Civil Engineering Reference
In-Depth Information
Figure 13.1
Idealization of a plane frame: (a) a typical plane frame; (b) idealized structure.
13.2(a). The axis
x
* coincides with the reference axis of the member and is
directed from end node O
1
to end node O
2
. The
y
*- and
z
*-axes are mutually
perpendicular to the
x
*-axis, with
y
* lying in the plane of the frame. The
purpose of the analysis is to determine the changes in nodal displacements in
global directions and, for each member, the internal forces at its ends along
the six local coordinates 1* to 6*. De
fi
ne a number of cross-sections, arbitrar-
ily spaced; the
rst section is at node O
1
and the last section is at node O
2
(Fig.
13.3(a) ). For each cross-section, the geometry (including the areas
A
ns
and/or
A
ps
of the reinforcement layers and their depths) and the parameters {
fi
σ
O
,
γ
}
in
,
de
ning the distribution of the initial stress (Fig. 13.3(b) ) are part of the
given data. External applied loads on an individual member are given at
the same sections in directions of the local axes. Also, external forces may be
given as nodal forces in the directions of the global axes. Figure 13.3(b) shows
the positive sign convention for
fi
σ
O
and
γ
and the normal force
N
and the
bending moment
M
.
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