Civil Engineering Reference
In-Depth Information
Figure 1.2
Shear stresses in an elastic I-section
stress over a width
t
w
, so the shear force per unit length is
vt
w
. This is
named the
shear flow
, and has the symbol
v
L
. From these results,
v
L,12
=
VA
f
(
h
-
t
f
)/(2
I
)
(1.17)
Consideration of the longitudinal equilibrium of the small element 1234
in Fig. 1.2 shows that if its area
t
w
t
f
is much less than
A
f
, the shear flows
on planes 1-4 and 2-3 are each approximately
v
L,12
/2, and the mean shear
stress on these planes is given approximately by
τ
14
t
f
=
τ
12
t
w
/2
This stress is needed for checking the resistance of the concrete slab to
longitudinal shear.
Repeated use of Equation 1.15 for various cross-sections shows that the
variation of longitudinal shear stress is parabolic in the web and linear in
the flanges, as shown in Fig. 1.2.
The second example is the elastic beam shown in section in Fig. 1.3.
This represents a composite beam in sagging bending, with the neutral
axis at depth
x
, a concrete slab of thickness
h
c
, and the interface between
the slab and the structural steel (which is assumed to have no top flange)
at level 6-5. The concrete has been transformed to steel, so the cross-
hatched area is the equivalent steel section. The concrete in area ABCD is
