Civil Engineering Reference
In-Depth Information
Figure 13.5
Analysis of fixed-end forces and numerical integration: (a) typical nonprismatic
member; (b) released structure; (c) temperature rise that varies nonlinearly
over the height of a typical cross-section; (d) deflected shape.
here the
xed-end forces {
A
r
} at the six coordinates shown in Fig. 13.2(a)
caused by the temperature rise.
Apply the force method (Section 4.2), using as a released structure a canti-
lever
fi
xed at the right-hand end O
2
(Fig. 13.5(b) ). Equations (13.19) to
(13.21), and Equation (13.22) (with
Q
1
to
Q
3
set equal to zero), can be used to
give the required
fi
fi
xed-end forces; the values of
ε
O
and
ψ
at any section, to be
substituted in Equation (13.21), can be determined by:
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