Design for serviceability of prestressed concrete - Concrete Structures: Stresses and Deformations - page 417

non-prestressed reinforcement ratio required for control of residual crack
opening. Again, homogenous uncracked sections are assumed in calculating
∆ σ σ perm .

The magnitude of the transient stress

and

erent from structure to
structure, depending upon the type of live load and the climate. As example,
consider a bridge continuous over three spans: 0.7 l , l and 0.7 l and having a
box or open cross-section shown in Fig. 12.2(a) or (b). A temperature rise
varying over the depth as shown in Fig. 12.4, produces at the section at the
middle of the interior span the stress distributions 2 shown in Fig. 12.5. Here
the span is varied between l

∆ σ is di ff

= 30 and 90 m, maintaining the span to thickness

l

ratio ⁄ 20. It can be seen that in this case, the maximum tensile stress due

to temperature rise is of the order 2 MPa (0.3 ksi) and occurs near the bottom
fi

=

h

bre. The temperature distribution in Fig. 12.4 may be representative of the
condition in the afternoon of a summer day in moderate climate. A distribu-
tion of the same shape, but with half the temperature values and the sign
reversed (representing drop of temperature) may appear in the night or in the
early morning in winter. This drop in temperature produces at the section
over the interior supports the stress distributions shown in Fig. 12.5, with the
stress values multiplied by

0.5. Here the maximum tensile stress is again
close to 2 MPa (0.3 ksi), occurring at the top

−

bre. It is to be noted that
because of the roller supports, the constant part of the temperature rise
shown in Fig. 12.4 produces no stress. In calculation of the stresses presented
in Fig. 12.5, the coe

fi

cient of thermal expansion is taken equal to 10 × 10 −6
per degree Celsuis (5.6 × 10 −6 per degree Fahrenheit) and the modulus of
elasticity is considered equal to 30 GPa (4400 ksi). The stresses presented are
the sum of self-equilibrating stresses and stresses due to statically
indeterminate moment. (See Example 10.1.)
In the same bridges the maximum stress ∆ σ trac due to exceptionally heavy

load 3 (convoy weighing 4000 kN (900 kip) ) is between 1.8 and 4.7 MPa (0.26

Figure 12.4 Distribution of temperature rise over the height of a bridge cross-section used
in the analyses whose results are shown in Fig. 12.5.