Civil Engineering Reference
In-Depth Information
Figure 2.16
Transformed section of steel and concrete beam
The numerical values, chosen to be typical of a composite beam, are
given in Section A.2. Substitution in Equation 2.27 gives the relation
between
s
and
x
for a beam of depth 0.6 m and span 10 m as
10
4
s
=
1.05
x
−
0.0017 sinh(1.36
x
)
(2.28)
The maximum slip occurs at the ends of the span, where
x
=
±
5 m. From
Equation 2.28, it is
0.45 mm.
The results obtained in Sections 2.2.1 and 2.2.2 are also applicable to
this beam. From Equation 2.6, the maximum slip if there were no shear
connection would be
±
8.1 mm. Thus the shear connectors reduce end
slip substantially, but do not eliminate it. The variations of slip strain and
slip along the span for no interaction and partial interaction are shown in
Fig. 2.3.
The connector modulus
k
was taken as 150 kN/mm (Appendix A). The
maximum load per connector is
k
times the maximum slip, so the partial-
interaction theory gives this load as 67 kN, which is sufficiently far below
the ultimate strength of 100 kN per connector for the assumption of a
linear load-slip relationship to be reasonable. Longitudinal strains at mid-
span given by full-interaction and partial-interaction theories are shown
in Fig. 2.17. The increase in extreme-fibre strain due to slip, 28
±
10
−6
,
×
Figure 2.17
Longitudinal strains at mid-span
