Civil Engineering Reference
In-Depth Information
1
12
(12)(20)
3
8000 in.
4
SOLUTION
I
g
e
6
(12)(20)
144
Bm
weight
(150)
250 lb/ft
Deflection Immediately after Cables Are Cut
(1.2
175,000)(6)(12
30)
2
(8)(4
Pe
2
8
EI
due to cable
0.638
a
10
6
)(8000)
250
12
30)
4
(384)(4
10
6
)(8000)
0.142
b
(5)
(12
4
384
EI
5
w
due to beam weight
Total deflection
0.496
a
Additional Deflection Comments
Long-term deflections can be computed as previously described in Chapter 6. From the
preceding example it can be seen that, not counting external loads, the beam is initially
cambered upward by 0.496 in.; as time goes by, this camber increases due to creep in the
concrete. Such a camber is often advantageous in offsetting deflections caused by the su-
perimposed loads. In some members, however, the camber can be quite large, particularly
for long spans and where lightweight aggregates are used. If this camber is too large, the
results can be quite detrimental to the structure (warping of floors, damage to roofing,
cracking and warping of partitions, and so on).
To illustrate one problem that can occur, it is assumed that the roof of a school is being
constructed by placing 50-ft double T's made with a lightweight aggregate side by side over
a classroom. The resulting cambers may be rather large, and, worse, they may not be equal in
the different sections. It then becomes necessary to force the different sections to the same
deflection and tie them together in some fashion so that a smooth surface is provided for roof-
ing. Once the surface is even, the members may be connected by welding together metal in-
serts, such as angles that were cast in the edges of the different sections for this purpose.
Both reinforced concrete members and prestressed members with overhanging or
cantilevered ends will often have rather large deflections. The total deflections at the free
end of these members are due to the sum of the normal deflections plus the effect of sup-
port rotations. This latter effect may frequently be the larger of the two, and, as a result,
the sum of the two deflections may be so large as to affect the appearance of the structure
detrimentally. For this reason, many designers try to avoid cantilevered members in pre-
stressed construction.
19.10
SHEAR IN PRESTRESSED SECTIONS
Web reinforcement for prestressed sections is handled in a manner similar to that used for
a conventional reinforced concrete beam. In the expressions that follow,
b
w
is the web
width or the diameter of a circular section, and
d
is the distance from the extreme fiber in
