Civil Engineering Reference
In-Depth Information
∆
F
1
(
t
,
t
0
)
=
(70.24 × 10
−9
)
−1
(
−
8266 × 10
−6
)
=−
117 700 kip-in.
Step 5
The stress changes in the period
t
0
to
t
are (Equation (4.6) ):
0.177
0.296
−
3.059
0.537
0.427
−
1.539
{
∆
A
}
=
+
10
−6
(
−
117 700)
=
ksi.
−
7.785
1.324
−
27.659
88.428
−
4.530
−
9.084
Addition of these stress changes to the stress values at time
t
0
gives
the total stress distribution at time
t
at the section above the central
support (Fig. 4.13(c) ). It is interesting to compare the initial stress
(
0.485 ksi) introduced by prestressing at time
t
0
to the remaining com-
pression at time
t
in the present example and in Example 2.7 (Fig.
2.16(c) ). In the present example the remaining compression in concrete
at time
t
dropped to almost zero.
−
4.8 General
The stresses in all reinforced or prestressed concrete structures, statically
determinate or indeterminate, change with time due to the e
ects of creep,
shrinkage of concrete and relaxation of prestress steel. In a statically
determinate structure, the distribution of stresses over the area of concrete
and reinforcement in any section varies with time, but the resultant of stresses
in the two components combined remains unchanged. This is not the case
with statically indeterminate structures, where statically indeterminate reac-
tions are produced, causing gradual changes in the stress resultants in the
sections.
The force method, employed in this chapter to analyse the time-dependent
internal forces, is intended for computations by hand or using small desk
calculators. It is, of course, possible to prepare computer programs to do
parts of the computations or all the computations for a certain type of struc-
ture (for example, continuous beams). However, for a more general computer
program, it is more convenient to use the displacement method, which is the
subject of the following chapter.
ff
Notes
1 For more detailed presentation and examples, see reference mentioned in note 3
of Chapter 3.
2 See reference mentioned in note 3 of Chapter 3.
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