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Experimental and Numerical Modelling of Cellular Beams with Circular and Elongated Web Openings at Elevated Temperatures El-Hadi Naili*, Ali Nadjai, Sanghoon Han, Faris Ali and Sengkwan Choi University of Ulster, Jordanstown Compus, School of Built Environment Shore Road, Co-Antrim, Northern Ireland, BT37 0QB, UK e-mail*:
[email protected] ABSTRACT This paper describes an experimental and numerical study at elevated temperatures on the behaviour of full scale composite floor cellular steel beams with circular and elongated web openings. A total of three specimens, comprising three different steel geometries and loading conditions were tested at elevated temperatures. Finite element models were established with both material and geometrical non-linearity to compare with the experimental results. This paper also demonstrates the capability of a developed simple design approach in comparison with numerical modelling, experimental tests and existing design software used by the Steel Construction Institute (SCI). Keywords: Cellular steel beams, Circular and elongated web openings, Fire testing, FE modelling
1. INTRODUCTION Cellular beams (CBs) are currently being widely used in multi-storey buildings where, as well as reducing the total weight of the steelwork, they decrease the depth of floors by accommodating pipes, conduits and ducting. They are also used in commercial and industrial buildings, warehouses, and portal frames. CBs produced by modern automated fabrication processes can be competitive for the construction of both floor and roof systems. Their widespread use as structural members has prompted several investigations into their structural behaviour. Lawson [1] presented a design method for simply-supported composite beams with rectangular openings in the web at ambient temperature. The design method is based on plastic analysis of the cross-sections, considering the moment transfer by Vierendeel action across openings. Chung et al. [2] have investigated the Vierendeel mechanism in steel beams with circular web openings based on analytical and numerical studies. Chung and Lawson [3] have presented a simplified design method in the format of application rules to Eurocode-4 [4] for the design of simply-supported composite beams with large web openings. Liu and Chung [5] have carried out a non-linear finite element analysis (FEA) investigation on steel beams with various shapes and sizes of web openings. Details of this design method are fully presented in a complementary paper [6]. Bailey [7] has investigated the temperatures experienced by the web-posts on cellular beams by carrying out preliminary indicative fire tests on unprotected and protected cellular and solid-web steel beams. Bitar et al. [8] proposed a model for web post resistance based on experimental studies and numerical investigations which covers symmetrical and unsymmetrical sections. Lawson et al. [9] developed a design method for composite asymmetric cellular beams, which is not fully covered by existing design rules. Nadjai et al. [10, 11] carried out full-scale fire tests and numerical studies at both ambient and elevated temperatures. Four specimens, comprising two different steel geometries and loading conditions were tested at elevated temperatures. Vassart et al. [12] have conducted an extensive parametric study based on the tests results of four full-scale fire tests that have been conducted on composite cellular beams with circular and/or
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elongated web openings [13]. They have developed an analytical model that can be used for the prediction of the critical temperature of cellular beams. A full scale fire test has been performed recently on a composite floor for analysing the possibility of tensile membrane action to develop when the unprotected steel beams in the central part of the floor are made of cellular beams [14]. This paper presents the experimental and numerical studies on cellular beams with circular and elongated web openings at elevated temperatures which have the potential to provide essential data in several areas currently lacking systematic research. The target of this study is to investigate and understand the performance and failure mechanisms under a standard heating regime of cellular beams with temperature distribution through the specimens. 2. TEST PROGRAMME The tests were carried out on three full-scale composite cellular steel beams of 4.5 m span length. They were fabricated from standard hot-rolled steel sections, subjected to one or two point loading, using three different geometries. 2.1. Specimens Details The following types of beams have been tested: a)
b)
c)
Test 1A: An asymmetrical composite cellular beam was produced on the basis of UB 356 × 171 × 57 as a top tee section and of UB 610 × 305 × 179 as a bottom tee section having a finished depth of 555 × 171/305 ACB × 118 kg/m (see Figure 1). The diameter of the cells was 375 mm at 600 mm centres. Test 2A: A symmetrical composite cellular beam was produced on the basis of UB 457 × 191 × 74, having a finished depth of 550 × 191 CB 74 kg/m (see Figure 2). The diameter of the cells was 335 mm at 600 mm centres. Test 3A: An asymmetrical composite cellular beam was produced on the basis of UB 356 × 171 × 57 as a top tee section and of UB457 × 191 × 74 as a bottom tee section having a finished depth of 555 × 171/191 ACB × 65.5 kg/m (see Figure 3). The diameter of the cells was 375 mm at 600 mm centres.
The steel grade of the beams was given as S355. All the tests used a 150 mm thick × 1100 mm wide concrete slab, using normal-weight concrete (Grade 35 N/mm2). The slab reinforcement consisted of welded wire mesh reinforcement A142 having yield strength of 460 N/mm2. The interaction between the slab and beam was ensured in all specimens by the use of shear connectors of 19 mm diameter studs at height 95 mm. They have been equally distributed in one row with a distance of 150 mm over the beam length. The degrees of shear connection calculated are 0.53, 0.73 and 0.73 for the specimens 1A and 2A and 3A, respectively. Holorib sheets HR 51/150 with a thickness of 0.9 mm have been used as sheeting. The measured yield stress from a tensile yield stress from a tensile test was fy = 327 N/mm2. Applied load Beam detail:
4500 mm span 375 DIA @ 600 spacing − 150 mm slab thickness 555 Deep ACB S355 − 356 × 171 × 57 Top, 610 × 305 × 179 bot 30 No 19 DIA stud × 95 long @ 150 C/C = 4350 Elastic moment capacity of cellular steel beam, Ms = 487.22 kNm Plastic moment capacity of cellular steel beam, Mc = 718.60 kNm
Top tee: Tee depth = 255.0 mm Web thickness = 8.1 mm Flange width = 172.2 mm Flange thickness = 13 mm Bottom tee: Tee depth = 300.0 mm Web thickness = 14.1 mm Flange width = 307.1 mm Flange thickness = 23.6 mm
Figure 1. Details of the asymmetrical composite beam 1A.
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Applied load
Beam detail:
4500 mm span 335 DIA @ 600 spacing − 150 mm slab thickness 550 Deep CB S355 − 457 × 191 × 74 30 No 19 DIA stud × 95 long @ 150 C/C = 4350
Tee depth = 550.0 mm Web thickness = 9.0 mm Flange width = 190.4 mm Flange thickness = 14.5 mm
Elastic moment capacity of cellular steel beam, Ms = 611.65 kNm Plastic moment capacity of cellular steel beam, Mc = 652.01 kNm
Figure 2. Details of the symmetrical composite beam 2A. Applied load
Beam detail: Top tee: Tee depth = 255.0 mm Web thickness = 8.1 mm Flange width = 172.2 mm Flange thickness = 13 mm
4500 mm span 375 DIA @ 600 spacing − 150 mm slab thickness 555 Deep CB S355 − 356 × 171 × 57 top, 457 × 191 × 74 bot 30 No 19 DIA stud × 95 long @ 150 C/C = 4350 Elastic moment capacity of cellular steel beam, Ms = 481.45 kNm Plastic moment capacity of cellular steel beam, Mc = 572.34 kNm
Bottom tee: Tee depth = 300.0 mm Web thickness = 9.0 mm Flange width = 190.4 mm Flange thickness = 14.5 mm
Figure 3. Details of the asymmetrical composite beam 3A. Concrete compressive strength was measured at different stages of time: after 2 weeks and 28 days using a compressive strength calibrated machine at the University of Ulster. During the testing days, the concrete compressive strength was found approximately equal to 35 N/mm2. The geometry data of the beams tested are given in Table I. Table I. Geometry data
Span (mm) Top tee width (mm) Top tee depth (mm) Bottom tee width (mm) Bottom tee depth (mm) Overall depth (mm) Number of circular cells Number of elongated cells Number of cells with infill Number of cells with semi infill Overall number of cells Cell diameter (mm) Cell spacing (mm)
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Beam 1A 4500 172.2 255 307.1 300 555 6 1 0 2 7 375 600
Beam 2A 4500 190.4 275 190.4 275 550 3 2 1 0 4 335 600
Beam 3A 4500 172.2 255 190.4 300 555 7 0 1 0 6 375 600
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2.2. Mechanical Loading Two beams were tested under one point loading and one beam was tested under two-points loading; both ends of the beams were simply-supported. The beams were designed at ambient temperature in order to determinate the failure load. The applied loads during the fire tests were considered equal to the load ratio of 30% that depends on the standard ISO curve used during the test. The load ratio represents 30% of the failure load found from the pre-design at cold condition and by taking into account the loading applied during the previous tests conducted at Ulster University as reference [11]. During the fire tests, the composite cellular beams 1A, 2A and 3A were subjected to 200 kN, 150 kN and 150 kN constant loading, respectively. 2.2.1. Initial Design based on the SCI documentation The specimens were pre-designed using software which is based on the SCI documentation [15] for the design of composite cellular beams and gives a linear elastic response in order to evaluate the failure load at cold conditions. Vierendeel bending, web post buckling and horizontal shear are considered as the main failure modes of the three specimens. Table II gives the unity factor which is the degree of utilisation of the beams in the failure modes and the failure loads. From the results, the Vierendeel mechanism occurs at the initial stage of failure before buckling of the web post and the beams fail because of Vierendeel bending. The failure loads evaluated by the software are based on the first stage of failure only during the elastic phase of response. 2.2.2. Finite Element modelling at ambient temperature Geometrically nonlinear finite element analysis have been carried out using the the commercial FEA package Diana with non-linear material properties in order to simulate the complete behavior of cellular beams at cold condition and validate how well it can predict the failure load by comparing predictions with the previous cold tests [11] which were used as reference. Shell elements with the ability to handle large strains, large deformations, and plasticity were used to model the cellular steel beams. Solid-brick elements were used in the analysis to improve the rate of convergence, incorporating a smeared crack approach for the concrete, to model the composite slab. For only the evaluation of failure load at ambient temperature, full interaction between the cellular steel beam and the concrete slab was assumed in the model and the steel decking shape and the shear studs were not considered in the model. This assumption is also justified from test observations [10] which confirmed that no stud failure occurred before web-post buckling of the beam. Figures 4 & 5 show the predicted load-deflection- relationships and the ultimate failure loads of the beams. A linear elastic response can be seen in the load deflection curves at the initial loading stage. The first yield occurs at a load level of approximately 382 kN, 245 kN and 432 kN for beams 1A, 2A and 3A, respectively (approximately 58%, 54% and 76% of the ultimate failure load determined by FEA). By introducing a web imperfection into the model, the sections failed at a smaller load and the failure mechanism was closer to a Vierendeel mechanism with web post buckling, as expected. The maximum deflection just before failure was between 10 mm and 20 mm, which should not exceed a value of span/200 [16]. 2.2.3. Simple approach A simple method was proposed by Chung et al. [2] to provide a rule for practical design of cellular steel beams. The failure load can be estimated by considering that the beam alone contributes to the strength Table II. Software results
Beam 1A Beam 2A Beam 3A
Vierendeel bending 90% 102% 111%
Web post buckling 51% 35% 73%
Horizontal shear 102% 44% 88%
Failure load (kN) 382 245 432
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800
Load applied (kN)
700 600 500 400 300 200 CB - with slab (no imperfection) CB - with slab (imperfection) Failure load (software based on SCI - 382 kN)
100 0 0
(a) Deflected shape of beam 1A
20
40
60 80 100 Deflection (mm)
120
(b) Load versus deflection of beam 1A 800 700 Load applied (kN)
600 500 400 300 200 CB - with slab (no imperfection) CB - with slab (imperfection) Failure load (software based on SCI - 245 kN)
100 0
(c) Deflected shape of beam 2A
0
20
40 60 80 Deflection (mm)
100
120
(d) Load versus deflection of beam 2A
Figure 4. Loading versus Deflection and failure loads of composite cellular Beam 1A and 2A.
of the specimen and the beam and slab act independently of each other, although it may estimate a conservative value for the load carrying capacity. In this case, the slab is considered as a uniform distributed loading along the length of the beam. The method uses an empirical shear moment interaction formula as follows: Vsd V o,Rd
2.5
M + sd M o,Rd
2.5
≤1
(1)
where, Vsd, applied shear force, Vo,Rd, shear capacity of cellular section, Msd, applied moment, Mo,Rd, moment capacity of cellular section. This formula can be represented to give a simple empirical design rule to estimate the moment capacity of a cellular section, Mvo,Rd, under a global shear force, Vsd, against the Vierendeel mechanism as follows:
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800
Load applied (kN)
700 600 500 400 300 200 CB - with slab (no imperfection) CB - with slab (imperfection) Failure load (software based on SCI - 435kN)
100 0 0
20
(a) Deflected shape of beam 3A
40 60 80 Deflection (mm)
100
120
(b) Load versus deflection of beam 3A
Figure 5. Loading versus Deflection and failure load of composite cellular Beam 3A.
MVo, Rd
V 2.5 = M o, Rd . 1 − Sd Vo, Rd
0.4
(2)
≥ M Sd
The failure loads found by this method and the properties of cellular beams are given in Table III below. 2.2.4. Results comparison Table IV shows that both the FEA and the simple approach produce similar outcomes regardless of the different loading cases for beams 1A and 2A. The values obtained by the software based on the SCI approach, which gives a linear elastic response, are conservative when compared against the failure loads obtained by the FEA and the simple approach because the failure loads evaluated by the SCI software are based on the first stage of failure only in the elastic phase of the response. The failure load of Beam 2A obtained by the SCI software is very conservative because of the Vierendeel mechanism that occurs at the initial stage of failure in Beam 2A which includes two elongated openings compared to the other two beams. Table III. Properties summary and failure loads
Beam 1A Beam 2A Beam 3A
Mo,Rd(kNm) 718.60 611.65 572.34
Vo, Rd (kN) 409.00 370.94 299.00
Mvo, Rd(kNm) 562.02 5217.75 461.53
FL (kN) 574 450 396
Table IV. Comparison of the failure load results
Beam 1A Beam 2A Beam 3A
Simple approach (kN) 574 450 396
Software based on SCI (kN) 382 245 432
Diana FEM (kN) [640; 690] [430; 480] [540; 600]
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3. TESTS RESULTS 3.1. Tests Duration The three fire tests were carried out under the ISO834 fire curve. Only the lower side of the slab and the steel section were fire-exposed. Table V shows the duration of the fire tests and the failure times: 3.2. Temperature Distribution and Deflection The average temperature distribution along the steel profile of the three specimens is shown in Figures 7 & 8. The average temperature of top flange is the coldest part of the steel profile with a significant thermal gradient due to the slab on the top of it, and only the bottom part is exposed to fire comparing to the other parts of the steel section that were fire-exposed on 3 sides. The maximum temperature values were recorded in the web, reaching up to 830°C in Test 1A after 49 minutes and up to 795°C in Test 2A and Test 3A after 39 minutes. Figures 7 & 8 show the mid-span deflections recorded during the three tests; the beam responds linearly due to the severe rise in temperature until about 20 minutes in Test 1A, by which time the furnace temperature had risen to over 780°C and until about 15 minutes in both Test 2A and Test 3A when the temperature was around 730°C. After these points the beams started to lose strength and the rate of deflection began to gradually increase as the temperature in the furnace reached over 860°C in Test 1A and around 800°C in both Test 2A and Test 3A. The rate of deflections of Beam 2A and Beam 3A begin to gradually increase after this point due to the deterioration of the beam properties until about 24 and 26 minutes respectively, when the beams deflection is recorded at furnace temperature around 800°C. Between 20 and 25 minutes, for both Beam 2A and Beam 3A rate of deflection started to increase rapidly up until the point of failure at 39 minutes, by which time the beams had deflected by 249 mm and 253 mm at furnace temperature around 870°C, respectively. The deflection of the Beam 1A continued to rise more rapidly as the beam lost more strength and stiffness up until the point of failure after 49 minutes at furnace temperatures around 920°C, with the deflection recorded equal to 254 mm.
Table V. Duration of fire tests
Heating Phase (min) Failure Time (min)
Test 1A 60 49
Test 2A 43 39
a e 10 mm b 1
c d
n o
g P 10 mm
i j k
2
140 mm
5 mm 5 mm 5 mm
50 mm The figure shows the thermocouple locations on web-post 1 from left side. 66 thermocouples 2 × 10 mm were used on the steel section (Test 1A)
A
C
l
h f
140 mm
3 off 4 off 2 off
B
m
Test 3A 50 39
5 mm
A 50 mm
5 mm 5 mm
C
B 12 Thermocouples were located on the slab and shear studs
Figure 6. Typical thermocouple locations on the steel and slab (Test 1A).
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0 −50
800 Deflection (mm)
Average temperature (°C)
1000
600 400 Bot flange Bot web Top web Top flange Mean furnace temperature ISO834 curve
200
−100 −150 −200 −250
Mid-span deflection
−300
0 0
10
20 30 40 50 60 70 Time (minutes) (a) Time vs. temperature in the steel of test 1A
0
10
20 30 40 50 60 Time (min) (b) Time vs. deflection of beam 1A
Figure 7. (a) Time versus temperature in the steel and (b) deflection - Test 1A.
0
1000 900
−50
700 600 500 400 Bot flange Bot web Top web Top flange Mean furnace temperature ISO834 curve
300 200 100
Deflection (mm)
Average temperature (°C)
800
−100 −150 −200 −250 Mid-span deflection −300
0 0
10
20 30 Time (minutes)
40
50
0
(a) Time vs. temperature in the steel of test 2A
20
30 40 Time (min)
50
60
(b) Time vs. deflection of beam 2A
0
1000
−50
800
600
400 Bot flange Bot web Top web Top flange Mean furnace temperature ISO834 curve
200
Deflection (mm)
Average temperature (°C)
10
−100 −150 −200 −250 Mid-span deflection −300
0 0
10
20
30
40
50
60
0
10
20
30
40
50
Time (minutes)
Time (min)
(c) Time vs. temperature in the steel of test 3A
(d) Time vs. deflection of beam 3A
60
Figure 8. (a) Time versus temperature in the steel and (b) deflection - Test 2A and (c) time versus temperature in the steel and (d) deflection - Test 3A.
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Test 1A: Web post buckling and vierendeel bending failure mechanisms
Test 2A: Vierendeel bending associated with web post buckling failure mechanisms
Test 3A: Web post buckling failure mechanism
Figure 9. Deformed beams after fire tests. 3.3. Failure Mode All sections of the fire tests failed due to the fact that they lost strength and stiffness due to the rise in temperature. Figure 9 below shows the failure mechanism observed in the tests. The buckling of the web posts begins to occur before the final point of failure as the steel beam temperatures exceed 600°C, at which point the steel has less than half of its design strength and its Young’s modulus is reduced to about 20% of the room temperature value. When the furnace temperature is around 750°C, the Young modulus decreases more rapidly than the steel strength limit which is the cause the failure modes. The main failure mode in Test 1A and Test 2A was the Vierendeel bending associated with the buckling of the web posts of the steel section. Web post buckling was the main failure mode in the Test 3A. 4. FINITE ELEMENT MODEL FOR FIRE CONDITIONS The cellular steel beam sections and slab were modelled using solid-brick elements and heating elements in order to add a temperature dependent mesh over top of the structural mesh. Both the steel deck, as a bottom layer, and the reinforcing mesh, as a layer within the concrete, were included. To simulate the tests as accurately as possible the beams were split into different areas.
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Different time/temperature curves were introduced to the model according to the average thermocouple reading recorded in the tests for the bottom flange, bottom web, upper web, upper flange, bottom layer of steel decking and concrete slab. A smeared cracking model was used for concrete which is characterized by the use of combining tension softening, tension cut-off and shear retention to analyze a concrete structure under loading. Tension cut-off has one of two options to consider, either constant or linear performance under loading, as shown in Figure 10. An implicit analysis was conducted in two steps, where the load was applied in the first step and the temperature was applied in the second step. Crack 1
σ2
Crack 2
ƒt
σ2 ƒt
ƒt
σ1
ƒt
ƒc
σ1
ƒc
(a) Constant
(b) Linear
Figure 10. Criteria for tension cut-off in smeared cracking FE model. 60
Time (min)
50 40 30 20 Test data FEM- DIANA
10 0 0
50
100 150 200 250 Deflection (mm)
(a) Deflection at mid-span versus time
(b) Deformed shape and failure mechanism
50 40 30 20 10
Test data FEM- DIANA
0 0
50
100 150 200 250 Deflection (mm)
(c) Deflection at mid-span versus time
(d) Deformed shape and failure mechanism
Figure 11. Comparison of FEM models and test results (a & b) Beam 1A and (c & d) Beam 2A.
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50
Time (min)
40 30 20
Test data FEM - DIANA
10 0 0
50
100 150 200 Deflection (mm)
250
(a) Deflection at mid-span versus time
(b) Deformed shape and failure mechanism
Figure 12. Comparison of FEM model and test result - Beam 3A.
.156E9 .954E8 .35E8 −.254E8 −.858E8 −.146E9 −.207E9 −.267E9 −.327E9 −.388E9
Figure 13. Axial stress distribution in elements (N/m2 ) - Beam 2A.
Figures 11 & 12 show the load-deflection curves compared between FE models and the experimental tests and the output deformed shape of FEM analysis which can be compared with the actual failure modes of the three specimens. The approach of numerical modelling agrees reasonably well with the experimental fire test results. The failure mode that has taken place in Beam 1A is due to the web posts buckling and Vierendeel bending, as was seen in the fire test. During the initial stage of loading, the Vierendeel mechanism tends to develop, starting due to the cellular geometry of specimen. Finally, the beam fails by flexural web post buckling. The axial stress distribution in the elements at the early stages of failure is shown in Figure 13. From the results, the stress concentration around the openings can help to determinate the critical sections in the three beams tested. For Beam 2A, the stress concentration in the bottom part of the web around the elongated opening near the circular opening is in tension to a greater extent than the other parts of the web around openings and the stress concentration in the top part of the elongated openings is higher than in the web post. From these observations and analysis, the failure mode of Test 2A has clearly been the Vierendeel mechanism, as expected associated with web post buckling. 5. CONCLUSION This paper describes an experimental and numerical study of the behaviour of three CBs with circular and elongated web openings at elevated temparatures. Flexural web post buckling was the main failure mode in Test 1A of an asymmetrical composite beam in the area of moment and shear interaction. Only the top part of the web resists the loading due to the high asymmetrical geometry of the steel beam of composite section 1A. Similar failure occurred in Test 3A of an asymmetrical composite beam.
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Veirendeel bending associated with the buckling of the web post were the main failure modes in Test 2A of a symmetrical composite beam. The FEM modelling predicted well the structural behaviour and fire resistance of each of the test specimens. The models can be used for further parametric studies using long span beams in order to extend existing fire design rules. Based on the observations and analysis of stress distributions and deflected shapes in the three tested beams with different geometries, the critical sections of CBs can be applied to evaluate the effective length for analytical modeling of web post failures. REFERENCES [1] R.M. Lawson, Design for openings in the webs of composite beams, CIRIA/SCI publication P068 (1987). [2] K.F. Chung, T.C.H. Liu, A.C.H. Ko, Investigation on Vierendeel mechanism in steel beams with circular web openings, Journal of Constructional Steel Research. 57 (2001) 467–490. [3] K.F. Chung, R.M. Lawson, Simplified design of composite beams with large web openings to Eurocode 4, Journal of Constructional Steel Research. 57 (2001) 135–164. [4] ENV 1994-1-1: Eurocode 4: design of composite steel and concrete structures. BSI. (1994). [5] T.C.H. Liu, K.F. Chung, Steel beams with large web openings of various shapes and sizes: finite element investigation, Journal of Constructional Steel Research. 59 (2003) 1159–1176. [6] K.F. Chung, C.H. Liu, A.C.H. Ko, Steel beams with large web openings of various shapes and sizes: an empirical design method using a generalised moment-shear interaction curve, Journal of Constructional Steel Research. 59 (2003) 1177–1200. [7] C. Bailey, Indicative fire tests to investigate the behaviour of cellular beams protected with intumescent coatings, Fire Saf. J. 39 (2004) 689–709. [8] D. Bitar, T. Demarco, P.O. Martin, Steel and non composite cellular beams – Novel approach for design based on experimental studies and numerical investigations, brochure EUROSTEEL (2005). [9] R.M. Lawson, J. Lim, S.J. Hicks, W.I. Simms, Design of composite asymmetric cellular beams and beams with large web openings, Journal of Constructional Steel Research. 62 (2006) 614–629. [10] A. Nadjai, Performance of Cellular Composite Floor beams at ambient temperatures, FireSERT, Test report, (2005). [11] A. Nadjai, O. Vassart, F. Ali, D. Talamona, A. Allam, M. Hawes, Performance of cellular composite floor beams at elevated temperatures, Fire Saf. J. 42 (2007) 489–497. [12] O. Vassart, C.G. Bailey, G. Bihina, M. Hawes, A. Nadjai, C. Peigneux, W.I. Simms, J.M. Franssen, Parametrical study on the behaviour of steel and composite cellular beams under fire conditions, Proceedings of the Sixth International Conference on Structures in Fire (SiF’10) (2010). [13] G. Bihina, B. Zhao, O. Vassart, Cellular composite beams at elevated temperatures, Application of Structural Fire Engineering, Prague, Czech Republic (2009). [14] O. Vassart, C.G. Bailey, M. Hawes, A. Nadjai, W.I. Simms, B. Zhao, T. Gernay, J.M. Franssen, Large-scale fire test of unprotected cellular beam acting in membrane action, Proceedings of the Sixth International Conference on Structures in Fire (SiF’10) (2010). [15] The Steel Construction Institute, Design of Composite and Non-Composite Cellular Beams (1994). [16] BS 5950-1: 2000, Structural use of steelwork in building, Part 1: Code of practice for design rolled and welded sections.
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