Design with stainless steel rebars applying Eurocode 2 - Outokumpu

RESEARCH REPORT

No. VTT-S-06464-11

September 15, 2011

Design with stainless steel rebars applying Eurocode 2 Requested by: Outokumpu Oyj

RESEARCH REPORT No. VTT-S-06464-11

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Customer/ Requested by Outokumpu Oyj PL 140 02201 Espoo Order

8.4.2010, Eero Nevalainen

Contact person

VTT Expert Services Ltd Senior research scientist Matti Pajari P.O. BOX 1001, FI-02044 VTT Tel. +358 20 722 6677 Fax + 358 20 722 7003 Email [email protected]

Assignment

Design with stainless steel rebars applying Eurocode 2 - How to do it?

1 BACKGROUND

Traditionally, the concrete structures reinforced with stainless steel have been designed applying design rules developed and verified for structures reinforced with carbon steel. When doing so, the nonlinear stress-strain relationship of the stainless steel has been modelled by a bilinear relationship used for the carbon steel. Most likely, this approach has resulted in an uneconomical design because the full potential of the stainless steel has not been exploited. On the other hand, it is also possible that in some cases the safety has been lower than that desired. This may be the case when the prevailing failure mode has been the compression failure of the concrete.

2 AIM

The aim is to study the applicability of the design rules, developed for concrete structures reinforced with carbon steel, to those reinforced with stainless steel and to compare the load-carrying resistance of structures reinforced with stainless steel with those reinforced with carbon steel. Three cases have been analysed: 1. Bending resistance of a beam cross-section 2. Bending resistance of a bridge deck cross-section 3. Bending and compression resistance of a column cross-section. The stainless steel grades considered are 1.4162 (LDX), 1.4362 and 1.4311. Two different carbon steels are used as reference: one with yield limit 500 MPa (C500) and the other with yield limit 620 MPa (C620). Carbon steel C620 is beyond the scope of Eurocode 2 [1]. The aim of considering C620 here is only to illustrate what happens, if the design rules of Eurocode 2 are applied to stainless steel LDX without modification. Instead of whole structures, cross-sections have been studied to simplify the calculations and to make it easy to interprete the results. Another reason is that the amount of steel needed in the section subjected to the ultimate loading is roughly proportional to the amount of reinforcement necessary for the whole structure. Furthermore, there are not enough data to take into account the real properties of the stainless steel when calculating the deflections, designing the shear reinforcement, designing the anchorage of the reinforcement etc.

The use of the name of VTT Expert Services Ltd or the name Technical Research Centre of Finland (VTT) in any other form in advertising or publication in part of this report is only permissible with written authorisation from VTT Expert Services Ltd.


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3 STRESS-STRAIN RELATIONSHIP 3.1 Measured relationship For each stainless steel grade, ten stress-strain curves were measured from 20 mm rebars (SFS-EN ISO 6892-1). The test results are documented in [3] and illustrated in Figs 1 ... 6. The sampling data provided by the the steel producer are given in App. A. A relatively wide scatter is typical of all stainless steels but within one coil the scatter remains much smaller, see Figs 7 - 9.

Stress [MPa]

1.4162 900 800 700 600 500 400 300 200 100 0

8M 11M 18F 24B 38B 56F 57-1 57-5 57-10

0

5

10

57-15 20

15

Strain [%]

Fig. 1. Measured stress-strain curves for stainless steel 1.4162 (LDX).

1.4162 800

Stress [MPa]

700 8M 11M 18F 24B 38B 56F 57-1 57-5 57-10 57-15

600 500 400 300 200 100 0 0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

Strain [%]

Fig. 2. Initial part of previous figure on a large scale.



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Stress [MPa]

1.4362 900

C13F

800

C14R

700

C26F

600

C48F C62F

500

C16B1 C16B4

400 300

C16B7

200

C16B11

100

C16B15

0 0

5

10

15

20

25

30

Strain [%]

Fig. 3. Measured stress-strain curves for stainless steel 1.4362. 1.4362 C13F C14R C26F C48F C62F C16B1 C16B4 C16B7 C16B11 C16B15

900

Stress [MPa]

800 700 600 500 400 300 200 100 0 0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

1,8

Strain [%]

Fig. 4. Initial part of previous figure on a large scale. 1.4311 900 800 C1F Stress [MPa]

700

C2R

600

C4F

500

C5R

400

C6F C3B1

300

C3B4

200

C3B7

100

C3B11 C3B15

0 0

5

10

15

20

25

30

Strain [%]

Fig. 5. Measured stress-strain curves for stainless steel 1.4311. The use of the name of VTT Expert Services Ltd or the name Technical Research Centre of Finland (VTT) in any other form in advertising or publication in part of this report is only permissible with written authorisation from VTT Expert Services Ltd.


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1.4311 900 800 C1F Stress [MPa]

700

C2R

600

C4F

500

C5R

400

C6F C3B1

300

C3B4

200

C3B7

100

C3B11 C3B15

0 0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

1,8

Strain [%]

Fig. 6. Initial part of previous figure on a large scale. 1.4162 900 800 Stress [MPa]

700 600 500

57-1 57-5

400

57-10 57-15

300 200 100 0 0

2

4

6

8

10

12

14

16

18

20

Strain [%]

Fig. 7. Behaviour of specimens taken from coil 57. 1.4362 900 800 Stress [MPa]

700 600

C16B1

500

C16B4

400 300

C16B7 C16B11

200

C16B15

100 0 0

5

10

15

20

25

30

Strain [%]

Fig. 8. Behaviour of specimens taken from coil 16. The use of the name of VTT Expert Services Ltd or the name Technical Research Centre of Finland (VTT) in any other form in advertising or publication in part of this report is only permissible with written authorisation from VTT Expert Services Ltd.


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1.4311 900 800 Stress [MPa]

700 600

C3B1

500 300

C3B4 C3B7 C3B11

200

C3B15

400

100 0 0

5

10

15

20

25

30

Strain [%]

Fig. 9. Behaviour of specimens taken from coil 3. 3.2 Ramberg-Osgood model for stainless steel The modified Ramberg-Osgood (R-O) expression

σ ⎛σ ε= + α 0 ⎜⎜ E0 E0 ⎝ σ 0 σ

⎞ ⎟⎟ ⎠

n

(1)

approximates the constitutive behaviour (stress-strain relationship) of the stainless steel. It tells how the stress σ and strain ε in a loaded rebar are related. The first term on the right represents a linear stress-strain behaviour with elasticity modulus E0. The second term is an increment to the elastic strain. It increases with σ and is responsible for the concave nonlinearity of the curve. Parameters E0, α, σ0 and n are calibrated to fit with test results in the strain range in which the highest accuracy is needed. For structural stainless steel and stainless steel reinforcement this range is different. This difference is discussed in Chapter 4. Consequently, it may be uneconomical to apply the same parameters to the structural stainless steel and stainless steel reinforcement. If n > 1, which is normally the case, E0 is the initial tangent modulus of the curve determined by Eq. (1). At σ = σ0, Eq. (1) becomes

ε=

σ0 E0

+α

σ0 E0

(2)

In other words, while σ0/E0 represents the elastic deformation at this point, the plastic deformation is equal to α times elastic deformation. σ0 is often set = 0,2% yield limit of the steel. Then

α

σ0 E0

= 0 ,002

(3)



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In Eq. (1) the plastic deformation ασ0/E0 is scaled by (σ/σ0)n. The effect of n is illustrated in Figs 10 and 11 in which n is varied and the other R-O parameters are kept constant. As can be seen, n controls the rate of strain hardening. 900 800 Stress [MPa]

700

n = 16 n = 13 n = 10

600 500 400 300

σ0 = 600 MPa E0 = 180 GPa α = 0,5

200 100 0 0

1

2

3

4

5

Strain [%]

Fig. 10. Effect of n on strain hardening. 700

Stress [MPa]

600 n = 16 n = 13 n = 10

500 400 300

σ0 = 600 MPa E0 = 180 GPa α = 0,5

200 100 0 0

0,2

0,4

0,6

0,8

1

Strain [%]

Fig. 11. Initial part of previous figure on a larger scale.

3.3 Ramberg-Osgood parameters determined from measured curves Table 1 gives the numerical values of the parameters in Eq. (1). They have been determined by trial and error. Figs 12 - 17 illustrate the fit. Attempts have been made to make the curves representative in the relevant strain range which is 2,0...2,8% for the considered bridge deck sections and 0,3...1,8% for the other sections. The use of the name of VTT Expert Services Ltd or the name Technical Research Centre of Finland (VTT) in any other form in advertising or publication in part of this report is only permissible with written authorisation from VTT Expert Services Ltd.


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The constitutive Ramberg-Osgood models for beam and columns sections are compared with carbon steel models in Fig. 18. Table 1. Experimental values of R-O parameters. Steel E0 [GPa] σ0 [MPa]

α

1.4162 (LDX) 170 600 0,6 15 (18)*

1.4362

1.4311

170 570 0,5 11 (13)*

160 480 0,6 11 (13)*

n * The values in parentheses are only used for bridge deck sections

Stress [MPa]

1.4162 900 800 700 600 500 400 300 200 100 0

R&O 8M 11M 18F 24B 38B 56F 57-1 57-5 57-10 57-15

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

Strain [%]

Fig. 12. LDX. R-O curve for beam and column section.

1.4362 C13F C14R C26F

800 700

C48F C62F

Stress [MPa]

600 500

C16B1 C16B4

400 300

C16B7 C16B11 C16B15

200 100

R&O

0 0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

1,8

Strain [%]

Fig. 13. 1.4362. R-O curve for beam and column section. The use of the name of VTT Expert Services Ltd or the name Technical Research Centre of Finland (VTT) in any other form in advertising or publication in part of this report is only permissible with written authorisation from VTT Expert Services Ltd.


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1.4311 C1F

700

Stress [MPa]

C2R

600

C4F

500

C5R C6F

400

C3B1

300

C3B4

200

C3B7 C3B11

100

C3B15 R&O

0 0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

1,8

Strain [%]

Fig. 14. 1.4311. R-O curve for beam and column section.

Stress [MPa]

1.4162 900 800 700 600 500 400 300 200 100 0

8M 11M 18F 24B 38B 56F 57-1 57-5 57-10 57-15 R&O

0,0

0,5

1,0

1,5

2,0

2,5

3,0

Strain [%]

Fig. 15. LDX. R-O curve for bridge deck sections. 1.4362 C13F

Stress [MPa]

800

C14R

700

C26F

600

C48F

500

C62F C16B1

400

C16B4

300

C16B7

200

C16B11

100

C16B15 R&O

0 0

0,5

1

1,5

2

2,5

3

Strain [%]

Fig. 16. 1.4362. R-O curve for bridge deck sections. The use of the name of VTT Expert Services Ltd or the name Technical Research Centre of Finland (VTT) in any other form in advertising or publication in part of this report is only permissible with written authorisation from VTT Expert Services Ltd.


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1.4311 800 C1F

Stress [MPa]

700

C2R

600

C4F

500

C5R

400

C6F C3B1

300

C3B4

200

C3B7

100

C3B11 C3B15

0 0

0,5

1

1,5

2

2,5

3

R&O

Strain [%]

Fig. 17. 1.4311. R-O curve for bridge deck sections.

800 700

Stress [MPa]

600 500 LDX

400

1.4362

300

1.4311

200

C500

100

C620

0 0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

2,0

Strain [%]

Fig. 18. Comparison of R-O curves for beams and columns with carbon steel curves.

4 COMPARISON OF STRUCTURAL STAINLESS STEEL AND STAINLESS STEEL REINFORCEMENT IN CONCRETE STRUCTURES For structures made of structural stainless steel the high ductility allows large deformations in the ultimate limit state. For example, the bending resistance is controlled by the strength rather than by the deformation, which makes the accurate stress-strain behaviour unimportant in the ultimate limit state. It is more important to know the stress-strain relationship in service conditions, i.e. below appreciable yielding. In a steel section the deformations attain their maximum and minimum values at the outer surfaces and all intermediate strain The use of the name of VTT Expert Services Ltd or the name Technical Research Centre of Finland (VTT) in any other form in advertising or publication in part of this report is only permissible with written authorisation from VTT Expert Services Ltd.


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values between the outer surfaces. Therefore, in the service conditions, the approximative constitutive law should be as accurate as possible for the intermediate strains, too. For rebars, the situation is different. They are placed close to the outer surfaces where they work effectively. It follows that in service conditions all steel deformations on the tension side tend to be of the same order as the maximum strains in a stainless steel beam. On the compression side the elastic properties of the rebar are less important because the amount of steel is small and because the deformation is controlled by the properties of the concrete mainly. For these reasons, the stress-strain behaviour for small deformations is unimportant when calculating the deflections etc. Contrary to the steel beams, the ultimate resistance of a concrete beam is sensitive to deformations on the compression side. A bended concrete beam is not likely to fail due to the rupture of the rebars but by crushing of the concrete in compression. The ultimate strain of the concrete in compression is low, typically -0,0035 for ordinary concrete. Increasing the steel strain on the tension side reduces the depth of the compressed concrete block and the total compressive force carried by the concrete. Since the tensile force in the steel and the compressive force in the concrete must be equal, it follows that the strain of the steel is typically quite low at failure. To be able to accurately evaluate the resistance, the constitutive law needs to be known beyond 0,2% yield limit, say until 2 - 5% elongation but not further. The different demands and different production methods mean that it would be uneconomical to use the same R-O parameters both for structural and reinforcing stainless steel, even if the chemical composition is the same in both cases. For the rebars, it may also be economical to use different parameters for small strains and large strains. It is obvious, that the R-O parameters for structural stainless steel given in Eurocode 3 [2] cannot be applied to stainless steel reinforcement without revision.

5 PRINCIPLES OF DESIGN CALCULATIONS 5.1 General The resistances calculated using the Ramberg-Osgood curves are compared with the resistances calculated using the same amount of carbon steel. The standard procedures of Eurocode 2, more specifically EN 1992-1-1, are applied using the recommended values for the nationally determined parameters. This means e.g. partial factors 1,15 and 1,5 for the steel and concrete, respectively. The amount of steel in the main reinforcement is varied by varying the number of bars. Since stress-strain curves were only measured for 20 mm thick bars, the bar thickness is set equal to 20 mm in all calculated beam and column sections even if thicker bars would have been more practical. For the bridge The use of the name of VTT Expert Services Ltd or the name Technical Research Centre of Finland (VTT) in any other form in advertising or publication in part of this report is only permissible with written authorisation from VTT Expert Services Ltd.


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deck sections, the material properties measured for 20 mm bars have been applied to all thicknesses of stainless rebars. 5.2 Constitutive model for carbon steel The design curves for steels C500 and C620 are illustrated in Figs 19 and 20.

Carbon steel C500 800

Stress [MPa]

700 600

Assumed behaviour

500 Design model

400

σ

300

σ / 1,15

200 100 0 0,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

Strain [%]

Fig. 19. Design model for carbon steel C500.

Carbon steel C620 800

Stress [MPa]

700

Assumed behaviour

600 Design model

500 400

σ

300

σ / 1,15

200 100 0 0,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

Strain [%]

Fig. 20. Design model for carbon steel C620. 5.3 Rough constitutive model for stainless steel



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It has been a common practice to apply the design rules developed for carbon steel reinforcement also to the design of the stainless steel reinforcement. This is equivalent to calculating the resistance assuming that the steel has the same 0,2% yield limit as the stainless steel and taking all other parameters from the carbon steel. To evaluate the error of this approximation, all concrete sections have also been analysed assuming carbon steel with 0,2% proof strength 620 MPa which roughly equals that of stainless steel LDX. Fig. 21 illustrates this method which is here called traditional. Stainless steel 800 Traditional assumption

Stress [MPa]

700

Measured curve

600 500 400

Traditional design model

300 200

σ

σ / 1,15

100 0 0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

Strain [%]

Fig. 21. Design model in accordance with Eurocode 2. Draw a straight line through the origin with the slope of 200 GPa, draw a roughly horizontal straight line through the 0,2% proof strength and move the latter line downwards to take into account the partial factor of 1,15. 5.4 Constitutive model for stainless steel Based on the test results, the stress-strain curves used for the stainless steel in the design calculations have been elaborated according to the following principles: 1. For each stainless steel, approximate the constitutive behaviour by Ramberg-Osgood model 2. For each Ramberg-Osgood curve, find the design curve by dividing the stress by a partial factor = 1,15 (safety factor), see Fig. 22. Fig. 22 illustrates how the design curve is obtained from the fitted RambergOsgood curve by stress reduction. This method is overconservative for small strains but due to the varying slope of the curve, some kind of reduction may be necessary also for stresses below the factored 0,2% proof strength (= strength divided by safety coefficient). This is different from the carbon steel for which the slope is practically constant until yielding or close to the 0,2% proof strength. This subject is further discussed in the conclusions.



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Fig. 22 also illustrates the difference between the present approach and the traditional one which is similar to that applied to carbon steel.

Stainless steel 800 Traditional design model

Stress [MPa]

700 600

R-O model

Design model

500 400

σ

300

σ / 1,15

200 100 0 0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

Strain [%]

Fig. 22. Obtaining design model from fitted R-O curve.

6 BEAM SECTION The bending resistance of a rectangular beam section shown in Fig. 23 is considered. In this report Txy refers to a rebar which is xy mm thick, e.g. T20 is 20 mm thick. The lower reinforcement is placed in two layers when necessary. Fig. 24 shows the results. "Most feasible range for carbon steel" in Fig. 24 indicates the most likely amount of carbon steel used in ordinary beams. A higher amount would not enhance the bending resistance, and three bars or less would mean that it would often be economical to reduce the depth of the concrete section and to increase the amount of reinforcing steel. 400 600 560

2T12 C500

Concrete C40

80 40

A st,2 A st,1



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Fig. 23. Section of considered beam. The upper reinforcement is the same in all cases: two 12 mm thick carbon steel rebars C500. The number of bars (amount of steel) and steel in the lower reinforcement are varied. C500

Beam Section

C620

1200

LDX 1.4362

1000

400

600 600

MRd [kNm]

1.4311

800

400 Most feasible range for carbon steel

200 0 4

6

8

10

12

14

16

18

20

22

24

Number of bars T20

Fig. 24. Bending resistance vs. number of 20 mm bars.

Fig. 24 shows that below a certain amount of rebars it would be safe to design stainless steel reinforcement as carbon steel reinforcement with yield strength equal to the 0,2% proof stress of the stainless steel. In the present beam the upper limit would be 8 bars for LDX and 1.4362 (carbon steel C620), and 11 bars for 1.4311 (carbon steel C500). This is good news to the existing structures. With a small or moderate amount of reinforcement no risks related to the bending resistance exist even if the real stress-strain behaviour of the stainless steel has been replaced by a relationship typical of carbon steel. On the other hand, the same approach, when applied to heavily reinforced beams, seems to result in an overestimation of the bending resistance. This is not, however, the whole truth, because applying the safety factor 1,15 to the initial part of the stress-strain curve may be considered too conservative. Fig. 25 shows the stress-strain combinations for stainless steel LDX and carbon steel C500 at failure (= ultimate stress and strain). In other words, Fig. 25 illustrates, how much of the strength of the steel can be exploited when calculating the bending resistance. In all cases the failure mode has been compression failure of the concrete. At a given steel strain, the tensile force T in the reinforcement increases with the amount of the steel. The compressive force C in the concrete must be equal to T. It follows that at a given steel strain, the concrete strain has to increase with increasing amount of steel. Since the concrete, unlike steel, is a brittle material, there is a relatively low upper limit for the concrete strain. It follows that with increasing amount of steel the ultimate steel strain and steel stress decreases. Consequently, less use can be made of the high strength of the stainless steel. Despite this, when considering The use of the name of VTT Expert Services Ltd or the name Technical Research Centre of Finland (VTT) in any other form in advertising or publication in part of this report is only permissible with written authorisation from VTT Expert Services Ltd.


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the bending resistance only, LDX seems to be mechanically competitive when compared with carbon steel C500.

LDX - Carbon steel 800 16 bars

Stress [MPa]

700 600 500

14 bars

LDX

10 bars

20 bars

4 bars

6 bars

22 bars

400 16 bars 14 bars

300

Carbon

10 bars

6 bars

20 bars b 22 bars

200 100 0 0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

2,0

Strain [%]

Fig. 25. Stress and strain at ultimate load for LDX and C500 reinforcement. 6 COLUMN SECTION Two cases have been analysed according to Eurocode 2: one with reinforcement Ast = 1885 mm2 (3 + 3 T20), shown in Fig. 26, and the other with reinforcement Ast = 6283 mm2 (10 + 10 T20). 380 Concrete C30 380

60

60 A st /2

A st /2

Fig. 26. Column section with 3 + 3 T20 rebars. The interaction diagrams for the cross-sections are shown in Fig. 27. Only with very low normal force, i.e. in beam-like columns, has the stainless steel mechanical advantage over the carbon steel C500. On the other hand, as shown in Fig. 28, with typical combinations of normal force N and bending moment M, the performance of LDX and that of 1.4162 are close to the performance of carbon steel C500.



5

380

C620 C620 C500 C500 LDX LDX 1.4362 1.4362 1.4311 1.4311

380

4 NRd [MN]

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3 2 1 0 0

100

200

300 MRd [kNm]

400

500

600

Fig. 27. N-M interaction diagrams for different steels. The thick and thin lines represent the heavy (10 + 10 T20) and light (3+3 T20) reinforcement, respectively.

P 380 380

5

NRd [MN]

4 3

C500 C500 LDX LDX 1.4362 1.4362 1.4311 1.4311

Q 2

Typical use

1 0 O 0

100

200

300 MRd [kNm]

400

500

600

Fig. 28. Previous figure without steel C620. Most common load cases are in sector POQ.

7 BRIDGE DECK SECTIONS A cantilevered, simply supported, reinforced concrete bridge from Eastern Finland is chosen for comparison, see Fig. 29. The consideration is restricted to two sections: A-A in the mid-span and B-B at support. Instead of the whole cross-section, a longitudinal cut with width 600 mm is considered. The The use of the name of VTT Expert Services Ltd or the name Technical Research Centre of Finland (VTT) in any other form in advertising or publication in part of this report is only permissible with written authorisation from VTT Expert Services Ltd.


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original reinforcement in the bridge has been transformed into equivalent reinforcement in the cuts, see Figs 30 and 31.

B

A

B

A

Fig. 29. Cantilevered bridge. Elevation.

60

A st,2 = 982 mm2 (2 T25)

700

Concrete C40

56

A st,1 = 1538 mm2 600

(4,9 T20)

Fig. 30. Section A-A at mid-span. T25 is a 25 mm rebar of carbon steel C500, the material of the lower, 20 mm rebars T20 is varied.

60

A st,2 = 1817 mm2 (3,7 T25)

700

Concrete C40

56

A st,1 = 1256 mm2 600

(4 T20)

Fig. 31. Section B-B, support. T25 is a 20 mm rebar of carbon steel C500, the properties of the lower, 20 mm rebars T20 are varied.



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The calculation models for the bending resistance of sections A-A and B-B are summarized in Table 2. Stainless steel is only used in the lower reinforcement. The results are shown in Figs 32 and 33. Table 2. Materials and amount of steel in considered cases. Upper reinforcement Steel Amount [mm2]

Section

Span (A-A)

C500

Support (B-B)

C500

Lower reinforcement Steel Amount [mm2] C500 1.4162 1.4362 1538 1.4311 C620

982

C500 1.4162 1.4362 1.4311 C620

1817

1256

In the span the section behaves in the same manner as a beam section with a small amount of reinforcement. At mid-span the reinforcement ratio ρ =Ast/(bd) equals 0,0040. This corresponds to 2,8 bars in Fig. 24. As predicted by extrapolation of curves in Fig. 24, LDX and 1.4162 perform mechanically better than C620, and 1.4311 better than C500. As expected, at support the quality of the compression (lower) reinforcement has no effect on the resistance which is controlled by the unchanged upper reinforcement.

Bridge deck, span

Resistance [kNm]

700 600

C500

500

C620 LDX 1.4362

400 300

1.4311

200 100 0 0

200

400

600

800

0,2% proof strength [MPa]



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Fig. 32. Section A-A at mid-span. Effect of steel specification of lower (tension) reinforcement on bending resistance. Bridge deck, support

Resistance [kNm]

700 600 C500 C620 LDX

500 400

1.4362 1.4311

300 200 100 0 0

200

400

600

800

0,2% proof strength [MPa]

Fig. 33. Section B-B at support. Effect of steel specification of lower (compression) reinforcement on bending resistance. 8 DISCUSSION The stress-strain relationship (constitutive law) of the reinforcing steel affects the mechanical resistance of concrete structures. This effect has been studied in three structural sections, one of which belongs to a beam, one to a column and one to a nonprestressed bridge. As a byproduct, data about the applicability of the present Eurocode 2 design method to the hot-rolled stainless steel reinforcement has been obtained. The main tension reinforcement in the calculated cases has been made of stainless steel 1.4162 (LDX), stainless steel 1.4362, stainless steel 1.4311 or carbon steel C500 with 0,2% proof strength = 500 MPa. In addition, a hypothetical carbon steel C620 with 0,2% proof strength = 620 MPa has been studied to give an impression, what happens if a concrete structure with LDX reinforcement is calculated using the design method of Eurocode 2, developed for carbon steel, without modification. The stress-strain relationship of each stainless steel was measured from 10 test specimens, and the lowest measured values were used to find a RambergOsgood approximation for that steel. To bridge deck sections, RambergOsgood parameters different from those used for beams and columns were applied. This was necessary to improve the accuracy of the model at large strains which were present in the bridge sections but not in the beams and columns. It would be safe to replace the Ramberg-Osgood curve by a multilinear broken line as shown in Fig. 34. As can be seen, a trilinear curve is a good approximation close to the 0,2% proof stress, but it is clearly too conservative below and above this zone. The zone between 300 and 400 MPa is important The use of the name of VTT Expert Services Ltd or the name Technical Research Centre of Finland (VTT) in any other form in advertising or publication in part of this report is only permissible with written authorisation from VTT Expert Services Ltd.


20 (22)

because the service stresses tend to be there and the deflections with stainless steel reinforcement tend to be greater than those with carbon steel reinforcement. Therefore, the constitutive model should neither underestimate nor overstimate the real stiffness of the reinforcement. A broken line with three linear lines is far from ideal in this sense. 800 Ramberg-Osgood 700 Trilinear Stress [MPa]

600 500

Bilinear

400 300 200 100 0 0,0

0,5

1,0

1,5

2,0

Strain [% ]

Fig. 34. Ramberg-Osgood curve compared with bi- and trilinear curves. A multilinear curve comprising n straight lines (say n > 10) would be accurate enough. Instead of giving the coordinates of n points (2n parameters) , it would be easier to specify four parameters to fix the Ramberg-Osgood curve. When this is done, any number of corner coordinates of a broken line can be calculated and the stress at any strain value interpolated. This further supports the use of Ramberg-Osgood model as the primary design model. The results confirm that replacing the curved stress-strain relationship of a stainless steel with a bilinear curve of Eurocode 2 is no good idea even if the real 0,2% yield strength is replaced by a considerably lower value. If this is done, a lot of the potential of the stainless steel is lost, and the design of columns and heavily reinforced beams may still be on the unsafe side. From purely mechanical point of view, stainless steel grades LDX (1.4162) and 1.4362 have advantage over carbon steel C500 in beams and slabs with light or medium reinforcement because in such structures the higher strength of the stainless steel can be exploited. This advantage is pronounced e.g. in bridges in which the deflection control often necessitates deeper concrete sections than what would be necessary to resist the bending moment. In heavily reinforced beams and in all columns, LDX and 1.4362 seem to be less effective than carbon steel C500. This is actually not the case but a consequence of the partly overconservative application of the safety factor to the initial part of the stress-strain relationship. Fig. 35 illustrates the design models for LDX and C500 used in the calculations. There are good reasons why the initial part of the LDX model The use of the name of VTT Expert Services Ltd or the name Technical Research Centre of Finland (VTT) in any other form in advertising or publication in part of this report is only permissible with written authorisation from VTT Expert Services Ltd.


21 (22)

could be replaced by an alternative curve as shown Fig. 35. If this alternative design curve is adopted, the comparison between LDX and carbons steel reinforcement for beam and column sections would look like that shown in Figs 36 and 37. Hence LDX would be more effective than C500 almost in all cases of practical importance. This means that to give the same mechanical resistance, the amount of LDX rebars can be lower than that of carbon steel rebars.

Stainless steel 800 R-O model

Stress [MPa]

700 Alternative

600

Design model

500 400

C500, design model

σ

σ0,2 / 1,15

300 200

σ / 1,15

In calculations

100 0 0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

Strain [%]

Fig. 35. Alternative design model for stainless steel. σ0,2 is the 0,2% yield limit. The initial part of the model used in calculations is indicated by dashed line.

Beam Section C500

1200

C620 LDX

800

400

600 600

MRd [kNm]

1000

400 200

Most feasible range for carbon steel

0 4

6

8

10

12

14

16

18

20

22

24

Number of bars T20

Fig. 36. Bending resistance of beam sections calculated using alternative design curve shown in Fig. 35 for LDX and Eurocode 2 for carbon steel. The use of the name of VTT Expert Services Ltd or the name Technical Research Centre of Finland (VTT) in any other form in advertising or publication in part of this report is only permissible with written authorisation from VTT Expert Services Ltd.

RESEARC CH REPORT No. VTT-S-006464-11

P

380 380

5

22 (22)

NRd [MN]

4

C5 500

3

C6 620

Q 2

LD DX

Typica al use

1 0 O 0

100 0

200

300 MRd [kNm]

400

500

60 00

Fig. 37. 3 N-M innteraction diagrams for f columnn sections calculated using alternative designn curve sho own in Fig. 35 for LDX X and Euroccode 2 for carbon c steel. 9 CONCL LUSIONS

The reesults confirrm that the present Eu urocode 2 iss far from id deal if appllied as such to t the designn of concreete structurees reinforcedd with stain nless steel rebars. r If the stress-strainn relationsh hip of stainlless steel iss determined using thee 0,2% l tensilee strength and a elasticitty modulus 200 GPa ass for carbonn steel, yield limit, the am mount of thhe steel in most m cases will w either bbe overconservative orr nonconserrvative. Thiis drawback k can be overcome byy using mo odified Ram mbergOsgoo od expressioon for the stress-strain n relationshhip. Changees to the present p practicce are necesssary both in Eurocodee 2 and in thhe product standard. Espoo o, 15.9.20111

Lassee Mörönen Team m Manager

Matti Pajjari Senior Exxpert

Infoormation of test specim mens, steel grades 1.436 62 and 1.43111

Appendix

EN 1992-1-1. Eurocode E 2:: Design off concrete structures. s P Part 1-1: General G rulees and ruless for Buildin ngs. 2 EN 1993-1-4. Eurocode 3: Design n of steel structuress. Part 1-4 4:General rules. suppllementary rules for staiinless steelss. 3 Tensile tests of 20 2 mm hot rrolled ribbeed reinforcing bars maade from sta ainless steell. Test Reporrt No. VTT--S-01366-1 1. VTT Exp pert Servicees Ltd, 20111.

Referencees 1

Distributioon

Custom mer Archiv ve

Original O Original O

The use of the e name of VTT Expert Services s Ltd or the nam me Technical Re esearch Centre of Finland (VTT T) in any other form f in advertisiing or missible with wrritten authorisation from VTT Exxpert Services Ltd. L publication in part of this report is only perm

RESEARCH APPENDIX

REPORT

No.

VTT-S-06464-11

1 (2)

Information of test specimens, steel grade 1.4162 -

Date of casting Heat Length Diameter

January 1, 2010 E91404 100 cm 20 mm

Test specimens provided by Outokumpu Stainless Ltd, Sheffield

Number of bars 3 3 3 3 3 3 20

Coil 8 11 18 24 38 56 57

Mark on bar F or M or B F or M or B F or M or B F or M or B F or M or B F or M or B 1, 2, … , 20

Tested sample M M F B B F 1, 5, 10 , 15


RESEARC CH APPENDIX

REPORT

No.

VTT-S-0646 64-11

2 (2)

Informattion of tesst specim mens, stee el grades s 1.4362 and a 1.431 11 Test specim mens providded by

Tested speccimens. Cxxx = Coil xx, Byy = bar yy, F = fro ont, R = rear.

C13F C14R C26F C48R C62F C16B1 C16B4 C16B7 C16B11 C16B15 C1F C2R C4F C5R C6F C3B1 C3B4 C3B7 C3B11 C3B15

Material 1.4362 " " " " " " " " " 1.4311

Identificcation AV190 0766/01, E1001410, BF2 20012710, 20 2 mm " " " " " " " " " AV186 6273/01, E991141, BF20007805, 20 mm

1.4311

AV186 6273/01, E991141, BF20007805, 20 mm

The use of the e name of VTT Expert Services s Ltd or the nam me Technical Re esearch Centre of Finland (VTT T) in any other form f in advertisiing or missible with wrritten authorisation from VTT Exxpert Services Ltd. L publication in part of this report is only perm