Advances in Steel Structures - part 41 docx

FLEXURAL STRENGTH FOR NEGATIVE BENDING AND VERTICAL SHEAR STRENGTH OF COMPOSITE STEEL SLAG-CONCRETE BEAMS Qing-li Wang, Qing-liang Kang and Ping-zhou Cao College of Civil Engineering,

380 V Enjily et al

experiments involving a span of 500mm leading to results significantly below the colTesponding curve for the 1000mm span

TABLE 2 TEST RESULTS FOR THE ULTIMATE LOADS OF CHANNEL SECTIONS WITH THE WEB IN COMPRESSION

Experiment Section Size Yield Young's Experimental F u l l Experimental BS5950 Experimental Span D/t ratio Reference (D*B*t) Strength Modulus Failure Load Plastic Failure Load/ Failure Failure Load/ (mm)

(N/mm 2) (N/ram 2) (kN) Load (kN) Full Plastic Load BS5950

Y1 60* 24"1.6 210.0 199300 i.30 1.043 1.247 1.041 1.248 1000 36.500 Y2 75* 32"!.6 210.0 199300 2.20 1.877 !.172 1.830 1.202 I000 45.875 Y3 90* 40"1.6 210.0 199300 3.30 2.958 1.116 2.952 1.118 1000 55.250 Y4 105" 48"1.6 210.0 199300 4.80 4.284 i.120 4.257 1.127 1000 64.625 Y5 120" 56"1.6 210.0 199300 6.40 5.856 !.093 5.692 1.124 1000 74.000 Y6 135" 64"1.6 210.0 199300 8.20 7.674 !.068 7.209 1.138 1000 83.375 Y7 160" 80"1.6 210.0 1 9 9 3 0 0 12.10 12.043 !.005 10.470 1.158 1000 99.000 Y8 210"105"1.6 210.0 1 9 9 3 0 0 19.60 20.850 0.940 16.243 1.207 1 0 0 0 130.250 Y9 240* 120* 1.6 210.0 1 9 9 3 0 0 24.20 27.281 0.890 20.130 1.202 1 0 0 0 149.000 YIO 270"135"1.6 210.0 1 9 9 3 0 0 30.50 34.273 0.813 24.166 1.262 1 0 0 0 167.750

YI 1 300"150"1.6 210.0 1 9 9 3 0 0 33.90 41.704 0.793 28.305 1.198 1 0 0 0 186.500

1 30* 8"1.6 232.5 198700 0.26 0.285 0.913 0.285 0.913 500 17.750

2 45* 16"1.6 232.5 198700 i.39 1.172 1.181 1.169 1.189 500 27.125

3 60* 24"1.6 232.5 198700 3.05 2.693 1.132 2.689 1.134 500 36.500

4 75* 32"1.6 232.5 198700 5.48 4.850 1.130 4.842 1.132 500 45.875

5 90* 40"1.6 232.5 198700 8.41 7.642 1.101 7.620 1.104 500 55.250

6 105" 48"1.6 232.5 1 9 8 7 0 0 11.25 11.068 1.010 10.942 1.028 500 64.625

7 120" 56"1.6 232.5 1 9 8 7 0 0 11.68 15.129 0.772 14.537 0.803 500 74.000

8 135" 64"i.6 232.5 1 9 8 7 0 0 13.46 19.825 0.679 18.332 0.734 500 83.375 P6 160" 80"1.6 !83.0 1 9 6 0 0 0 18.10 24.488 0.739 21.841 0.829 500 99.000 P7 210"105"1.6 1 8 3 0 1 9 6 0 0 0 24.00 42.388 0.566 20.855 1.151 500 130.250 P8 240* 120 * 1.6 1 8 3 0 1 9 6 0 0 0 25.20 55.470 0.454 26.690 0.944 500 149.000 P9 270"135"1.6 1 8 3 0 1 9 6 0 0 0 27.90 70.310 0.397 33.180 0.841 500 167.750 P! 0 300* 150* 1.6 1 8 3 0 1 9 6 0 0 0 25.90 85.689 0.302 39.801 0.651 500 186.500

Theoretical Analysis

Discounting the results at 500mm spacing because of local crushing, sections with a web/thickness ratio less than 100 carried the full plastic moment Sections with larger ratios failed by compression in the web forming a 'pitched roof' yield pattern Using Murray's theory and the mechanisms shown in figure 8 a theoretical prediction of the behaviour was made Full details of the procedure are found in Enjily (1984) A typical comparison between theory and experiment is given in figure 9

Discussion

From the experimental results at 1000mm it can be seen that for web/thickness ratios less than 100 that

Experimental Investigation into Cold-Formed Channel Sections in Bending 381

Figure 7: Typical experimental curves, web in compression

Figure 8" Theoretical model for beams with web in compression

382 V Enjily et al

Figure 9: Comparison of theory against experiment for specimen Y8

the channels were able to carry their full plastic moment At 500mm span, a local crushing failure mode occurred before the full plastic moment was reached for web width/thickness ratios between 65 and 100 It is likely that if loading is such as to prevent local crushing that a design approach is to allow full plastic moments to be applied for ratios less than 100

When moments of resistance are calculated by use of BS5950 (see Table 2) it can be seen that again BS5950 is conservative However as the discrepancy does not exceed 26% the results from BS5950 are a good estimate of failure load

For plain channels with their flanges (i.e unstiffened elements) in compression the full plastic load can

be used for flange/thickness ratios below 16 BS5950 is excessively conservative for flange/thickness ratios above 10

For plain channels with their webs (i.e stiffened element) in compression full plastic moment can probably be achieved for web/thickness ratios of up to 100 At ratios in excess of this figure BS5950 gives a good conservative prediction of performance

REFERENCES

BS5950 Structural use of steelwork in building Part 5: Code of practice for design of cold formed sections BSI London 1987

Enjily V (1985) The inelastic post-buckling behaviour of cold-formed sections, Ph D Thesis, Oxford

Brookes University (formerly Oxford Polytechnic)

Enjily V., Beale R.G and Godley M.H.R (1998) Inelastic Behaviour of Cold-Formed Channel

Sections in Bending Proc 2 "a Int Co~f On Thin-walled Structures, Research & Development,

Singapore, 1998, 197-204

Little G H (1982) Complete collapse analysis of steel columns, hTt J Mech Sci 24, 279-98

Murray N W (1984) Introduction to the theory of thin-walled structures, Clarendon Press, Oxford Rhodes J and Harvey J.M (1976) Plain channel sections in compression and bending beyond the

ultimate load Int J Mech Sci 18, 511-519

Rhodes J (1982) The post-buckling behaviour of bending elements Proc Sixth Int Speciality Conf

On Cold-Formed Steel Structures, St Louis, 135-155

Rhodes J (1987) Behaviour of Thin-Walled Channel Sections in Bending Proc Dynamics of

Structures Congress '8 7, Orlando, 336-351

Composite Construction

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FLEXURAL STRENGTH FOR NEGATIVE BENDING AND VERTICAL SHEAR STRENGTH

OF COMPOSITE STEEL SLAG-CONCRETE

BEAMS

Qing-li Wang, Qing-liang Kang and Ping-zhou Cao College of Civil Engineering, Hohai University, Nanjing, 210098, China

ABSTRACT

This paper is part of a summary on a series of tests and studies of 6 simply supported and 12 continuous composite steel slag-concrete beams Using simple plastic theory and conversion of the steel member cross-section shape from " I " to rectangle, calculation formula of flexural strength of continuous composite beams for negative bending is obtained and this formula can provide accurate results no matter the cross-section neutral axis of the composite beam lies in the web or in the top flange of the steel member Main factors affecting the strength of composite beams for vertical shear such as concrete slab, nominal shear span-ratio and force ratio, are discussed in this paper It is necessary considering the effect of the concrete slab when calculating the strength of composite beams for vertical shear Bending moment-ratio should be considered for continuous composite beams

KEYWORDS

Composite steel slag-concrete beams, flexural strength for negative bending, vertical shear strength, conversion of cross-section, nominal shear span-ratio, force ratio

INTRODUCTION

This paper is part of a summary on a series of tests and studies of 6 simply supported and 12 continuous composite steel slag-concrete beams These tests indicate that at flexural failure around the interior prop of the continuous composite beams the concrete slab cracks and the stress in the main part of the steel member exceeds the yielding stress The simple plastic theory is suitable to calculate the flexural strength of continuous composite beams for negative bending Main factors affecting the strength of composite beams for vertical shear are approached It is necessary considering the effect of concrete slab when calculating the strength of composite beams for vertical shear, and the bending moment-ratio must be considered for continuous composite beams These are proved by the tests Comparison of the composite steel slag-concrete beam with the composite steel common-concrete beam will be presented in another paper

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386 Q.-L Wang et al

FLEXURAL STRENGTH FOR NEGATIVE BENDING

The following method of calculating the flexural strength for negative bending, M'p, avoids the complexities that arise in some other methods when the steel member cross-section is not geometrically symmetric about its centroidal axis as shown in Figure 1 (a) It can provide accurate results no matter the cross-section neutral axis of the composite beam lies in the web or in the top flange of the steel member The main step of this is a conversion of the steel member cross-section shape from " I " t o rectangle as shown in Figure 1 (a) which is the initial cross-section considered and (b) which is the conversed cross-section and during which following rules must be obeyed:

(1) The relative position of the steel member center axis to the composite cross-section keeps unchanged;

(2) The steel member cross-section area keeps unchanged and

(3) The steel member inertia moment about its center axis keeps unchanged

Figure 1: Cross-section conversion of the steel member and stress

distribution of the composite cross-section

New rectangle steel member cross-sectional dimensions are given by

ts = x/A.~ /O2Is )}

where d s and t s = the depth and breadth of the conversed rectangle cross-section respectively; I s = the steel member inertia moment about its centroidal axis; A s = the steel member cross-section area

At flexural failure, the whole of the concrete slab may be assumed to be cracked, and simple plastic theory is applicable, with all the steel at its design yield stress of frd for longitudinal reinforcement

and fsd for steel member respectively The stresses are as shown in Figure 1 (c), and are separated into two sets: those in Figure 1 (d) which correspond to the plastic moment of resistance of the rectangle steel member alone, M ps, which is given by

and those in Figure 1 (e) The longitudinal force, F r , in Figure 1 (e) is

Flexural Strength for Negative Bending and Vertical Shear Strength

Fr =~rfr~

387

(3)

where A r = the cross-section area of longitudinal reinforcement within the effective breath of the concrete slab

The flexural strength for negative bending is given by

in which d, d r = the depths of the center axis of the steel member and the longitudinal reinforcement below the top of the concrete slab respectively as shown in Figure 1 (a) and

Asf~a - Fr

2tsf sa

is the depth of tension zone of the rectangle steel member

VERTICAL SHEAR STRENGTH

It is very difficult estimating the exact strength of composite beams to vertical shear theoretically for it

is influenced by a lot of factors In reinforced concrete beams, its vertical shear strength is taken into account even concrete cracks, for composite beam the strength of concrete slab for vertical shear should not be neglected too If the cross-section area of concrete slab and force ratio are relative small and the steel member resists the main vertical shear, then it is feasible and convenient for calculation neglecting the effect of the concrete slab Whereas a composite beam designed appropriately, the part

of concrete slab should not be too small, the result would be too conservative if neglecting the effect of the concrete slab

Main Influence Factors

In this paper vertical shear strength is derived based on test results with theoretical analysis, considering the main influence factors and the calculation model of the reinforced concrete beams Tests by the author and others show:

(1) The vertical shear strength increases as the cross-section area and the axial compressive stress of the concrete slab increase This is because concrete is not homogeneous material, which leads to the unusual shear stress distribution on cracked section of the concrete slab and very rough interface of crack, and there are friction and occlusive mechanism in the crack which will provide some vertical shear strength;

(2) Force ratio, ~ , could embody the contribution of the concrete slab and especially the longitudinal reinforcement inside it to the whole vertical shear strength of the composite beams, which is usually used in the negative moment region of continuous composite beams

where fry = the yielding stress of the longitudinal reinforcement and fy = the yielding stress of the steel member The effect of the concrete slab enhances as force ratio increases mainly due to the effect of pin to concrete slab and restriction to crack of the longitudinal reinforcement;

388

(3) Nominal shear span-ratio, 2',

Q.-L Wang et al

M

Vh'

in which M , V = the bending moment and vertical shear on the composite cross-section respectively, h '= the whole depth of the composite beam; There is decrease trend of the vertical shear strength of the composite beams as 2' increases when 2' < 4;

(4) The vertical shear strength increases as the transverse reinforcement ratio and the tension yielding stress of the transverse reinforcement increase and

(5) Bending moment ratio, m, must be considered for continuous composite beams

where M- = the negative moment of a point of inflection; M § = the positive moment of a point

of inflection

Vertical Shear o f Strength

Although there are not effective compositive actions on the prop cross-section of simply supported composite beams and the interior prop cross-section of continuous composite beam, functions of the steel member could be added to that of the concrete slab The following formulas imitate that of the reinforced concrete beams

For simply supported composite beams subjected to concentrated loads at midspan the vertical shear strength, V,, is provided by the steel member and the concrete slab together

where Vs = the vertical shear strength of the steel member alone, which is given by

where d , , t, = the depth and breadth of the web of the steel member respectively; V c = the vertical

shear strength of the concrete slab alone, which is given by

wherebc, h c = the effective breadth and depth of the concrete slab; fc = the axial compressive

strength of concrete; p,, = the transverse reinforcement ratio; f~v = the yielding stress of the transverse reinforcement; a and b = the coefficients decided by tests, a = 0.2 and b = 1.5

For continuous composite beams subjected to concentrated loads at midspan moment-ratio must be considered and then

Flexural Strength for Negative Bending and Vertical Shear Strength 389

l + m Figure 2 shows the comparisons of V, with V~st and V~est with V s The averages of Vu/Vtest and V,~s,/Vs are 0.935 and 1.401 for simply supported beams (1 6), 0.978 and 1.3 for continuous beams

(7 12) respectively

Figure 2: Comparisons of V u with V, est and V~est with V s

CONCLUSIONS

(1) Simple plastic theory is suitable for calculating the flexural strength for negative bending of continuous composite steel slag-concrete beams with compact steel member cross-section Calculation formula presented in this paper can provide accurate solutions even the neutral axis of the composite cross-section lies in the top flange of the steel member

(2) Vertical shear strength of composite beam increases as the cross-section area and the axial compressive stress of the concrete slab and force ratio increase There is decrease trend of the vertical shear strength of composite beams as nominal shear span-ratio increases when 2'< 4 Bending moment ratio must be considered for continuous composite beams

(3) Results of calculation with formula about vertical shear strength of composite beams have good accordance with that of test, concrete slab can provides 28.6%V u and 23.1%Vu for simply supported and continuous beams respectively

REFERENCES

Company, Beijing, China, 1989

2 GBJ17 89, Steel Structure Design Code, Construction Industry Publishing Company, Beijing,

China, 1990

3 JBJ12m82, Light Reinforced Concrete Structure Design Rule, Construction Industry Publishing

Company, Beijing, China, 1982

4 Johnson, R P (1984) Composite Structures of Steel and Concrete, Volume 1: Beams, Columns, Frames and Applications in Building, Granada, London, England

Deformation Behavior of Continuous Composite Beams, Ph.D Dissertation, Northeastern

University, Shenyang, China, July 1998