Civil Engineering Reference
In-Depth Information
Variation in bending resistance along a span
In design, the bending resistance of a simply-supported beam is checked
first at the section of maximum sagging moment, which is usually at mid-
span. For a steel beam of uniform section, the bending resistance else-
where within the span is then obviously sufficient; but this may not be so
for a composite beam. Its bending resistance depends on the number of
shear connectors between the nearer end support and the cross-section
considered. This is shown by curve ABC in Fig. 3.16, because the
x
-
coordinate is proportional to the number of connectors.
Suppose, for example, that a beam of span
L
is designed with partial
shear connection and
n
/
n
f
0.5 at mid-span. Curve ABC is re-drawn in
Fig. 3.17(a), with the bending resistance at mid-span,
M
Rd,max
, denoted by
B. Length BC of this curve is not now valid, because shear failure would
occur in the right-hand half span. If the connectors are uniformly spaced
along the span, as is usual in buildings, then the axis
n
/
n
f
is also an axis
x
/
L
, where
x
is the distance from the nearer support and
n
is the number of
connectors effective in transferring the compression to the concrete slab
over a length
x
from a free end. Only these connectors can contribute to
the bending resistance
M
Rd,x
at that section, denoted E in Fig. 3.17(b). In
other words, bending failure at section E would be caused (in the design
model) by longitudinal shear failure along length DE of the interface
between the steel flange and the concrete slab.
Which section would in fact fail first depends on the shape of the
bending-moment diagram for the loading. For uniformly-distributed load-
ing, the curve for
M
Ed,x
is parabolic, and curve OFB in Fig. 3.17(a) shows
that failure would occur at or near mid-span. The addition of significant
point loads (e.g., from small columns) at the quarter-span points changes
=
Figure 3.17
Variation of bending resistance along a span
