Civil Engineering Reference
In-Depth Information
No interaction
k
i
= 0
Partial interaction
k
i
= d
V
i
/d
u
s
Slip,
u
s
Complete interaction
k
i
= ∞
Slip strain, d
u
s
/d
x
FIGURE 7.20
Slip and slip strain distribution in a simply supported composite beam.
need not be considered in the flexural analysis. The strain distribution through a com-
posite steel and concrete beam is shown in
Figure 7.21
for no, partial, and complete
interaction.
Transformed section methods may be used to determine cross section stresses at
service load levels since complete interaction allows for a linear elastic analysis (elas-
tic
E
s
and
E
c
)
, with the same stress and strain profile (Gere and Timoshenko, 1984).
The modular ratio,
n
=
E
s
/E
c
, can be established and used as the transformation ratio
for steel and concrete elements. However, long-term dead load stresses do not remain
constant with time because of creep and shrinkage of the concrete deck. The dead
load stresses will increase in the steel elements. Long-term effects are considered by
a simplified approach to shrinkage and creep that uses a plastic modulus
n
cr
=
3
n
(Viest, Fountain and Singleton, 1958).
The elastic stress distribution will also depend on how load is transferred to the
composite steel concrete span (i.e., dependent on construction scheme). If the steel
κ
h
c
ε
si
=
ε
ci
ε
si
ε
ci
ε
si
ε
ci
κ
d
u
s
/d
x
κ
h
s
d
u
s
/d
x
d
u
s
/d
x
=
0
No interaction
k
i
=
0
Partial
interaction
k
i
=
d
V
i
/d
u
s
Complete
interaction
k
i
=
∞
FIGURE 7.21
Strain profile through composite beam at various connection stiffness (no,
partial or complete interaction) (
κ
is the curvature of the beam.
