Simply-supported composite slabs and beams - Composite Structures of Steel and Concrete - page 52

M pr = 1.25 M pa [1 − ( N c / N pa )] ≤ M pa (3.17)

M Rd = N c z + M pr (3.18)

3.3.2 Resistance of composite slabs to longitudinal shear

For profiled sheeting that relies on frictional interlock to transmit longit-
udinal shear, there is no satisfactory conceptual model. This led to the
development of the shear-bond test, described in Section 2.8.1, and the
empirical ' m - k ' method of design, where the shear resistance is given
by an equation based on Equation 2.33, in the British code [19], or on
Equation 2.32, in EN 1994-1-1. With the safety factor added, the Eurocode
equation is

V ,Rd = bd p [ mA p /( bL s ) + k ]/ γ Vs (3.19)

where m and k are constants with dimensions of stress, determined from
shear-bond tests, and V ,Rd is the design vertical shear resistance for a
width of slab b . This must exceed the vertical shear at an end support at
which longitudinal shear failure could occur in a shear span of length L s ,
shown by line 2-2 in Fig. 2.19.
For uniformly-distributed load on a span L , the length L s is taken as
L /4. The principle that is used when calculating L s for other loadings is
now illustrated by an example.

Calculation of L s
The composite slab shown in Fig. 3.4(a) has a distributed load w per unit
length and a centre point load wL , so the shear force diagram is as shown

Figure 3.4 Calculation of L s for composite slab