ISSN 1831-9424 (PDF) ISSN 1018-5593 (Printed)
Rules on high strength steel (RUOSTE)
Research and Innovation
EUR 28111 EN
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EUROPEAN COMMISSION Directorate-General for Research and Innovation Directorate D — Key Enabling Technologies Unit D.4 — Coal and Steel E-mail:
[email protected] [email protected] Contact: RFCS Publications European Commission B-1049 Brussels
European Commission
Research Fund for Coal and Steel Rules on high strength steel (RUOSTE) Prof. Dr.-Ing. Markus Feldmann Nicole Schillo, Simon Schaffrath Rheinisch Westfälische Technische Hochschule Aachen, Germany (RWTH) Institute of Steel Structures Mies-van-der-Rohe-Str.1 D-52074 Aachen
Kuldeep Virdi AU Aarhus University
Timo Björk, Niko Tuominen LUT Lappeenranta University of Technology
Milan Veljkovic, Marko Pavlovic, Panagiotis Manoleas LTU Luleå University of Technology
Markku Heinisuo, Kristo Mela TUT Tampere University of Technology
Petri Ongelin, Ilkka Valkonen, Jussi Minkkinen, Juha Erkkilä Ruukki Rautaruukki Oyj
Eva Pétursson, Matthias Clarin SSAB SSAB EMEA
Alfred Seyr Voest Voestalpine Krems GmbH
LászlóHorváth, Balázs Kövesdi, Pál Turán, Balázs Somodi BME Budapesti Müszaki és Gazdaságtudományi Egyetem
Grant Agreement RFSR-CT-2012-00036 1 July 2012 – 30 June 2015
Final report Directorate-General for Research and Innovation
2016
EUR 28111EN
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More information on the European Union is available on the Internet (http://europa.eu). Cataloguing data can be found at the end of this publication. Luxembourg: Publications Office of the European Union, 2016 Print ISBN 978-92-79-61984-7 PDF ISBN 978-92-79-61983-0
ISSN 1018-5593 ISSN 1831-9424
© European Union, 2016 Reproduction is authorised provided the source is acknowledged. Printed in Luxembourg Printed on white chlorine-free paper
doi:10.2777/885050 KI-NA-28-111-EN-C doi:10.2777/908095 KI-NA-28-111-EN-N
Table of contents INTRODUCTION AND SUMMARY ............................................................. 7 1
MATERIAL DUCTILITY CRITERIA ...................................................... 9 1.1 1.2
INTRODUCTION ................................................................................ 9 NET SECTION TENSILE RESISTANCE ........................................................ 9
1.2.1 1.2.2 1.2.3 1.2.4 1.2.5
1.3
RESISTANCE OF BOLTED CONNECTIONS MADE OF HSS ................................. 17
1.3.1 1.3.2 1.3.3 1.3.4
1.4
General Information .......................................................................... 9 Net section tensile tests ..................................................................... 9 Numerical Parametric Studies ........................................................... 12 Conclusions for Net Section Resistance .............................................. 15 Statistical evaluation ....................................................................... 16 General Information ........................................................................ Literature survey summary and experimental programme .................... Tests and observations .................................................................... Statistical evaluation .......................................................................
17 17 18 19
ROTATIONAL CAPACITY OF HSS BEAMS ................................................... 20
1.4.1 General Information ........................................................................ 1.4.2 Material properties and geometry ...................................................... 1.4.3 Assessment of rotational capacity in design ........................................ 1.4.4 Conclusions for beams in bending ..................................................... 1.4.5 Numerical Studies – I-sections.......................................................... 1.4.6 FE analysis of rotation capacity of hollow section beams ...................... 1.4.6.1 Validation of 4-point bending experiments by FEA ...............................
20 21 23 25 25 26 26
1.4.6.2 Parametric study of HSS and MS compact hollow section beams ........... 29 1.4.6.3 Conclusions on rotational capacity of hollow section HSS beams ........... 32
1.4
MATERIAL LAWS FOR FEM SIMULATION .................................................. 33
1.4.1 1.4.2
1.5
MATERIAL PROPERTIES AT ELEVATED TEMPERATURES .................................... 43
1.5.1 1.5.2 1.5.3 1.5.4 1.5.5 1.5.6
2
Material modelling using damage mechanics ...................................... 33 Material modelling using ductile material model .................................. 37 General Information ........................................................................ Tested materials ............................................................................. Testing equipment .......................................................................... Test Results ................................................................................... Ductility behaviour at elevated temperatures ...................................... Conclusions ....................................................................................
43 43 43 44 45 46
STABILITY ...................................................................................... 49 2.1
RESIDUAL STRESS MEASUREMENTS ....................................................... 49
2.1.1 2.1.2 2.1.3
2.2
LOCAL BUCKLING TESTS .................................................................... 53
2.2.1 2.2.2 2.2.3 2.2.4 2.2.5 2.2.6 2.2.7 2.2.8 2.2.9
2.3
General Information ........................................................................ 49 Work program ................................................................................ 49 Conclusions for residual stress measurements .................................... 51 General Information ........................................................................ Local buckling tests conducted .......................................................... Test results .................................................................................... Evaluation according to EC3-1-5 ....................................................... Evaluation using a modified general method ....................................... Conclusions for local buckling tests.................................................... Influence of overstrength on local buckling ......................................... Alternative resistance function to Winter Curve ................................... Safety Assessment for plate buckling .................................................
53 53 54 57 58 58 60 61 62
GLOBAL BUCKLING TESTS ................................................................... 64
2.3.1 2.3.2
General Information ........................................................................ 64 Experiments conducted at BME ......................................................... 65
Page 3
2.3.3 2.3.4
2.4
Numerical modelling of HSS hollow section columns ............................ 71 New findings related to global buckling .............................................. 72
INTERACTION TESTS ......................................................................... 75
2.4.1 Design and fabrication ..................................................................... 2.4.2 Material characterization .................................................................. 2.4.3 Test setup and procedure ................................................................. 2.4.4 Experimental Results ....................................................................... 2.4.5 Evaluation according to Eurocode ...................................................... 2.4.6 Numerical Model ............................................................................. 2.4.6.1 Material Model ................................................................................
75 76 76 77 78 81 82
2.4.6.2 Assessment of geometric and structural imperfections ......................... 83 Geometric imperfections ............................................................................. 83 Residual Stress implementation................................................................... 84 2.4.7 2.4.8 2.4.9
3
TUBULAR JOINTS ............................................................................ 89 3.1 3.2
INTRODUCTION ............................................................................... 89 REDUCTION FACTOR TEST ................................................................... 89
3.2.1 3.2.2 3.2.3 3.2.4 3.2.5
3.3 3.4 3.5 3.6 4
Comparison FE-results and experimental results ................................. 85 Parametric studies .......................................................................... 85 Summary for Interaction tests .......................................................... 88
Used tubes and joints in reduction factor and fillet weld tests ............... Welded specimen coupon tests ......................................................... S500 reduction factor tests .............................................................. S700 reduction factor tests .............................................................. S960 reduction factor tests ..............................................................
89 92 93 94 96
THROAT THICKNESS TESTS .................................................................. 97 DETAILED STUDY OF S960 X-JOINTS UNDER TENSION ............................... 103 DISCUSSION ................................................................................ 106 CONCLUSION................................................................................ 107
CASE STUDIES .............................................................................. 109 4.1
BACKGROUND ............................................................................... 109
4.1.1 General ........................................................................................109 4.1.2 Cost factors ...................................................................................110 4.1.3 Beams and columns .......................................................................111 4.1.4 Constraints of tubular trusses ..........................................................111 4.1.5 Floors in high rise buildings – composite beams with HSS ...................114 4.1.5.1 Analysis parameters .......................................................................114 4.1.5.2 Optimisation criterions and procedure ...............................................116 4.1.5.3 Calculation of relative costs .............................................................118
4.2
RESULTS..................................................................................... 119
4.2.1 4.2.2 4.2.3 4.2.4 4.2.5 4.2.6 4.2.7
4.3 5
Welded beams ...............................................................................119 Welded box columns ......................................................................121 Tubular trusses ..............................................................................123 Effect of fire protection on optimized structures .................................125 Effect of new design rules for optimal trusses ....................................126 Innovative frame system for commercial building...............................127 Possible cost reductions for floors in high rise buildings.......................128
CONCLUSIONS .............................................................................. 130
DESIGN GUIDE AND PROPOSED AMENDMENDS ............................ 133 5.1 5.2 5.3 5.4
INTRODUCTION ............................................................................. 133 NET SECTION RESISTANCE ................................................................ 133 MATERIAL REQUIREMENTS ................................................................ 133 MATERIAL PROPERTIES AT ELEVATED TEMPERATURES .................................. 133
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5.5 5.6 5.7 5.8 5.9 5.10
BOLTED CONNECTIONS .................................................................... 134 GLOBAL BUCKLING CURVES ............................................................... 134 LOCAL BUCKLING RESISTANCE ............................................................ 135 INTERACTION OF LOCAL AND GLOBAL BUCKLING ....................................... 135 TUBULAR JOINTS ........................................................................... 135 DESIGN RECOMMENDATIONS FOR FLOORS IN HIGH-RISE BUILDINGS ................ 136
6
REFERENCES ................................................................................. 139
7
LIST OF FIGURES .......................................................................... 143
8
LIST OF TABLES ............................................................................ 147
9
LIST OF ABBREVIATIONS ............................................................. 149
Page 5
Page 6
INTRODUCTION AND SUMMARY The partly by the RFCS funded project RUOSTE consisted of three technical Work packages to evaluate reasonable material requirements for high strength steel in the construction business, investigate their properties in respect of stability cases and construction issues of welded tubular joints. Additionally, case studies and sustainability analysis were conducted to judge the financial and environmental benefits of high strength steel towards mild steels. The studies focused on steel grades S500-S960.
On behalf of the technical part, it could be confirmed that for un-notched cross-sections in tension the full net section resistance 𝐴𝑛𝑒𝑡 ∙ 𝑓𝑢 can be achieved, and thus the reduction factor 0.9 can be neglected. However, 0.9 should still be used for notched cross-sections. This concerns clause 6.2.3(2) of current EN 1993-1-1 [3] for cross-sections with holes. The material requirements given in clause 3.2.2 of current EN 1993-1-12 [4] regarding the yield ratio fu/fy and elongation at ultimate load εu were found to be relievable, proofed by parametric numerical studies which allowed for the usage of artificial stress-strain curves. For elevated temperatures, the existing yield strength reduction factors (given in Table 3.1 and Table E.1 of current EN 1993-1-2 [5]) proofed to be optimistic, which can be also found for mild steels. However, as the behaviour of high strength steels proofed to be very similar to that of mild steels, the same reduction factors could be used for both. The existing end-distance requirements given in clause 3.5 and 3.6 of current EN 1993-18 of [6] were confirmed, although different models developed by Može and Beg [7] might lead to more economical design. Experiments on the rotational capacity of welded I-beams indicated that plastic-plastic design and the cross-section classification rules for Class 1 in 5.2 of current EN 1993-1-1 [3] are applicable for steel grades up to S700. For steel grade S960 the situation was less pronounced: the experiments indicated that elastic-plastic design and the cross-section classification rules for Class 2 in current EN 1993-1-1 [3] could be applicable, but additional tests would be necessary to give clear recommendations. Extensive residual stress measurements on welded box and tubular sections confirmed lower relative residual stress values for high strength steel members. For local buckling the current resistance curve given in clause 4.4 of current EN 1993-1-5 [8] proofed to be optimistic, which could be also found for mild steel tests. Statistical analysis of all available data (mild and high strength steel stub column tests) suggested a necessary 𝛾𝑀 higher than 1.0. Discussion in Working Group EN 1993-1-5 (subgroup of CEN/TC250/SC3) agreed on aiming at a value of 1.1. However, at the time being, no final conclusion was drawn. Global buckling tests and accompanied finite element calculations suggest higher possible buckling curves for the high strength steel material: based on statistical evaluation, buckling curve b could be used for all welded box sections (S500 up to S960). This curve could also be confirmed for the cold-formed structural hollow sections (S500 up to S960). Although afflicted with some scatter, the experiments on the interaction behaviour of local and global buckling showed acceptable results using the rules of EN 1993-1-1 [3]. For tubular joints, where a reduction factor of 0.8 is to be applied on the joint resistance according to [6] 7.1.1 (4) of current EN 1993-1-12 [4], was found to be 1.0 for S500, and 0.9 for S700. For S960, 0.8 could be used. The throat thickness requirement was found to be also reducible for high strength steel: while the full-strength requirement in 7.3.1(4) of current EN 1993-1-8 [6] leads to 1.6 t, 1.0 t could be used for S500 tubes. Respectively, for S700 throat thickness 1.2 t instead of 1.65 t can be recommended, and for S960 1.4 t instead of 1.73 t could be used. Numerical case studies on welded beams and tubular trusses revealed that by using the present design rules of Eurocode 3, substantial weight and cost savings can be obtained by
Page 7
employing HSS. The actual savings depend strongly on the application, but in general, the savings become greater as the load and span of the structure increase. For example, for welded I-beams, S500 provides about 15-20% lighter solutions than S355, and S700 yields weight reduction of 25-30%. However, in some cases, no benefit is gained from higher strength. Comparison of minimum cost designs obtained for different steel grades revealed that up to 10-20% savings can be reached by HSS, although, again, the actual savings are casespecific. In many cases, HSS actually yielded more expensive solutions than S355. One reason for this is that HSS requires substantially larger full strength welds than mild steels, which has a significant impact on the manufacturing cost. This partially negates the savings in weight. This can be circumvented by employing hybrid solutions, where the web of the beam (or braces of trusses) is made of S355 and HSS is utilized in the chords. Virtually in all cases, the minimum cost design was a hybrid structure. Sustainability analysis of selected structures obtained by optimization showed that the environmental impact depends mainly on the production of plates and tubes. For welded beams, this means that the environmental impact is largely proportional to the amount of material used. For trusses, the welds play a more important role, which means that, similarly to costs, the reduction of environmental impact obtained from material savings is partially negated by increased impact of the welds for HSS.
Page 8
MATERIAL DUCTILITY CRITERIA
1 1.1
Introduction
To secure ductile behavior and ductile failure of steel structures is a major objective throughout Eurocode 3. Depending on load scenario and structural system, the conditions herefore might vary, however, it is necessary to establish general requirements for steel to apply the design rules. The current requirements seem too restrictive and not appropriate for high strength steel. In the following sections, the requirements for net section resistance, bolted connections and rotational capacity are evaluated and reassessed.
1.2 1.2.1
Net Section Tensile Resistance General Information
EN 1993-1-1 [3] as well as EN 1993-1-12 [4], reduce the net section resistance to 90 % of the full plastic carrying capacity by applying 𝑁𝑡,𝑅𝑑 =
0.9 ∙ 𝐴𝑛𝑒𝑡 ∙ 𝑓𝑢 𝛾𝑀2
(2.1)
The factor 0.9 is based on fracture mechanics [9] and rather old tests, mainly on lower strength steel grades. Previous research on modern steels with centre holed tests (CHT) and bolted connections suggest that the 0.9 factor could be omitted [10], while the 0.9 factor was derived also for centre notched tests (CNT). These tests react more unfavourable due to the sharp notch. However, they have to be taken into account, because: Due to fatigue loading sharp notches are likely to occur in the area of bore holes etc. Notches from manufacturing processes are likely to occur 1.2.2
Net section tensile tests
Tests were conducted by the University of Budapest and Ruukki Metals Oy, the dimensions are shown in Figure 1-1. The hole diameters in the specimens define a certain grade of damage, thus allowing for the evaluation of the ultimate strength of the net section to be achieved. This includes also the verification in how far the steel material is able to redistribute stress and strain in locally heavy loaded areas. For both centre holed tensile (CHT) - and centre notched tensile (CNT) specimens five different ratios of net section to gross section were selected. The diameter d, to specimen width w, ratio for the CHT-specimens covers the range 0.1 to 0.5 in 0.1 steps. For the CNT specimens the ratio 2a/w was selected to be 0.1, 0.2, 0.3, 0.45 and 0.6 where 2a is the total width of the weakening notch (= hole + 2 pre-cracks). The stress-strain characteristics of the four materials used are shown in Table 3. While the S700 material fulfils all criteria of EC3-1-12 [4] if the rules were applied on S960, only the elongation at fracture criterion is met. The yield strength ratio would have been met by the direct quenched material (I), while the quenched and tempered steel (II) would be slightly lower. Table 1-1: Engineering stress-strain curves and evaluated material parameters from MCs
Material
S700 I S700 II S960 I S960 II
fy
fu
fu/fy
Agt
[N/mm²] [N/mm²] 727 802 1.10 753 843 1.12 1060 1161 1.09 1018 1053 1.03
[%] 7.1 9.3 3.9 5.3
KV
KV
Impact toughness [J] 20°C
Impact toughness/Area [J/mm2] 20°C 72
120 72 132 128
188 206
Page 9
Task 1.1: Net Section Tensile Tests - 1 Material: S700MC or S690Q 120
CHT specimen (Center Hole Tension) 100
d/w = 0,1
d/w = 0,2
d/w = 0,3
d/w = 0,4
40
32
24
8
d/w = 0,5
50
16
Contour to be water cutted 400 100
8 80
CNT specimen (Center Notch Tension) 2a/w = 0,1
2a/w = 0,2
2a/w = 0,3
2a/w = 0,45
50
Detail see right
2 8
6
20
8
2a/w = 0,6
32
16 36
48
100
24
Cracks to be established by cyclic loading
Figure 1-1: Geometry CHT wide plate tests The fractured specimens of one test series (S960 I) are shown in Figure 1-2. The typical crack development in the net section can be identified: while for a specimen without hole a certain angle develops, this angle gets flatter with increasing hole diameter and thus decreasing net section. For a larger net section ratio, the plastic strain is more localized and the remaining crosssection is fully under tension. With smaller holes and more material to distribute stresses and strain, the percentage of shear stresses increase and thus the angle of fracture gets steeper.
Figure 1-2: Fractured wide plate specimens (S960 I) The ultimate load achieved was evaluated with respect to the ultimate resistance Agross*fu. The results are shown in Figure 1-3. For the specimens with holes, all tests showed the same characteristic: the ideal resistance (depicted with the straight line) is reached more or less exact in all cases. This can be observed regardless of the actual yield-strength ratio. In the tests comprising holes and notches (two lower diagrams of Figure 1-3, material “II” in both cases), the S960 specimens reached Anet*fu (and did not meet the requirements [4]) while the S700 specimens did not reach Anet*fu, although the requirements of [4] were met. The CharpyV values show however much lower values for S700II than for S960II, which is in correlation to the ability of the material to distribute strains and stress.
Page 10
CHT S700 II 1.0
0.8
0.8 Fu/(Agross*fu)
Fu/(Agross*fu)
CHT S700 I 1.0
0.6 0.4 0.2
0.6
0.4 0.2
0.0 0.0
0.2
0.4
d/w
0.6
0.8
1.0
0.0 0.0
0.2
d/w
0.6
0.8
1.0
CHT 960 II
1.0
1.0
0.8
0.8
Fu/(Agross*fu)
Fu/(Agross*fu)
CHT S960 I
0.4
0.6 0.4 0.2
0.6 0.4 0.2
0.0 0.0
0.2
0.4
d/w
0.6
0.8
1.0
0.0 0.0
0.2
0.4
d/w
0.6
0.8
1.0
Figure 1-3: Comparison of experimental tests with net section resistance
Page 11
1.2.3
Numerical Parametric Studies
The ultimate strength of tension loaded steel elements is governed by: Plastic instability to the point where geometric sectional reduction equals material hardening (Considère-criterion) and the occurrence of damage on a microscopic level that may onset the plastic instability. Using a damage mechanics approach, parametric studies were conducted to evaluate reasonable ductility requirements. The basic resistance damage curve was taken from former RFCS-project PLASTOTOUGH [14] and is characterized by the equivalent plastic strain to the triaial state. This curve was fitted in the numerical model to match the experimental results. As an example, the procedure is shown in Figure 1-4. The basic curve from [14] (A) is given in an exponential form and scaled into (B) until the resulting Force-Displacement curve for the evaluated CHT tests show the same characteristic due to the correct initiation of damage and degradation.
Figure 1-4: Scaling effect of damage curves on damage initiation. To assess the Anet –resistance and rules given in [3] and [6], derived from the Considèrecriterion a number of nominal material curves were derived, where the fu/fy-ratio as well as the uniform elongation were prescribed. The resulting true stress-strain curves were used first for the calculation of round bar tension tests, for which the engineering stress-strain curves were assessed. With this approach the Considère-criterion was assessed backwards and confirmed. An example for three different nominal true stress-strain curves, with the corresponding engineering stress-strain curves from the round bar tests are shown in Figure 1-5. 1200
stress [N/mm²]
1000 800
𝜎 𝜀
600
𝑑𝜎 𝑑𝜀
400 200
𝜀𝑢
𝜀𝑢
𝜀𝑢
0
0
0.1
0.2
0.3
0.4
0.5
strain [-] Figure 1-5: Principle methodology to assess nominal material curve [36], without damage
Page 12
In Table 1-2, the requirements of the fabrication codes [74][12] are compared with the requirements of the building code [4] to identify the lower limits. Subsequently, a parametric study with the parameters of Table 1-3 was carried out. Table 1-2: Miminum values according to [4] and [11][12] Min fy Steel
t ≤ 8mm [N/mm²]
Min fu
fu/fy
[N/mm²]
[74][11]
fu/fy [4]
εf
εu
[74][11]
[4]
[%]
[%]
S690Q
690
770
1.12
1.05
14
4.9
S700MC
700
750
1.07
1.05
12
5
S960MC
960
980
1.02
1.05
7
6.8
S960Q
960
980
1.02
1.05
10
6.8
The required values for fu/fy are taken from the fabrication codes [11] and [12]. These were either used directly, or even reduced for the parametric study. The uniform elongation was varied between 3 and 6 % for S700 material and between 4 and 8 % for S960 material. The Young’s Modulus was taken for all curves with 210000N/mm² up to f y. In the plastic area, the stress-strain relation is described by the Hollomon equation:
𝜎𝑡 = 𝑘𝐿 ∙ 𝛷𝑛
(2.2)
The respective parameters and assessed fu/fy-ratio and uniform elongation εu are summarized in Table 1-3. Table 1-3: Definition of nominal material curves S700
fu/fy
εu,eng
n
kL
1.03
6
0.693
1.03
5
0.6474
1.03
4
1.03
fu/fy
εu,eng
n
kL
460.788
1.02
8
0.8345
830.657
403.743
1.02
6.8
0.802
762.366
0.5901 337.3861
1.02
6
0.7759 708.9033
3
0.5149 261.7079
1.02
4
0.6849
1.05
6
0.5739
1.05
8
0.6513 684.9336
1.05
5
0.5248 350.5858
1.05
6.8
0.6077 610.3839
1.05
4
0.4655 291.2531
1.05
6
0.5739
555.645
1.05
3
0.3922 227.0486
1.05
4
0.4655
399.694
404.315
S960
536.455
For each configuration, a round bar tensile test was calculated first, resulting e.g. in Figure 1-6. These 16 curves were then used to recalculate wide plate tensile tests, using the calibrated model from the numerical studies. Three cases were investigated per configuration: a specimen without hole, one with 8 mm and one with 16 mm. The results were evaluated in respect to two issues: 1. Can Anet x fu be reached? 2. Is plastic instability significantly affected by damage induced crack initiation?
Page 13
1000 S700_1.03_3
true stress, st [N/mm²]
900 800
st = s0 + AetB
700 600
dst det
500 400 0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
true strain, et [-]
fu = 1:03 fy
Figure 1-6: Evaluation of S700 curve, fu/fy=1.03, εu= 3 %
S700,
500
d0mm : Anet *fu
Force [kN]
450 400 350
d8mm : Anet *fu
6% 5% 4% 3% Fu
d16mm : Anet *fu
300
crack ini 250
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Displacement [mm]
fu = 1:02 fy
Figure 1-7: S700, fu/fy=1.03, varying εu
S960,
d0mm : Anet *fu
Force [kN]
650 600 550
d8mm : Anet *fu
d16mm : Anet *fu
500
8% 6.8 % 6% 4% Fu crack ini
450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Displacement [mm] Figure 1-8: S960, fu/fy=1.02, varying εu
Page 14
Figure 1-7 and Figure 1-8 show exemplarily the results for some of the parametric studies. It can be observed that in all cases, even for very low fu/fy ratios the net section resistance could be reached. The specimens without holes/perturbations reached their net section resistance closely, while wide plates with hole showed more over strength, as the localization of strains might lead to localized higher strains and subsequently higher stresses. The integral of the stresses over the loaded area leads thus to higher strength. For the specimens without holes, the plastic instability was in all cases dominant, which can be seen in the previous figures as the ultimate load (black triangle) occurs well before the crack initiation (yellow dot). As soon as a small hole is used the crack initiation moves before the ultimate load. However, the Anet x fu resistance could be reached in all cases. 1.2.4
Conclusions for Net Section Resistance
Experimental and numerical investigation suggest that omitting 0.9 in the net section resistance calculation is possible, providing the existence of sufficient material toughness and no sharp notches in the member. For notched structures the following formula still applies: 𝑁𝑡,𝑅𝑑 =
0.9 ∙ 𝐴𝑛𝑒𝑡 ∙ 𝑓𝑢 𝛾𝑀2
(2.3)
For structures without sharp notches 1.0 can be used: 𝑁𝑡,𝑅𝑑 =
1.0 ∙ 𝐴𝑛𝑒𝑡 ∙ 𝑓𝑢 𝛾𝑀2
(2.4)
In the present studies it could be shown that lower f u/fy ratios and lower εu properties are possible, provided again no notches exist (e.g. no fatigue loading) and a sufficient material toughness can be guaranteed. For a quantification, however, further steps are necessary, such as: Evaluation of nominal or statistically secured material curves (i.e. true stress-strain curves). The methodology and several of these nominal curves were already used in the present report. Derivation of nominal damage curves. Can be derived artificially based on KVrequirements and respective numerical simulations of Charpy-V experiments. Investigation of other geometries (e.g. eccentrically holes) Regarding the material toughness, an upper shelf criterion would be necessary to define the necessary toughness at room temperature. Impact toughness tests carried out within the Ruoste-Project showed the influence of this property. εu of a material is depending on the combination of Considère-criterium, Hollomon or Ludwik equation (true stress-strain curve) and associated damage curve. In the studies within Ruoste, assumptions for the damage curves had to be made based on former projects (i.e. PLASTOTOUGH). For the implicit studies, it was aimed to use estimated lower boundary curves to include a safety margin. εu is a result of the three equations. Provided sufficient material toughness members, the parametric studies (see 1.2.3) lead to the following conclusions for lower limits: -
For S700: fu/fy could be reduced to 1.03 and εu to 3 %
-
For S960: fu/fy could be reduced to 1.02 and εu to 4 %
For un-notched members of all steel grades the net section resistance could be assessed with: 𝑁𝑡,𝑅𝑑 =
𝐴𝑛𝑒𝑡 ∙ 𝑓𝑢 𝛾𝑀2
(2.5)
For notched members (e.g. fatigue loaded) the net section resistance can be assessed with:
Page 15
𝑁𝑡,𝑅𝑑 =
1.2.5
0.9 ∙ 𝐴𝑛𝑒𝑡 ∙ 𝑓𝑢 𝛾𝑀2
(2.6)
Statistical evaluation
Statistical evaluation of the test results were made according to EN 1990, Annex D [13]. Three equations have been considered for the statistical evaluation. To include the uncertainty of steel grade and fabrication of element, the coefficients of variation VXi were used which are determined on the basis of prior knowledge. The same values were used as for the evaluation of the current version of design formulas for bolted connections [6]: variation coefficient for hole diameter: Vd0=0.005, variation coefficient for material strengths: Vfy=Vfu=0.005, variation coefficient for plate thickness Vt=0.005, variation coefficient for width: Vb=0.005. The estimated partial factor M is a ratio between the rk characteristic and rd design value. In the design formulas all the variables are defined with their nominal and characteristic values, too. The material strengths are given with their characteristic values, but the geometrical values are given as their nominal values. In such a case a suitable adjustment should be made, this final partial factor is indicated as M*. The details of the used procedure can be seen in [10] based on [13]. The results of CHT and CNT tests were evaluated in separated groups. In each group separate data sets have been created based on the single steel grades. Statistical evaluation of the CHT data group (Centre Hole Tension specimen): The evaluated population consisted of the executed tests and the test results from the above mentioned literature [10]. The results are shown in Table 1-4. The b correction factor is slightly less than 1.0. The required value of the partial factor has not reached the M2 value in the current EN (M2 =1.25) even though the omitted 0.9 reduction factor, which shows in accordance with [10] that this formula is applicable for the net section resistance in our studied cases. Table 1-4 – Results of statistical evaluation.- Eq (2.5) Model
Anet x fu
Data set
No. tests
kn
kd
b
V
M
M*
S690 & S700
34
1.71
3.37
0.987
0.018
1.132
1.154
S960
10
1.92
4.53
0.998
0.013
1.133
1.141
HSS all
44
1.69
3.29
0.989
0.017
1.132
1.151
Statistical evaluation of the CNT (Centre Notch Specimen) data group: The evaluated population was restricted thus to the results of the tests carried out within the Ruoste-project. Table 1-5 – Results of statistical evaluation of CNT result group Model
0.9.fu.Anet
Anet fu .
Data set
No. tests
kn
kd
b
V
M
M*
S700
5
2.33
7.78
1.040
0.017
1.146
1.110
S960
6
2.17
6.35
1.089
0.011
1.133
1.045
HSS all
11
1.89
4.35
1.074
0.028
1.145
1.080
S700
5
2.33
7.78
0.936
0.017
1.146
1.233
S960
6
2.17
6.35
0.980
0.011
1.133
1.161
HSS all
11
1.89
6.35
0.966
0.028
1.145
1.200
Page 16
The scatter of data is similar to that of the CHT group; it can be observed that the correction factor is consequently less than 1.0 with the use of Anet . fu. The calculated partial safety factor is less than the value of M2 in the current EN (M2 =1.25) in all cases.
1.3
Resistance of bolted connections made of HSS
1.3.1
General Information
Experiments were conducted to check the applicability of design rules given in the current EN 1993-1-8 [6] and EN 1993-1-12 [4] for bolted connections made of HSS material. Focus was laid on steel grades S700 and S960. The design tensile resistance of the net section may be determined by: 𝑁𝑡,𝑅𝑑 =
0.9 ∙ 𝐴𝑛𝑒𝑡 ∙ 𝑓𝑢 𝛾𝑀2
(2.7)
The design resistance for bearing failure can be calculated by: Nb,Rd =
k1 αb fu dt
(2.8)
γM2
where 𝛾𝑀12 and 𝛾𝑀2 are the partial safety factors, both given with 1.25 as recommended value. The conducted experiments as well as test results from literature review were used to verify the code rules given in [3] and [4] with focus on net section resistance according to Eq. (2.7) and on minimum end/edge distances on bolted connections. 1.3.2
Literature survey summary and experimental programme
According to previous publications [2][7][15], the present Eurocode design formulas are on the safe side for HSS bolted connections. Moreover, they are partially conservative with the net section resistance. The literature shows that high strength steels – even when not meeting the fu/fy ratio ductility requirement given in [4] – have demonstrated significant local ductility through large deformations. Based on the literature review, more accurate formulas are needed for more efficient design. The test programme conducted within Ruoste comprised double shear bolted connection tests with S960 material and single shear connection tests with S700 and S960 material. All specimens were produced by Rautaruukki. The steel grades used in the tests were S700 MC and S960 QC. Material properties according to the Ruukki’s material certificates: yield strength 727 MPa and 1060 MPa, tensile strength 802 MPa and 1161 MPa, respectively. For all tests the same bolt (d = 27 mm, grade 10.9 and 12.9) and bolthole diameter (d0 = 30 mm) were used. In the configuration S the tests were designed as single shear connections and in the configuration D as double shear connection. The plates of all specimens had a nominal thickness of t = 8 mm. The parameters are summarized in Table 1-6. Figure 1-9 shows the dimensions of the specimen. Table 1-6 : Testing programme b e2/d0 [mm] 1.2 60 72 80 90 110
1.00 1.20 1.33 1.59 1.83
x x x
Double Shear Tests Material S960 e1/d0 1.5 2.0 2.5 3.0 x x x x
x x
x x x x x
x x x
Single Shear Tests
No 3 4 4 4 2
1.2 x x x
Material S960 e1/d0 1.5 2.0 2.5 x x x
x
x x
3.0 x
No 2 4 2 2 0
1.2 x x x
1.5
x
Material S690 e1/d0 2.0 2.5
x x
x x
3.0 x x
No 1 3 4 2 0
Five different edge distances (e2 = 30, 36, 40, 45 and 55 mm) and five end distances (e1 = 36, 45, 60, 75 and 90 mm) have been investigated. The designation symbol of the specimen
Page 17
includes the configuration (S or D), the material (7-S700; 9 - S960), plate width b and end distance e1 (both in mm). 1.3.3
Tests and observations
Tests were carried out in a 1000 kN hydraulic testing machine, using displacement controlled loading. The relative displacements were measured by inductive displacement transducers (IDT). The bolts were snug tightened to ensure that the load was transferred primarily by bearing and not by friction. All of the specimens were subjected to static tensile force until the fracture of the plate occurred. In Figure 1-9 the experimental setup can be seen.
Figure 1-9: Different test arrangements for D and S configuration The following load-displacement diagrams (Figure 1-10 and Figure 1-11) show the test results for the specimens made of S960 material. The S700 tests show similar behaviour with more ductility. In general it can be observed that the bearing failure is more ductile behaviour than the net section failure which, however, occurs at lower force level. Comparing the double and single sheared configurations, the latter specimen failed at larger deformations.
Figure 1-10: Load-displacement diagrams for S960 D configuration – left the net section and right the bearing failure modes
Figure 1-11: Load-displacement diagrams for S960 S configuration – left the net section and right the bearing failure modes Concerning the minimum end (e1) and edge (e2) distances, for both minimum 1.2d0 is allowed according the current EN 1993-1-8 [6]. In our test series the minimum end distance was e1 = 1.2d0, but specimens with e2 = 1,0d0 and e2 = 1.2d0 were also examined.
Page 18
Specimens with e2 = 1.0d0 all failed at the net section and are marked with red colour in the Figures. Specimens with the minimum allowed edge/end distances (e1 = 1.2d0 and simultaneously e2 = 1.2d0) all failed by splitting/bearing failure. Comparing the test results with the calculated resistances according the current Eurocode rules (without partial factor) shows the following: -
Figure 1-12 shows the test results of S960 S and D specimen with continuous lines, the calculated resistances with dashed and dash-dotted lines (same colour);
-
the calculated resistances are always on the safe side, the bearing resistances even more;
-
the transition between the failure modes according EN (plotted by dashed red line in Figure 1-12 is quite different from the experienced transition zone, which lies in the red shaded area. It shows that the real failure mode cannot be correctly predicted according to the current EN calculations using Eq.(2.7) and Eq.(2.8).
Figure 1-12: Comparison of the test results with calculated resistances acc. Eq. (2.7) and Eq. (2.8) 1.3.4
Statistical evaluation
Based on the tests results carried out in this project and the already published experimental test results, a statistical analysis has been performed according to EN 1990 Annex D. At the calculation of the theoretical resistance all partial factors have been set to 1.0. The current EN-models based on Eq. (2.7) for net section resistance and Eq. (2.8) for bearing resistance were extended with two additional models for each failure mode.
net section failure, modified Eq. (2.7): 𝑁𝑢,𝑅𝑑,𝑚𝑜𝑑 =
net section plastic failure formula:
𝑁𝑛𝑒𝑡,𝑝𝑙,𝑅𝑑 =
bearing resistance according [15]:
𝑁𝑏,𝑅𝑑 =
bearing resistance according [7]:
𝑁𝑏,𝑅𝑑 =
𝐴𝑛𝑒𝑡 𝑓𝑢 𝛾𝑀2 𝐴𝑛𝑒𝑡𝑓𝑦
𝛾𝑀 𝑘1 𝑘2 𝑓𝑢 𝑑𝑡 𝛾𝑀2 𝑘𝐵 𝛼𝑑 𝑓𝑢 𝑑𝑡 𝛾𝑀
(2.9) (2.10) (2.11) (2.12)
Separately in each failure mode they were compared in a two-level procedure. The test results were classified to above mentioned failure modes in the first level according to the real/experienced failure mode, in the second level according to the calculated resistances.
Page 19
Figure 1-13: Evaluation of the resistances acc. the current EN Eq. (2.7) and Eq. (2.8)
Figure 1-14: Statistical evaluation of the resistances acc. Eq. (2.9) and Eq. (2.11) The Figure 1-12 shows that the models according the current EN, the Eq. (2.7) and Eq. (2.8) do not fit the results, the bearing resistance formula significantly underestimates the failure load with large b correction coefficient. They are clearly conservative and need refinement. The net section resistance model Eq. (2.9) fits better with the experimental results than the others (see Figure 1-14) with practically b = 1.0 correction factor; and M =1.14 and M*=1.17 partial factor would be sufficient for the required safety level. Concerning the bearing resistance, Eq. (2.11) and Eq. (2.12) are the “best-fit” models. Eq. (2.11) (see Figure 1-14) needs smaller b correction coefficient and larger partial factor (b = 1.05 and M*=1.16) while Eq. (2.12) the opposite – larger correction and smaller partial factor.
1.4 1.4.1
Rotational capacity of HSS beams General Information
Beams made from high strength steel are supposed to have lower rotational capacity, and have been thus excluded from plastic/plastic design according to [3][4]. The advantages of a HSS cross-section Class 1 beam could hitherto not be exploited. Although the material properties of high strength steel show lower strain hardening than mild steels, combined with the actual ductility it might be still sufficient to reach the respective
Page 20
cross-section classification. To examine this, in the research presented here, two test series were conducted to assess: First, the rotational capacity, aiming at fulfilling cross-section Class 1 requirements and thus permitting plastic/plastic design. Second, the achievement of Mpl, aiming at fulfilling cross-section Class 2 requirements and thus allowing elastic/plastic design. Here, the limit of Class 2 to Class 3 for beams in bending was evaluated The basic dimensions and applied measuring equipment used for the 3 and 4 point bending tests are shown schematically in Figure 1-15. The prevention of lateral-torsional buckling was achieved by large steel brackets at the points of load-introduction. Due to the different widths of the upper and lower flanges only the upper flange was restrained laterally as this part of the section is subjected to compression and therefore prone to lateral deflection. A steel profile of HEB 200 was constrained to the fixed brackets. An additional stainless steel plate covered with grease was attached to the profile in order to allow smooth gliding of the upper flange along the HEB 200 beam to deflect in the vertical direction. However, the stainless steel plates were removed as indentations occurred by the tested beam. In order to assure the vertical displacement of the beams without load-transferring friction, a sufficiently thick grease layer was applied directly on the steel girders. At the supports, the lower flanges were constrained by two lateral supports at each side. For Tests 9 to 17 (single-symmetric tests), upper and lower flange were restrained. The lateral restraints are situated below the load introduction, i.e. at midspan for the 3 point bending test and at a distance of 350 mm left and right from midspan for the 4 point bending tests. A drawing of the basic setup is depicted in Figure 1-15.
Figure 1-15: Test-setup, schematically 1.4.2
Material properties and geometry
The beams are all 2900 mm long and welded in the workshops of the respective steel producer with matching welds. The main material properties from the material test certificates are summarized in Table 1-7. The denomination of the tests include the test sequence, indication of loading (3P = 3
Page 21
point-bending, 4P = 4 point-bending), the nominal yield strength and the height of the web and the width of the flange, as well as the thickness of the web. The specimens of this series were all double-symmetric and made of one steel plate material. The requirements given in EC3-1-12 regarding the A5 strain at fracture are fulfilled by all steels investigated, even if applied on S960. The fu/fy-ratio is fulfilled by the S700 steel grades. From the investigated 3 different batches of S960, one would be under the threshold of 1.05 with 1.04. The requirement regarding the elongation at ultimate load (Agt) is in no case fulfilled. Table 1-7: Material properties of tests beams Test
Producer
01_3P_S960_160_140_8 02_3P_S700_160_140_8 03_3P_S700_160_110_6 04_3P_S960_160_110_6 05_4P_S700_160_110_6 06_4P_S960_160_110_6 07_4P_S700_160_140_8 08_4P_S960_160_140_8 09_3P_S960_240_70_6 10_3P_S960_250_70_6 11_3P_S700_275_80_6 12_3P_S700_290_80_6 13_3P_S700_385_105_8 14_3P_S700_365_100_8 15_3P_S960_330_95_8 16_3P_S960_320_90_8 17_3P_S960_240_70_6 Upper Flange, 15mm Upper Flange, 15mm
SSAB Ruukki Ruukki SSAB Ruukki SSAB Ruukki SSAB SSAB SSAB Ruukki Ruukki Ruukki Ruukki Ruukki Ruukki SSAB Ruukki SSAB
t [mm] 8.07 8.12 5.99 6.08 5.99 6.08 8.12 8.07 6.08 6.08 5.99 5.99 8.12 8.12 8.04 8.04 6.08 15 14.83
fy [N/mm²] 985 738 746 1010 746 1010 738 985 1010 1010 746 746 738 738 1060 1060 1010 751 1000
fu [N/mm²] 1044 818 829 1053 829 1053 818 1044 1053 1053 829 829 818 818 1160 1160 1053 812 1052
fy/fu 1.06 1.11 1.11 1.04 1.11 1.04 1.11 1.06 1.04 1.04 1.11 1.11 1.11 1.11 1.09 1.09 1.04 1.13 1.05
Agt [%] 5.3 4.7 4.4 4.9 4.4 4.9 4.7 5.3 4.9 4.9 3.2 3.2 4.7 4.7 4.2 4.2 4.9 5.39
A5 [%] 15 15.3 13.7 16 13.7 16 15.3 15 16 16 13.7 13.7 15.3 15.3 11.8 11.8 16 17.9 15
The actual dimensions of the specimens are reported in Table 1-8 and show only minor variations to the nominal ordered seizes. Table 1-8: True dimension of the delivered specimens Upper Flange Web Test Width Height Width Height [mm] [mm] [mm] [mm] 1 139.95 14.81 8.14 161.62 2 140.51 14.76 7.88 160.44 3 110.41 15.11 6.17 160.32 4 109.78 14.74 6.21 159.60 5 110.29 15.16 6.14 160.16 6 109.91 14.79 6.20 159.48 7 140.13 14.72 7.85 160.55 8 139.91 14.83 8.14 161.57 9/17 68.94 6.22 6.19 239.11 10 68.96 6.21 6.17 285.05 11 80.05 6.09 6.10 275.11 12 79.82 6.05 6.05 289.91 13 105.03 8.07 8.03 384.78 14 99.94 8.10 8.13 364.64 15 94.30 8.08 8.00 329.55 16 89.17 8.07 8.03 319.84
Lower Flange Width Height [mm] [mm] 120.98 8.06 119.96 7.94 119.89 6.11 119.24 6.21 120.08 6.12 119.14 6.14 120.05 7.91 121.24 8.07 69.41 6.21 68.88 6.22 80.10 6.08 80.13 6.08 105.13 8.09 99.99 8.09 94.15 8.07 89.38 8.04
Page 22
1.4.3
Assessment of rotational capacity in design
To reach Mpl a certain rotational capacity is necessary, which depends not only on the crosssection, but also on the system itself (frame, continuous beam, etc.). The most unfavourable system is considered to be a continuous beam, and for this the general assumed minimum requirement Rreq = 3 has been adopted by EC. The actual rotational capacity is defined as: 𝜑𝑟𝑜𝑡 − 𝜑𝑝𝑙 𝑅𝑎𝑐𝑡 = 𝜑𝑝𝑙
(2.13)
The evaluation regarding the rotational capacity of the beams is summarized in Table 1-9. The first 8 tests, which aimed at high rotations by avoiding local failure modes due to a thick upper flange in the compression zone, show always higher rotations for S700 specimens compared to their S960 counterpart. The plastic hinge was reached by all these specimens but slightly missed by Test 06 (M/Mpl = 0.99), in consequence no rotational capacity could be evaluated. Rotations are in general lower for 3-point bending tests (combined with higher strains), thus the 4-point bending tests show higher rotational capacity although here the Mmax/Mpl values are lower. Theoretically, the 4-point bending tests are not supposed to achieve cross-section Class 1 behaviour as the hardening cannot be exploited due to an even strain distribution and thus avoidance of strain peaks. Specimens for Tests 09 to 16 were designed to be very slender to assess the cross-section Class 2-3 limits. Due to the slenderness, the specimens were prone to lateral torsional buckling, and the test-setup had to be modified several times to avoid or decrease stability issues. A configuration, which proved to be successful and could be repeated was used for specimens 13 to 16. Specimen 09 was reused in Test 17. Although the failure mode of Specimen 09 initially was by elastic lateral torsional buckling, localized plastic deformations could not be avoided. For further evaluation purposes of rotational capacity therefore only specimens 01 to 08 are taken into account. The 4P-bending tests 05, 07 (S700) and 08 (S960) had to be aborted due to testing rig limits. In Table 1-10 the normalized moment-rotation curves are depicted, with the sequential number of the test in the upper left corner of each cell. Table 1-9: Test results regarding rotational capacity φmax,
Mmax
Mpl
Mmax/Mpl
01_3P_S960_160_140_8 02_3P_S700_160_140_8 03_3P_S700_160_110_6 04_3P_S960_160_110_6 05_4P_S700_160_110_6 06_4P_S960_160_110_6 07_4P_S700_160_140_8 08_4P_S960_160_140_8 09_3P_S960_240_70_6 10_3P_S960_250_70_6
[kNm] 294.5 222.1 172.5 218.6 166.5 210.8 217.4 287.3 79.7 195.0
[kNm] 278.5 201.4 157.7 212.7 157.7 212.7 201.4 278.5 195.9 204.0
[-] 1.06 1.10 1.09 1.03 1.06 0.99 1.08 1.03 0.41 0.96
[°] 5.64 9.85 9.09 8.33 13.55 10.14 13.00 9.26 1.51 2.21
[-] 1.48 3.61 3.40 1.66 5.04 4.97 2.42 0.00 0.00
11_3P_S700_275_80_6
164.7
188.3
0.87
2.64
0.00
12_3P_S700_290_80_6
169.7
202.0
0.84
1.25
0.00
13_3P_S700_385_105_8 14_3P_S700_365_100_8 15_3P_S960_330_95_8 16_3P_S960_320_90_8 17_3P_S960_240_70_6
466.4 431.4 507.7 434.5 179.4
465.6 422.0 502.7 467.8 195.9
1.00 1.02 1.01 0.93 0.92
2.12 1.99 2.19 2.07 2.16
0.69 0.83 0.22 0.00
Test
left/right
Ract
Ultimate Failure ductile Crack at midspan LTB LTB LTB LTB ductile ductile LTB LTB LTB / Local instability/Bucklg LTB / Local instability/Bucklg Buckling/ LTB LTB LTB
Page 23
Table 1-10: Normalized Moment-Rotation Curves 02 07 3PS7001601408
4PS7001601408
1
1
0.8
0.8
M/Mpl [-]
M/Mpl [-]
1.2
0.6
act. = 3.61
0.4 0.2 0
0.6
act. = 4.96
0.4 0.2
0
1
2
3
4
0
5
/ pl [-]
0
1
2
03
1
0.8
0.8
M/Mpl [-]
1
0.6
act. = 3.40
0.4
0
6
0.6
act. = 5.03
0.4 0.2
0
1
2
3
0
4
0
1
2
3
/ pl [-]
4
5
6
/ pl [-]
01
08 4PS9601601408
3PS9601601408 1
1
0.8
0.8
M/Mpl [-]
M/Mpl [-]
5
4PS7001601106
0.2
0.6
act. = 1.47
0.4
0
0.6
act. = 2.41
0.4 0.2
0.2 0
0.5
1
1.5
2
0
2.5
0
0.5
1
04
1.5
2
2.5
3
3.5
/ pl [-]
/ pl [-]
06 3PS9601601106
4PS9601601106
1
1
0.8
0.8
M/Mpl [-]
M/Mpl [-]
4
05 3PS7001601106
M/Mpl [-]
3
/ pl [-]
0.6
act. = 1.65
0.4
act. = -
0.4 0.2
0.2 0
0.6
0
0.5
1
1.5
/ pl [-]
2
2.5
3
0
0
0.5
1
1.5
2
2.5
3
3.5
/ pl [-]
While the S700 could achieve R=3 in all test configurations, the S960 displayed as expected lower rotational capacity in test 04. In the corresponding 4P bending test, the Mpl was slightly missed. Test 01 was aborted before reaching the final rotational capacity. It has to be pointed out, that the usage of stiffeners would increase the rotational capacity.
Page 24
1.4.4
Conclusions for beams in bending
According to EC3, stiffeners should be applied to members at points of concentrated loads when coping with structures of cross-section Class 1. These were not applied in the first series, and thus better rotational capacity could be expected if used. However, the possible influence of welding, especially in regard to the rather thin plate material used within this study, led to the decision to avoid stiffeners. The rotational capacity, R=3, was achieved by all specimens made from S700 in the first series with single symmetric specimens. None of the S960 specimens reached R=3, but 2 out of 4 had to be aborted due to the large deflections and corresponding testing rig issues. One test (06_4P_S960_160_110_6) did not reach Mpl. However, for the lower steel grades, S700 and consequently S500, within the scope of the tested geometries, the restrictions given in [4] for plastic design might be considered as overconservative. For the second series, containing double symmetric specimens, the stability failure mode lateral torsional buckling was usually present, as the aim of dimensioning the specimens at the limit between Class 2 and 3 in combination with the available plate thickness 6 and 8 mm led to very slender structures. With the introduction of bolted stiffeners, 4 remaining tests were used for further evaluations (Tests 12 to 16). Of these, two were made of S700 and two of S960. While two still failed due to lateral torsional buckling, they could achieve their M pl. Both S700 specimens and one S960 achieved Mpl, while one S960 did not, failing by an interaction of local buckling and lateral torsional buckling. The results indicate here that the current cross section class limits for beams in bending for S700 are applicable, provided lateral torsional buckling can be excluded. For S960 the rules might be applicable, but further experiments are recommended. The material properties regarding fu/fy ratio and elongation at fracture was achieved by all steel grades, one material set of S960 had a slightly lower yield-strength ratio than required with 1.04. The corresponding specimen (4) did reach Mpl, but did fail before R=3 due to lateral torsional buckling. The uniform elongation was in all cases lower than the EC-requirement, but the overall behaviour seemed not to be influenced by this fact. 1.4.5
Numerical Studies – I-sections
For the I-section tests conducted, a numerical study using finite-difference approach was used. Figure 1-16 shows the moment-curvature plots for sections 01,04,10,15, and 16. Without doing any analysis, it is clear that, theoretically, these sections display considerable ductility. Figure 1-17 shows the results for the other two S960 sections tested. It should be noted that deeper sections reach maximum moment capacity at a lower curvature, since the limiting condition is the maximum strain in the section. In Figure 1-17 shown also are the curvature values corresponding to the Plastic Moment of resistance of Section 08. Using a customary definition of ductility as the ratio of the upper and lower curvatures at which the plastic moment is obtained, the ductility ratio is of 3.6.
Figure 1-16: Moment-curvature results for tested sections 01, 04, 10, 15 and 16.
Page 25
Figure 1-17: Moment-curvature results for tested sections 06 and 08 Table 1-11 shows a comparison between theoretical and observed maximum moment capacities. Where lateral-torsional buckling was observed, the experimental values are obviously lower. In most cases, however, close agreement is obtained between the two values. Table 1-11: Theoretical and experimental moment capacities 01
04
06
08
10
15
16
17
Theoretical
298.0
217.7
216.1
298.5
266.5
505.7
470.3
206.6
Experiments
294.5
218.6
210.8
287.3
195.0
507.7
434.5
179.4
1.4.6
FE analysis of rotation capacity of hollow section beams
Influence of the ultimate strength/yield ratio, fu/fy, on the bending resistance and rotation capacity of HSS hollow section beams was investigated and cross-section classification limits were accessed. The experimental data available on 4-point bending experiments performed in Australia and Europe on tubular section beams were firstly validated by FEA before the same model was used in the parametric analysis. 1.4.6.1
Validation of 4-point bending experiments by FEA
The finite element model created by ABAQUS, the finite element software package [16], is used for validation of 4-point bending experiments of hollow section beams performed by two research groups. Wilkinson & Hancock experiments [17] were performed on small-scale mildsteel beams with spans of 1.3 and 1.7 m and beam experiments by HAMK [18] have spans from 3 m to 6.8 m, see Figure 1-18. In both set of experiments cold-formed hollow sections are produced in continuous forming (CF) process. Loading was applied in both experiments by a spreader beam supported by “side plates” welded to the web of the tested beam.
a) Wilkinson and Hancock [17]
b) HAMK experiments [18]
Figure 1-18: 4-point bending experiments used for validation by FEA.
Page 26
The exact geometry of specimens with the side plates (the loading plates) and welds was modelled in FEA in order to avoid any uncertainties about boundary and loading conditions, see Figure 1-19. The vertical plane symmetry boundary conditions were used along the beam and in the mid cross-section, meaning that ¼ of the beam was modelled.
Figure 1-19: FE model of 4-point bending experiments. Shell elements with linear interpolation functions and reduced integration in ABAQUS, S3D4r, were used for the beam. The loading plates and welds are modelled with continuum solid elements C3D8R and shell-solid coupling was applied by tie constraint surface pairs. Several analysis approaches offered in ABAQUS [16] were tested in this study: a) RIKS archlength method, b) General/Static and c) quasi-static explicit dynamic. It was found that for the analysed problem the General/Static solver with load application by displacement control gives optimum performance between the robustness, calculation time and quality of the results. Standard convergence problems were overcome by introducing automatic stabilization method with default value of dissipated energy fraction equal to 0.0002. Exact material properties obtained in coupon tensile tests of each specimen in bending experiments were considered in FEA. Different material properties are used for the flange and the web, according to coupon tests results The analysis was carried out considering three ways to model initial imperfections: - equivalent imperfections given in the form of the Eigen-mode obtained in the buckling analysis and assuming amplitudes according to common practices, - direct use of measured imperfections, - modelling of the welding induced geometric imperfections and residual stresses. It was found that the welding induced imperfections, see Figure 1-20, and the consideration of those lead to more accurate prediction of the local buckling failure modes and the rotation a capacity than the state of art model of the imperfections.
ew ew
ew
TB [rad]
t
ew
= bw,eff ∙ ew TB∙t
ew
a a) induced strain distribution
b) induced strain vs. angular distortion TB
Page 27
c) temperature field
d) von Mises stresses
e) out of plane deformations
Figure 1-20: Welding induced strains applied in FE model of RHS 140x140x6 Comparisons of FEA and results of experiments of 4-point bending of hollow section beams made by Wilkinson & Hancock [17] and HAMK [18] are shown in Figure 1-22 and Figure 1-23, respectively. Ultimate resistance was well estimated by FEA even if no imperfections were applied. However, the rotation capacity was overestimated and in most cases the obtained failure mode in FEA did coincide with experiments because the local buckling occured in the mid-span of the beam. Modelling influence of welding gives very good results in terms of prediction of rotation capacity. Also the characteristic failure mode obtained in experiments, local buckling near the loading plates, was obtained in each case of FEA, see Figure 1-21.
Figure 1-21: Local buckling near the loading plates - failure mode obtained in FEA with welding induced imperfections: RHS 140x140x6
Page 28
1.4 1.2
1.0
Non-dimensional moment (-)
Non-dimensional moment (-)
1.2
0.8
0.6
No imperfections
Welding induced imperfections Residual stresses
0.4
Welding & residual stresses 0.2
1.0
0.8 No imperfections Welding induced imperfections Residual stresses Welding & residual stresses
0.6 0.4 0.2 0.0
0.0 0.0
0.5
1.0 1.5 2.0 Non-dimensional curvature (-)
2.5
0
3.0
1
2
a) SHS 100x100x3
3
4 5 6 7 8 9 Non-dimensional curvature (-)
10
11
12
b) RHS 150x50x4
Figure 1-22: Comparison of non-dimensional moment-rotation curves: Wilkinson & Hancock experiments [17] vs. FEA 160
180 160 140
120
100
Force (kN)
Force (kN)
120
80 No imperfections
60
Welding induced imperfections
80 No imperfections Welding induced imperfections
40
40
Residual stresses
Residual stresses
20
Welding & residual stresses
Welding & residual stresses 0
0 0
20
40
60 80 100 Deflection (mm)
a) RHS 150x100x4
120
140
160
0
100
200
300 400 500 Deflection (mm)
600
700
b) SHS 140x140x6
Figure 1-23: Comparison of load-deflection curves: HAMK experiments [18] vs. FEA 1.4.6.2
Parametric study of HSS and MS compact hollow section beams
A Parametric study of the rotation capacity and bending resistance of SHS and RHS sections made of HSS was subsequently performed, considering various material properties. Previously validated FE model of 4-point bending test with welding induced imperfections was used for the parametric study. The parametric study was performed using single span 5.8 m beam in the 4-point bending test set-up with the length of the constant bending moment region CBM = L/3 = 1932 mm. Five square hollow sections (SHS) and nine rectangular hollow sections (RHS) were chosen such that the flange slenderness was in a range between 16 – 60 in order to validate crosssection class limits according to the EN1993-1-1 [3], see Table 1-12.
Page 29
Table 1-12: Hollow sections considered in the parametric study
Section shape (aspect ratio)
Flange slenderness
Height Width Thick. d
b
t
(mm) (mm) (mm)
cf/te (-) S355 S460 S500 S700 S960
160
160
10
16.0
18.2
19.0
22.4
26.3
150
150
8
19.4
22.0
23.0
27.2
31.8
140
140
6
25.0
28.4
29.7
35.1
41.1
150
150
6
27.0
30.8
32.1
38.0
44.5
160
160
5
35.6
40.6
42.3
50.1
58.6
150
100
6
19.9
23.6
27.6
180
120
6
24.8
29.3
34.4
180
120
5
30.6
36.2
42.4
180
120
4
39.4
46.6
54.6
240
160
5
42.3
50.1
58.6
200
100
6
19.9
23.6
27.6
RHS
200
100
5
24.8
29.3
34.4
d/b=2.0
240
120
5
30.6
36.2
42.4
240
120
4
39.4
46.6
54.6
SHS d/b=1.0
RHS d/b=1.5
Two sets of materials: the mild-steel (MS) and the high-strength steel (HSS) were defined using generic stress-strain curves, see Figure 1-24 for HSS. Materials with minimum requirements of EN1993-1-1 (fu/fy = 1.1; Ag = 15ey; A5 = 15%) and EN1993-1-12 (fu/fy = 1.05; Ag = 15ey; A5 = 10%) were analysed for the MS and HSS, respectively. In the case of HSS, the nominal materials conforming to the design code requirements were compared to the possible increases and decreases of ultimate strength/yield ratio in range fu/fy = 1.0 – 1.3, see Figure 1-24.
Engineering stress (N/mm2)
1000
800
600 S960 - real material S960 - fu/fy=1.1; Ag=6.9%; A=10% S960 - fu/fy=1; Ag=6.9%; A=10% S700 - real material S700 - fu/fy=1.1; Ag=5.0%; A=10% S700 - fu/fy=1; Ag=5.0%; A=10% S500 - real material S500 - fu/fy=1.1; Ag=3.6%; A=10% S500 - fu/fy=1; Ag=3.6%; A=10%
400
200
0 0.00
0.05
0.10 0.15 Engineering strain (-)
0.20
0.25
Figure 1-24: Generic high-strength steel (HSS) materials used in the parametric study compared to the results of coupon tests. An Example of results of 4-point bending FEA on SHS beams for S700 and S960 is presented in Figure 1-25. In all analysed cases local buckling of the compression flange, followed by the
Page 30
buckling of the web in the compression zone occurred near the loading plates as in reference experiments. Results are consistent considering obtained ultimate bending resistance and rotation capacity in function of steel grade and ultimate strength/yield ratio of the material. 1.25 Non-dimensional bending resistance: Mu/Mpl (-)
8
d/b=1.0 - S700: fu/fy=1.300; Ag=5.0%; A5=10% d/b=1.0 - S700: fu/fy=1.200; Ag=5.0%; A5=10% d/b=1.0 - S700: fu/fy=1.100; Ag=5.0%; A5=10% d/b=1.0 - S700: fu/fy=1.050; Ag=5.0%; A5=10% d/b=1.0 - S700: fu/fy=1.025; Ag=5.0%; A5=10% d/b=1.0 - S700: fu/fy=1.000; Ag=5.0%; A5=10%
Rotation capacity: R = ku/kpl - 1 (-)
7
0.75 10
Class 3
Class 2
Class 1 - EC3 limit
1.00
20 30 33 38 40 42 Flange slenderness: c/te (-)
6 5 4 3 2 1 0
50
10
a) Non-dimensional moment
20
30 33 38 40 42 Flange slenderness: c/te (-)
50
b) Rotation capacity
Figure 1-25: Cross section classification for generic SHS S700; fu/fy = 1.0 – 1.3 Cross-section Class 1 and Class 2 flange slenderness limits, obtained considering rotation capacity R > 3 and resistance criteria Mu/Mpl > 1 are summarized in Table 1-13. The Class 1 and Class 2 limits are presented in function of the steel grade and the ultimate strength/yield ratio of the material in Figure 1-26. Both criterions show high nonlinear dependence on the ultimate strength/yield ratio. The Class 1 criterion, shown in Figure 1-26b clearly justifies the EN1993-1-12 [4] limitation of the ultimate strength/yield ratio to 1.05 as the rotation capacity criterion is rapidly reduced below this limit. No significant influence of the steel grade to the Class 2 limit is observed. Higher influence of the steel grade on the rotation capacity, i.e. Class 1 limit is observed in Figure 1-26b. Table 1-13: Obtained HSS Class 1 and Class 2 flange slenderness limits in function of steel grade and ultimate strength/yield ratio Ultimate
Class 1 limit considering
Class 2 limit considering
strength/yield ratio
rotation capacity criterion: R > 3
resistance criterion: Mu/Mpl > 1
fu/fy (-)
S500
S700
S960
S500
S700
S960
1
27.9
26.6
/
26.6
28.4
31.8
1.025
30.8
29.0
27.6
32.5
32.6
34.2
1.05
31.4
30.2
29.3
34.7
35.1
36.2
1.1
32.3
31.2
30.2
38.1
38.4
39.0
1.2
33.2
32.0
30.8
41.7
41.5
41.8
1.3
34.4
32.9
31.4
43.5
43.7
44.5
Page 31
35
Flange slenderness limit for R > 3
Flange slenderness limit for Mu > Mpl
45
40
38 35 35 S500 S700 S960
30
a) Resistance criterion – Class 2
30 30 S500 S700 S960
1.18
1.10 25 1.00 1.05 1.10 1.20 1.30 Over-strength value: fu/fy (-)
33
1.40
1.30
25 1.00 1.05 1.10 1.20 1.30 Over-strength value: fu/fy (-)
1.40
b) Rotation capacity criterion – Class 1
Figure 1-26: Required ultimate strength/yield ratio of the HSS material to satisfy current EC3 SHS flange slenderness limits Considering the minimum EN1993-1-12 [4] requirement for the ultimate strength/yield ratio fu/fy=1.05, Class 1 and Class 2 flange slenderness limits 30 and 35, respectively, are obtained. The obtained limits for HSS are higher compared to the limits for mild steels if the minimum design code requirements of the material are considered. However, in order to achieve the section Class 1 and Class 2 flange slenderness limits given as 33 and 38 in EN19931-1 [3], respectively, minimum required ultimate strength/yield ratio of the HSS material is 1.30. This limit is governed by the rotation capacity criterion, see Figure 1-26b. 1.4.6.3
Conclusions on rotational capacity of hollow section HSS beams
Welding of the loading plates at the cross section, where the concentrated forces are applied, has strong influence on geometric imperfections. FEA validation of a series of experimental results clearly showed the dominating influence of welding induced imperfections compared to the influence of residual stresses and bow-out imperfections due to cold forming. Cross section class limits were obtained from the results of FE parametric study considering strength and rotation capacity of the simple beam in 4-point bending test. For the mild steel beams, having ultimate strength/yield ratio in range fu/fy = 1.25 – 1.4, flange slenderness limits given in EC3 for class 1 and class 2, 33 and 38, respectively, are satisfied for S355, but lower cross-section class 1 flange slenderness limit 29 is obtained for S460. This complies with findings of Wang et al. [19] and Taras et al. [20]. However, the classification of hot-formed tubular sections in Class 1 was considered to be critically by [21]. Influence of the HSS steel grade and the ultimate strength/yield ratio on hollow section class limits of HSS are analysed and it was found that the ultimate strength/yield ratio has rather strong influence on resistance and rotation capacity: 1. Considering the minimum requirement for the ultimate strength/yield ratio of HSS in [4] fu/fy =1.05, Class 1 and Class 2 flange slenderness limits are 30 and 35, respectively. The obtained limits for HSS are higher compared to the limits for nominal mild steel properties obtained in this study. 2. In order to achieve the section Class 1 and Class 2 flange slenderness limits given in Eurocode 3 as 33 and 38, respectively, minimum required ultimate strength/yield ratio of the HSS material is fu/fy > 1.10, 1.30, respectively.
Page 32
1.4
Material Laws for FEM Simulation
1.4.1
Material modelling using damage mechanics
The load capacity of steel is influenced - aside from plastic instability – additionally by material damage. Assuming ductile behaviour (upper shelf), crack initiation and crack growth will develop under plastic strain. Voids will emerge, grow and finally coalesce as depicted in Figure 1-27.
F
F
F
F F
F nucleation of voids
growth of voids
coalescence of voids
Figure 1-27: Schematic presentation of ductile damage evolution of steel [26] This damage mechanism, however, is usually not part of commercial finite element calculations. To take this phenomenon into account, damage mechanics models can be used. Several are available and distinguished e.g. by loading (monotonic, cyclic), fracture behaviour (cleavage, ductile), implementation of damage (coupled, uncoupled) and general approach (micromechanically, phenomenological) [27]. For the simulations conducted within the study presented here, a coupled damage model for phenomenological assessment of ductile fracture under monotonic loading was used. The definition of crack initiation is based on damage pl curves, where the critical equivalent plastic strain e D is defined as a function of the stress triaxiality . If the integral of strain-increment
e Dpl
de
pl
divided by the critical equivalent plastic strain
results in or exceeds 1, ductile crack initiation is reached [28].
de
(2.14)
pl
e pl = 1 D
The critical equivalent plastic strain
e Dpl = a e b + c
e Dpl
can be written as: (2.15)
The characteristic trend of a damage curve is depicted in Figure 1-28 (left). The parameters a, b and c from equation (2.15) can be derived from coupon tests with different damage grade, different notch sizes, respectively. However, recent research [29] revealed unsafe results using an exponential expression for stress-triaxiality 0.4 . This is found to be due to a change of the failure mode from void coalescence to shear fracture. In this case, an extension from 2D
Page 33
to a 3D damage-curve is necessary, which contains (aside from invariant of the stress deviator, the so-called Lode-angle
)
the influence of the 3rd
.
Figure 1-28: Characteristic damage resistance curve (left) and Stress-strain curve with progressive damage degradation [16] After crack initiation, the degradation of material stiffness is defined in the used model by the scalar damage variable D. It describes the grade of degradation starting at the crack initiation (D=0) until failure of the element at D=1. To enhance convergence of simulations, it is possible to delete elements which reached a lower value than 1. By defining D, the actual stress-tensor can be derived by multiplying the Young’s modulus E with (1-D). An example is depicted in Figure 1-28 (right). The dotted line shows the stress development without damage consideration, while the continuous line displays the stress curve under consideration of degradation of material stiffness. However, problems arise when implementing damage progression in FE-programs on the basis of a stress-strain relationship. When a structure is subjected to extreme loading conditions, the initial smooth distribution of strain tends to localize due to geometrical effects (e.g. necking) or material instabilities (e.g. micro cracking). In a meshed model, this means that strain increasingly concentrates on an ever decreasing number of elements and, thereby, introducing a strong mesh dependency. A proposal to reduce this mesh dependency consists of expressing material behaviour after damage initiation in terms of a stress-displacement relation, thus replacing the element length dependent strain dimension by the equivalent plastic displacement. The equivalent plastic displacement value ūpl is obtained in incremental terms by the following equation: 𝑢̅̇𝑝𝑙 = 𝐿 ∙ 𝜀̇𝑝𝑙
(2.16)
where 𝜀̇𝑝𝑙 is the incremental plastic strain and L represents a characteristic length, which is calculated in terms of the element size. Consequently, as depicted in Figure 1-29, the evolution of the damage variable D progresses as a function of the respective equivalent plastic displacement. In this case, the damage evolution is expressed in a linear form, therefore, the softening of the yield stress will also degrade linearly until a complete loss of load-carrying capacity (σy = 0) occurs.
Page 34
Figure 1-29: Damage variable progression and yield stress softening The area under the yield stress softening curve in Figure 1-29 (right) represents the specific fracture energy proposed by Hillerborg [30]. By using brittle fracture concepts, he defines the energy required to open a unit area of crack, Gf, as a material parameter. As shown in Figure 1-30, it enables the regulation of the degradation rate.
Figure 1-30: Variation of fracture energy levels on (a) single element and (b) wide plate model. The variation of fracture energy levels depicted in Figure 1-30 shows that higher energy values required to originate additional crack surfaces lead to slower degradation rates. On the left (a), the figure illustrates these effects on a single element subjected to tension and in (b) the same effects implemented on a wide plate model. This parameter constitutes a practical calibration tool when adjusting the declining slope of the force-displacement curve derived from the FE-models after damage starts to affect material behaviour. A further regulating damage parameter is established in order to limit the magnitude of incurring degradation on the elements of the FE-model. Maximum degradation, Dmax, combined with subsequent element deletion once Dmax is reached allows for the pinpointing indication of global failure in FE-models. Figure 1-31 shows the corresponding effects. On the left, Figure 1-31(a) shows a single, damage afflicted finite element with maximum degradation Dmax = 0.5 loses in a sudden drop all load-carrying capacity due to its deletion after Dmax is reached. On the right in (b), the figure shows the influence D has in a wide plate model: while the degradation keeps constant, the initiation of rupture (deletion of elements) starts at lower displacement values.
Page 35
Figure 1-31: Variation effects of maximum degradation on (a) single element and (b) wide plate model. After the geometrical considerations and the input of material data follows the meshing of the model. At first, the establishment of continuum solid three dimensional element types responds to its suitability when performing stress analysis without a predominance of bending loads. The effect of the interpolation order between the nodes of the elements, which enables the calculation of DOF (degrees of freedom) at other points beside the nodes, is studied by performing the same calculation with linear 8-node bricks (C3D8R) and also with quadratic 20node bricks (C3D20R) available in ABAQUS finite element program. Figure 1-31 shows the plotted results of those calculations and it becomes evident that no distinguishable differences and, therefore, no loss in accuracy is to be recognized until the force-displacement curve has already undergone a substantial plastic deformation. The damage initiation starts here per definition when the force-displacement curve of the damage-free FE model detaches from the actual force-displacement curve derived from the tests (“damage initiation” in Figure 1-31. This critical point is utilised to derive the damage curve and takes place before the clearly recognizable bifurcation between the forcedisplacement curves obtained by FE-models with C3D8R and C3D20R elements. This recognition assures that the derived damage curves are independent of the chosen order of interpolation. Furthermore, the option of adopting elements with reduced integration to compute quantities over the volume of the element is also evaluated (the “R” at the end of the element name distinguishes reduced-integration elements). Figure 1-32 shows that the difference between the force-displacement curve of the FEmodel with fully-integrated 8-node bricks (C3D8) and the one with reduced-integrated elements (C3D8R) is negligible within the relevant displacement range. Taking these considerations into account, the ultimate choice for C3D8R elements to model the tensile tests with wide plates is based mainly on the reduction of computational time.
Figure 1-32: Effects of element type variation on force-displacement curve and meshed wide plate model.
Page 36
In order to assure reliable solutions during calculations when material and geometrical nonlinearities constitute basic properties of the implemented FE-model, a suitable computation method is required. ABAQUS offers the Riks method for these particular cases. Treating the load magnitude as an additional unknown, this method solves simultaneously for loads and displacements, providing solutions regardless of unstable or stable responses of the model. To measure the progress of the solution, ABAQUS uses the arc length, “l”, along the static equilibrium path in load-displacement space. The loading remains proportional during computation and the solution outputs a load proportionality factor λ for each increment which, when applied to the initial reference load Pref, provides the effective load magnitude [16]. 1.4.2
Material modelling using ductile material model
A similar, but alternative method for deriving material properties has been developed using an implicit numerical solver. Quasi-static analysis was made using explicit dynamic solver in ABAQUS FE software package [16], providing reliable solution for complicated geometries and high level of nonlinearities. Explicit solver does not have usually convergence problems, such as the implicit static solver, in models when significant nonlinear behaviour is present. Therefore, this procedure is practical for analysis of joints. Calibration procedure for ductile damage material model in Abaqus, developed by Pavlovic et al. [22], was used, based only on results of a coupon test. Parameters of ductile damage initiation criterion and damage evolution law were derived analysing undamaged and damaged material responses in the coupon test taking into account localization of plasticity. Uniaxial stress state is a necessary precondition for the coupon specimen.
Engineering Stress (MPa)
Applicability of the material model was then validated by comparing FEA results to experimental results of S700MC and S960Q SSAB centre hole specimens (CHT). Results of the coupon tests are presented in Figure 1-33. The main requirement was to have identical mesh size at least in the critical cross-section of the coupon specimen and in the plate with the hole. The gauge in coupon tests was l0 = 80 mm.
1100 1000 900 800 700 600 500 400 300 200 100 0
S700MC (SSAB) S960Q (SSAB)
0
5
10
15
20
Engineering Strain (%) Figure 1-33: Nominal stress-strain curves from the coupon tests Finite element (FE) model of the coupon tests was made in order to calibrate the parameters of the ductile damage material model. Geometry and the boundary conditions of the model are shown in Figure 1-34a. Eight node hexahedral solid elements with reduced integration (C3D8R) and the size of 1.5 mm were used in the central zone of the model, see Figure 1-34b.
Page 37
symmetry BC: Ux=Ry=Rz=0
kinematic coupling to a reference point
symmetry BC: Uz=Rx=Ry=0
load application by imposed translation
a) geometry and BCs
b) the mesh
Figure 1-34: The FE model of the coupon specimen Ductile damage material model in Abaqus is based on reduction of initial material modulus of elasticity E, in function of artificial damage scalar D as shown in Figure 1-35. The damage model is defined by two sets of parameters: damage initiation criterion and damage evolution law. The damage variable D takes values form 0 to 1 from the onset of damage until the complete damage. The onset of damage is defined by the damage initiation criterion and it depends on stress triaxiality , is similar to as it is analytically defined by the Considère criterion.
Figure 1-35: Ductile damage material model The elastic behaviour of the material is defined with initial modulus of elasticity E0=214 GPa, which is defined in experiments, and Poisson’s ratio v=0.3. The hardening part of the material behaviour is defined by the plasticity curve while the softening part and the failure are governed by the ductile damage model. Parameters of ductile damage initiation criterion and damage evolution law are derived analysing undamaged and damaged material response in the tensile test, as described by Pavlović et al. [22]. Firstly, the plasticity curve is defined by transforming the engineering stress-strain curve shown in Figure 1-33 to the true stressstrain curve shown in Figure 1-36 (damaged response shown with the dash-dot line).
Page 38
1600
1400
True stress (MPa)
1200
Critical damage, "rapture" point (Dr =Dcr )
Damage initiation, "necking" point (Dn=0)
1000 damaged resp. 800
600 Total damage, "fracture" point (Df=1)
uniaxial plastic strain at the onset of damage
400
200
accumulated plastic strain 0 0
0.1
0.2
0.3
0.4
0.5
Localized true plastic strain (-)
Figure 1-36: Damage extraction procedure and the input plasticity curve – S700MC The undamaged material response is obtained assuming ideal plastic-constant engineering stress after the onset of damage, i.e. at the strain corresponding to ultimate tensile strength. Transforming the constant engineering stress to the true stress-strain data, the curve presented with the solid line in Figure 1-36, is obtained. The damage initiation criterion is defined as equivalent plastic strain at the onset of damage which depends on stress triaxiality Eq. (1.16) [22]. Damage initiation in Abaqus is e pl 0
also strain rate dependent, but in the quasi-static analysis used here this it is neglected. Uniaxial true plastic strain at the onset of damage e npl = 0.0985 is obtained from Figure 1-36 for S700MC and e npl = 0.0536 for S960Q as the plastic strain at which the ultimate tensile strength is obtained. The damage initiation criteria for both materials are shown in Figure 1-37a.
e 0pl ( ) = e npl exp 1.5 ( 1 / 3)
(1.16)
0.20
S700MC S960Q
0.15
0.0985
0.10 0.05
0.00 -0.67 -0.33 0.00
0.33 0.67 1.00 Stress triaxiality (-)
1.33
a) damage initiation criteria
1.67
Damage variable (-)
0.25
uniaxial tension
Equivalent plastic strain at the onset of damage (-)
0.30
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Dcr
S700MC
S960Q
0.0
0.2 0.4 0.6 0.8 Equivalent plastic displacement (mm)
1.0
b) damage evolution law
Figure 1-37: Input curves for ductile damage material models
Page 39
Once the damage initiation criterion is defined, the plasticity curve and the damage evolution law for use in the ductile damage material model can be derived from experimental results of the coupon test taking into account the localization of plastic strains after offset of damage (necking).
Figure 1-38: Comparison of experimental and FEA results of coupon tests – S700MC The procedure used in Pavlović et al. [22] is based on an engineering approach and the localization of the plasticity in the necking zone of the coupon specimen. Several parameters, depending on material behaviour and the FE mesh, influence material characteristics. The parameters are described in detail in [22] and the values used in this study are below: 1.
initial gauge length l0 = 80 mm;
2.
average necking zone length lloc = 6.0 mm (4.5 mm for S960Q);
3.
localization rate factor L = 0.45;
4.
damage eccentricity factor D = 2.1;
5.
finite element size LE=1.0 mm;
6.
finite element size factor S = 0.92 (assuming LR = 0.8 mm, see [22]);
7.
element type factor E = 2.5 (2.5 to 3.2 for C3D8R elements [22]).
With the above listed set of parameters, the damage evolution laws for S700MC and S960Q are shown in Figure 1-37b. Values of those parameters were calibrated by matching the experimental stress-strain curve to the curve obtained from the FE model, see the example for S700MC in Figure 1-38. Very good agreement was obtained, especially in the softening part of the curve. Geometry of the plated specimen with 8 mm centre hole is shown in Figure 1-39. Symmetry boundary condition is used only through the mid plane of the plate thickness. Load was applied as displacement on the upper wide part of the specimen corresponding to the grip area in a testing machine which is constrained to a reference point. Similarly the lower grip area is constrained to a reference point having all the 6 degrees of freedom restrained. The same element size and type (length 1 mm, C3D8R element) were used in the coupon specimens and plated specimens. This is important because FEA is used to calibrate the damage material model parameters of the coupon specimen using the same elements. Four elements were defined through the (one half) thickness of the plate. In the wide zone of the specimen where no propagation of material damage is expected, mesh size was increased to 5 mm in order to reduce the calculation time.
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a) whole model (CHT-700-24)
b) the mesh
Figure 1-39: The FE models of the plated specimens Comparisons of the load-displacement curves of experiments and FEA are given in Figure 1-40 and Figure 1-41. Very good agreement of FEA and the experimental results was obtained considering ultimate loads and initiation of fracture. For both materials, FEA results for the specimens without the centre hole fit almost perfectly well to the experimental results. Slightly higher resistances in FEA of specimens with centre hole may hypothetically be addressed to disregard of residual stresses and possible micro cracks due to hole drilling in the FEA. 500 CHT-700-0 CHT-700-8 CHT-700-16 CHT-700-24 CHT-700-32 CHT-700-40
Force [kN]
400 300 200 Experimental FEA
100 0 0
2
4
6
8 10 12 Displacement (IDT) [mm]
14
16
18
20
Figure 1-40: Experimental vs. FEA load-displacement curves of CHT plate specimens S700MC
Page 41
700 600 Experimental FEA
Force [kN]
500 400
CHT-960-0 CHT-960-8 CHT-960-16 CHT-960-24 CHT-960-32 CHT-960-40
300 200 100 0 0
2
4
6 8 Displacement (IDT) [mm]
10
12
14
Figure 1-41: Experimental vs. FEA load-displacement curves of CHT plate specimens - S960Q Plated specimens after testing in experiments and corresponding FEA are shown in Figure 1-42. The diagonal fracture line in the plated specimens is the consequence of development of diagonal pattern of principal stresses due to the geometry of the specimen. This phenomenon was well reproduced in FEA using the described damage material model. The Mises stresses and the crack development are shown in Figure 1-43.
a) experiments (all specimens)
b) FEA (CHT-960-0 and CHT-960-16)
Figure 1-42: Comparison of experimental and FEA fractured modes of the plate specimens, S960Q
a) Elastic
b) Plastic
c) Necking
d) Rapture
e) Fracture
Figure 1-43: Development of stresses and fracture in specimens CHT-700-0
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400
500
350
450 400
300
200
Force [kN]
Force [kN]
350
250 A1 - Exp. A4 - Exp. A1 & A4 - FEA A2 - Exp. A3 - Exp. A2 & A3 - FEA
150 100 50
300 250 A1 - Exp. A4 - Exp. A1 & A4 - FEA A2 - Exp. A3 - Exp. A2 & A3 - FEA
200 150 100 50
0
0
0
200
400 600 800 Strain [mm/m x103 ]
a) S700MC (CHT-700-24)
1000
0
200
400 600 800 Strain [mm/m x103 ]
1000
b) S960Q (CHT-960-24)
Figure 1-44: Local strains in specimen with 20 mm centre hole In the locations A1-A4 around the hole, longitudinal strains were measured in experiments. Experimental and FEA results at these locations are compared in Figure 1-44. In this zone longitudinal strains are highly increased (localized) due to the necking. Satisfactorily agreement between experimental and FEA results proved applicability of the damage material model used in this study.
1.5 1.5.1
Material properties at elevated temperatures General Information
Main purpose of this task was to determine mechanical properties of high-strength steels at high temperatures. The nominal yield strengths of the tested specimens in this research were 700 N/mm2 and 960 N/mm2. The test series were quite small and the main aim was to study whether the behavior of these specified HS steels is similar to lower steel grades and if their mechanical properties fulfill the requirements for structural steel at elevated temperatures as stated in EN 1993-1-2 [5]. 1.5.2
Tested materials
Both tested materials, S700QL and S960QC are hot-rolled steels and manufactured by the Finnish company Rautaruukki Corporation. The test specimens are graded as high-strength steels. There were 35 test pieces of both steel grades. Before any testing all the test pieces were measured and verified that they are in accordance with the standard SFS-EN 6892-1 and -2 [23][24]. S700QL is quenched and tempered (Q) and low-temperature tough (L) steel [46], which meets the requirements of S690QL in standard EN 10025-6 [45]. The test specimens were cut out from thicker hot-rolled steel sheet with nominal thickness of 20 mm. S960QC is quenched (Q) and cold-formable (C) steel [46] which fulfills the requirements of prEN 10149-2:2013. The test specimens are cut out from a hot-rolled steel sheet with nominal thickness of 8 mm. 1.5.3
Testing equipment
Testing equipment is the same one as Jyri Outinen has used in his research [31][32]. The testing equipment is shown in Figure 1-45. In the oven there are three separately controlled resistor elements, which ensure stable air temperature. The resistors are controlled by
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temperature-controlling unit. The air temperature in the oven is measured with three separate temperature-detecting elements. The steel temperature was measured accurately from the test specimen using temperature-detecting element that was fastened to the specimen during the heating process. Differences between air temperatures and steel temperatures were taken into account. Load cell
Test specimen
Resistor elements
Heat insulation
Tension bar Rigid support Extensometer Figure 1-45: Testing equipment 1.5.4
Test Results
To verify the room temperature properties the tensile tests were carried out according to SFS-EN ISO 6892-1. Tensile tests were carried out as strain rate-controlled loading with a strain rate being 0.006 s-1. Results are shown in Table 1-14 with requirements from standards prEN10149-2:2013 and EN 10025-6. Two test pieces of both steel grades were used in room temperature tests. Table 1-14: Material properties at room temperatures Test
S960
S700
Measured
Requirement
Measured
Requirement
Modulus of elasticity E (MPa)
208600
-
205200
-
Yield stress ReH (MPa)
1098
960
833
690
Ultimate stress Rm (MPa)
1189
980-1250
880
770-940
Transient state tensile tests were carried out with two repeated tests at each load level. A thermal elongation of the structural steel was taken into consideration by the EN1993-1-2. In the temperature-strain relationship, the thermal elongation was subtracted from the total strain. A heating rate in the transient tests was 20 °C/min. The test specimen was heated until the temperature was 950°C or until the breaking of the test specimen. Additionally to transient tests, steady state tensile tests at some stress levels were carried out for both materials with one test at each temperature level. In the steady state tests, the same heating rate (20 °C/min) was used as in the transient tests, until the temperature rose
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to the specified value. After temperature rising there was two minutes waiting time before carrying out the tensile tests. The reduction of yield strength compared to the actual measured room temperature yield strength is presented in Figure 1-46.
Figure 1-46: Test results of yield strength fy,. Comparison of the reduction factors for S700 and S960. Test values compared to the actual, measured values at room temperature. Test results of measured actual yield strength at elevated temperatures and corresponding Eurocode values are shown in Figure 1-47.
Figure 1-47: Test results of yield strength fy, for S700 and S960. Stress-temperature values 1.5.5
Ductility behaviour at elevated temperatures
For high-strength steels like S700 and S960 the elongation at fracture in room temperature can be much below 20% (For example, for S960 the elongation at fracture in room temperature is generally approximately at the level of 7-10%). Thus it is obvious that they cannot reach the fire design requirement of 20% at time t=0 (ie. at temperature of 20°C). However, it is anticipated herein that the evaluations and conclusions provided by the other Tasks & Work Packages in Ruoste will prove that grades S700 and S960 have a sufficient material ductility in room temperature. Consequently, their ductility is thereby proven to be sufficient also for fire situation at time t=0, no matter that the fire design requirement 20% is not met. Next, when the temperature rises, Figure 1-48 shows that the ductility systematically increases together with the temperature, reaching the required 20% criterion at temperature of 600°C (and with higher temperatures even reaching and exceeding 50% elongation), thereby satisfying the provisions of EN1993-1-2 for fire design. Thus, as the material has sufficient ductility in the beginning of fire at time t=0, and reaches the 20% criterion of EN1993-1-2 at temperature of 600°C, it is reasonable to conclude that the ductility is sufficient also between these two ‘phases’.
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Figure 1-48: S960QC: Stress-Strain (steady state) curves As it comes to the high strength steels and the ductility of joints in fire situation, reference can be made to the PhD thesis of Xuhong QIANG, done in Delft University 2013 [33], where Qiang has studied endplate joints made of different steel grades up to and including S960: the rotation capacity of high strength steel endplate connections in fire is proven sufficient (based on the generally accepted sense that a minimum of 40-50 mrad ensures “sufficient rotation capacity” of a partial-strength bolted joint), which guarantees the ductility and safety of steel structures using connections made of high strength steel under fire condition. Moreover, the rotation capacity with high strength steels can be even higher (due to the general tendency to use thinner plate materials) compared to the thicker mild steel endplate. 1.5.6
Conclusions
28 transient tests were carried out of both steel grades S700QL and S960QC. Furthermore, some steady state tests were carried out to verify transient state test results. The steady state tests results were a little bit higher than the transient state tests as usually. Material properties at high temperatures analyzed from the tests are presented in Table 1-15 and Table 1-16. Table 1-15: Material properties of S700QL at high temperatures Temperature [°C] 20 100 200 300 400 500 600 700 800 900 1000
ky,θ EC3-1-2 1 1 1 1 1 0.78 0.47 0.23 0.11 0.06
ky,θ Tests 1.00 0.94 0.84 0.67 0.42 0.20 0.07 0.04
kp0.2,θ EC3-1-2 1 1 0.89 0.78 0.65 0.53 0.30 0.13 0.07 0.05
kp0.2,θ Tests 1.00 0.90 0.80 0.67 0.65 0.49 0.32 0.10 0.05 0.04
0.04
-
0.03
-
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Table 1-16: Material properties of S960QC at high temperatures Temperature [°C] 20 100 200 300 400 500 600 700 800 900 1000
ky,θ EC3-1-2 1 1 1 1 1 0.78 0.47 0.23 0.11 0.06 0.04
ky,θ Tests 1.00 0.99 0.94 0.93 0.87 0.64 0.37 0.18 0.06 0.04 -
kp0.2,θ EC3-1-2 1 1 0.89 0.78 0.65 0.53 0.30 0.13 0.07 0.05 0.03
kp0.2,θ Tests 1.00 0.79 0.75 0.65 0.38 0.18 0.11 0.04 0.03 -
The obtained reduction factors are lower (ca. 15%) than given in EN 1993-1-2. The obtained results should be compared not only to Eurocode provisions, but also to test results from literature and to different steel grades. The test results presented in Table 1-15 and Table 1-16 are put in Figure 1-49 which is taken from the QIANG, Delft University 2013 [33].
Figure 1-49: Yield strength reduction factors from literature and results from Ruoste With regard to Figure 1-49, it should be noticed that the old test results by Outinen and Mäkeläinen are in their studies obtained by using nominal room temperature yield strength as the reference value, why the presented values for the reduction factors may be somewhat too high. If all results in Figure 1-49 would be presented in the ‘same scale’ (ie. calculated using the actual room temperature yield strength as the reference) the results would settle quite well on the same level with the Ruoste results. Within the scatter (which is typically large for these kind of tests) most of the results would settle 0-15% below the EC prediction. The fast conclusion might be (although perhaps premature) that EC’s reduction factors are in general too optimistic and should be further reduced ca. 10% for all steel grades. Normally the yield strength of structural steels is in average 10-20% over the nominal strength. Thus, EC’s reduction factors, when applied to the nominal strength - as the case is in design calculations - predict quite well the actual strength at elevated temperatures. This seems to be the general approach with the current EN 1993-1-2 reduction factors. This would also be the result with the tested steels S700 and S960. From this it can also be concluded that the same reduction factors can be used for S700 and S960 as for the mild steels. Ductility behavior of high-strength steel grades S700 and S960 – although not being in the actual scope of this research and thereby not specifically tested herein – is briefly discussed. It can be concluded that steel grades S700 and S960 have sufficient ductility in fire situation.
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Page 48
STABILITY
2 2.1
2.1.1
Residual Stress Measurements General Information
Residual stresses have a major influence on the stability behaviour of steel members. The effect of the residual stresses are considered in the buckling curves and in the magnitude of the equivalent geometric imperfections used in the FEM based design methods. Based on the previous research results the effect of residual stresses on the high strength steel members (HSS) are less severe than in the case of normal strength steel (NSS) members. Therefore the application of the existing buckling curves developed for NSS members may lead to uneconomic design for HSS members. At the same time the application of the equivalent geometric imperfections proposed for NSS members can underestimate the resistance of HSS members. Therefore the general aim of this research report is to investigate the residual stress distribution and its extreme values in case of HSS box section members. The effect of the steel grade and the geometrical properties were investigated and design residual stress models were developed for the design of HSS members. The residual stresses have significant influence on the mechanical characteristic of steel structural members especially on the global and local buckling behaviour of compressed columns. Several design models are adopted in the steel design guidelines in Eurocode, ANSI/AISC 360-10 and Chinese code GB500017-2003 etc.; the applicability of these residual stress distributions are questionable in case of high strength steel structures due to the following three reasons: -
the material properties and manufacturing process of HSS sections are different from those ones used for NSS, the maximum tension residual stress in the weld region can be lower than the yield strength (fy), while for NSS section it is normally taken as fy, the current models do not take into account the cross section geometry, however, several previous test results show that residual stresses are strongly dependent on the width-to-thickness ratio (b/t) of the cross section.
Residual stress measurements were carried out on squared cross-sections, both on welded and cold-formed sections. During the measurements the longitudinal residual stress patterns were determined. The measurements were carried out using the sectioning technique and the deformations were recorded with electric strain gauges. The test specimens were delivered by three different manufacturers (Ruukki, SSAB and VoestAlpine) using three different material types (S500, S700, S960). The typical values of the residual stress patterns were studied as functions of the yield strength and the geometric properties of the tested cross-sections. The current test results were compared to the results of previous experiments and improved residual stress models were developed for welded and cold-formed square hollow sections, which models are based on the previous and current test results and usable for various steel grades from S500 to S960. 2.1.2
Work program
A total number of 17 residual stress measurements were carried out at the Budapest University of Technology and Economics Department of Structural Engineering using specimens from grades S500 to S960. Additionally, 5 extra cold-formed specimens were investigated from S420 and S460 material grades provided by Ruukki. The residual stresses were measured by the widely used “sectioning technique”. From the total number of 17 basic test specimens 10 specimen geometries belonged to local buckling and interaction tests. 7 specimen geometries belonged to the global buckling tests, aiming to investigate the global buckling behaviour of HSS compressed columns made from HSS square hollow sections. Table 2-1 gives an overview of the test matrix of the residual stress measurements. Two specimens are tested twice in order to check the reliability of the testing method.
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Table 2-1: Experimental research program Analysed basic Number of specimens duplication 2.2; 2.6 10 0 Task 2.4 7 2 Sum
17
2
Tests on S420 and S460 specimens 0
Total number of tests 10
5
14
5
24
Table 2-2 summarizes the geometry and the material properties of the tested 17+5 specimens. The CF9-120×6_R specimen was tested twice using the sectioning method, the specimen CF9-150×7_R was tested once with sectioning and a second time using an alternative residual stress measurement method (“Laser-Falconeye” method) to check the reliability of the “sectioning technique”. From the total number of the 22 different section types 13 specimens were cold-formed and 9 specimens were welded sections. The cold-formed specimens were produced by VoestAlpine and Ruukki. The welded specimens were produced by Ruukki and SSAB. Three test specimens were manufactured from S420, two specimens from S460, seven specimens form S500, 2 specimens are made from S700, and 8 pieces from S960 steel material. The width of the cross section varied between 100 and 250 mm. The thickness of the analysed sections were between 3 - 8 mm. The width to thickness ratio (blok/t) was between 13.75 - 60.5. Table 2-2: Investigated cross section geometries and material properties. Cold-formed blok/t PerMate(bProSign WP b t fy fu formed rial 2×rout) ducer test /t CF4.2-100×3_R 2.4 100 3 28.67 Ruukki 458 552 1 CF4.2-120×6_R S420 2.4 120 6 15.33 Ruukki 506 551 1 CF4.2_150×5_R 2.4 150 5 25.60 Ruukki 479 561 1 CF4.6_150×8_R 2.4 150 8 14.00 Ruukki 508 563 1 S460 CF4.6_120×4_R 2.4 120 4 25.00 Ruukki 559 598 1 CF5-120×6_V 2.4 120 6 15.67 VoestA 624 656 1 CF5-130×4_V S500 2.2; 2.6 130 4 28.00 VoestA 573 649 1 CF5-200×5_V 2.2; 2.6 200 5 35.60 VoestA 567 648 1 CF7-150×8_R 2.4 150 8 13.75 Ruukki 742 839 1 S700 CF7-150×4_V 2.2; 2.6 150 4 32.50 VoestA 799 874 1 CF9-120×6_R 2.4 120 6 15.33 Ruukki 1088 1182 1+1 CF9-150×7_R S960 2.4 150 7.1 16.62 Ruukki 1114 1199 1+1* CF9-120×4_R 2.2; 2.6 120 4 24.50 Ruukki 1049 1207 1 Welded W5-120×6_R 2.4 120 6 18.00 Ruukki 1 546 636 W5-150×6_R 2.4 150 6 23.00 Ruukki 1 S500 W5-195×6_R 2.2; 2.6 195 6 30.50 Ruukki 563 636 1 W5-250×4_S 2.2; 2.6 250 4 60.50 SSAB 624 692 1 W9-120×6_S 2.4 120 6 18.00 SSAB 1005 1047 1 W9-120×6_R 2.2; 2.6 120 6 18.00 Ruukki 1 W9-170×6_R S960 2.2; 2.6 170 6 26.33 Ruukki 1 992 1084 W9-220×6_R 2.2; 2.6 220 6 34.67 Ruukki 1 W9-250×6_R 2.2; 2.6 250 6 39.67 Ruukki 1 Manufacturing process of test specimens The welded specimens were welded from four plates using welds only in the corner zones (Figure 2-1). The width of the plates B and D were equal to the width of the cross section (b), and the original width of the sides A and C were equal to the distance between the inner sides of B and D (b-2×t) aiming to get a square hollow section with equal dimensions. Weld toes
Page 50
were placed on side A and C. Since the weld position has influence on the residual stress distribution, therefore its position has importance in further studies.
Figure 2-1: Welded specimens The manufacturing process of the cold-formed specimens was the “continuous forming” process, which includes the following main steps: -
(i) roll-forming of the straight strip first into a circular open tube,
-
(ii) joining the edges of the open tube by welding,
-
(iii) flattening the tube walls to form the desired rectangular shape
Testing method The allowable residual stress measurement techniques can be classified into two groups, which are the “destructive” and the “non-destructive” methods. The principle of the destructive methods is the releasing of the stresses. After or during the relaxation it is necessary to measure the difference between the relaxed and the stressed state. The non-destructive methods are recent developments. To carry out the residual stress measurement the sectioning method was used in the current project, as it is the most popular and most economical residual stress measuring method reported by several researchers in the past. Using the sectioning method, the specimen is cut in strips and then the strain changes between the cut and original phases are measured. Sectioning in strips gives information about the stress levels in the plane of the plate and the layering shows how the stresses vary through the thickness of the specimen. 2.1.3
Conclusions for residual stress measurements
Residual stresses on welded box sections 1. The current test results show that the maximum tensile residual stresses can reach the actual yield strength in case of S500 specimens and in a few cases also for the S960 material as well, however for S960 specimens the tension residual stress generally does not reach the yield stress. 2. The test results and the evaluation of the previous residual stress measurements show that the maximum tensile residual stress can be a function of the plate thickness and for larger plate thicknesses the maximum residual stress can be lower than the yield stress. This tendency is independent of the steel grade and is not a feature of HSS materials. 3. The test results show that the average compression residual stresses are independent of the steel grade. This means that the compression residual stresses do not increase linearly by increasing the yield strength. 4. The test results show that the compressive residual stresses depend on the b/t ratio and the plate thickness (t) of the investigated specimen. 5. Based on the test results and the statistical evaluation of 80 residual stress measurements executed on steel grades from S460 –S960 design residual stress models were developed. The shape of the residual stress distribution, the extreme values (σrt maximum tensile stress, σrc average compression stress) are given in the
Page 51
model depending on the parameters: fy, b0/t ratio and wall thickness (t). The width of the tension and compression zones can be also determined by equilibrium equation. 6. The general shape of the developed residual stress model for welded box sections is presented in Figure 2-2.
For all analyzed steel grades
Figure 2-2: Developed residual stress model for welded sections.
7.
The proposed residual stress model can be expressed by the following equations:
𝜎rt = Min 1,132 − 0,033 ∙ 𝑡 ∙ 𝑓𝑦 ;𝑓𝑦 . If t ≤ 6: 𝜎rc = 20 − 5𝑡 − (14000 ∙
1 𝑡−2
(3.1) 𝑏
−1
− 800) ∙ ( 0) ,
(3.2)
𝑡
𝑏
−1
If t ≥ 6: 𝜎rc = 20 − 5𝑡 − 4620 − 320𝑡 ∙ ( 0) ,
(3.3)
𝑡
8. The proposed general residual stress model (Model 3) estimates the real values by the following average differences: maximum tensile stress: 11.7%, average compression stress: 0.5%, width of the compression zone: 0.4%. Residual stresses of cold-formed sections 1. The current test results show that the membrane residual stresses can be neglected in the case of cold-formed square hollow section specimens produced by the “continuous forming” manufacturing method. 2. The bending residual stresses can be approximated by an average constant residual stress distribution in the flat plates as well as in the corner zone which can be calculated depending on the maximum yield strength. 3. The residual stresses for cold-formed HSS products are significantly different from the Normal Strength Steels (NSS). The test results show that the residual stresses normalized by the yield strength are much smaller for HSS sections than for NSS products. 4. While the normalized residual stresses for NSS sections are almost constant for steel grades of S235 - S420, the normalized residual stresses are decreasing by increasing steel grade. This favours HSS members and results in smaller residual stresses compared to the yield strength. 5. The reason of the different residual stresses depending on the yield strength between HSS and NSS sections can be explained by the different σ - ε diagram and the different plastic cyclic behaviour of the NSS and HSS material. Thus the square hollow section products are manufactured by two plastic deformations (i) producing circular section (ii) producing square section, the largest part of the material is bent in two different directions. This is similar to a plastic cyclic loading. The known enlarged Bauschinger
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6. 7.
8. 9.
effect of the HSS material can indicate that the target plastic deformation can be reached in the second deformation process on a smaller stress level, resulting in smaller residual stresses in the specimens. The tests showed that the average residual stresses in the flat plate parts are independent from the b/t ratio of the analyzed section. However the residual stresses in the middle plate part are slightly smaller than the residual stresses close to the corner zone. This result shows that the difference depends on the b/t ratio. The measured average residual stresses in the corner zones are 55% of the average residual stresses in the flat plate parts. The general shape of the developed residual stress model for cold-formed box section is presented in Figure 2-3.
Figure 2-3: Developed residual stress mode for cold-formed sections. 10. The proposed residual stress model can be given by the following equations: σrb,flat = ± (1.28 −
2.2 2.2.1
𝑓𝑦 1270 𝑀𝑃𝑎
) ∙ 𝑓𝑦 and σrb,corner = ±0.55 ∙ σrb,flat
(3.4)
Local Buckling Tests General Information
Previous research on local buckling of high strength steels showed an apparently optimistic prediction of resistance according to [8]([59][60][61]). However, similar results could be shown for mild steels [62] and the overall number of tests on high strength steel can be considered low. To increase the existing results and information, stub column tests with varying load scenarios and slenderness were conducted. Tests included S960 specimens aiming at an inclusion of these steel grades in further EC developments. To calculate the local buckling resistance according to [8] leads to an extensive procedure due to effective cross-section calculations and - especially in case of unsymmetrical loaded specimens - to unrealistic assumptions. As an alternative, a modified general method approach is introduced allowing for simplification by using the global buckling curves [3]. The improved resistance due to local buckling behaviour is taken into account by an effective imperfection factor and is based completely on gross-cross-section values. A similar approach has been used in assessing interaction of lateral-torsional buckling and local buckling of beams with tapered cross-section [67]. 2.2.2
Local buckling tests conducted
To investigate local buckling behaviour, 34 welded box sections and 41 structural hollow sections were used as quadratic stub columns. The sections were made of S500MC, S700MC and S960Q, with a varying non dimensional local slenderness between 0.64 up to 1.55 (welded) and 0.66 up to 1.32 (structural hollow sections). Extensive imperfection measurements were undertaken and analysed.
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The material properties obtained are given in Table 2-3 to Table 2-5. Table 2-3: Material properties of welded stub columns from material certificates Steel t fy fu, fu/ fy εu 15* A80 fy,actual/E (min 10%) [mm] [N/mm²] [N/mm²] [-] [%] [%] [%] S500M 4 615 690 1.12 10.64 4.35 17.35 S500M 6 562 634 1.12 12.1 4.00 25.45(A60) S700M 6 760 822 1.08 12.92 5.42 20.04 S960Q 6 991 1083 1.09 3.12 7.08 9.42 Table 2-4: Material properties, strength requirements of cold-formed specimens 1 2 3 4 5 fu, Steel b t fy,flat fy,corner fu,flat fu/ fy [mm] S500
S700 S960
130 200 200 110 150 150 100 120 120
4 5 4 4 4 7 4 4 3
[N/mm²] 584 614 537 616 533 597 729 786 804 891 1106 1210 981 990 1051 1227 1050 1094
corner
[N/mm²] 652 739 609 741 599 740 794 920 857 1091 1197 1389 1096 1156 1207 1412 1168 1246
6 fu,c/ fy,c
[N/mm²] 1.12 1.20 1.16 1.20 1.12 1.22 1.09 1.17 1.07 1.22 1.08 1.14 1.11 1.16 1.14 1.15 1.11 1.13
Bold: fulfilled criterion Table 2-5: Material properties, strain requirements of cold-formed specimens 1 2 3 7 8 9 10 A εu, 15* (min Steel b t εu Acorner fy,nom/E corner
10%)
S500
S700 S960
[mm] 130 200 200 110 150 150 100 120 120
4 5 4 4 4 7 4 4 3
[%] 10.08 10.43 11.09 11.71 6.22 1.18 1.37 1.68 1.63
[%] 1.69 2.33 1.94 1.80 2.11 1.16 1.23 1.45 1.63
[%] 3.57 3.57 3.57 5.00 5.00 6.86 6.86 6.86 6.86
[%] 29.55 21.63 30.87 25.74 13.49 7.8(t) 9.4(t) 9.8(t) 8.8(t)
[%] 9.43 12.23 10.90 7.96 7.56 13.3(t) 12.4(t) 11.4(t) 13.2(t)
Bold: fulfilled criterium 2.2.3
Test results
The achieved ultimate loads 𝐹𝑢 and stress-ratio 𝛹 are summarized in Table 2-6 for the welded specimens and in Table 2-7 for the cold-formed specimens. For each configuration (displayed in the denomination with steelgrade_width_thickness) four, five respectively, tests were conducted. The specimens were concentrically and eccentrically loaded, which is characterized by the stress-ratio 𝛹. The eccentricity was measured by 2x2 strain gauges at opposite faces of the specimens (face 2 and face 4). The averaged strain of the two strain gauges of the less loaded face (face 2) is divided by the averaged strain of the higher loaded one (face 4). 𝜓=
𝑠𝑡𝑟𝑎𝑖𝑛𝑓𝑎𝑐𝑒4 𝑠𝑡𝑟𝑎𝑖𝑛𝑓𝑎𝑐𝑒2
(3.5)
Page 54
CF-S500-200-4-1
Force [kN]
1000
750
500
5% Fy : 0.51 0.49 10% Fy : 0.49 0.51 Fu: 0.52 0.48 10% 0.96
250
0 -0.1
0
0.1
0.2
0.3
0.4
0.5
SG1 SG2 SG3 SG4 0.6
0.7
0.8
0.9
e [%]
Figure 2-4: Example for strain/ eccentricity evaluation The strains on opposite faces were evaluated at a total load of 10 % of the theoretical yield load, which was also used as alignment load (see also Figure 2-4). At this level, the specimen response is still in the elastic range and no significant 2nd-order effect exists. Table 2-6: Local buckling test results, Test No. 𝐹𝑢 S500_195_6 1 2261 2 2275 3 2216 4 2341 S700_180_6 1 2716 2 2686 3 2017 4 2721 5 2785 S960_120_6 1 2931 2 2970 3 1970* 4 2622 S960_220_6 1 3178 2 3184 3 2359 4 3196
welded sections 𝛹 Test 0.92 S500_250_4 0.96 0.68 0.95 0.85 S700_260_6 0.99 0.25 0.93 0.96 1.00 S960_170_6 0.98 0.00 0.73 0.99 S960_250_6 0.96 0.20 0.96
No. 1 2 3 4 1 2 3 4 5 1 2 3 4 1 2 3 4
𝐹𝑢 1086 1083 1056 902 2666 2670 2579 2199 2661 3382 3362 3447 2241 ** 3289 2867 2526
𝛹 0.95 1.00 0.71 0.32 0.96 0.97 0.69 0.33 0.95 0.98 1.00 0.92 0.18 0.96 0.95 0.54 0.27
*tension at one face at 10% yield strength; **failure of measuring equipment For the concentrically loaded specimens, the load was normalized to the plastic crosssection resistance and the displacement to the length of each specimen. The results are shown for the 3 investigated steel grades in Figure 2-5. For stocky section, a more or less distinctive ultimate load can be identified, followed by a sharper drop of the curve. With increasing slenderness, the load-displacement response becomes flatter and the ultimate load is reached at an earlier stage of displacement with respect to the specimen length.
Page 55
1.2
1.2
1
1
0.8
67p= 0.783
𝜆̅𝑝 =0.783
0.6
N/Npl
N/Npl
0.8
= 0.851 𝜆̅𝑝67p=0.851 0.6
0.4
0.4
67p= 1.256
67p= 1.554
𝜆̅𝑝 =1.554
0.2
0
0
𝜆̅𝑝 =1.256
0.2
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
0
0.01
0
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
0.01
Displacement/length
Displacement/length 1.2 1
𝜆̅𝑝 =0.656
150x150x7
1 0.8
𝜆̅𝑝 =0.937
p
67p= 0.937
0.6
𝜆67̅𝑝p==1.234 1.234
0.4
120x120x4 𝜆̅𝑝 =0.961
0.6
𝜆̅𝑝 =1.317
120x120x3
0.4
𝜆̅𝑝
7 6=1.411 p= 1.411 0.2
0.2
0
𝜆̅𝑝 =0.783
𝜆̅𝑝 =0.641 67 = 0.641 N/Npl
N/Npl
0.8
100x100x4
0
0
0.002 0.004 0.006 0.008
0.01 0.012 0.014 0.016 0.018
0.02
0
0.0025
0.005
0.0075 /L
Displacement/length
0.01
0.0125
0.015
Figure 2-5: Normalized Load-Displacement curves for welded S500 (top-left), S700 (topright) S960 (bottom-left) and S960 cold-formed specimens (bottom-right) Table 2-7: Local buckling test results, cold-formed sections 𝐹𝑢 𝛹 Test No. Test S500_130_4 1 773 * S500_200_5 2 1214 0.99 3 829 0.24 4 1025 0.58 5 1173 0.85 S500_200_4 1 1097 0.98 2 1109 0.87 3 1087 0.80 4 974 0.49 5 813 0.15 S700_110_4 1 1099 0.91 S700_150_4 2 1011 0.91 3 921 0.48 4* 651 0.00 5 699 0.03 S960_150_7 1 4345 0.94 S960_100_4 2 4396 0.95 3 4262 0.90 4 4430 0.93 S960_120_4 1 1372 0.96 S960_120_3 2 1360 1.00 3 975 0.13 4 796 0.21
No. 1 2 3 5
1 2 3 4 5 1 2 3 4 1 2 3 4
𝐹𝑢 1689 1693 1594 1535
𝛹 0.94 0.98 0.76 0.58
1113 1120 1043 1009 1021 1448 1443 889 1117 838 833 834 844
0.93 0.98 0.65 0.38 0.53 0.86 0.98 0.04 0.56 0.99 0.95 0.86 0.96
It is striking that with increasing steel grade the scaled displacement increases as well at ultimate load. This might be attributed to the increasing proportion of elastic displacements.
Page 56
The displacement is calculated geometrically from the 3 string pots at the point of load introduction of the specimen. 2.2.4
Evaluation according to EC3-1-5
To assess the local buckling resistance [8] assumes for each plate hinged boundary conditions and thus a buckling factor k = 4. However, the consideration of bending on the stub column leads to an increased k-value, as the adjacent faces of the most loaded plate act as an additional clamping. For the assessment of the elastic critical load, this value can be derived by using the Opensource programme CUFSM, which uses the Finite-Strip-Method to calculate the critical load of a given structure [51]. With the input of Young's modulus (210.000 MPa), the cross-section geometry and the load pattern ψ, a load amplification factor is given as output, defining the critical load but also the buckling factor k, as we know that 𝜎𝑐𝑟 = 𝑘 ∙ 𝜎𝐸 where σcr equals the critical stress and σE the equivalent buckling stress. Using strictly [8], the more unloaded opposite plate might be calculated with k=4, resulting in a higher φ than for the most loaded plate, due to the modified k. But as the latter plate will buckle first, the actual load on the opposite plate is lower, which can be taken into account using a modified slenderness, defined in [8], equation (4.4): (3.6)
𝜎𝑐𝑜𝑚,𝐸𝐷 𝜆̅𝑝,𝑟𝑒𝑑 = 𝜆̅𝑝 √ 𝑓𝑦 /𝛾𝑀0 The slenderness is assessed by: 𝜆̅𝑝 = √
𝑓𝑦 𝑏̅/𝑡 = 𝜎𝑐𝑟 28.4 ∙ 𝜀 ∙ √𝑘𝜎
(3.7)
Thus, the reduction factor ρEC of the most loaded plate is assessed with the k-factor derived from the Finite-Strip-Analysis, while the k-values (and subsequently the ρ-values) of the opposite and adjacent faces are set dependant on the first one. The reduction factor ρEC can be calculated according to [8] with: 𝜌𝑊𝑖𝑛𝑡𝑒𝑟 =
(𝜆̅𝑝 − 0.055 3 + 𝜓 )
(3.8)
𝜆̅2𝑝
We can calculate then: 𝜌𝑢𝑛𝑙𝑜𝑎𝑑𝑒𝑑 = 𝜌𝐸𝐶
(𝜆̅𝑝,𝑢𝑛𝑙𝑜𝑎𝑑𝑒𝑑 − 0.22)/(𝜆2̅𝑝,𝑢𝑛𝑙𝑜𝑎𝑑𝑒𝑑 ) (𝜆̅𝑝,𝑙𝑜𝑎𝑑𝑒𝑑 − 0.22)/(𝜆2̅𝑝,𝑙𝑜𝑎𝑑𝑒𝑑 )
And: 𝜌𝑝𝑠𝑖 = 𝜌𝐸𝐶
̅𝑝,𝑝𝑠𝑖−0.055 3+𝜓 )/(𝜆 ̅2 ) (𝜆 𝑝,𝑝𝑠𝑖
(3.7)
(3.9)
̅𝑝,𝑙𝑜𝑎𝑑𝑒𝑑−0.22)/(𝜆 ̅2 (𝜆 𝑝,𝑙𝑜𝑎𝑑𝑒𝑑 )
As the load carrying capacity of each plate depends on the force distribution which correlates with the reduction factor, an iterative process is used to calculate the reduction factor ρEC which corresponds to the achieved ρexp and thus to the ultimate load in the experiments (Fu). The following equation has thus to be fulfilled: 𝐹𝑢 = 𝜌𝐸𝐶
f𝑢 ∙ 𝐴𝑒𝑓𝑓 ∙ 𝐴 /𝑊 {𝜌 = 𝜌𝐸𝐶 } 1 + 𝑧𝑒𝑓𝑓 𝑒𝑓𝑓 𝑒𝑓𝑓 𝑒𝑥𝑝
(3.10)
where the effective properties are depending on the ρ-values and zeff additionally on the load eccentricity. This calculation alternative was used for the welded sections as well as for the cold-formed sections .The plate length is here assessed by using the actual plate length b2t-2ri.
Page 57
2.2.5
Evaluation using a modified general method
In the herein used modified general method it is aimed to use the basic approach of the buckling curve to include not only global, but also local buckling. The slenderness can be calculated by: (3.11)
𝛼𝑢𝑙𝑡 𝛼𝑐𝑟𝑖𝑡
λ̅ GM =√
Where 𝛼𝑢𝑙𝑡 is in this case the theoretically achievable, elastic resistance load on the full cross-section, while 𝛼𝑐𝑟𝑖𝑡 is here the critical load taken from the CUFSM-calculations, which allow for the assessment of the real global mode, including mixed modes of coupled instabilities [51]. With this approach, the global slenderness of the member is assessed.
To calculate the reduction factor 𝜌𝐺𝑀 , the interim factor 𝜑𝐺𝑚 is first calculated by: 𝛼∗
∗ 2∙ 𝑐𝑟𝑖𝑡 𝛼𝑐𝑟𝑖𝑡 𝛼 𝜑𝐺𝑚 =0.5 [1+αeff (𝜆̅𝐺𝑀 -1.2+ ) +𝜆̅𝐺𝑀𝑐𝑟𝑖𝑡 ] 𝛼𝑐𝑟𝑖𝑡
and: αeff =𝛼
∗ 𝛼𝑐𝑟𝑖𝑡
(3.12)
(3.13)
𝛼𝑐𝑟𝑖𝑡
𝛼 is taken from the buckling curve for welded box sections from [3] as 0.34. To take into account the torsional rigidity of the plate subjected to local buckling, this value is modified by 𝛼∗ multiplication with 𝑐𝑟𝑖𝑡. In principle, this ratio is the same as the ratio of the buckling factor k* 𝛼𝑐𝑟𝑖𝑡
(without torsional rigidity) and k (with torsional rigidity): 𝑘∗ 𝑘
∗ 𝛼𝑐𝑟𝑖𝑡
=𝛼
𝑐𝑟𝑖𝑡
=
𝑚 4 ) +𝑛4 𝛼1 2 𝑚 [ +𝑛2 ] 𝛼1
(
(3.14)
.
Where 𝛼1 is the ratio of length to width of the considered plate, m the number of half-waves in the longitudinal direction and n the half-wave number in the width-direction (assumed to be 1 in all cases). m was taken to as 3, since the length was in all specimens approximately 3x the width. For pure local buckling, the ratio tends then to be 0.5. The resulting αeff coincides with the imperfection factor 𝛼 for flexural buckling if the influence of torsional rigidity on the magnification factor 𝛼𝑐𝑟𝑖𝑡 for 2nd order effects is negligible. Used in Eq. (6), this leads back to the formula given in [8] for local buckling. Consequently, the reduction factor 𝜌𝐺𝑀 results in:
1
𝜌𝐺𝑀 = √
(3.15) 𝛼∗ 2∙𝛼𝑐𝑟𝑖𝑡
𝜑𝐺𝑀 + 𝜑𝐺𝑀 2 − 𝜆̅𝐺𝑀𝑐𝑟𝑖𝑡 2.2.6
Conclusions for local buckling tests
In this report three topics were approached: first the material properties of high strength steel compared to the requirements given in [4]. Second, the evaluation of local buckling behaviour in comparison with [8] and third the introduction of a modified general method approach to simplify the design for local buckling. The material property requirements given in [4] were fulfilled by S500 and S700 plate material and the flat face material of the tubes. Applying the same requirements to the corner material, the fu/fy-ratio criterion is fulfilled but the elongation at fracture min. 10% would not have been achieved by the S700 material and part of the S500. Elongation at ultimate load would naturally not be achieved by any material.
Page 58
Applying the same requirements on S960 material shows insufficient strain capacity at ultimate strength. However, the performance in the investigated field of local buckling was not affected. The over-strength of material increases the ultimate carrying capacity from a factor equal to the over-strength in the stocky range, where the squash-load determines the failure mode. Towards the slender area, the effect of over-strength reduces non-linearly until converging to half of the fy,act/fy,nom-value. Relying on the over-strength, which is not required in the fabrication codes and cannot be guaranteed by a global market, seems inappropriate in terms of the Eurocode safety concept. To assess the local buckling resistance of tubular sections, the critical load was assessed in all cases using the finite-strip program CUFSM. The results when increasing the buckling width from b-2t-2ri to b-3t is of major impact: In the stocky range, the already safe results increase to a conservative reduction factor of partly over 25 %, while the unsafe slenderness limit shifts from 0.8 to 1.1. However, this approach seems to be quite random: the real buckling width would be b-2t-2ri, so b-3t is supposed to take the rotation of the corners partly into account. But the ratio of these two values is highly dependent on the real cross-section dimension, and thus no constant safety value can be achieved with this approach. It seems more advisable in consequence, to calculate with the known buckling width and assess the corner influence e.g. with CUFSM. In all cases, the effective width approach [8] tends to overestimate the resistance of plates against local buckling with increasing slenderness. This could be already observed in other studies [59][60][61], including mild steels [62] and is thus not a specific problem of high strength steels. The actual reduction factors ρ achieved in the experiments are shown in Figure 2-6, with the scaled results depicted in Figure 2-7. The effective width approach tends to underestimate the resistance of plates against local buckling for the welded sections in the stocky range by 6 % and overestimates the resistance with increasing slenderness (higher than 1) with a mean value of 6 %. For the cold-formed sections, EC gives in the stocky group in average 4 % and in the slender group 9 % unsafe results. The modified general method is in general 6 % on the safe side for the cold-formed sections and overestimates the resistance similar to EC with 7 % in the stocky area, but in the slender area for sections with 𝜆̅𝑝 ≥ 1, the resistance prediction is in average accurate.
1.4 EC3-1-5 welded cold-formed
1.2
1 0.8 0.6 0.4
0.60
0.80
1.00 6𝜆7̅𝑝p
1.20
1.40
1.60
Figure 2-6: Actual plate buckling resistance/reduction factor compared to EC3-1-5 The herein introduced modified general method aims to combine the design check of global and local buckling. This leads to reduced efforts concerning the calculation (one design check instead of separate global and local calculations). The return of a local buckling check to the European buckling curves leads to a check on the gross-cross-section. Thus, an extensive calculation process on an effective cross-section including calculation of a shift of the centroid can be neglected.
Page 59
1.4 GM EC-w EC-cf
1.3 1.2
1.1 1 0.9 0.8 0.7
0.60
0.80
1.00 6𝜆7p̅
1.20
1.40
1.60
𝑝
Figure 2-7: Comparison re/rt using EC and a modified general method approach GM, all specimens 2.2.7
Influence of overstrength on local buckling
Evaluating the resistance according to [8], and using actual properties from measurements, the resistance curve proves to be non-conservative for all steel grades alike. Although the resistance curve of [8] is questioned in this report in respect to the safety assessment required by Eurocode 0 [13], it is assumed that the majority of structures, which is made of mild steels, profit considerably from their over-strength fy,act/fy,nom. But with increasing yield strength, the over-strength reduces in general. The over-strength of high strength steel material was recently assessed by Baddoo in scope of the RFCS-project HILONG in [47], where fy is defined as the 0.2 % proof strength. The main results are summarized in Table 2-8. It can be seen, that aside from the yield strength, the fabrication is of crucial importance. For mild steels, [48] proposed a formula to derive the over-strength ratio, resulting in 1.2 for S235 and 1.13 for S355. Only two European Steel Producers were investigated in his study, but the values were taken nonetheless for the evaluations performed in the present study as they seem to be within an acceptable scatter. Table 2-8: Overstrength of material in dependence of steel grade ([47]) σ0.2 (fy ) – Yield Stress Steel S420 S460 S500 S690 S700 S760 S900 Grade Mean 458.5 513.5 586.4 791.1 808.1 798.6 1047 [N/mm²] Overstrength 1.09 1.12 1.17 1.15 1.15 1.05 1.16 ratio OSR St. Deviation 17.49 25.64 33.81 47.82 56.36 23.88 84.08 [N/mm²] C.O.V. No. Samples
S960
S1100
995.2
1093
1.04
0.99
37.2
78.62
3.82%
4.99%
5.77%
6.05%
6.97%
2.99%
8.03%
3.74%
7.19%
35
1052
15
546
66
9
20
34
11
For linear functions, as e.g. for the net section resistance, the nominal yield strength can easily be taken into account. In case of local buckling, the resistance is non-linear, and moreover, the slenderness changes and thus the reduction factor ρ. A higher (or actual) yield strength will lead to a higher 𝜆̅𝑝 value, and subsequently to a lower ρ value. The absolute
Page 60
resistance ρ x fy might be similar therefore for a structure using nominal and actual values. This depends on the absolute values, the over-strength existing, as well as on the slenderness looked at. Figure 2-8 shows on the left hand side how the actual slenderness changes towards the nominal slenderness: with increasing over-strength, the slenderness increases as well, leading to steeper curves in the respective diagram. On the right hand side, we can see that at the same time the reduction factor decreases. To quantify the absolute advantage in the carrying capacity using actual material properties, the nominal slenderness was drawn over the ratio of the actual to nominal resistance in Figure 2-8. The result is clearly dependent on the slenderness: While in the stocky area, where the squash-load defines the ultimate resistance, the benefit in carrying capacity equals the over-strength ratio, it decreases non-linear in the constructional relevant slenderness area until converging to a certain value. For S960, where the over-strength is assessed with 1.04, the gain tends to 1.02 in the very slender area, while for S235 the gain changes from 1.2 to 1.1. Also for the other steel grades it can be said that the reduction in gain tends to be half of the original over-strength. 1000
1.18
𝑁 𝑓𝑦 ∙ 𝜌 [ ] 2 [mm] f y " ; 𝑚𝑚
700 600 500
S235 - 1.20 S355 - 1.13 S500 - 1.17 S700 - 1.15 S960 - 1.04
1.16 1.14
; nom " f y;nom
800
nom nom nom nom nom act act act act act
𝑓𝑦,𝑎𝑐𝑡 ∙ 𝜌𝑎𝑐𝑡 ; act " f ∙y;act 𝑓𝑦,𝑛𝑜𝑚 𝜌𝑛𝑜𝑚
S235 S355 S500 S700 S960 S235 S355 S500 S700 S960 -
900
400 300
1.12 1.1 1.08 1.06
200
1.04
100 0 0.5
1.02
1
1.5
2
2.5
3
7 6 p̅
𝜆𝑝
1
1.5
2
2.5
7 6 p;nom 𝜆̅𝑝,𝑛𝑜𝑚
Figure 2-8: Evaluation of overstrength on the absolute resistance (left) and the actual gain in resistance in dependence of the slenderness (right) 2.2.8
Alternative resistance function to Winter Curve
The data produced within the research project of the authors and the collected data from literature resulted in 157 data sets. All data was derived from stub column tests and are shown in Figure 2-9. Different approaches were evaluated to depict the best mean function for the available test data. The resulting curves in comparison with the test data are shown in Figure 2-10. With a complete empirical approach, a function is searched for which predicts the results best in all slender ranges. The function was found to be of exponential character. ̅
𝜌 = 2.235 𝑒 −1.582 𝜆+0.288
Page 61
3
Figure 2-9: Resistance curve according to [8] compared with available test data (all welded stub columns)
Figure 2-10: Available test data in comparison with different best-fit functions 2.2.9
Safety Assessment for plate buckling
The study at hand deals mainly with high strength steel material (S500 up to S960). The tests performed within the Ruoste project suggest the existing local buckling resistance curve to be very optimistic, which is supported by further studies (e.g. [59][63][64][61]). However, looking at test results from steel grades below a yield strength of S500 and mild steels (up to S420), the prediction by Eurocode proved to be optimistic as well [62]. In consequence, the problem of safe assessment of local buckling resistance is not confined to high strength steels. For evaluation purposes therefore various steel grades were included. The data included in this study is based completely on square stub columns. Additionally, the research of [64] comprises square and rectangular specimens. In 1947, Winter published his work on “Strength of Thin Steel Plates Compression Flanges'' [52] and adapted his formula in 1968 [53], which is still the fundamental basis for the resistance curve in the current design code [8]. These tests were conducted in two test series on thin steel members, first on inverted U-sections, and second on two bolted U-sections, forming an I-section. Additional tests from Sechler [54] were included in his evaluations. The semi-empirical resistance curve was derived as a mean function of the tests. Given the safety standard requirements of [13], either a mean function and a safety factor M or a lower bound curve would be necessary. In this section the assessment of a design safety M* relating to local buckling is derived. More detailed information can be found in [55].
Page 62
∗ To derive the design safety factor 𝛾𝑀 , first a simplified approach with constant Coefficients ∗ of Variations CoV's, taken from literature [56], was used. 𝛾𝑀 , yielded here in 1.41 when considering all available test data from literature and the tests presented in this study for the resistance curve provided in [8].
Table 2-9: Assumed constant coefficient of variations Parameter
Label
Value
Plate thickness
Vt
0.05
Plate width
Vb
0.005
Plate length
Vl
0.005
Yield strength
Vfy
0.07
The assumption of a simple additive function is thus not recommendet. [13] gives the possibility to assess Vrt for complex functions by evaluation of the local sensitivity of each variable (thickness, yield strength, width): 𝑉𝑟𝑡 =
𝑉𝐴𝑅[𝑔𝑟𝑡 𝑋 ] 2 𝑔𝑟𝑡 (𝑋𝑚 )
1
𝑗
2
𝜕𝑔𝑟𝑡 = 2 × ∑( × 𝜎𝑖 ) 𝑔𝑟𝑡 (𝑋𝑚 ) 𝑖=1 𝜕𝑋𝑖
(3.16)
This equation was used in the study presented here. Moreover, using constant Coefficient's of Variation (CoV's) yields in some cases to unrealistic assumptions: e.g. if we take Vt (for the plate thickness) as 5%, and assess the fractile-value for a normal distribution at 3-times the standarddeviation, this would mean for a nominal plate thickness of 6 mm that 16% of investigated plates would be below the tolerance limit given in EN 10029 (0.3 mm). More reasonable CoV's were thus chosen, where the Vt and Vfy are dependent on the mean material thickness and yield strength, respectively. The function for Vt is shown in the following equation: 𝑉𝑡 = 𝑚𝑖𝑛 (0.05; 0.3
1
1 ) 𝑡𝑚𝑒𝑎𝑛 3
(3.17)
The scatter of gathered experimental data and the investigated resistance model is however ∗ still considerably high. This leads for the current resistance curve of [8] to a 𝛾𝑀 of 1.30. The evaluation of the tests carried out within Ruoste shows less scatter when compared with the resistance curve than the test results taken from literature. This might be due to the additional data which allowed to include the bending portion in the specimens. As these data was not available for all other experiments, a separated safety assessment was carried out for ∗ only these 34 tests. Additionally, the resulting 𝛾𝑀 proved to be very sensitive to the CoV for the plate thickness Vt. Assuming that the used plates would fulfil tolerance class B of EN 10029, we would assume that no sample is thinner than the nominal value -0.3 mm. This could ∗ significantly reduce scatter and leads thus to a 𝛾𝑀 value of 1.18. When assuming that the actual thickness t scatters around a nominal value +5%, resulting ∗ in a lower limit of scatter equalling the nominal value of t, the lowest 𝛾𝑀 value could be achieved with 1.07. However, the minimal thickness of the plate has to be guaranteed on consequence. When evaluating the reduced data set with the derived best-fit exponential function (see ∗ 2.2.8) the lowest 𝛾𝑀 of 1.08 (all test data, scatter of t around the nominal value of t) could be achieved. Further and detailed information on this study may be found in [55].
Page 63
2.3 2.3.1
Global buckling tests General Information
The application range of the current EN 1993-1-1 [3] for column (flexural) buckling of steel structures is limited to ordinary steel materials up to the grade of S460. The EN 1993-1-12 [4] gives design background for materials up to grade of S700, however, for the determination of the column buckling resistance the same rules are applicable for materials between steel grade S460 - S700 as for the S460 materials. The determination of the global (flexural) buckling resistance is highly important in the design of HSS structures, because due to the high yield strength smaller cross sections can be used. This results in more slender structural elements, which can be sensitive to stability failure. According to previous research results [75][76] the flexural buckling behaviour of HSS structures is less severe than in case of NSS structures. The difference comes from the different residual stresses, different material properties and geometric imperfections. Several previous investigations and the residual stress measurements in the RUOSTE project also showed that the residual stress amplitudes are smaller for HSS structures compared to the yield strength than in case of NSS members. On the other hand the reduction due to the flexural buckling is governed by the ratio of residual stress to the yield strength, rather than the magnitude of residual stress itself. Therefore it is expected that a higher column buckling curve could be used for HSS members than for NSS members, consequently the design using HSS structures could be more economical. The general aim was to investigate the column (flexural) buckling behaviour of HSS columns having square box sections up to S960 steel grade. The investigation covered cold formed and welded hollow section members, which were separately handled, thus different buckling curves could be used. The investigated specimens covered the relative slenderness range between 0.54 < λ < 1.49. The specimen’s geometries were designed to ensure a quasi-uniform distribution by the test results within the studied slenderness region. Parallel to the experimental research program a numerical investigation was carried out to determine the flexural buckling resistance of HSS hollow section columns and to investigate the differences between NSS and HSS members. In frame of the numerical investigations the differences in the flexural buckling behaviour were investigated, which comes from (i) the different yield strength, (ii) the different residual stress pattern and (iii) the different steel material properties (stress – strain diagram). Based on the current and the previous experimental results found in the international literature and based on the current numerical investigations the differences in the flexural buckling behaviour of HSS and NSS members were identified, studied and evaluated. Finally based on the experimental and numerical investigations design buckling curves can be proposed for cold formed and welded HSS hollow section members separately. The literature survey showed that the previous experimental and numerical investigations prove that box section columns made from HSS material provides significantly larger resistances than the columns having the same geometry but made from NSS material. It means that the buckling behaviour of the HSS columns are more favourable than for NSS columns which can lead to the application of higher buckling curves for columns made from HSS material. The previous investigations explained the differences between the NSS and HSS columns by the following three reasons: residual stresses are smaller for HSS members compared to NSS members, geometric imperfections are not larger for HSS member than for NSS sections, even smaller due the better manufacturing control and improved quality, different material properties, which contains increased yield and ultimate strength, but also different character for the stress – strain relationship. These differences can have large impact on the buckling behaviour of hollow section columns and therefore improved column buckling curves are needed for HSS box section columns. These differences are also valid for welded as well as for cold formed cross section columns. However, the importance of the three terms have different weights depending on the manufacturing process. Therefore they should be separately handled. In the international literature, only 2 experimental research programs have been found investigating the flexural buckling behaviour of welded box section columns made from S460
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steel material and only one test program on S690 and S960 steel materials. The total number of the tested specimens were for S460 material 12 specimens, for S690 6 specimens and for S960 only 3 specimens, which can be treated as a relative small number of available previous experimental results. For cold formed section columns only one investigation is found in the international literature carried out by the company SSAB on cold formed hollow section columns made from a double steel grade of S355 and S420. A total of 39 cold-formed hollow section specimens were tested under axial loading. The experimental research programme was extended by numerical calculations. The first option for column buckling curve determination is based on an experimental way performing real tests, or numerical simulations using real residual stresses and geometric imperfections, which are approximated using Monte Carlo simulations technique. Using this evaluation process based on the test results and numerical calculations the buckling curve representing the characteristic value of the buckling resistance can be determined by statistical evaluation. The second option is to carry out numerical simulation applying residual stresses and initial geometric imperfection with amplitude of L/1000. It is proved in the international literature for NSS structures that these assumptions are shown to represent an excellent approximation of a characteristic value (in a probabilistic sense) of the buckling reduction factor, taken to be equal to the mean value minus two standard deviations of (Monte Carlo) experimental results plotted over the nominal slenderness. Therefore, full consistency with the column buckling case is given. In frame of the current RUOSTE research project buckling curves for HSS members were determined in both ways, therefore a combined experimental and numerical research program was carried out. 2.3.2
Experiments conducted at BME
A total number of 26+28=54 flexural buckling tests were carried out at Budapest University of Technology and Economics Department of Structural Engineering. 26 test specimens were investigated having steel grades between S500 – S960. Additional to this originally planned test program complementary investigations (28 tests) were made of S420 and S460 steel grades as well. The aim of the complementary tests was to give reference and comparison background to the test results made on HSS members (S500 – S960) and to increase the investigation range. The test specimens are produced by three steel manufacturers (Ruukki, SSAB and VoestAlpine). From the 26 test specimens 17 columns were made from cold-formed, and 9 from welded cross sections. The additional 28 specimens made from S420 and S460 steel grades were all cold formed sections. All the tested specimens fulfilled the requirements of the cross-section Class 3, thus no Class 4 sections were investigated. The investigated global slenderness range was between λ=0.52-1.49. A total of 6 different cross sections were investigated from welded hollow section specimens, using three different material grades (S500, S700 and S960). The test matrix is presented in Table 2-10. Table 2-10: Test specimens for welded hollow section [mm]. Welded specimens Specimen # Leff b t material producer 6 2940 120 6 S500 Ruukki 7 2440 120 6 S500 Ruukki 8 2140 150 6 S500 Ruukki 17 2940 140 6 S700 SSAB 18 1641 140 6 S700 SSAB 9 2940 180 8 S700 Ruukki 10 2940 120 6 S960 SSAB 11 1340 120 6 S960 SSAB 12 2740 160 8 S960 Ruukki
λgl 1.04 0.84 0.60 0.96 0.54 0.79 1.43 0.65 1.01
A total of 12 different cross section types made from cold formed square hollow sections are investigated using 5 different steel grades (S420, S460, S500, S700 and S960). The original aim of the RUOSTE project was to investigate specimens within the range of S500 – S960, but it seemed more appropriate to extend the investigated parameter range by the steel
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grades of S420 and S460. The extended analysis can give more information through the comparison of the test results with other previous test results made in different laboratories and test setup (using different hinges) and supported to investigate the effect of the yield strength on the buckling behavior of HSS columns. The nominal geometries of the investigated test specimens and their global slenderness are summarized in Table 2-11. Table 2-11: Test specimens for cold formed square section [mm]. Cold-formed specimens Specimen 1/1, 2/1, 3/1, 4/1, 5/1, 6/1, 7/1, 8/1, 9/1, 10/1, 11/1, 12/1, 13/1, 14/1,
#
1/2 2/2 3/2 4/2 5/2 6/2 7/2 8/2 9/2 10/2 11/2 12/2 13/2 14/2
Specimen
#
1a, 1b, 1c 13 14 2a, 2b 15a, 15b 16a, 16b 3a, 3b 4a, 4b 5a, 5b
Leff
bnom
tnom
material
producer
λgl
2939 2739 2938 2640 2939 2540 2040 2639 2239 1240 2939 2240 2940 2540
100 100 120 120 150 150 150 80 80 80 120 120 150 150
3 3 6 6 5 5 5 5 5 5 4 4 8 8
S420 S420 S420 S420 S420 S420 S420 S460 S460 S460 S460 S460 S460 S460
Ruukki Ruukki Ruukki Ruukki Ruukki Ruukki Ruukki Ruukki Ruukki Ruukki Ruukki Ruukki Ruukki Ruukki
1.11 1.04 1.00 0.90 0.76 0.65 0.52 1.49 1.26 0.7 1.03 0.78 0.8 0.7
Leff
bnom
tnom
material
producer
λgl
2946 2640 1940 2940 2940 2140 2940 2940 1840
120 140 140 120 150 150 120 150 150
6 8 8 6 8 8 6 7 7
S500 S500 S500 S700 S700 S700 S960 S960 S960
VoestA Ruukki Ruukki Ruukki Ruukki Ruukki Ruukki Ruukki Ruukki
1.11 0.85 0.63 1.20 0.96 0.71 1.46 1.16 0.72
Tested specimen number 2 2 2 2 2 2 2 2 2 2 2 2 2 2 Tested specimen number 3 1 1 2 2 2 2 2 2
The total number of the specimens could be divided into 8 groups based on material properties and the manufacturing type (Welded S500/S700/S960, Cold-formed S420/S460/S500/S700/S960). Each group had at least 3 different types of specimens with different geometries. The analysed specimens were in the relative slenderness range between 0.52 < λ < 1.5. Within each group the stockiest specimen’s slenderness was between 0.5 < λ < 0.8, the second slenderness range was between 0.8 < λ < 1.00 and the specimens with the highest slenderness were in the range between 1.00 < λ < 1.5 (see Table 2-12).
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Table 2-12: Slenderness distribution of tested specimen Global slenderness – λgl Type
Coldformed
Welded
Mat.
Stockier
Medium
Slenderer
S420 S460
0.5-0.8
0.9-1.0
1.0-1.15
0.6-0.8
0.8-1.05
1.2-1.5
S500
0.63
0.85
1.11
S700
0.71
0.96
1.20
S960
0.72
1.16
1.46
S500
0.60
0.84
1.04
S700
0.54
0.79
0.96
S960
0.65
1.01
1.43
For all specimens the following measurements were carried out: -
residual stresses for each specimen types for all analysed steel grades, global geometric imperfections (out-of-plane straightness) for each specimens, loading eccentricities calculated for each specimens from strain gauge measurements, material properties for each analysed steel grade and plate thickness measured by coupon tests. load-displacement diagrams regarding longitudinal and lateral displacements, stress distribution within the plate parts to check the local buckling phenomenon, ultimate flexural buckling resistance for each specimens.
Material properties of the test specimens The measured material properties of all the specimens were considered in the evaluation procedure. For several specimens the manufacturers provided the measured material properties based on tensile coupon tests. In most of these cases the measured values provided by the manufacturer were used for the evaluation. In case of the other specimens where no information about the material properties was available from the manufacturers additional tensile coupon tests were made. The coupon test specimens were cut out by water cutting from the end of those specimens that were used previously for the residual stress measurements. Table 2-13: Measured material properties for welded specimens [MPa]
Type
Material
Welded
S500 S700 S960
Specimen #
Producer
6 7 8 17, 18 9 10, 11 12
Ruukki Ruukki Ruukki SSAB Ruukki SSAB Ruukki
Coupon test made by BME BME BME SSAB BME SSAB, BME BME
Plate fy fu 558,5 639 524 630 551,5 638 670 735 741 803 1005 1047 1073 1153
Table 2-14 summarizes the measured average material properties for all the cold formed test specimens.
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Table 2-14: Measured material properties for cold formed specimens [MPa]
Material
S420
S460
S500 S700 S960
Specimen 1/1, 1 /2, 2/1, 2/2 3/1, 3/2, 4/1, 4/2 5/1, 5/2, 6/1, 6/2, 7/1, 7/2 8/1, 8/2, 9/1, 9/2, 10/1, 10/2, 11/1, 11/2, 12/1, 12/2 13/1, 13/2, 14/1, 14/2 1a,1b,1c 13,14 2a,2b 15a,15b 16a,16b 3a,3b
Test Producer made by Ruukki Ruukki
Ruukki Ruukki
Plate fy fu 458 552 506 551
Ruukki
Ruukki
479
561
Ruukki
Ruukki
508
563
Ruukki
Ruukki
601
655
Ruukki
Ruukki
559
598
Voest Ruukki Ruukki Ruukki Ruukki Ruukki
BME Ruukki Ruukki Ruukki Ruukki Ruukki
624 614 742 751 741 1088
656 662 839 834 830 1182
Corner fy fu
Edge of plate fy fu
672 815 951 1109 1271 -
691 -
Test set-up and testing method The specimens were tested between cylindrical testing rigs which provided hinged support conditions in one direction and fixed support conditions in the perpendicular direction. The flexural buckling always occurred in the hinged direction. During all the tests the following data were measured:
stress distribution in bottom cross-section (20 cm away from the end of the column) using 4 strain gauges, stress distribution in top cross-section (20 cm away from the end of the column) using 4 strain gauges, stress distribution in middle cross-section using at least 8 strain gauges, rotation of the bottom hinge using two displacement transducers, rotation of the top hinge using two displacement transducers, axial displacement using two displacement transducers (uz1, uz2), lateral displacement in the direction of buckling plane using two displacement transducers (uy1, uy2), lateral displacement in the direction perpendicular to buckling plane using one displacement transducer (ux).
Geometrical imperfections and loading eccentricities The exact geometry of the test specimens were measured prior to the buckling tests, including thus the initial global imperfections. The shape and magnitude of the imperfection was measured on each corner of all the specimens. The magnitude of the imperfections were determined for all the specimens in both directions and normalized to the total length of the tested specimen. The measured out-of-straightness imperfections are significantly smaller than the manufacturing tolerance given by the Eurocode (L/750). Clear increasing tendency could be observed in case of the cold formed specimens depending on the global slenderness, but there was no clear tendency depending on the steel grade. Larger global slenderness indicates usually larger out-of-straightness imperfection, but its maximum value for the cold formed specimens was found to be smaller than L/2500. In case of the welded specimens, for most the average out-of-straightness imperfection was equal to L/5000, except two specimens, which had significantly larger imperfections having a maximum amplitude of L/1500, but what was still below the manufacturing tolerance. The average magnitude of the out-of-straightness imperfection was L/3200 for the welded and L/8300 for the cold formed
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specimens. These average values are only informative values, because the magnitudes are strongly dependent on the global slenderness and manufacturing process. Beside the out-ofstraightness of the specimens the loading eccentricities were also measured in the tests. After the determination of the end-eccentricity the total imperfections were calculated by the outof-straightness of the specimen plus the average of the upper and lower end-eccentricities. The total geometric imperfections applied in the tests are presented in Figure 2-11 for the welded and in Figure 2-12 for the cold-formed specimens. The results show that for the welded specimens there are two specimens where the applied imperfection is approximately the double (L/500) of the imperfection what is the bases of the European buckling curves (L/1000). This fact wa considered later in the evaluation process of the test results. However, from the 9 welded test specimens for two specimens the applied imperfection was close to the L/1000 value, and for 5 specimens the total imperfection amplitude was close to L/2000. In case of the cold formed specimens 7 columns had larger imperfections than L/1000, and the average imperfection magnitude was equal to L/1800. However, it should be mentioned that the exact placement of the specimens into the loading equipment is quite difficult, and therefore it is almost impossible to guarantee the exact L/1000 imperfection magnitude. BME tried to ensure in the experimental research program the approximation of the L/1000 imperfection magnitude and measured the exact values of the imperfections. Its effect is considered in the evaluation process of the test results.
Figure 2-11: Maximum imperfection magnitudes for welded specimens
Figure 2-12: Maximum imperfection magnitudes for cold formed specimens
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Evaluation of the flexural buckling test result From the measured ultimate resistances the buckling reduction coefficient (χtest) was determined using the expression of Eqs. (3.18): 𝜒𝑡𝑒𝑠𝑡 =
𝑁𝑡𝑒𝑠𝑡 𝐴𝑡𝑒𝑠𝑡 ∙ 𝑓𝑦,𝑡𝑒𝑠𝑡
(3.18)
The calculated buckling reduction factors (χtest) for the welded specimens with smaller b/t ratio than 30 are plotted in Figure 2-13 as a function of the global slenderness ratio together with the column buckling curves of the EN1993-1-1. The previous test results available in the international literature are also shown in the diagrams. The comparison shows, that all the measured resistances are significantly larger than the expected values based on the buckling Curve c, what is in accordance with the previous test results found in the international literature for welded HSS box columns. The results also show that the lowest reduction factor belongs to the specimens of Wang et al, which were made on S460 steel grades. All the test results based on the real value of the buckling reduction factor for higher steel grades than S500 are over the column buckling Curve a according to EN1993-1-1. It can be also observed, that the current results fit well the general tendency of the previous test results and the current test program significantly increases the previous test database related to the flexural buckling of HSS welded hollow section columns. Based on the present experiments the column buckling Curve b sufficiently met the safety criteria of the EN1990 Annex D using the γM1* equal to 1.00, and the 2.3% lower quantile of the experimental results is 6% higher than the resistances calculated by the column buckling Curve b.
Buckling reduction-coefficient (χtest)
1,2
1 Euler
0,8
a0 curve (EC) a curve (EC) b curve (EC)
0,6
c curve (EC) S500
0,4
S700
S960 Rasmussen S690
0,2
Ban et al. S960
Global slenderness (λ)
Wang et al. S460
0 0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
1,8
2
Figure 2-13 –Buckling reduction factors for welded specimens (χtest) The calculated buckling reduction factors (χtest) for the cold formed HSS hollow section specimens are presented in Figure 2-14 depending on the global slenderness ratio. The comparison shows that all the measured resistances are significantly larger than the expected values based on the buckling Curve c, what is in accordance with the previous test results found in the international literature. The results show that the lowest reduction factor belongs to the specimens made on S420 steel grade. There are two test results giving lower resistances for the steel grade of S700, but for these two specimens the applied geometric imperfections are larger than L/1000. All the test results even for these two cases are above the column buckling Curve b according to EN1993-1-1 using the test values for the geometry and the material properties.
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Based on the present test results the buckling Curve b sufficiently met the safety criteria for the S500, S700, S960 specimens; γM1* is 0.99 and the 2.3% lower quantile of the experimental results is 6% higher than the resistances of the buckling Curve b. The same statement can be done for the S460 material grade as well; γM1* is 0.97 and the 2,3% lower quantile of the experimental results is 9% higher as the resistance level of the buckling Curve b. It means that based on the RUOSTE test results the buckling Curve b is applicable to S460, S500, S700, S960 material grades in case of cold formed hollow section columns.
Figure 2-14 –Buckling reduction factors for cold formed specimens (χtest) 2.3.3
Numerical modelling of HSS hollow section columns
The aim of the executed research was to investigate the structural behaviour and to determine the flexural buckling resistance of compressed welded and cold-formed hollow section columns using a numerical model. The analysed numerical model was developed using the finite element software Ansys 14.0. The numerical modelling is based on a full shell model using four node thin shell elements. The ultimate loads were determined by geometrical and material nonlinear analysis using equivalent geometric imperfections (GMNIA). In the numerical model both the global and the local imperfection shapes were modelled. The shape of the global imperfection was a half-sinus wave shape. The shape of the local imperfection was a continuous sinus wave on each side along the longitudinal axis. The number of the half waves was equal to the L/b ratio rounded up, where L is the actual length of the specimen, b is the cross-section width. Previous research results showed that a numerical analysis using L/1000 as the amplitude of global imperfection gives close results to the Monte Carlo analysis based calculations, therefore we used this consideration in the numerical models. For the basic value of the local imperfection’s amplitude b/1000 was used. Since in the parametric study the buckling phenomenon is studied, always the global imperfection is considered as the leading imperfection with the amplitude of L/1000. The local imperfection was considered as the accompanying imperfection, so its magnitude was multiplied by 0.7. Aside from geometric imperfections also residual stresses were applied. The proposed residual stress model of the RUOSTE project was used. To define the HSS material models the Ramberg-Osgood material model was applied. Based on the S500, S700 and S960 material tests done by Ruukki, a value of n=14 could be determined, which gave the best fit for the measured material properties. Based on the S700 and S960 material tests carried out by SSAB, n=30 for the Ramberg-Osgood parameter gave the best fit to the results of the coupon tests. The aim of the numerical parametric study was to obtain the appropriate buckling curve for welded hollow section columns made from high strength steel material. As a first step the
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effect of the different properties of NSS and HSS material grade was studied and evaluated in frame of a numerical parametric study. The following properties were found to have significant effect on the buckling behaviour:
the yield strength, the residual stress pattern (value of the compression residual stresses), the material model law (character of the stress – strain curve).
In the executed research work the effect of these properties were assessed separately. In each parametric study only one property was changed, all the other relevant properties were kept as constant. A second parametric study was executed using the realistic material and residual stress properties for HSS welded columns. Based on this study appropriate buckling curves are proposed for steel grades of S500, S700 and S960. 2.3.4
New findings related to global buckling
General remarks Based on the international literature there are two different ways to develop applicable column buckling curves. The first method is based mainly on laboratory test results where the statistical evaluation ensures the required safety level of the applicable column buckling curve. The second method is based on numerical simulations, which gives immediately the applicable column buckling curve using predefined imperfections and residual stresses. In frame of the RUOSTE research project applicable buckling curves for HSS members were determined using both ways. Applicable buckling curves for HSS welded box sections Results based on the laboratory tests: -
-
-
-
In case of the welded specimens the average out-of-straightness imperfection was equal to L/4500, which is significantly smaller than the manufacturing tolerance (L/750). No clear tendencies could be observed depending on the steel grade in the out-of-straightness imperfection, which means that for the HSS members the same out-of-straightness imperfection shapes can be used as for the normal strength steel members. This observation suggests that the same geometric imperfection shape and magnitude can be used in FE calculations for HSS members as for NSS members. It has positive consequences on the buckling behaviour of HSS members. All the test results evaluated based on the measured material properties results in buckling reduction factors over the column buckling Curve a according to EN1993-1-1 [3] for steel grades between S500 – S960. Based on the statistical evaluation of the test results the column buckling Curve b sufficiently meets the safety criteria of the EN1990 Annex D using the γM1* equal by 1.00, and the 2.3% lower quantile of the experimental results is 6% higher than the resistances calculated by the buckling Curve b. Based on the statistical evaluation of the current test results the column buckling Curve c met the safety criteria of the EN1990 Annex D for the S420. It has to be mentioned that the number of the executed tests did not make it possible to make the statistical evaluation for all the analysed steel grades separately. The separated evaluation is therefore made based on the numerical simulations.
Results based on the numerical simulations The aim of the numerical parametric study was to obtain the appropriate buckling curve for welded hollow section columns made from HSS material with smaller b/t ratio than 30. The following conclusions can be drawn for welded hollow section columns: -
the buckling reduction factor of HSS columns can be higher due to the increased yield strength,
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-
-
-
the buckling reduction factor of HSS columns can be higher due to the magnitude of the compression residual stresses (in case of HSS grades the residual compression stresses does not increase linearly with the yield strength), the buckling reduction factor of HSS columns can be higher because the residual stresses results in smaller resistance decrease in case of Ramberg-Osgood type material models than in case of material models having clear yield plateau, the buckling reduction factor of HSS columns could be smaller because the RambergOsgood type material model can have negative effect on the buckling resistance depending on the slenderness range and steel grade.
The results of the numerical simulations show there are three phenomena that increase and there is one phenomenon that decreases the buckling reduction factor of HSS columns compared to NSS material grades. Using the verified numerical model a further parametric study is executed analysing 7 different square hollow section columns using the input parameters which are the bases of the simulation based ECCS column buckling curve development. Based on the numerical simulations the following final conclusions are drawn: -
-
The results of the simulations showed, that for cross sections which belongs to the Class 1 – Class 3 the column buckling curves are independent of the investigated cross section geometry in the whole analysed material grade range (S235 - S960), if the b/t ratio is smaller than 30. The obtained buckling resistances for the S500 and S700 steel grades are always higher than the ECCS column buckling Curve b. The obtained buckling resistances for the S960 steel grade are always higher than the ECCS column buckling Curve a. Results also prove the applicability of the ECCS column buckling Curve c for steel grades S235 – S355, as currently proposed by the EN1993-1-1 [3]. The simulation results are also compared to previous design methods found in the international literature. Based on the numerical simulations an enhanced imperfection modification factor according to Eq. (a) is applicable for steel grades between S500 S960 for welded hollow section columns. However it should be mentioned, that the design method using modification of the α parameter depending on the steel grade can be criticized theoretically, because it does not consider the differences in the material characteristic change between the NSS and HSS materials, but it seems usable for NSS and HSS columns separately. 0.6
235 𝑀𝑃𝑎 𝛼 = 0.49 ∙ ( ) 𝑓𝑦
(3.19)
The results of the current numerical simulations are in harmony with the results of the laboratory tests and the statistical evaluation of the measured column buckling resistances as made in frame of the RUOSTE project. At the same time all the results are in harmony with the previous test results and numerical simulations found in the international literature. However, the current investigations enlarge the investigated parameter range (S420 – S960), using the same methodology for the evaluation of all the steel grades, making it possible to observe the differences in the buckling behaviour between steel grades, and determine its reasons, which are unique in this topic. Applicable buckling curves for HSS cold-formed sections Results based on the laboratory tests -
In case of the cold formed specimens the average measured out-of-straightness imperfection is equal to L/11000, which is significantly smaller than the manufacturing tolerance (L/750). Clear increasing tendency can be observed depending on the global slenderness, but there are no clear tendencies depending on the steel grade. This observation suggests to adopt the same geometric imperfection shape and magnitude
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in FE calculations for HSS members as for NSS members, which has positive consequence on the buckling behaviour. The lowest reduction factor belongs to the specimens made on S420 steel grades. Application of higher steel indicates clear increase in the buckling reduction factor. All test results for the analysed steel grades (S420 – S960) are located above the buckling Curve b using the actual values for the geometry and the material properties. If only the test results regarding steel grades of S500 – S960 are considered with smaller geometric imperfections than L/1000 all the reduction factors are located over the column buckling Curve a. Using the nominal values in the evaluation process all the test results are located above the column buckling Curve a0. Based on the statistical evaluation of the current test results the column buckling Curve b sufficiently met the safety criteria of the EN1990 Annex D for the S500, S700, S960 specimens. The calculated value of γM1* is 0.99 and the 2.3% lower quantile of the experimental results is 6% higher than the resistances of the buckling Curve b. The same statement can be also done for the S460 material grade as well, with γ M1* equal by 0.97 and the 2.3% lower quantile of the experimental results is 9% higher as the resistance level of the column buckling Curve b. It has to be mentioned that the number of the executed tests did not allow making the statistical evaluation for all the analysed steel grades separately. The separated evaluation is therefore made based on the numerical simulations.
-
-
-
-
Results based on the numerical simulations According to the numerical parametric study the following conclusions are made for cold formed hollow section columns:
the buckling reduction factor of HSS columns can be higher due to the increased fy, the buckling reduction factor of HSS columns can be higher due to the magnitude of the bending residual stresses (in case of HSS grades the residual bending stresses does not increase with the yield strength), the buckling reduction factor of HSS columns could be smaller because the RambergOsgood type material model can have negative effect on the buckling resistance depending on the slenderness range and steel grade.
The results of the numerical simulations show there are two phenomena that increase and there is one phenomenon that decreases the buckling reduction factor of HSS columns compared to NSS material grades. Using the verified numerical model a further parametric study is executed analysing different square hollow section columns using the input parameters which are the bases of the simulation based ECCS column buckling curve development. Based on the numerical simulations the following final conclusions are drawn: -
-
The simulations showed that for cross sections which belong to cross section Class 1 – Class 3, the column buckling curves are independent of the investigated cross section geometry in the whole analysed steel grade range (S235 - S960). The obtained buckling resistances for the S500 and S700 steel grades are always higher than the ECCS column buckling Curve b. The obtained buckling resistances for the S960 steel grade are always higher than the ECCS column buckling Curve a. Results also prove the applicability of the ECCS column buckling Curve c for steel grades S235 – S355, as currently proposed by the EN1993-1-1 [3]. The simulation results are also compared to previous design methods found in the international literature. Based on the numerical simulations an enhanced imperfection modification factor according to Eq. (b) is applicable for steel grades between S500 S960 for cold formed hollow section columns. However it should be mentioned, that the design method using modification of the α parameter depending on the steel grade can be criticized theoretically, because it does not consider the differences in the material
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characteristic change between the NSS and HSS materials, but it seems usable for NSS and HSS columns separately (see eq. 3.19). The results of the current numerical simulations are in harmony with the results of the laboratory tests and the statistical evaluation of the measured column buckling resistances as well made in frame of the RUOSTE project. In the same time all the results are also in harmony with the previous test results and numerical simulations found in the international literature. However the current investigations enlarge the investigated parameter range (S420 – S960), use the same methodology for the evaluation of all the steel grades, make possible to observe the differences in the buckling behaviour between steel grades, and determine its reasons, which are unique in this topic. The proposed design buckling curves can be applied for cold finished cold formed hollow section columns.
-
2.4
Interaction Tests
2.4.1
Design and fabrication
The welded sections were provided with matching welding strengths, i.e. the yield strength of the seams were similar to the yield strength of the specimens. They were fabricated according to [68]. After sawing, the specimens were milled flat at the ends providing a best possible even surface. Head plates were avoided to introduce no further residual stresses. The specimens were designed such that local buckling was decisive before global buckling. The local buckling slenderness was kept constant: the global buckling slenderness was varied by a changing overall length. This aimed at a slight transition from plain local buckling to global buckling failure. The test-matrix is shown in Table 2-15. Table 2-15: Test-matrix for interaction tests Nominal Dimensions Actual Dimensions CrossSpecimen Cross-section Thickness Length ̅ 𝜆𝑝,𝑛𝑜𝑚 Steel section Length [mm] [mm] t [mm] [mm] [mm]
𝜆̅𝑐,𝑛𝑜𝑚
S500
160 160 4
1400
160.5
159.25
4.06
1399
0.976
0.341
“
160 160 4
1600
159.75
159.5
4.08
1599
0.976
0.390
160 160 4
1800
160.0
159.25
4.03
1800
0.976
0.439
160 160 4
2000
160.0
159.0
4.01
2000
0.976
0.488
160 160 4
2200
4.0
2198
0.976
0.536
“
160 160 4
2300
159.0
159.0
3.96
2301
0.976
0.609
S960 “
140 140 4
470
140.25
137.0
3.95
470
1.174
0.182
“
140 140 4
730
138.5
136.5
4.18
728
1.174
0.283
140 140 4
1300
3.96
1299
1.174
0.504
140 140 4
1400
139.0
137.75
4.0
1399
1.174
0.542
140 140 4
1500
139.5
138.5
3.91
1499
1.174
0.581
140 140 4
1700
141.0
137.5
3.97
1699
1.174
0.659
140 140 4
1900
138.5
137.0
3.97
1899
1.174
0.736
“
159.25 159.25
139.25 137.75
Page 75
The name of specimens were defined as follows:
01_W_S500_160_4_1400 sequential number
Fabrication_Steelgrade_width_thickness_length
The welded sections were provided by Ruukki (S500M) and SSAB (S960Q). 2.4.2
Material characterization
Table 2-16 summarizes the material properties taken from the material certificates provided by the respective steel producers. The bold values in Table 2-16 indicate the fulfilment of the requirements of the code [4]: the S500M material fulfilled all requirements. Applying the same criteria to S960, the elongation at fracture criterion was matched, while the yield strength ratio was slightly lower than required. The elongation at fracture would have been 35 % lower than asked for. Table 2-16: material properties of the welded specimens Steel
t
fy
fu,
fu/ fy
S500M S960Q
[mm] 4.03 4.11
[N/mm²] 562 980/962*
[N/mm²] 640 1024
[-] 1.14 1.045
εu [%] 12 4.45
15* fy,nom/E [%] 3.57 6.85
A5 (min 10%) [%] 25.3 12
*bold: fulfilled criteria 2.4.3
Test setup and procedure
The tests aimed at having local buckling before global buckling to trigger the failure mode. The specimens were put between steel plates to avoid the indentation of the base plate and the load introduction from above. The testing machine was a Zwick/Roell with 5 MN static loading capacity. For the load introduction a special plate with roughness category N2 was produced by Ruukki, to allow for the transfer of the load from the hydraulic jack via the cup and ball bearing to the specimen. The cup and ball bearing ensured a constant direction of the load, even if large rotation would occure. At the bottom, the specimen was placed on a plate which fitted in dimensions to the specimen to achieve a centrically build-in specimen. Below the plate, a roller bearing was used to control the direction of global buckling. The build-in specimen is shown in Figure 2-15, together with details of the constraints. The distance from the specimen to the centre of rotation was on the top 225 mm (52.5+72+41+40=205+head plate) and 103 mm (83+20mm) at the bottom. Each specimen was equipped with 6 strain gauges: 2x 2 in the middle at two opposite faces, and 1x 2 at the top of the specimen close to the load introduction (29.5 cm from above for the specimens longer than 1000 mm, else 16.5 cm). 3 string pots were used to measure the vertical displacement, were two were placed above the roller. One was placed in the middle of the specimen to measure the horizontal deflection.
Page 76
cup and ball bearing
2x1 strain gauges
specimen string pot (horizontal)
2x2 strain gauges
Plate, fitting in specimen
3 string pots
Roller bearing
Figure 2-15: Test-setup with build in specimen, overview (left) and constraint execution (right)
2.4.4
Experimental Results
The measured load-displacement curves are shown in Figure 2-16 for the S500 specimens (𝜆̅𝑝 = 0.976) and in Figure 2-17 for the S960 specimens (𝜆̅𝑝 =1.174).
Page 77
It can be observed that with increasing length/ global slenderness the initial stiffness decreases, accompanied with a decreasing ultimate load. The shape of drop after reaching the ultimate load indicates the failure mode: while for the short specimens the drop is very smooth (local buckling) for the longer ones it occurs more sudden (global buckling). The S960 columns were more slender in both categories, locally and globally. This leads to a more distinguishable behaviour, i.e. the transition between both failure modes is clearer to identify.
Figure 2-16: Load-displacement curves for S500 specimens
Figure 2-17: Load-displacement curves for S960 specimens
2.4.5
Evaluation according to Eurocode
The effective width is calculated by taking the nominal width (as the mean values of the measured width do insignificantly deviate from the nominal values) and real thickness (mean value of all four faces) into account (𝑏̅ = 𝑏 − 2𝑡). The slenderness 𝜆̅𝑝 is calculated according to [8] with:
Page 78
𝜆̅𝑝 = √
(3.21)
𝑓𝑦 𝑏̅/𝑡 = 𝜎𝑐𝑟 28.4 ∙ 𝜀 ∙ √𝑘𝜎
kσ is taken to 4, assuming hinged boundary condition for the faces, neglecting the interaction of the adjacent plates. The reduction factor ρ is then calculated with the well-known Winter-formula: 𝜆̅𝑝 ≤ 0.673:
ρ=1
𝜆̅𝑝 > 0.673:
ρ=
̅𝑝 −0.22 𝜆 ̅2𝑝 λ
(3.22)
Applied on the plate width, the effective cross-section properties are evaluated and used to calculate Npl for the global slenderness 𝜆̅𝑐 . The critical load Ncr is however assessed using the gross cross-section values. (3.23)
𝐴𝑒𝑓𝑓 ∙ 𝑓𝑦 𝜆̅𝑐 = √ 𝑁𝑐𝑟
The subsequent calculation procedure does not differ from the known global buckling check: 𝜒𝑐 =
(3.24)
1 𝜙 + √𝜙² −
using:
𝜆2̅𝑐
𝜙 = 0,5[1 + 𝛼(𝜆̅𝑐 − 0,2) + 𝜆̅2𝑐 ]
The factor is then applied on the plastic resistance of the member: 𝑁𝐸 ≤ 1,0 𝜒𝑐 ∙ 𝐴𝑒𝑓𝑓 ∙ 𝑓𝑦
(3.25)
Or, under consideration of bending: 𝑀𝑦,𝐸𝐷 + Δ𝑀𝑦,𝐸𝐷 𝑁𝐸𝑑 𝑀𝑧,𝐸𝐷 + Δ𝑀𝑧,𝐸𝐷 + 𝑘𝑦𝑦 + 𝑘𝑦𝑧 ≤ 1,0 𝑁𝑒𝑓𝑓,𝑅𝑘 𝑀𝑦,𝑒𝑓𝑓,𝑅𝑘 𝑀𝑧,𝑒𝑓𝑓,𝑅𝑘 𝜒𝑦 ∙ 𝜒𝐿𝑇 ∙ 𝛾𝑀1 𝛾𝑀1 𝛾𝑀1 𝑀𝑦,𝐸𝐷 + Δ𝑀𝑦,𝐸𝐷 𝑁𝐸𝑑 𝑀𝑧,𝐸𝐷 + Δ𝑀𝑧,𝐸𝐷 + 𝑘𝑧𝑦 + 𝑘𝑧𝑧 ≤ 1,0 𝑁𝑒𝑓𝑓,𝑅𝑘 𝑀𝑦,𝑒𝑓𝑓,𝑅𝑘 𝑀𝑧,𝑒𝑓𝑓,𝑅𝑘 𝜒𝑧 ∙ 𝜒𝐿𝑇 ∙ 𝛾𝑀1 𝛾𝑀1 𝛾𝑀1
(3.26)
(3.27)
Table 2-17 summarizes the specimens with their length, which is taken here as the distance between the centres of rotation of the top and bottom support (225 mm + specimen length + 103), and the main slenderness values (locally and globally) as well as their critical load for local and global failure modes.
Page 79
Table 2-17: Slenderness and critical loads for specimens CrossLength 𝜆̅𝑝,𝑛𝑜𝑚 𝜆̅𝑝,𝑎𝑐𝑡 Steel section [mm] [mm]
𝜆̅𝑐,𝑎𝑐𝑡
𝑁𝑐𝑟,𝑐/𝐸𝐶
𝐹𝑐𝑟,𝑝/𝐸𝐶
S500
160 160 4
1728
0.976
1.035
0.447
7031
1278
“
160 160 4
1928
0.976
1.035
0.498
5648
1278
160 160 4
2128
0.976
1.035
0.550
4636
1278
160 160 4
2328
0.976
1.035
0.602
3874
1278
160 160 4
2528
0.976
1.035
0.550
3285
1278
“
160 160 4
2628
0.976
1.035
0.749
3040
1278
S960
140 140 4
728
1.174
1.193
0.287
26255
1483
“
140 140 4
1058
1.174
1.193
0.416
12413
1483
140 140 4
1628
1.174
1.193
0.641
5250
1483
140 140 4
1728
1.174
1.193
0.680
4660
1483
140 140 4
1828
1.174
1.193
0.720
4164
1483
140 140 4
2028
1.174
1.193
0.798
3383
1483
140 140 4
2228
1.174
1.193
0.877
2803
1483
“
A comparison of the results using the effective width approach with the experimental results is shown in Table 2-18 The ratio of the experimental results (re) over the theoretical results (rt), plotted over the slenderness, is also depicted in Figure 2-18. The Eurocode approach delivers a larger scatter in resistance prediction and seems conservative in the more slender range.
1.3 EC3-1-1 1.2
re/rt
1.1 1 0.9 0.8 0.25
0.3
0.35
0.4
0.45
0.5 7 𝜆 6̅
0.55
0.6
0.65
0.7
0.75
Figure 2-18: Experimental results scaled to resistance model EC
Page 80
Table 2-18: Ultimate loads achieved in experiments and calculated
2.4.6
Test
Fu,exp [kN]
Fu,EC,1-1,eff [kN]
Fu,EC,1-1,eff / Fu,exp
01_W_S500_160_4_1400
848.6
1007
0.843
02_W_S500_160_4_1600
880.3
987
0.892
03_W_S500_160_4_1800
883.9
966
0.915
04_W_S500_160_4_2000
858.2
944
0.909
05_W_S500_160_4_2200
828.9
921
0.900
06_W_S500_160_4_2300
826.5
908
0.910
07_W_S960_140_4_0470
1444.1
1438
1.003
08_W_S960_140_4_0730
1400.4
1391
1.006
09_W_S960_140_4_1300
1390.5
1275
1.090
10_W_S960_140_4_1400
1396.6
1252
1.115
11_W_S960_140_4_1500
1382.5
1228
1.125
12_W_S960_140_4_1700
1340.7
1176
1.139
13_W_S960_140_4_1900
1305.4
1121
1.164
Numerical Model
For the numerical studies the finite-element programme Ansys 16.0 was used. The model consisted of shell181 elements, which depicted a four-node element with six degrees of freedom at each node (Figure 2-19).
Figure 2-19: Definition of shell element used in Ansys [5] As constraints, hinged conditions and a clamping along one axis (preventing from torsional modes) were used at the bottom of the column, whereas on the top the same boundary conditions were used but free in longitudinal direction. Load was applied as displacement in longitudinal direction. The used solver follows the arc-length method and involves the tracing of a complex path in the load-displacement response into the buckling/post buckling regimes (Figure 2-20). It is assumed that all load magnitudes can be controlled by a single scalar parameter (that is, the total load factor). Mathematically, the arc-length method can be viewed as the trace of a single equilibrium curve in a space spanned by the nodal displacement variables and the total load factor. Therefore, all options of the Newton-Raphson method are still the basic method for the arc-length solution. As the displacement vectors and the scalar load factor are treated as unknowns, the arc-length method itself is an automatic load step method [5].
Page 81
As an example, the finite element model of specimen S960_140x140x4_1300 is shown in Figure 2-21 with its mesh and boundary conditions.
Figure 2-20: Basics of arc-lenght method
Figure 2-21: Ansys FE-Model for experiment S960_140x140x4_1300 2.4.6.1
Material Model
The material model used in the numerical simulations were derived from the coupon tests provided by the steel suppliers. Using the known equations to assess the true stress-strain relations, the Hollomon equations were used to fit and extrapolate the final material curve for Ansys. The used true stress-strain curves can be found in Figure 2-22 and Figure 2-23.
True stress:
𝜎𝑡 = 𝜎 1 + 𝜀
True strain:
𝜀𝑡 = 𝑙𝑛 1 + 𝜀
Hollomon:
𝜎𝑡,𝐻𝑜𝑙𝑙 = 𝑘𝐻 ∙
(3.28) (3.29) 𝑛 𝜀𝑡 𝐻
(3.30)
Page 82
800
2
s [N/mm ]
600 400 Engineering Curve True Engineering Curve Hollomon Extrapolation
200 0
0
2
4
6
8
10
e [%]
Figure 2-22: Ansys Input S500
1200
s [N/mm2]
1100 1000 900 800
Engineering Curve True Engineering Curve Hollomon extrapolation
700 600 0
2
4
e [%]
6
8
10
Figure 2-23: Ansys Input S960 While the S500 material exposed a small yield plateau, the S960 material could be extrapolated using Hollomon directly from fy. The parameters for the Hollomon equation could be derived as summarized in Table 2-19. Table 2-19: Hollomon parameters Steel S500 S960
kH 584.3 991.6
nH 0.084 0.049
The Young’s Modulus was assumed to be 210,000 N/mm² in both cases until reaching the yield strength stated in the material certificate. 2.4.6.2
Assessment of geometric and structural imperfections Geometric imperfections
An Eigen-Buckling analysis was carried out in a first step. The first mode was applied then in the model with the amplitude 𝑒0 , calculated with developed in [70]. The global imperfection was applied by displacement controlled loading in the middle of the column, using the amplitude: length of the column/ 750 (which equals the geometric tolerance limit from the fabrication code).
Page 83
Figure 2-24: Local buckling imperfection shape (scaled) Residual Stress implementation Basic approach to incorporate residual stresses from welding was the model used in ENV 1993, taken from [69]. The amplitude of the tension residual stress was adjusted according to the measurements which were undertaken within the Ruoste project (detailed information can be found in [70]). The amplitude of the compression residual stress was calculated assuming equilibrium of forces. The factor multiplied with the actual yield strength is summarized in Table 2-20 (the actual yield strength stated here might differ from the material coupon test which is due to the fitting process for the true stress-strain curve achieved for the material model used in Ansys, see also section 0). An example with the resulting applied residual stress is shown in Figure 2-25. Table 2-20: Residual stress assumptions for tensile strength in the corners Steel
fy,actual [𝑁/𝑚𝑚²]
𝜎𝑡 [𝑁/𝑚𝑚²]
S500
555
0.85 fy,actual
S960
980
0.55 fy,actual
Figure 2-25: Residual Stress Plot for S960_140x140x4_1300
Page 84
2.4.7
Comparison FE-results and experimental results
The finite-element model described was used to evaluate the 13 experimental test results for calibration purposes. The main results are presented in Table 2-21. Table 2-21: Main Results from interaction tests Test
Fu,exp [kN]
Fu,FE [kN]
Fu,FE/Fu,exp
01_W_S500_160_4_1400
848.6
974
1.148
02_W_S500_160_4_1600
880.3
967
1.098
03_W_S500_160_4_1800
883.9
963
1.089
04_W_S500_160_4_2000
858.2
945
1.101
05_W_S500_160_4_2200
828.9
935
1.128
06_W_S500_160_4_2300
826.5
9143
1.106
07_W_S960_140_4_0470
1444.1
1368
0.947
08_W_S960_140_4_0730
1400.4
1473
1.052
09_W_S960_140_4_1300
1390.5
1303
0.937
10_W_S960_140_4_1400
1396.6
1330
0.952
11_W_S960_140_4_1500
1382.5
1256
0.909
12_W_S960_140_4_1700
1340.7
1276
0.952
13_W_S960_140_4_1900
1305.4
1247
0.955
The developed finite element model showed good compliance in terms of ultimate loads achieved in the simulations compared with the experiments. A better fitting would be possible when varying the structural and geometrical imperfections, however, it was aimed at a general model for the implementation of those. Thus, a mean conformity of resistance prediction was preferred towards individual fitting. 2.4.8
Parametric studies
After the calibration of the numerical model, a parametric study was conducted to assess the influence of the material specific issues such as yield plateau length and ultimate to yield strength ratio. Nominal material curves were used as proposed by Eichler [71]. The mathematic description of the material curves were derived from a database containing 100 stress-strain curves of S235 up to S890. The fabrication processes included untreated, normalized, quenched and tempered as well as thermomechanical rolled steels. The length of the yield plateau can be estimated acc. to [71] with: Δ𝜀𝑙 = 0.0375 (1 −
𝑓𝑦 ) 𝐸
(3.31)
Using the Hollomon equation: 𝜎𝑡𝑟𝑢𝑒 = 𝑘𝑙 𝜀 𝑛 + Δ
(3.32)
With: Δ = −𝑘𝑙 (𝑙𝑛 1 + Δ𝜀𝑙 ) + 𝑓𝑦 (1 +
𝑓𝑦 ) 𝐸
(3.33)
The coefficients for the 0.05 confidence level, 0.50 and 0.95 could be derived then (depicting a lower and upper limit, and the mean function) as summarized in Table 2-22.
Page 85
Table 2-22: Reference true stress strain curves in dependence of confidence level 𝑛 [-] 𝑘𝐿 [-] Confidence Level 0.2932 𝑓𝑦 + 535 −0.0984 ∙ 10−3 𝑓𝑦 + 0.1188 0.05 0.7206 𝑓𝑦 + 553 −0.1897 ∙ 10−3 𝑓𝑦 + 0.2291 0.50 1.1948 𝑓𝑦 + 573 −0.2744 ∙ 10−3 𝑓𝑦 + 0.3314 0.95 The inclination and curvature resulting from these formulas were adopted, assuming that fy equals always the nominal yield strength fy,nom. Their influence was then evaluated for the ultimate load.
Figure 2-26: Artificial stress-strain curves for parametric studies For S500 material, additionally different yield plateau lengths 𝜀𝐿 were investigated for the mean stress-strain curve (0.50 confidence level), shown in Table 2-23. For lower, mean and upper limit equations (Table 2-22) the yield plateau length was varied first using the suggested yield length plateau by Eichler [71], additionally with the yield plateau from the original Ruukki material of the experiments and finally with an interpolated value from both length values (see Figure 2-26). For S960, no yield plateau was used at all. The ultimate load and the vertical displacement at ultimate load were evaluated. The vertical displacement was divided by the length of the column to assess the mean strain in the column at failure load. The results on S500 material are summarized in Table 2-23 and for the S960 material in Table 2-24.
Page 86
Table 2-23: fy=500 N/mm²: Variation of hardening and yield plateau length εL column
Length [mm] fu,act [N/mm²] εu [-]
Equation Eichler [19]
εL [-] = 0.01875
fu,act [N/mm²] εu [-] fu,act [N/mm²] εu [-] fu,act [N/mm²]
Interpolat ed between Eichler and Ruukki material
εu [-] εL [-] = 0.01073
fu,act [N/mm²] εu [-] fu,act [N/mm²] εu [-] fu,act [N/mm²]
Scaled Ruukki Material
εL [-] = 0.00296
εu [-] fu,act [N/mm²] εu [-]
1400
1600
1800
2000
2200
2300
496
Fu,FE [kN]
925.76
930.60
908.57
890.38
883.54
864.79
0.093
δ/length
0.00206
0.00201
0.00196
0.00195
0.00193
0.00191
550
Fu,FE [kN]
925.76
930.60
908.57
890.38
883.54
864.79
0.165
δ/length
0.00206
0.00201
0.00196
0.00195
0.00193
0.00191
642
Fu,FE [kN]
925.76
930.83
908.57
890.38
883.54
864.79
0.235
δ/length
0.00206
0.00201
0.00196
0.00195
0.00193
0.00191
530
Fu,FE [kN]
925.81
930.87
908.61
890.41
883.59
864.82
0.085
δ/length
0.00206
0.00201
0.00196
0.00195
0.00193
0.00191
619
Fu,FE [kN]
925.92
930.96
908.67
890.49
883.68
864.90
0.157
δ/length
0.00206
0.00201
0.00196
0.00195
0.00193
0.00191
712
Fu,FE [kN]
925.81
930.87
908.61
890.41
883.59
864.82
0.228
δ/length
0.00206
0.00201
0.00196
0.00195
0.00193
0.00191
555
Fu,FE [kN]
925.89
928.26
903.97
886.73
878.80
860.41
0.077
δ/length
0.00206
0.00198
0.00201
0.00197
0.00193
0.00191
778
Fu,FE [kN]
925.98
933.09
908.76
890.64
0.220
δ/length
0.00206
0.00201
0.00196
0.00199
Table 2-24: fy=960 N/mm²: Variation of hardening and yield plateau length εL column
length [mm]
1300
1400
1500
1700
1900
962
Fu,FE [kN]
1392.62
1240.90
1258.33
1191.66
1205.71
1168.39
0.0292
δ/length
0.00449
0.00424
0.00417
0.00411
0.00390
0.00365
fu,act [N/mm²]
1019
Fu,FE [kN]
1458.16
1297.86
1324.80
1250.94
1270.85
1241.08
εu [-]
0.053
δ/length
0.00428
0.00398
0.00389
0.00389
0.00365
0.00342
fu,act [N/mm²]
1120
Fu,FE [kN]
1471.71
1307.65
1334.56
1260.01
1278.15
1245.12
εu [-]
0.075
δ/length
0.00459
0.00414
0.00406
0.00399
0.00371
0.00342
fu,act [N/mm²] εu [-] Equation Eichler [19]
730
The results show that for S500 material, the achieved ultimate loads are almost unaffected by the actual tensile strength fu: no matter which of the scaled engineering stress-strain curves was used, the ultimate/ failure load for a given member length remained the same. The same can be concluded for the corresponding uniform elongation 𝜀𝑢 . The length of the yield plateau 𝜀𝑢 proofed also to be of no influence neither on the ultimate load nor on the scaled end-shortening of the column δ/length.
Page 87
Although it is obvious in global terms that the yield strength is not reached because of the CSC4 section, it is nonetheless interesting here that local plastifications do not lead to differing results. For the S960 material study, the results do differ a bit, showing low, but slightly noticeable changings in ultimate load and end-shortening. This might be due to the fact, that for S500 the yield plateau smoothens the differences, as all specimen have to follow the same path in the material curve on the yield plateau length. The end of the plateau is probably not reached, or at least not far exceeded. On the other hand, reaching (locally) the yield strength in the S960 material leads directly into the hardening path such that here the influence of different hardening coefficients is more pronounced. It can be concluded, however, that the hardening characteristic of the material is of low up to no influence on the behaviour of columns. 2.4.9
Summary for Interaction tests
The comparison of the experimental test data with the effective width method given in Eurocode gave acceptable results, however, combined with a comparable high scatter. The general method introduced within this study, which gave good results for the limit case of local buckling, showed to be too optimistic in the resistance prediction for the coupled instability case. This might be mainly attributed to the fact that the method is so far developed for open sections. Further research is planned to improve the reliability.
Page 88
3
TUBULAR JOINTS
3.1
Introduction
Welded tubular trusses made of hollow sections are very typical structures in steel construction along with trusses made of variety of I-beams. However, tubular members have several advantages over I-beams, including more uniform properties between different axis, less area for painting and easiness of use as composite columns Figure 3-1 illustrates these properties.
Figure 3-1: Shape and paint surface on different kind of steel sections [72] Currently, the majority of trusses made in Europe are made from S355J2H steel grade. There are several reasons for this, including that high strength hollow sections are not as widely available as mild grades. Also there are clear technical barriers induced in Eurocode 3 (see 4.1.1) which leads to situation that trusses made of high strength hollow sections are not economical nor practical to manufacture in spite of the clear benefits they would offer, including reduced material usage and costs, longer spans and smaller environmental impact. Two issues were investigated regarding tubular joints within Ruoste: first, EC requires to apply reduction factors on the base material of 0.9 for S 420 and S 460 and 0.8 for S500 and above. This reduction factor almost prevents using HSS in construction, when S500 is reduced to S400 and S700 to S560 level. Other major obstacle is the throat thicknesses of fillet welds: EC3 gives very conservative weld sizes for HSS fillet welds, which increases welding costs very much.
3.2
Reduction factor test
In reduction factor tests, the validity of different failure modes according to current EC3 [6] were tested. The joints were designed and fabricated such that the weld would not be the critical part of the joint. For different steel grades the joint dimensions were kept similar if possible, despite the fact that the cross section class of joint may change between steel grades of tubes. 3.2.1
Used tubes and joints in reduction factor and fillet weld tests
In Table 3-1, the tested tube dimensions and actual yield strength of material used are shown. The true thickness of the tube is shown in parentheses next to the nominal value. True strength values are from material certificates delivered by manufacturers. For two tubes there were no material certificates available but they were not the critical components of the specimens. The values seen in Table 3-1 were used when the comparisons of test result and EC3 joint capacity were made.
Page 89
Table 3-1: Nominal and true values of tested tubes
4 (4.15)
Yield strength [MPa] 557
Ultimate strength [MPa] 634
Ultimate elongation [%] 28,3
100
4 (4.12)
522
624
27,6
100
6 (5.99)
553
648
26,0
S500
Width [mm]
Height [mm]
Thickness [mm]
Voestalpine
80
80
Voestalpine
100
Voestalpine
100
SSAB
120
120
4 (4.19)
604
671
20
Voestalpine
120
120
6 (6.04)
566
640
21,2
Voestalpine
130
130
4 (4.19)
X
X
X
Voestalpine
150
150
5 (5.15)
548
651
28,1
SSAB
150
150
6 (5.93)
546
597
20
SSAB
150
150
8 (7.84)
595
646
20
510
620
24
Filler Material
Union Ni 2,5
S700
Width [mm]
Height [mm]
Thickness [mm]
Yield strength [MPa]
Ultimate strength [MPa]
Ultimate elongation [%]
SSAB
80
80
4 ( 3.98)
864
878
13
Voestalpine
100
100
5 (4.82)
725
813
21,7
SSAB
100
100
6 (5.89)
772
844
12
SSAB
120
120
4 (3.83)
836
861
13
SSAB
120
120
6 (5.95)
741
830
13
Voestalpine
130
130
4 (3.92)
X
X
X
Voestalpine
150
150
5 (5.06)
762
846
23,2
SSAB
150
150
6 (5.89)
748
856
15
SSAB
150
150
8 (7.85)
751
834
14
740
18
Filler Material
Union NiMoCr
S960
Width [mm]
Height [mm]
SSAB SSAB SSAB SSAB SSAB SSAB SSAB SSAB SSAB SSAB
80 100 100 120 120 140 150 150 150 150
80 100 100 120 120 140 150 150 150 150
Filler Material
Thickness [mm] 4 4 6 4 6 4 5 6 7 8
(3.94) (3.98) (5.95) (3.81) (5.94) (4.00) (4.97) (5.91) (6.90) (7.79)
Union X96
680 Yield strength [MPa] 1176 996 1071 1162 1093 1070 1080 1006 1180 1050
Ultimate strength [MPa] 1220 1108 1151 1206 1176 1133 1193 1156 1244 1163
930
980
Ultimate elongation [%] 7 8 9 7 8 11 10 10 8 10 14
In Table 3-2 the ranges of welding parameters are shown. These values are depending on the type of joints. Heat input of welding (or rather cooling rate) was not taken as variable in testing but is definitely important factor, because it has impact on the softening of base material (heat affected zone, HAZ).
Page 90
Table 3-2: Ranges for welding parameters used in the tests Steel grade
Min/m ax
Current [A]
Voltage [V]
Welding speed [mm/min]
Heat input [kJ/mm]
min
250
26.6
480
0.83
max min
250
28.1
240
1.76
240
24.5
600
0.59
max min
255
26.6
400
1.02
240
24.5
600
0.59
max
255
26.6
400
1.02
S500 S700 S960
In Table 3-3 reduction factor test results are shown with the comparison of EC3 predicted capacity of joint. Table 3-3: Reduction factor test results Max. Cross Capacity Force in section acc. EC3 test class [kN] [kN]
Chord [mm]
Cross section class
Brace [mm]
RX1
100x100x4
1
100x100x4
1
518
718
RX2
150x150x5
3
100x100x4
1
158
498
RX3
150x150x5
3
120x120x4
3
245
686
RX3
150x150x5
3
120x120x4
3
245
679
RX4
150x150x6
1
130x130x4
4
458
921
RX5
150x150x5
3
150x150x5
3
307
815
RX6
150x150x5
3
100x100x4
1
171
227
RX7
150x150x5
3
120x120x4
3
253
339
RK1
150x150x5
3
80x80x4
1
304
376
RK2
120x120x6
1
100x100x6
1
683
715
RK3
150x150x5
3
80x80x4
1
304
377
RK4
150x150x5
3
80x80x4
1
304
397
RX1
100x100x5
1
100x100x5
1
869
1154
RX2
150x150x5
4
100x100x6
2
214
445
RX3
150x150x5
4
100x100x7
4
335
723
RX3
150x150x5
4
120x120x4
4
335
728
RX3
150x150x5
4
120x120x4
4
335
592
RX4
150x150x6
2
130x130x4
4
623
916
RX5
150x150x5
1
150x150x5
4
356
935
Joint / Steel grade
S500
S700
Failure mode in test weld toe /general failure mode weld toe /general failure mode weld toe /general failure mode weld toe /general failure mode weld toe /general failure mode chord web failure chord web failure/ chord face failure chord web failure/ chord face failure chord face failure compression side chord face failure chord face failure compression side chord face failure compression side weld toe /general failure mode/weld chord face failure weld toe /general failure mode weld toe /general failure mode weld toe /general failure mode weld toe /general failure mode chord web failure
Page 91
RX6
150x150x5
1
100x100x5
1
214
266
RX7
150x150x5
1
120x120x4
4
355
388
RK1
150x150x5
4
80x80x4
1
412
394
RK2
120x120x6
1
100x100x6
1
889
982
RK3
150x150x5
4
80x80x4
1
412
440
RK4
150x150x5
4
80x80x4
1
412
412
RX1
100x100x4
4
100x100x4
4
947
816
RX2
150x150x5
4
100x100x4
4
294
396
RX3
150x150x5
4
120x120x4
4
459
725
RX3
150x150x5
4
120x120x4
4
459
511
RX4
150x150x6
4
140x140x4
4
1441
1202
RX5
150x150x5
4
150x150x5
4
244
808
RX6
150x150x5
4
100x100x4
4
292
276
RX7
150x150x5
4
120x120x4
4
453
428
RK1
150x150x6
4
80x80x4
1
688
515
RK2
120x120x6
1
100x100x6
1
1280
951
RK3
150x150x6
4
80x80x4
1
688
545
RK4
150x150x6
4
80x80x4
1
688
459
S960
3.2.2
chord web failure/ chord face failure chord web failure/ chord face failure chord face failure compression side chord shear failure chord face failure compression side chord face failure compression side weld toe chord side chord face failure/punching shear weld toe /general failure mode weld toe /general failure mode weld toe /general failure mode chord web failure chord web failure/ chord face failure chord web failure/ chord face failure chord face failure tension side chord shear failure/ chord face failure chord face failure tension side chord face failure tension side
Welded specimen coupon tests
The joint behaviour and the capacity of welded hollow section joints are affected by nonlinear behaviour of joint geometry and material. Joint nonlinearity is often good thing in terms of capacity of weld itself. However, at the weld toe where the softening occurs, material is often highly stressed due to primary and secondary loading of joint. The coupon tests shown in Figure 3-2 are for studying the welded material without the geometrical effects from joint. Test specimens were cut from X1 type joints and machined smooth to have the shape of standard coupon test, but contained the same material zones as the original joint: weld, HAZ, cold formed corner and base materials (transversely and longitudinally) of the tube.
Figure 3-2: Idea of welded coupon test specimens
Page 92
Testing of these coupons was performed like normal coupon test specimens, but also the 3D Aramis measuring system has been used. Aramis enables measuring of local strains on fractured zone and based on that information the material models for FEA can be obtained. This kind of testing has been carried out for each steel grade. In Figure 3-3 the engineering stress-stain curves can be seen. Stress was calculated from force and initial area of cross section and strain obtained from axial extensometer. From those curves it can be seen that the material properties of welded S500 material are close to yield and ultimate strengths of base material, but the ultimate strain capacity has dropped approximately to half of the value available for base material of tube. Reason for this is the strain localisation next to the weld and therefore the strains from axial extensometer seems lower. Consequently, the decreasing percentage is highly depending on the reference length of the extensometer. In case of S960 steel grade the yield and ultimate stresses drop remarkably compared to the values gained from the base material. Similar behaviour could be seen in real joint capacities but the drop in joint capacities is even more significant due to stress concentration in joint and large displacements.
Figure 3-3: Tensile coupon tests for welded specimens - Engineering stress-strain 3.2.3
S500 reduction factor tests
Figure 3-4 illustrates the scatter of the 31 test results of S500 tubular joints (Ftest) compared to calculated capacities according to EC3 (FEC3). The solid line represents the capacities according to EC3 but without any reduction factor for S500 material and the dotted line represents the joint capacity with the material reduction factor of 0.8 according to EC3. The 31 test series included 19 joints for fillet welds capacity tests, where the throat thickness was set so small that it would be a critical part of the joint and the full capacity of the joint would not be reached. Most of the joints failed in the base material, but in some specimens the failure took place in the weld or in the fusion line. Those tests are discussed in section 3.3. As can be seen from the Figure 3-4 all the test results are well above both reference lines. The calculated capacities (EC3) seem conservative and there is no evidence for need to use any reduction factor for S500 material. It is worth noticing that the failure mode in the tests often differ to the EC3 calculated critical failure mode. The joint member cross section class is limited to 1 and 2 but the tests include also joint members with cross section class 3 and 4 and those results are indicated by circles in Figure 3-4. These tests were carried out in order to find out the validity of the cross section limitations. Basically the use of high strength steel enables the use of thinner profiles, leading to a reduced throat thickness.
Page 93
Figure 3-4: Test results compared to calculated capacities for joints made of S500 Statistical analysis of the test results have been performed for each steel grade. Because of a big scatter between test results and EC3 capacities the EC0 (EN 1990) way to do the statistical analysis obtains low reduction factors for S500 steel grade joints even though all the tested joint capacities are above the EC3 proposal. This problem was tackled by removing tests one by one starting from the best test capacity relation to EC3 capacity. Using this approach the optimum reduction factor was found as illustrated in Figure 3-5. The minimum γM* = 1.117 (γM* in figure) equals reduction factor of 0.9. But from the Figure 3-4 it can be seen that because all the results are above the current design recommendation EC3, the reduction factor could be set as 1.0. The recommendation of reduction factor 1.0 can be confirmed by the tensile test result of welded test specimens shown in Figure 3-3.
Figure 3-5: Calculating reduction factor for S500 tubular joints 3.2.4
S700 reduction factor tests
Figure 3-6 illustrates the scatter of the 35 results obtained from S700 tubular joints when tested capacities (Ftest) are compared to calculated values according to EC3 (FEC3). The solid line represents EC3 calculations without any material reduction factor and the dotted line represents EC3 the joint capacity with the material reduction factor of 0.8 for S700 according to EC3. The 35 tests includes 22 tests for fillet welds where the weld was set so small that it would be a critical part of the joint and the full capacity of joints would not be reached.
Page 94
The scatter of joint capacities made of S700 steel grade seems to be similar to the scatter of S500 tests. Some of the tests are close or under the line of EC3 capacity without reduction factor 0.8 for this material. However, the joints that are close to this reference line are so called throat-thickness-tests or cross section class 4 joints which is not acceptable for tubular joints. Two test results lie under the EC3–material-reduction-factor line, but these tests were special throat thickness tests and the full capacity of joint was not expected to be reached. The failure type in those tests were weld and fusion line failures. Those tests are not included in the statistical analysis of test results.
Figure 3-6: Test results compared to calculated capacities for joints made of S700 In Figure 3-7 the optimum γM* for S700 tubular joints was calculated as explained in the case of S500 joints. The minimum reduction factor would be 0.85. After removing the best test results compared to capacities calculated according to EC3, the remaining joints are mostly throat thickness tests and those joints are not expected to fulfil the maximum load capacity of joint. Because all the full- strength-weld joints in allowed cross section classes are above the reference lines, the reduction factor could be rounded to be 0.9. Extra tests were performed for S700 steel grade joints because during the project some reduction in strength due to cold ambient temperature was observed. The joint tested at room temperature was part of the fillet weld tests with undersized throat thickness where one pass welding was used. The weld was not the critical part of joint in any of the tests. The difference in load displacement behaviour between room and cold ambient temperature tests can be explained by the size effect of fillet weld and the strengthening of the material due to low ambient temperature. The (unofficial) deformation limits for joint displacement are also drawn in Figure 3-8 in order to have some acceptable rules for joint displacement. The minimum plastic limit for joint displacement is 1% and maximum acceptable total displacement is 3% of chord width. Because in this case the joint have braces in both sides of chord, the lower limit for total deformation of joint is 2 % of chord width [73]. The Figure 3-8 shows clearly the effect of cold ambient temperature for joint capacity in terms of load and displacement. Ultimate forces of each joint are above the calculated EC3 capacities but the differences of different temperature tests cannot be ignored. At the -40°C temperature test the ultimate load is 24% lower and the ultimate displacement 57% lower than at the -20°C temperature test.
Page 95
Figure 3-7: Calculating reduction factor for S700 tubular joints
Figure 3-8: Room temperature test vs. cold ambient temperature tests The welded specimen test results in Figure 3-3 confirm the need for reduction factor 0.9 of the material. The cross section class recommendation according to EC3 should also be obeyed. 3.2.5
S960 reduction factor tests
In Figure 3-9 test results of S960 tubular joints are shown. The results differ to the capacities of S500 and S700 tubular joints. One reason for difference is the cross section class which was often 4. The other reason is that 25 of specimens were throat thickness tests where the full capacity of joint could not be reached. The reason why the throat thickness tests obtained lower relative capacities than similar tests with S500 and S700 steel grade is the larger local softening of higher strength base material. The throat thickness tests did often not fail from the weld but along the fusion line of weld in brace or chord members, examples shown in Figure 3-11. The too small weld with high local stress concentrations might lead to unsafe design for ultra-high strength steel.
Page 96
Figure 3-9: Test results compared to calculated capacities for joints made of S960 The statistical analysis of S960 tubular joints is shown in Figure 3-10. In this case, the scatter of test results was reduced by removing one by one the best and the worst test result relations from the population of the results. The acceptance to do that can be seen from Figure 3-9 where the lowest capacity joints in relation to reference lines are cross section class 4 joints and throat thickness capacity tests. The optimum γM* is 1.26 which corresponds to a reduction factor of 0.8. The test results for welded test specimens in Figure 3-3 are just covering that factor. The cross section class recommendation according to EC3 should also be obeyed.
Figure 3-10: Calculating reduction factor for S960 tubular joints
3.3
Throat thickness tests
Throat thickness tests and test results are shown in Table 3-4.
Page 97
Table 3-4: Throat thickness tests Chord
Brace
Capacity acc. EC3
TTX1 TTX2 TTX3 TTX4 TTX5 TTX5 TTX6 TTX7 TTX7 TTX8 TTX8 TTK1 TTK1 TTK2 TTK2
150x150x8 150x150x5 150x150x8 120x120x6 150x150x8 150x150x8 150x150x8 150x150x6 150x150x6 150x150x6 150x150x6 150x150x5 150x150x5 150x150x5 150x150x5
100x100x6 120x120x4 80x80x4 80x80x4 100x100x6 100x100x6 100x100x6 80x80x4 80x80x4 100x100x4 100x100x4 120x120x4 120x120x4 100x100x4 100x100x4
398 245 298 226 398 398 398 359 359 254 254 455 455 379 379
Max. Force in test 679 647 476 454 803 618 842 646 622 637 616 563 577 447 499
TTK3
150x150x5
80x80x4
304
363
TTK3
150x150x5
80x80x4
304
441
TTK4
150x150x6
80x80x4
375
413
TTK4
150x150x6
80x80x4
375
408
TTX1 TTX2 TTX2
150x150x8 150x150x5 150x150x5
100x100x6 120x120x4 120x120x4
502 328 328
652 542 637
TTX3
150x150x8
80x80x4
382
532
TTX4 TTX5 TTX5 TTX6 TTX7 TTX7 TTX8 TTX8 TTK1
120x120x6 150x150x8 150x150x8 150x150x8 150x150x6 150x150x6 150x150x6 150x150x6 150x150x5
80x80x4 100x100x6 100x100x6 100x100x6 80x80x4 80x80x4 100x100x5 100x100x5 120x120x4
302 502 502 502 453 453 351 351 616
469 752 702 894 620 647 742 735 748
TTK1
150x150x5
120x120x4
616
779
TTK1 TTK2 TTK2 TTK2 TTK3 TTK3 TTK4
150x150x5 150x150x5 150x150x5 150x150x5 150x150x5 150x150x5 150x150x6
120x120x4 100x100x5 100x100x5 100x100x5 80x80x4 80x80x4 80x80x4
616 516 516 516 412 412 511
660 570 531 519 392 435 396
TTK4
150x150x6
80x80x4
511
353
TTX1
150x150x7
100x100x6
610
542
Joint / Steel grade
S500
S700
S960
failure mode in test weld weld weld weld weld
toe /general failure mode toe /general failure mode toe /general failure mode toe /general failure mode toe /general failure mode fusion line/weld weld toe /general failure mode weld toe /general failure mode weld toe /general failure mode chord face failure chord face failure weld weld weld / fusion line? weld chord face failure compression side chord face failure compression side chord face failure compression side chord face failure compression side weld toe /general failure mode weld toe /general failure mode weld toe /general failure mode toe of weld/general failure mode chord shear failure weld toe /general failure mode fusion line/weld weld toe /general failure mode weld toe /general failure mode weld toe /general failure mode chord face failure weld toe /general failure mode weld weld toe /general failure mode/weld weld toe /general failure mode chord face failure tension side chord face failure tension side chord face failure tension side chord shear failure; chord shear failure; weld toe /general failure mode weld toe /general failure mode/fusion line chord face failure/punching shear
Page 98
Joint / Steel grade
Chord
Brace
Capacity acc. EC3
TTX1
150x150x8
100x100x6
698
Max. Force in test 556
TTX2
150x150x5
120x120x4
453
627
weld toe /general failure mode
TTX2
150x150x5
120x120x4
453
535
punching shear
TTX2
150x150x5
120x120x4
453
608
TTX3
150x150x7
80x80x4
458
420
TTX3
150x150x8
80x80x4
698
491
punching shear chord face failure/punching shear weld/fusion line
TTX4
120x120x6
80x80x4
423
496
TTX5
150x150x7
100x100x6
610
632
TTX5 TTX5
150x150x8 150x150x8
100x100x6 100x100x6
698 698
722 520
TTX6
150x150x7
100x100x6
610
730
TTX6 TTX7 TTX7 TTX8 TTX8 TTK1
150x150x8 150x150x6 150x150x6 150x150x6 150x150x6 150x150x5
100x100x6 80x80x4 80x80x4 100x100x4 100x100x4 120x120x4
698 631 631 467 467 854
835 651 672 615 618 628
TTK1
150x150x5
120x120x4
854
619
TTK2 TTK2 TTK3 TTK3
150x150x5 150x150x5 150x150x6 150x150x6
100x100x4 100x100x4 80x80x4 80x80x4
712 712 688 688
416 340 474 400
TTK4
150x150x6
80x80x4
688
502
TTK4
150x150x6
80x80x4
688
454
failure mode in test weld/fusion line
weld toe /general failure mode chord face failure/punching shear weld/fusion line weld/fusion line chord face failure/punching shear weld/fusion line weld toe /general failure mode weld toe /general failure mode weld toe /general failure mode weld toe /general failure mode chord face failure tension side chord face failure/chord shear failure chord face failure tension side chord face failure tension side chord face failure tension side chord face failure tension side toe of weld/general failure mode/weld fusion line
Testing the capacities depend on throat thicknesses of fillet welds met the same problems as capacities of joints: the failure modes occurred in the tests differed from the theoretical calculation modes. Also the loss of strength in the softened areas of base material increased considerably with increasing steel grade. This caused problems especially when weld was significantly smaller compared to wall thickness of the brace member. This phenomena caused some fusion line failures which are basically weld failures with different failure angel. However, the throat thickness of fillet weld has still an effect on the capacity of fusion line failure. Typical fusion line failure modes are shown in Figure 3-11.
Page 99
Figure 3-11: Fracture in fusion line of joints TTX5 with tungsten plates steel grades S700 and S960 According to current EC3 the required throat thickness depends on steel grades according to Equation (1) and the calculated throat thicknesses are show in Table 3-5: The a/ti ratios for different steel grade according to current EC3Table 3-5.
a 2 w
M2 fy ti M 0 fu
(4.1)
Table 3-5: The a/ti ratios for different steel grade according to current EC3 Steel grade
Yield strength
Ultimate strength
w
γM2/γM0
a/ti
S355 S500 S700 S960
355 500 700 960
510 550 750 980
0.9 1.0 1.0 1.0
1.25/1.0 1.25/1.0 1.25/1.0 1.25/1.0
1.11 1.61 1.65 1,73
In next procedure the results from experimental tests and strength of fillet welds are fixed so that comparison could be made. The conventional calculation illustrated in equation (4.1) guarantees the strength of the weld is balance with the adjacent member independent on stress distribution around the joint perimeter as illustrated in Figure 3-12. If the throat thicknesses is decreased, the stress distribution and the effective area of joint should be considered.
Figure 3-12: Membrane and shell bending stress distribution around X- joint perimeter The uneven stress distribution is considered by using effective perimeter length Seff of the joint calculated according to equation 4.2. The load carrying capacity of fillet welds can be calculated using the effective perimeter of brace and true throat thickness of fillet weld, see equation 4.3. Ultimate strength of filler material is obtain from catalogue of filler material supplier (Böhler).
Page 100
S eff =
(4.2)
Ftest t i f u , frace
and (4.3)
Fu ,weld = S eff a f u 2 where Ftest = ultimate load carrying capacity from test Fbrace = theoretical ultimate load carrying capacity of brace member a= measured throat thickness of fillet weld (at 45° angle in weld) fu = ultimate (nominal) strength of filler material (available from filler metal supplier)
The calculated results are summarized in Table 3-6 and the results are shown graphically in Figure 3-13. Table 3-6: Calculation of fillet weld strength
Joint type and steel grade
S500
S700
S960
Brace member Total True circumf FM BM Load at Angle of Size of Widht Thickness EC3 Brace throat erence Tested Tensile Tensile Fu, weld x of brace Failure capacity capacity fracture thickness fracture fracture of Seff strength strength [kN] [kN] [°] [mm] Height tube [mm] brace [MPa] [MPa] [mm] [mm] [mm]
TTX1
100
5.92
FLB
398
1495
679
4.40
16
5.29
390
177
620
648
683
TTX2
120
4.19
TOWB
245
1329
647
4.48
70
3.35
473
230
620
671
904
TTX3
80
4.15
TOWB
298
823
476
4.03
58
3.07
313
181
620
634
639
TTX4
80
4.15
TOWB
226
823
454
4.04
78
2.45
313
173
620
634
611
TTX5
100
5.92
TOWB
398
1495
803
5.32
90
3.31
390
209
620
648
976
TTX5W
100
5.92
W
398
1495
618
10
6.03
390
161
620
648
610
TTX6
100
5.92
TOWB
398
1495
842
5.05
72
3.97
390
219
620
648
972
TTX8
100
4.12
TOWC
254
1010
637
5.35
0
5.92
393
248
620
624
1162
4.32
TTX8W
100
4.12
TOWC
254
1010
616
5.07
0
5.92
393
240
620
624
1065
TTK1 Gmin
120
4.19
W
455
1329
563
2.87
20
3.31
473
200
620
671
504
TTK1 Gmax
120
4.19
W
455
1329
577
2.60
27
2.81
473
205
620
671
468
TTK4
80
4.15
TOWC
375
871
413
3.34
0
5.92
313
148
620
671
434
TTK4W
80
4.15
TOWC
375
871
408
2.88
0
5.92
313
147
620
671
370
TTX1
100
5.92
W
502
1948
652
4.16
4
6.33
390
130
740
844
568
TTX5
100
5.92
FLB
502
1948
752
5.03
13
5.51
390
151
740
844
792
TTX5W
100
5.92
FLB
502
1948
702
4.06
4
5.90
390
140
740
844
597
TTX6
100
5.92
FLC
502
1948
894
6.49
0
10.25
390
179
740
844
1215 1080
TTX7
80
4.15
TOWB
453
1100
620
5.85
68
2.92
313
176
740
847
TTX7W
80
4.15
TOWB
453
1100
547
4.12
70
2.79
313
156
740
847
671
TTX8
100
4.82
TOWC
351
1535
742
6.47
0
5.92
392
189
740
813
1282
TTX8W
100
4.82
FLB
351
1535
735
2
4.78
392
188
740
813
691
TTK1 Gmin
120
3.88
W
616
1581
748
3.13
3.52
30
3.37
473
224
740
861
733
TTK1 Gmax
120
3.88
W
616
1581
660
2.92
24
3.54
473
198
740
861
604
TTX1
100
5.95
FLC
700
2669
556
5.16
15
6.37
390
81
980
1151
581
TTX3
80
3.94
FLC
525
1506
491
5.51
57
3.16
313
102
980
1220
780
TTX5
100
5.92
FLB
700
2656
722
4.36
18
8.03
390
106
980
1151
640
TTX5W
100
5.92
FLB
700
2656
520
4.11
11
6.98
390
76
980
1151
435
TTX6
100
5.92
FLC
700
2656
835
7.21
90
10.54
390
123
980
1151
1225 1062
TTX7
80
3.94
TOWB
631
1506
651
5.66
53
3.89
313
135
980
1220
TTX7W
80
3.94
TOWB
631
1506
672
3.62
69
3.52
313
140
980
1220
701
TTX8
100
3.98
TOWB
467
1734
615
6.25
58
3.83
393
139
980
1108
1208
TTX8W
100
3.98
TOWB
467
1734
618
4.55
62
3.29
393
140
980
1108
884
TTK4
80
3.94
TOWC
688
1506
502
2.26
15
2.91
313
104
980
1220
327
TTK4W
80
3.94
TOWC
688
1506
454
3.04
75
3.44
313
94
980
1220
398
W
Weld
FLB
Fusion line brace
FLC
Fusion line chord
TOWB Toe of Weld Brace TOWC Toe of Weld Chord
Page 101
Figure 3-13: Fillet weld tests compared to the expected values It can be seen from Figure 3-13 that the calculated and tested strengths matched well, if the failure occurred in welds. The agreement is less accurate, but still quite good if the failure took place in fusion line. The weakest correlation can be found, if failure occurred at weld toe in softened base material. Referring to steel grades, the best agreement can be found for S500, still quite a good for S700 and worst for S960. The calculations are made ignoring the safety factor M2 =1.25. As presented in section 3.2, the penetration of fillet welds has proven to be a problem with throat thickness tests. Generally the welds need to be small in order to be the weakest link of a welded joint. In order to obtain perfect fillet weld in terms on adequate penetration everywhere but not in root itself, a tungsten plates was set between the brace and chord members during the joint preparation and welding. In Figure 3-14 an example of tungsten plate test (S500) is presented with similar joint without tungsten plate. These examples are from the series of joints where the nominal throat thicknesses were 3, 4 and 5 mm. The joint with nominally 4 mm throat thickness was chosen as a reference joint for tungsten plate test. In this case there is no big difference in throat thicknesses between the two joints. The failure modes of the joints were different and the load carrying capacities differed significantly. The failure in joint without tungsten plate occurred at weld toe in brace member. The joint with tungsten plate, the failure took place in weld. The angle of the weld failure was not at the angle of 45° through the weld as assumed in EC3. The failures of S500 steel grade joints with and without the tungsten plate are shown in Figure 3-14. The weld failure plane is shown therein and differs from the current assumption of 45° critical failure plane. It was about 10° from the force direction. In the similar joints with tungsten plates in steel grades S700 and S960, the weld was not critical but the fusion lines on brace became more critical than weld as can be seen in Figure 3-11. In some cases the fusion line on chord side was critical in joints made of S700 and S960 steels. Fusion line fracture occurred in both joints, with or without tungsten plate, and significantly lowered the joint capacity. Defining the primary failure of joint was often difficult because the failure occurred in different parts of joint area, for example in fusion line and in weld itself. The primary failure was determined from fractured surfaces and the polished sections. Generally, both weld and fusion line failures were addressed as weld failures.
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Figure 3-14: S500 TTX5 joint tests without and with tungsten plate from estimated primary fracture area
3.4
Detailed study of S960 X-joints under tension
The capacities of tensile tests X-joint tests exceeded the requirement from EC3 with one exception. The failures took place at weld toe either on corner of brace member or by punching shear of chord flange as illustrated in Figure 3-16. In Figure 3-15 the tensile tested X-joints with same tube cross sections but different welding method and throat thickness were used. The black curve (X3_960) represent manually welded joint with nominally 6.5mm throat thickness using 3 passes. Red curve (X2TT_960) is distinguishing from previous case by using only one run resulting nominally 3 mm throat thickness. The blue curves (X2TT_960R1 and X2TT_960R2) represent similar joints but welded by using robotic process, which guarantees the constant heat input for the whole weld. As it can be seen from Figure 3-15 the robotic welding did not increase the capacity of joint and the larger throat thickness also increased the joint capacity. The difference between capacities could be explained with different failure modes between manually and robotic welded joints. The different failure modes can be seen in Figure 3-16.
Figure 3-15: Comparison of X-joint tensile test with similar tube dimensions but different welding method and throat thickness size
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Figure 3-16: Failure path in brace member (X2TT_960) and punching shear failure (X2TT_960R1) of X-joint made of S960 Hardness distributions of the manually welded specimens of different throat thicknesses are shown in Figure 3-17 and Figure 3-18. From that figure can be seen that multiple passes produce more even hardness distribution compared to the single pass welding and the width of the HAZ is larger. This could be one reason for higher load carrying capacity obtained by joints with bigger throat thickness. In these two cases the failure mode and path were similar.
Figure 3-17: Hardness distribution of hand welded X2TT_960 WPS-specimen (single pass welding)
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Figure 3-18: Hardness distribution of hand welded X3_960 WPS-specimen(multiple pass welding) The reasons for unexpected low load carrying capacity was tried to solve with SEM- analysis (Scanning Electron Microscope) but no clear reason was found. Results of SEM-analysis from the crack area of automatic robotic welded joint X2TT_960R1 are seen in Figure 3-19 and Figure 3-20 and in those figures the table of chemical compositions and the spectrum of molybdenum proves that there was no clear reason for lack of ductility found on fractured surface.
Figure 3-19: Chemical composition of fractured surface studied using SEM-analysis of robotic welded joint X2TT_960R1
Page 105
Figure 3-20: Results of SEM-analysis of robotic welded joint X2TT_960R1
3.5
Discussion
From the test results and FE-analysis can be concluded that welded tubular joints comprise potential and challenges for optimizing of the joint capacity. However, the test results also show that the capacity of the highest studied steel grades, S700 and S960 is limited by ultimate strain of material and the effects due to welding. Also the low ambient temperature reduced the deformation capacity of joints made of S700 steel grade compared to behaviour at room temperature. The recommendation for material reduction factors are shown in Table 3-7 including also the recommended minimum throat thicknesses. The proposal for reduction factors are given separately for each steel grade at tested temperatures. The values for reduction factor at low temperature and the recommended (tests proved adequate capacity) minimum temperature are inside the parentheses. The throat thicknesses are presented as relative values (a/ti-ratio). Given values indicate the ratio based either on applied brace force or on joint capacity. Table 3-7 Recommendations for reduction factors in tubular joints and for the sizes of fillet welds for different cases
Steel grade and current reduction factor
Recommendation for throat thickness a
Recommendations for reduction factors for tested steel grades
General Min allow. Min allow. Current min. allow. when brace when joint recommenda throat force based capacity base tion acc. EC3 Room Low thickness design is used design is used [mm] temperature temperature [mm] [mm] [mm]
S500 0.8
1.0
1.0 (-40°C)
3
1.0 ti
1.0 ti
1.61 ti
S700 0.8
0.9
0.9 (-30°C)
3
1.2 ti
1.2 ti
1.65 ti
S960 (0.8)
0.8
-
3
x
1.4 ti
1.73 ti
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The capacity of throat thicknesses seems to be difficult to predict and the drop of capacity was unexpectedly high when the steel grade of joint was increased from S500 upwards. Topic needs definitely more research because the calculations shown in Table 3-6 and Figure 3-13 do not take into account the true failure angle and therefore it is hard to determine the true needed throat thickness. From the S500 test results can be concluded that the material behaves safely and welding does not have any remarkable effect on the joint capacity, neither in room temperature nor at low ambient temperature. This is why for this steel grade the reduction factor of 1.0 can be recommended. Also the throat thickness tests show good load carrying and deformation capacity and therefore the throat thickness recommendations could be set to 1.0ti. This is potentially raising the question about the suitability of the reduction factor for welds made of milder steels. Based on similar type of tests this reduction can be used for joints made of steel grades S420-S460 and throat thicknesses for joints made of S355-S460. The results are presented in references [77] and [78]. However, the limits for cross section classes of tubes according to current EC3 must be obeyed concerning S500 and other steel grades (S700 and S960), too. For joints made of S700 steel grade, the reduction factor of 0.9 must be set because of a lack of deformation capacity in some joints and especially at low temperature tests. The ratio of throat thickness to brace wall thickness should be bigger than 1.2ti as shown in Table 3-7. This recommendation should eliminate the weld failures i.e. weld and fusion line failures and it also confirms that the load carrying and deformation capacities are sufficient. The filler material must be matching with the base material and heat input and cooling time recommendation given by steel manufacturers must be followed. The joints made of S960 did not reach the sufficient load carrying and deformation capacities. Consequently the reduction factor in Table 3-7 is set to 0.8. The low temperature test (-40°C) reduced the capacity of the joint remarkably. Based on these few tests the room temperature is the lowest safe temperature that could be recommended if the joints are prepared using current methods and parameters. For the throat thickness the minimum ratio of 1.4ti should be used. Due to low load and deformation capacities found in throat thickness tests, the throat thicknesses cannot be designed based on applied forces of brace members.
3.6
Conclusion
The objectives of this project was to have clear understanding about the need for reduction factors for materials used in tubular structures and to avoid the uneconomical throat thicknesses of joints when high strength steels are used. These two are the main barriers to use the high strength steels in tubular structures and to have effect on efficiency and economy of the structure. Both problems were tried to solve by testing joints for different failure modes according to current EC3. However, the failure modes were often different from the predicted ones especially for K-joints. This increased the scatter of test results but led also to very promising results for joints made of S500 and S700 steel grades. The problems occurred when joints made of S960 steel grade were tested. The throat thickness tests for S500 showed better capacities compared to their counterparts made of S700 and S960. For S960 material the problem seemed to be involved in heat input and cooling rate by welding. This could not be tackled even using the robotic welding for S960 steel grade joints. Also the low ambient temperature affected the joint behaviour by reducing the load and deformation capacities. Unfortunately, the planned 100 (106 done) tests with FEA for 3 different steel grades and 2 different main challenge was not enough to provide a clear answer for all original questions. Consequently more study and testing must be carried out especially for assessment of proper throat thicknesses. For these tests the welding should be done mechanically in order to have better control on welding parameters and to obtain constant throat thicknesses and penetration degrees along the joint perimeter. The dimensions for tested joints should be constant in order to avoid the effect of any extra geometrical factors on the results. Assessment of the prober throat thickness is difficult because real structure often contains residual stresses and strains. The residual stresses will be released during welding causing additional deformation and thus changing the joint geometry in groove. Residual stresses and strains also reduce the capacity of the joint. From the test results can be drawn a conclusion that the strength of weld (weld or fusion line) is not depending linearly on throat thickness or steel
Page 107
grade. This problems was not included in this research beforehand and it need more studies before more detailed conclusions can be drawn.
Page 108
CASE STUDIES
4 4.1
Background
4.1.1
General
The aim of this study was to find out by using optimization if the use of high strength steel (HSS) in typical structures results in more economical solutions than the use of regular S355 steel. The HSS steel grades were up to S960 including hybrids. In hybrid beams and columns the flanges are made of stronger steel than the webs. In hybrid trusses the chords are made of stronger steel than the braces. The structures considered were basic components of buildings such as welded beams and welded tubular trusses. A new innovative frame system for multi-purpose multi-story buildings and heavily loaded box-columns of power buildings were studied, too. In optimization the feasibility of the structures must be controlled with design rules. In this research the Eurocodes were used. The design rules include not only the requirements at the ultimate and the serviceability limit states (ULS, SLS, respectively), but also the information behind these rules, dealing with the geometrical entities of the structures, for example for the joints of tubular trusses. Feasibility of the structure is ensured in optimization by collecting all the rules as constraints of the problem. The optimization was performed in two phases: In the phase 1 the present design rules of Eurocodes were used and the steel grade was up to S700. In the phase 2 the steel grade was up to S960 and new design rules which were developed in this project were implemented into the optimization routines. Typically in optimization of steel structures the weight of the structure is chosen as an objective. When comparing different steel grades, the total manufacturing cost is a more relevant criterion than weight. In this study the manufacturing costs were calculated based on a generic feature-based cost calculation method including costs of all actions in the workshop, transport and site. The authors are not aware of a cost calculation method that covers the data for steel grade up to S960. In this study the industrial partners of the project gave the cost factors for materials and manufacturing in relation to S355 such that S960 could be included in the comparison. In all cases weight and cost optimal solutions were searched separately. Also steel grades were fixed in every run. The following costs are taken into account: material costs, blasting, cutting of plates, welds, sawing of final member to correct length, alkyd painting including drying time, transport (200 km supposed) and erection in site. Plasma cutting is used up to 30 mm and after that flame cutting is used for plates. The automated submerged-arc welding is supposed for beams and columns and the manual MAG welding for trusses. The erection costs are calculated assuming that 25 ton crane is used to lift the members vertically 10 m and 15 m horizontally and there exist 6 bolts at the both ends of the assemblies (beams, columns and trusses). In optimization the particle swarm optimization (PSO) algorithm was used (Mela & Heinisuo, 2014) because this has found to be rather suitable for these kinds of discrete non-linear optimization problems. The problems are discrete because the available plate thicknesses are discrete and the sizes of available tubes are discrete. The non-linearity is originating from the design rules in the constraints of the problems. The optimization problem has to be formulated into the mathematical form in order to solve it using any algorithm. For example the formulation of the optimization of the welded I-beam (WI-beam) is:
M Rd x 0, M Ed x V V x 1 pl, Rd 0 , 1 b, Rd 0 , VEd VEd min f(x) such that
1
(5.1)
Page 109
hw E k tw f yt
u x Aw x 1 0 , 0 , SLS u Ayt , eff x
where the function f(x) can be either weight or cost of the structure, x is the vector of design variables and the constraints include resistance checks for the moment, plastic shear, shear buckling and flange induced buckling of web in the ULS and finally the deflection limit in the SLS in this case. The notations follow Eurocodes. All cases were optimized in normal conditions and some cases were optimized in fire conditions using intumescent coatings. Sizing optimization was performed to all structures and for trusses also shape optimization was done. In shape optimization the height of the truss, the gap of the joints (only gap joints were considered) and locations of the joints along the chords were varying. It was found that by changing the locations of the joints some per-cents savings could be realized compared to the fixed geometry where the joints are located evenly at the chords. 4.1.2
Cost factors
The cost factors which varied depending on the steel grade and which were used in all cases are given in Table 5.1. Table 5.1 : Cost factors for HSS Tubular trusses, tube material 0.8 €/kg
S355
S500
S700
S960
Material cost factor
1
1.15
1.30
1.60
Sawing
1
1.15
1.3
1.5
Assembly by welding of braces to chords
1
1.25
1.5
2
Welded beams and columns, material 0.7 €/kg
S355
S500
S690
S960
Material cost factor
1
1.15
1.30
1.60
Flame cutting
1
1
1.1
1.2
Beam welding
1
1.25
1.5
2
The costs of other features of structures were fixed but e.g. the total cost of painting was dependent on the paint area of the structure. An example of the cost optimized welded Qbeam (WQ-beam) is shown in Figure 5.1. WQ-beams are used in slim floor constructions, so the paint is needed only at the bottom flange. The height of the WQ-beam was fixed to 400 mm.
Figure 4-1: Cost distribution (a), and cross-section (b), cost optimized one-span welded beam (WQ-beam), load 100 kN/m, span 6 m, top flange and web S355, bottom flange S500. In costs only the beam itself is taken into account, no fabrication costs of the joints at the ends and along the beam are present (Mela & Heinisuo, 2014b)
Page 110
4.1.3
Beams and columns
One-span simply supported beams and columns were optimized including hybrids. Two kinds of welded beams were considered: WI- and WQ-beams. The cross-section resistances of beams were checked in the ULS and in the SLS the deflections. This means that it was supposed that the top flanges of the beams were supposed to be supported in the lateral direction and no flexural-torsional buckling was present. In welded beams the pre-chamfer can be used, so the deflection limit was set as L/200 using the estimation of the SLS load. For beams the spans and loads varied but for the welded box (WB) columns the span was fixed as 12 m but the large axial loads were varying, and the moment in two directions was fixed. The moment simulates the effect of loads from beams along the column. For columns the interaction of buckling and moment was checked using EN 1993-1-1, Annex B. 4.1.4
Constraints of tubular trusses
The constraints of the trusses include all requirements of Eurocodes both for the members and for the joints. The feasibility of the members (check of fulfilment of the constraints) is done as the resistance checks including cross-section resistance checks and interaction checks for the moment and the axial force using EN 1993-1-1, Annex B. The feasibility check of the joints is a rather nasty task, because there exist a lot of rules dealing with the geometrical entities of the joints and resistance checks. Our ambitious goal in this project was to full-fill strictly all requirements of Eurocodes to welded tubular joints. It is believed by the authors, that this is the first time when truss optimization is completed in that scope. The constraints of N, K and KT joints are collected to Figure 5.2 and the constraints of T joints are collected to Figure 5.3. The notations follow Eurocodes. In the evaluation of the feasibility of the truss structural analysis must be done during iterations to get the stress resultants for the members and for the joints. The structural model should follow strictly the geometry of the truss. In this study Bernoulli-Euler beam finite elements were used. Following the rules of Eurocodes the eccentricity at the joints must be considered. The local analysis models of the joints are shown in Fig. 5.4.
Page 111
Figure 5.2: Constraints of welded tubular N, K and KT joints (collected by Petri Ongelin)
Page 112
Figure 5.3: Constraints of welded tubular T joints (collected by Petri Ongelin)
e e
g
g
g
Figure 5.4: Local analysis models of joints
Page 113
The structural analysis model was generated from the geometrical model, which is the only possibility to get the proper analysis model including exact eccentricities at the joints. The linear analysis was used for trusses. 4.1.5
Floors in high rise buildings – composite beams with HSS
Limitations of economical use of HSS in high rise buildings were derived using parametric study of optimum design of floor beams in a typical floor layout of a high rise building. Three types of I cross sections: monolithic mild steel (S355), monolithic high strength steel (S500 or S700) and hybrid (S355 + S500 or S700) were analysed. Also the steel floor beams are compared to composite HSS beams. 4.1.5.1
Analysis parameters
The parametric study of beam design was performed aiming to explore limitations of possible construction costs reductions in high rise buildings by using high strength steel floor beams. A range of L = 6 m to L = 16 m beam span was analysed in the parametric study. Such a wide range was used in order to cover the typical spans both for the residential and commercial high rise buildings (6 m – 10 m) and the multi-storey car parks (10 m – 16 m). In this way the potential of increasing spans in residential high-rise buildings by using HSS beams could be examined, too. The cross-section of the floor structures in the parametric study used is shown in Figure 4-2. Full depth concrete deck is supported by the steel beams. A welded section is adopted for the steel beam in order to allow optimisation of the cross section dimensions.
Figure 4-2: Floor structure cross-section with dimensions High strength steel (HSS) beams, grades S500 and S700, were compared to the common S355 mild steel (MS) beams. Steel beam design is optimized in span range from 6 m to 16 m considering design bending resistance in ultimate limit state (ULS) and deflection limits in serviceability limit state (SLS). As the concrete deck is mostly used in high rise buildings and car parks construction, the option to have composite beam is analysed as well. Monolithic MS and HSS composite beams analysed in the parametric study are shown in Figure 4-3d and e. In the case of hybrid composite beam the high strength steel is used only for the bottom flange, see Figure 4-3f. Contribution of HSS top flange to the plastic bending resistance of the composite beam would be negligible because the top flange is near the plastic neutral axis.
Page 114
a) MS – steel beam
b) HSS – steel beam
d) MS – composite beam
e) HSS – composite beam
c) Hybrid – steel beam
f) Hybrid – composite beam
Figure 4-3: Monolithic and hybrid cross sections A typical floor layout is assumed for the parametric study comprising of hc = 100 mm thickness full depth prefabricated concrete slab as the deck, supported by the steel beams at the distance of b = 4 m. Clear storey height is assumed as hcst = 2.8 m in order to calculate the possible indirect building cost reductions by reduction of the total storey height due to smaller depth of HSS beams Permanent loads acting on the floor of a building are the self-weight of the structure qsw = qa+qc, In this parametric study self-weight of the steel beams is unknown in advance and therefore is assumed as qa = 0.1 kN/m2. Real variation of this load is negligible compared to loads due to weight of the concrete, dead-weight and imposed loads. Additional dead weight loads are adopted as qG = 1.5 kN/m2. For this parametric study the imposed load in a high rise building is adopted as qk = 2.5 kN/m2 according to EN1991-1-1 [3] The same value of imposed load is required for a multi-storey car parks, category F, EN1991-1-1 [3] Table 6.8. Therefore the design value of the beam load to be used in the parametric study is calculated as:
kN qULS = 1.35 qa + qc + qG + 1.5qk b = 37.1 m
(5.2)
Deflection limits are checked with respect to imposed loads only, because pre-cambering is assumed for entire permanent self-weight and dead-weight loads.
kN qSLS.MS = qk b = 10 m
(5.3)
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4.1.5.2
Optimisation criterions and procedure
For the design optimisation of HSS floor beams in high rise buildings several aspects are considered in the parametric study regarding: the compact cross section limits, ultimate an serviceability limit states, engineering solutions and special failure modes which are characteristic for HSS monolithic and hybrid cross section beams. Bending of the single supported beam is considered as the governing ultimate limit state (ULS) criterion in the parametric study of optimum floor beam design. Several cross section classes are considered in the parametric study and therefore the design bending moment resistance is obtained using the appropriate plastic or elastic theory. Cross sections class 4 effective cross section resistance is obtained using simplified equation from [22], see Figure 4-4a:
(5.4) In the case of hybrid cross section with high strength steel flanges and mild steel web the characteristic plastic bending resistance of the cross section is obtained allowing higher plastic strains in the web compared to flanges, according to [22]:
(5.5) For the hybrid cross section of classes 3 and 4 the plastic strains in the web are allowed, see Figure 4-4b, provided that the yield strength of the flange is not more than double the yield strength of the web. Bending resistance of the class 3 and 4 hybrid cross section is obtained according to following equations:
(5.6) (5.7)
a) cross seciton classes 1 and 3
b) cross section classes 3 and 4
Figure 4-4: Design bending resistance of hybrid cross section [22] For purpose of iterative calculation in this parametric study the original flange induced buckling criterion from EN1993-1-5 [8] is transformed in a way to obtain the minimum required thickness of the web tw which satisfies the criterion: 2
bf tf hw tw fyf 0.3 E
3
(5.8)
Reduction of the beam cross section dimensions by introducing the HSS material lead to increased deflections compared to mild steel beams. Considering several national annexes:
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German, British, Swedish, an average deflection limit due to variable imposed load w3 = L/300 is adopted for this parametric study considering the beam pre-camber which accommodates all the permanent loads. In the parametric study, some limitations are introduced regarding the minimum dimensions of the cross section parts. This is done in order to make the fabrication possible and to follow some common engineering practice rules in steel structures. The adopted limitations are as follows: Minimum thickness of the web: fw,min = 4 mm Minimum thickness of the flange: tf,min = 6 mm Minimum weld throat thickness: aw,min = 3 mm Minimum width of the flange: bf,min=60 mm The parametric study is performed by varying the beam span to steel beam depth ratio in range L/b = 10 – 40. This range is assumed to be applicable for the wide range of spans, cross section types and materials that are analysed. In each case of certain span, cross section type, steel material and the span to depth ratio, thickness of the web tw and the flange tf are obtained in order to meet the targeted cross section class. Targeted slenderness of the flange f,trg and the web w,tgr were as follows:
f,trg =9.8 𝜀 and w,trg = 80 𝜀 for the cross-section Class CSC2 f,trg =13 𝜀 and w,trg = 200 𝜀 for the cross-section Class CSC4
Targeted slenderness of the web and the flange for the CSC2 were set close to upper bound limits for this class in order to achieve the most possible design optimisation. For the CSC4 the targeted slenderness limit of the flange f,trg was set to upper bound limit of the class 3 in order to keep the flange fully effective. In the preliminary parametric study, it was concluded that targeting CSC4 provides more reduction of steel quantity compared to CSC3, see Figure 4-5. It can be also concluded that targeting the web slenderness as high as possible gives the most optimal results in terms of required steel quantity. Therefore the targeted slenderness of the CSC4 web is set to an estimated optimum value of w,tgr = 200e.
Minimum steel quantity - Qmin (kg/sqm)
32
S355 S500 S700 25
18
11
4 50
75
100
125
150
175
200
225
250
Web slenderness (-)
Figure 4-5: Minimum required steel weight vs. web slenderness of the monolithic cross section steel beam, span 16 m. In case of composite beam, the steel cross section is in tension at ULS and therefore considered as compact. The same cross section dimensions are used as for the targeted CSC4 steel beam in order to obtain the most optimum results in terms of required steel quantity.
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For each specific cross section type, see Figure 4-3, and steel material, see Table 4-1, the design optimisation was performed in the range of the considered beam span to steel beam depth ratio L/b = 10 – 40. For each specific case the cross section dimensions were obtained iteratively in order to achieve 100% utilisation of either ULS or SLS criterion, whichever was dominant. Then for a certain beam span to steel beam depth ratio L/b the minimum required steel quantity was found. An example of design optimisation is shown in Figure 4-6 for the case of one MS (S355) and one HSS (S500) monolithic cross section of the steel beam with span L = 6 m and the targeted cross section class CSC4.
Figure 4-6: Design optimisation of the steel quantity with respect to ULS and SLS utilisation It can be seen that across the wide range of beam span to depth ratio different design criterions are dominant for different cases. At low span/depth ratios, up to 20, the ULS criterion is up to 100 % utilized (dotted lines) while the SLS criterion is not fully utilized (dashed lines). At high span/depth ratios the SLS criterion becomes dominant and reaches 100 % utilisation while the ULS criterion is not fully utilized. For each case in the parametric study the optimized design was obtained by seeking 100 % utilization of either ULS or SLS criterion. Since the design optimisation process is iterative the MathCad software package [40] was employed to effectively solve this task. Four iterations were calculated for each case. 4.1.5.3
Calculation of relative costs
For each case in the parametric study the required steel quantity per m 2 of the floor Q = A/b was calculated with respect to the area of the cross section A = 2bftf + hwtw, steel density = 7850 kg/m3 and distance between the beams b = 2 m. Lower required steel quantities were obtained in case of HSS and Hybrid sections compared to mild steel sections. The required steel quantity will directly affect the weight of the structure leading to possible reduction of indirect building costs related to: foundations, transport, welds, corrosion protection, etc. However, the reduction of direct material costs is less compared to the reduction of the steel quantity because of the higher market price of HSS material. Relative steel material prices in 2005 in Sweden and 2011 in Germany, according to [41] and [42], are shown in Figure 4-7a and b, respectively, as relative values with reference to S235 material, calculated from average market prices.
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Realtive price per tonne - ref. to S235
3 2.5 2 1.5 1 0.5 0 200
400 600 800 1000 Yield stenght - fy [N/mm2]
1200
a) Sweeden 2005 - Johansson [41]
b) Germany 2011 - Stroetmann [42]
Figure 4-7: Relative material cost according to average market prices with reference to S255 Relative material costs for S355, S500 and S700 materials are summarized in Table 4-1. Approximately 15 % reduction trend of relative HSS price can be observed in the time between 2005 to 2011. This trend can be attributed mostly to improved production process where thermo-mechanical treatment is used to achieve high-strength properties, see Figure 4-7b. For this parametric study, the relative steel prices of Stroetmann [42] are adopted. A weighted steel quantity Qw which can be used for quantifying the reduction of direct material costs is calculated in each case.
Qw = (2bftfpf + bwbtpw) / b
(5.91)
Quantity of the mild steel and HSS material were considered separately and weighted relative to their market prices. Relative market price of the mild steel material S355 was set as a reference value and relative material costs pHSS = 1.05 and pHSS = 1.25 are calculated for S500 and S700 steel grades, respectively, see Table 4-1. Relative material costs of the flange and the web, pf and pw, respectively, are set to pMS or pHSS, depending of the cross section type. Table 4-1: Recapitulation of the relative material costs Relative mat. cost – ref. S235J2 Steel grade Johansson Stroetmann (2005) (2011) S235J2 1 1 S355J2 1.23 1.035 S500M 1.46 1.08 S700M 1.72 1.3
4.2 4.2.1
used in the parametric study Relative mat. cost – ref. S355J2 Johansson Stroetmann (2005) (2011) 1 1 1.19 1.04 1.40 1.25
Results Welded beams
The cross-sections of WI- and WQ-beams are shown in Figure 4-8 with their variables. The beams are simply supported at their ends. The uniform load q in the ULS was 20, 60 and 100 kN/m and the spans L were 6, 8 and 10 m. In the SLS the design load was reduced to 75 % and the deflection limit was L/200. The dimensions of the WQ beam were restricted as hw+tt = 400 mm, bb = bt+260 mm and r = 90 mm. The height 400 mm is a mean height of hollow core concrete slab which is used in this slim floor construction.
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Figure 4-8: Welded beams, WI and WQ The objective function in optimization is the weight of the beam or the manufacturing cost of the beam. For beams and columns only the member is considered meaning that no fittings are taken into account in mass and cost calculations. The details of the manufacturing costs are given in (Mela & Heinisuo, 2014). The same method is used for the calculation of the manufacturing costs of columns and trusses. The constraints in optimization were moment and shear resistances and flange induced buckling of the web in the ULS. When defining the moment resistance of the WQ-beam, the reduction of the yield strength of the bottom flange fyb due to the lateral bending of the lip by the load q/2, is taken into account. The stress resultants and the deflections are calculated analytically and the resistances are calculated based on the Eurocodes. Full strength fillet welds are used. In hybrids the plastification of the web is allowed in all cross-section classes. For each plate 19 thickness alternatives varying from 5 to 100 mm are available. The widths of the plates range from 100 to 1000 mm in steps of 10 mm, meaning 91 possible values and 3x19x91 = 5187 possible solutions for each case. The population-based heuristic and stochastic PSO (Particle Swarm Optimization) was used in optimization (Mela & Heinisuo, 2014). Due to stochastic nature of the algorithm 10 runs with 100 particles in the swarm were carried out for each case. Typical development of the objective function during a run of PSO in three cases can be seen in Figure 4-9. The notation [grade of top flange]/[grade of web]/[grade of bottom flange] is used.
Figure 4-9: Convergence of PSO for WI-beams The smallest relative weight compared to S355/S355/S355 material combination was obtained by S960/S960/S960 WI-beam, as is shown in Table 4-2.
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Table 4-2: Summary of optimized WI-beams Weight optimized, relative weights, WD: with displacement limit, ND: no displacement limit. L: span [m], q: load [kN/m]. Materials
L=6 q=20
L=6 q=60
L=6 q=100
L=8 q=20
L=8 q=60
L=8 q=100
L=10 q=20
L=10 q=60
L=10 q=100
S355/S355/S355
100 %
100 %
100 %
100 %
100 %
100 %
100 %
100 %
100 %
WD: S960/S960/S960
98 %
81 %
72 %
99 %
77 %
66 %
95 %
76 %
66 %
ND: S960/S960/S960
74 %
63 %
62 %
70 %
62 %
58 %
63 %
61 %
55 %
94 %
95 %
Cost optimized, relative costs WD: S700/S355/S500
107 %
99 %
97 %
106 %
96 %
95 %
103 %
It can be seen, that for longer and more heavily loaded beams the weight savings increase ending up to 45 % savings with L = 10 m and q = 100 kN/m. The savings in cost are more modest, and for several span/load cases, no savings are achieved. The greatest cost savings (6%) are attained by the hybrid S700/S355/S500 for span of 10 m and load 60 kN/m. The results for WQ-beams are shown in Table 4-3. Again, significant weight savings (up to 52%) are obtained by S960, when the displacement constraint is not included. If the displacement constraint is active, less savings (in some cases none) are attained. For costs, no savings are achieved by HSS. In this case WD solution is not S960/S960/S960, but S960/S700/S960. The cross-sections of these two are very near to each other and this may be due to the stochastic nature of PSO. The height of the beam was limited to 400 mm and this implies larger weight savings in ND solution compared WD solution. Table 4-3: Summary of optimized WQ-beams Weight optimized, relative weights, WD: with displacement limit, ND: no displacement limit. L: span [m], q: load [kN/m]. Materials
L=6 q=20
L=6 q=60
L=6 q=100
L=8 q=20
L=8 q=60
L=8 q=100
L=10 q=20
L=10 q=60
L=10 q=100
S355/S355/S355
100 %
100 %
100 %
100 %
100 %
100 %
100 %
100 %
100 %
WD: S960/S700/S960
100 %
80 %
79 %
100 %
99 %
100 %
100 %
100 %
99 %
ND: S960/S960/S960
100 %
80 %
68 %
100 %
69 %
61 %
94 %
57 %
48 %
WD: S500/S355/S355
103 %
101 %
103 %
105 %
105 %
Cost optimized, relative costs 103 %
104 %
104 %
103 %
The preliminary results of the optimal HSS beams have been presented in (Mela & Heinisuo, 2013) and (Mela & Heinisuo, 2014b). 4.2.2
Welded box columns
In this case the hinge-ended 12 m long welded box (WB)-column were optimized. Three separate cases of axial design loads of 10, 20 and 30 MN, meaning rather high loads, acting with uniform bending moments of 500 kNm with respect to both principal axes are considered. These are typical columns in boiler plants, as is shown in Figure 4-10.
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Figure 4-10: Welded box columns (black) of boiler plant The design variables are the plate sizes, as shown in Figure 4-11. Double symmetric crosssections are considered. The cantilever parts of the flanges are a = 15 mm. The constraints in this case are the interaction equations of EN 1993-1-1, Annex B. Results are given in Table 5.4.
Figure 4-11: Variables of welded box columns Table 5.4 : Results of welded box column optimization. Weight optimization Cost optimization Relative weights Relative costs N=10 N=20 N=30 N=10 N=20 N=30 Materials MN MN MN MN MN MN S355/S355 100 % 100 % 100 % 100 % 100 % 100 % S500/S355 81 % 81 % 81 % 91 % 87 % 89 % S500/S500 78 % 76 % 75 % 96 % 89 % 89 % S700/S355 66 % 64 % 64 % 83 % 78 % 76 % S700/S500 65 % 62 % 62 % 90 % 80 % 79 % S700/S700 64 % 59 % 57 % 92 % 80 % 78 % S960/S500 56 % 51 % 51 % 93 % 79 % 77 % S960/S700 55 % 50 % 49 % 95 % 80 % 78 % S960/S960 55 % 49 % 46 % 101 % 83 % 77 %
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It can be seen that considerable weight and cost savings using HSS are obtained. For WBcolumns the cost savings are 17-24 % using hydrid S700/S355 ([flanges]/[webs]). 4.2.3
Tubular trusses
Two types of one span (36 m) Warren-type trusses were optimized separately: Type 1 truss with KT-joints (with verticals), Type 2 truss with K-joints (without verticals), see Figure 4-12. Two load cases were studied: moderate load 23.5 kN/m (~2 kN/m 2 snow, 6 m c/c distance) and heavy load 47 kN/m at the top chord. The symmetry of the truss structure was utilized and therefore all values are presented for half trusses. Hybrid trusses with different steel grades in chords and braces are considered and notation [grade in chords]/[grade in braces] is used. Trusses with different material in top and bottom chords were not considered. Steel grades varied from S355 (considered as regular steel, reference) up to S960.
Figure 4-12: Considered tubular trusses The design variables were member profiles, the height of the truss, the gap of the joints (only welded gap joints are considered and the same gap is supposed at each joint), and the locations of the joints at the top and bottom chords, meaning both sizing and shape optimizations were performed. The objectives in optimization were the weight of the truss and the costs of the truss and weight and cost optimizations were done separately. Costs were calculated based on the feature based cost calculation method. The constraints were taken from the Eurocodes and the design rules for S960 were supposed to be the same as for S700. The constraints included all design rules for tubular trusses both for members and joints. The optimization was done firstly using the existent design rules. At the second phase the new rules which were developed in the present research were implemented into the optimization to find out the cost effect of these new rules to final designs. At the first phase were considered design in normal and fire conditions and at the second phase only in normal conditions. The particle swarm optimization (PSO) algorithm was used in optimization. In Figure 4-13 is shown the convergence of PSO for Type 2 trusses (K-joints) with the load 47 kN/m and the span 36 m in three cases varying the material grades of the members and using population 200, iterations 200 and 10 runs. The objective was the costs.
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Figure 4-13: Convergence of PSO in truss optimization In these three cases using larger population, more iterations and runs, more cost efficient solutions could be found:
S700/S355 2482 € => 2295 €;
S700/S700 2842 € => 2496 €;
S960/S960 2891 € => 2661 €.
This illustrates the nature of PSO in this case. The final PSOs in the phase 2 were calculated as massive parallel runs with:
Type 1 (KT-joints), population 400, iterations 225, runs 75;
Type 2 (K-joints), population 400, iterations 200, runs 100.
These runs were approximately six times more extensive (i.e. six times more CPU time was spent to find the best solution) than in the phase 1. Although due to the limitations of the method, global optimum still cannot be guaranteed. Preliminary results of the phase 1 are given in (Tiainen et al. 2013) and (Tiainen et al, 2014). In general, Type 2 trusses are more economical and they are given in Table 4-4.
K, 23.5 kN/m Rel. weight
KT, 23.5 kN/m K, 47 kN/m KT, 47 kN/m
95 %
100 %
101 %
97 %
98 %
87 %
86 %
79 %
86 %
S960/S700
90 %
S960/S500
94 %
S960/S355
S700/S500
94 %
S960/S960
KT, 47 kN/m
91 %
S700/S355
K, 47 kN/m
104 % 106 %
S700/S700
KT, 23.5 kN/m
100 % 106 % 100 % 115 % 100 % 104 % 100 % 110 %
S500/S355
Rel. cost
S500/S500
K, 23.5 kN/m
S355/S355
Table 4-4: Overall best cost and weight relative to S355/S355 Type 2 truss (K-joints)
108 % 106 %
100 % 106 %
107 % 110 %
105 % 106 %
92 %
86 %
95 %
89 % 91 %
101 %
97 %
89 %
95 %
96 %
92 %
97 %
102 %
87 %
84 %
69 %
72 %
71 %
63 %
68 %
68 %
64 %
84 %
85 %
68 %
74 %
70 %
57 %
70 %
65 %
60 %
74 %
76 %
62 %
62 %
64 %
53 %
58 %
58 %
54 %
79 %
84 %
60 %
74 %
67 %
50 %
64 %
60 %
52 %
The best trusses in weight are the S960/S960 trusses. The weight savings relative to S355 trusses are up to 50 %. The hybrid solution S700/S355 seems to be good a combination for
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steel grades in trusses when the manufacturing cost is the objective. The cost savings are 10 % with the small load and 21 % with the large load. 4.2.4
Effect of fire protection on optimized structures
Three types of considerations including fire design were made: Cost optimization of welded I beams, weight optimization of WQ beams without fire protection and cost optimization of trusses. Cost optimization WI beams When fire protection resistance requirement R30 is applied, the HSS WI beams are still more expensive whereas hybrid beams provide marginal (1-5 %) savings for higher loads. The cost distribution is such that material takes 32-60 % of the total cost. Painting corresponds to 11-27 % and the share of welding varies from 6 to 20 %. Erecting the beams takes 8- 20 % of the total cost and cutting 5-9%. Blasting, sawing and transportation each has a very small (1-2 %) contribution to the cost. The thickness of the fire paint varies from 430 to 730 μm. The cost comparison for R30 and R60 seem quite similar. The S355 solutions are the most economical in most cases. The share of material is 31-54 %. Painting corresponds to 19-35 % and welding 5-17 %. The other cost factors have similar shares as R30. The paint thickness is substantially greater ranging from 880 to 1352 μm. Weight optimization of WQ beams Consider the minimum weight problem of an unprotected beam in fire. The resistance requirement is R30. The weight reduction obtained with HSS become greater than in room temperature in general. The S500 cross-sections provide material savings up to 10 % whereas up to 24 % savings can be attained with S700. Fire resistance is mainly achieved by increasing the thickness of the flanges. The moment resistance constraint is the most critical constraint. On the other hand, the utilization ratio of the shear resistance constraint is also over 90 % in several cases. The average increase in weight compared with the minimum weights in room temperature is 89 %. For the smallest load, the weight increase becomes greater when the span is increased, but for q=60 kN/m and q=100 kN/m, the opposite is true. Cost optimization of trusses The trusses were also optimized including fire design (see Figure Figure 4-14). Both type 1 and 2 were considered with loading of 23.5 kN/m. The PSO parameters were 400/300/8 for type 2 and 500/400/8 for type 1. In fire, hybrid trusses were not considered. The design variables were the same as with ambient temperature added with fire intumescent paint thickness that could have values d = 0, 200, 300, …, 1400, 1500 μm. The calculation of steel temperatures with 5 seconds time step is rather time consuming in optimization. Therefore, steel temperatures were calculated and stored in tables for each wall thickness t, paint thickness d and fire resistance time of 30 and 60 minutes. Results imply that with 30 minute fire resistance requirement there is no benefit of using HSS. In 60 minutes some benefit can be achieved. The weight reduction is rather high but due to high cost of intumescent paint, the cost reduction is smaller.
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Figure 4-14: Relative weight and cost of trusses, including fire design 4.2.5
Effect of new design rules for optimal trusses
In the present Eurocodes are given reduction factors for the resistance of tubular joints if the steel grade is larger than S355. For the steel grades S in the range S355 < S ≤ S460 the reduction factor is 0.9 and in the range S460 < S ≤ S700 the reduction factor is 0.8. In this project the following reduction factors have been proposed: S500 => 1.0, S700 => 0.9 and S960 => 0.8. Type 2 trusses (K-joints) with 47 kN/m load were re-optimized using these new values. Cost and weight optimizations were done with similar PSO parameters than before. All previous S960 steel grade trusses were already calculated using the 0.8 reduction factor, so they were not optimized again. New reduction factors resulted in as much as 5.7 % cost savings with S500 steel grade, but with S700 savings were less significant in the comparison with the optimal trusses with the present reduction factors. S700/S355 combination was still the most efficient one. On average the costs were 2.4 % lower. Weight savings were similar or slightly better. In this project has been proposed that the buckling curves can be changed from c to b from S460 onwards for cold formed hollow sections. Thus, the imperfection factor α could be reduced from 0.49 to 0.34. The buckling curve of S355 steel grade sections still remains the same value c. The trusses Type 2, 47 kN/m were re-optimized using these new imperfection factors. New buckling curves reduced costs 4.9 % in one case (S960/S500), but in other steel grade combinations the cost savings were more limited, the average being 1.4% cheaper. The cheapest steel grade combination became 1% cheaper. Weight savings were slightly more substantial across the board; new buckling curves resulted in 2.7 % lighter trusses on average. The same trusses Type 2, 47 kN/m were re-optimized once more using both the new reduction factors and the new buckling curves to show the overall effect of the new design rules. With both new reduction factors and new buckling curves as much as 7.6 % cheaper than before (S500/S500) and on average the trusses are 3.9 % cheaper. The cheapest truss (S700/S355) becomes 1.0 % cheaper. Weight drops 9 % in two cases and 5 % on average. This is a great result for HSS trusses.
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4.2.6
Innovative frame system for commercial building
The new innovative commercial building frame (see Figure 4-15) includes three components: tubular welded columns, WQ-trusses (top chord is WQ-beam, diagonals are tubes, bottom chord is plate) and tubular trusses on the roof. The frame is considered as nonsway. The slabs are pre-tensioned hollow core concrete slabs with 80 mm cover concrete. Loads and dimensions are presented in the enclosed drawing. The reference case is optimized using S355 steel grade. Other cases include S500 and S700 grades.
Requirement of client: 1:20
500
Commercial building, frames c/c 10800 mm (non-sway frame) Project: RUOSTE, Design by Markku Heinisuo, TUT, 26.9.2012 Requirement of client: characteristic: dead 1 kN/m2, snow 2 kN/m2
Tubular truss c/c 5.4 m
Requirement of client Live load 5 kN/m2
Fire requirement: R60 for all
w
Technical
3800
Requirement of client Live load 8 kN/m2
v
WQ truss c/c 10.8 m
400+80
Requirement: D=1000 mm
c/c 10800
Commercial
2500
c/c 10800
Requirement of client Live load 2.5 kN/m2
.
