Civil Engineering Reference
In-Depth Information
Any further increase in load will not increase the moment at the hinge (the increased
moment being carried in the adjacent spans). However, the prestress moments, both
primary and parasitic, are not affected by the formation of this elasto-plastic hinge. Of
course, if a complete hinge were to be introduced at a support, all moments including
M
P
at the hinge would become zero, and the
M
P
at the other supports in the beam
would be redefi ned.
6.4 The effect of parasitic moments on the beam reactions
The parasitic moments for a typical four-span beam are shown in Figure 6.2 and may
be labelled
M
p1
,
M
p2
and
M
p3
at the three internal supports, with the parasitic moments
being zero at the end supports. The variation of parasitic moment along the spans
creates shear forces in the beam, and reactions at the end of each span. In general, the
reactions and the shear forces are
(
M
p right
-
M
p left
)/
L
, where
L
= span length.
For instance, in the side span the reaction at the end support is (
M
p
1
- 0)/
L
1
, which
is an upwards reaction if
M
p
is positive. There is a corresponding downward reaction
on pier 1. The reactions at each end of span 2 are
±
(
M
p
2
-
M
p
1
)/
L
2
.
These reactions must all sum to zero, as no external vertical loads have been applied
to the beam.
The prestress primary moments,
Pe
, are internal forces, and although they apply
shear forces to the beams, they do not create reactions; the shear forces at the beam
ends are matched by equal and opposite vertical components of the prestress anchorage
force (
5.19
).
±
Figure 6.2
Reactions due to prestress parasitic moments
