Advances in Steel Structures - part 41 docx

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 Full 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
Load Failure Load
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 199300 12.10 12.043 !.005 10.470 1.158 1000 99.000
Y8 210"105"1.6 210.0 199300 19.60 20.850 0.940 16.243 1.207 1000 130.250
Y9 240* 120* 1.6 210.0 199300 24.20 27.281 0.890 20.130 1.202 1000 149.000
YIO 270"135"1.6 210.0 199300 30.50 34.273 0.813 24.166 1.262 1000 167.750
YI 1 300"150"1.6 210.0 199300 33.90 41.704 0.793 28.305 1.198 1000 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 198700 11.25 11.068 1.010 10.942 1.028 500 64.625
7 120" 56"1.6 232.5 198700 11.68 15.129 0.772 14.537 0.803 500 74.000

8 135" 64"i.6 232.5 198700 13.46 19.825 0.679 18.332 0.734 500 83.375
P6 160" 80"1.6 !83.0 196000 18.10 24.488 0.739 21.841 0.829 500 99.000
P7 210"105"1.6 183.0 196000 24.00 42.388 0.566 20.855 1.151 500 130.250
P8 240* 120 * 1.6 183.0 196000 25.20 55.470 0.454 26.690 0.944 500 149.000
P9 270"135"1.6 183.0 196000 27.90 70.310 0.397 33.180 0.841 500 167.750
P! 0 300* 150* 1.6 183.0 196000 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.
385
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 "to
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 )}
ds =~/12Is/As
(1)
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
M ps = f~a ts d2/4
(2)
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
M'p:Mm + Fr(d-ds/4+dt/2-dr)
(4)
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
a, = (5)
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.
~=Arfry/(Asfy )
(6)
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
,~ '=
~ (7)
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.
m
(8)
where M- = the negative moment of a point of inflection; M § = the positive moment of a point
of inflection.
Vertical Shear of 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
V. = V c + V~ (9)
where Vs = the vertical shear strength of the steel member alone, which is given by
V s =dwtwfy/V~
(10)
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

o/a )
Vc = -j-~+ b f ~ + P,~ f r~ bc hc
(11)
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
V, = Vc + V s
(12)
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
1. GBJ10 89,
Reinforced Concrete Structure Design Code,
Construction Industry Publishing
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
5. Qing-li Wang.
Practical Study and Theoretical Analysis on Mechanical Performance and
Deformation Behavior of Continuous Composite Beams,
Ph.D. Dissertation, Northeastern

University, Shenyang, China, July 1998.