Civil Engineering Reference
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forces calculated in this way may subsequently be employed to predict de
ec-
tions, but the presence of reinforcement should not be ignored in the calcula-
tion of axial strains and curvature from which the displacements can be
determined, as discussed in Chapters 2 and 3.
An alternative procedure of analysis using Equation (4.5) is discussed in
Section 4.5, in
wh
ich the presence of the reinforcement is accounted for in the
calculation of [
f
] and {
fl
∆
D
}.
Example 4.1 Shrinkage effect on a portal frame
Find the bending moment diagram in the concrete frame in Fig. 4.2(a)
due to shrinkage that gradually develops between a period
t
0
to
t
. The
frame has a constant cross-section; the moment of inertia of the
concrete area is
I
c
. Ignore deformations due to axial forces.
The analysis for this problem is the same as that for a drop of tem-
perature that produces a free strain equal to
ε
cs
(
t
,
t
0
). The only di
ff
erence
Figure 4.2
Analysis of internal forces caused by shrinkage in a plane frame: (a) frame
dimensions; (b) bending moment diagram.
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