Civil Engineering Reference
In-Depth Information
most constant throughout the member. The calculations for
M
u
for such members are less
accurate than for bonded members. Unless some ordinary reinforcing bars are added to
these members, large cracks may form which are not attractive and which can lead to
some corrosion of the prestress strands.
If a prestressed beam is satisfactorily designed with service loads, then checked by
strength methods and found to have insufficient strength to resist the factored loads (
M
u
1.2
M
D
1.6
M
L
), nonprestressed reinforcement may be added to increase the factor of
safety. The increase in
T
due to these bars is assumed to equal
A
s
f
y
(Code 18.7.3). The
Code (18.8.2) further states that the total amount of prestressed and nonprestressed rein-
forcement shall be sufficient to develop an ultimate moment equal to at least 1.2 times the
cracking moment of the section. This cracking moment is calculated with the modulus of
rupture of the concrete, except for flexural members with a shear and flexural strength
equal to at least twice that required to support the factored loads and for two-way, un-
bonded posttensioned slabs. This additional steel also will serve to reduce cracks. (The
1.2 requirement may be waived for two-way unbonded posttensioned slabs and for flex-
ural members with shear and flexural strength at least equal to twice that required by ACI
Section 9.2.)
19.9
DEFLECTIONS
The deflections of prestressed concrete beams must be calculated very carefully. Some
members that are completely satisfactory in all other respects are not satisfactory for prac-
tical use because of the magnitudes of their deflections.
In previous chapters, one method used for limiting deflections was to specify mini-
mum depths for various types of members (as in Table 4.1 of this textbook). These mini-
mum depths, however, are applicable only to nonprestressed sections. The actual deflection
calculations are made as they are for members made of other materials, such as structural
steel, reinforced concrete, and so on. However, the same problem exists for reinforced con-
crete members, and that is the difficulty of determining the modulus of elasticity to be used
in the calculations. The modulus varies with age, with different stress levels, and with other
factors. Usually the gross moments of inertia are used for immediate deflection calcula-
tions for members whose calculat
ed
extreme fiber stresses at service loads in the precom-
pressed tensile zone are
c
(ACI 18.3.3). Transformed
I
values may be used for
other situations as described in ACI Sections 18.3.3, 18.3.4, and 18.3.5.
The deflection due to the force in a set of straight tendons is considered first in this
section, with reference being made to Figure 19.11(a). The prestress forces cause a nega-
tive moment equal to
Pe
and thus an upward deflection or camber of the beam. This
L
de-
flection can be calculated by taking moments at the point desired when the conjugate
beam is loaded with the
M
/
EI
diagram. At the
L
the deflection equals
7.5
f
2
8
EI
a
Pe
2
EI
2
4
Pe
Should the cables not be straight, the deflection will be different due to the different
negative moment diagram produced by the cable force. If the cables are bent down or
curved, as shown in parts (b) and (c) of Figure 19.11, the conjugate beam can again be ap-
plied to compute the deflections. The resulting values are shown in the figure.
