Shear connection - Composite Structures of Steel and Concrete - page 41

Figure 2.20 Bending resistance of a composite slab

Figure 2.21 Definition of m and k

M u = VL s (2.29)

where V is the maximum vertical shear, assumed to be much greater than
the self-weight of the slab. A test specimen, of breadth b , should include
a number of complete wavelengths of sheeting, of total cross-sectional
area A p . Flexural failure is modelled by simple plastic theory, with all the
steel at its yield stress, f yp (Fig. 2.20), and sufficient concrete at 0.85 f c ,
where f c is the cylinder strength, for longitudinal equilibrium. The lever
arm is a little less than d p , but approximately,

M u ∝ A p f yp d p (2.30)

From Equation 2.29

V
bd

M
bd L

Af
bL

pyp

u

= ∝ (2.31)

p ps s

The strength f yp is not varied during a series of tests, and has no influence
on longitudinal shear failure. It is therefore omitted from the axes on
Fig. 2.21, and Equation 2.31 shows that flexural failure should plot as a
straight line through the origin, (1) in Fig. 2.21.
At low L s / d p , vertical shear failure occurs. The mean vertical shear
stress on the concrete is roughly equal to V / bd p . It is assumed in current