Special cases of uncracked sections and calculation of displacements - Concrete Structures: Stresses and Deformations - page 98

ρ ns . The negative sign indicates camber. It is clear that the camber will
be overestimated if non-prestressed steel is ignored. Also it can be seen
that the de

ection after creep, shrinkage and relaxation cannot be
accurately predicted by multiplying the instantaneous de

fl

fl ection by a

constant number, because such a number must vary with ρ ns and with

the creep, shrinkage and relaxation parameters.

E ects of varying creep and shrinkage parameters

It is sometimes argued that the e

ff

ort required for an accurate analysis
of the strain and the stress is not justi

ff

fi ed because accurate values of the

creep coe ε cs are not commonly available.

A more rational approach for important structures is to perform accur-
ate analyses using upper and lower bounds of the parameters

cient φ and the free shrinkage

φ and ε cs .

The analysis is repeated in the above example for the case ρ ns = 0.4

with 300 × 10 −6 ). The

results, shown in the last column of Table 3.2, indicate that reducing

φ = 1.5 and ε cs = − 150 × 10 −6 (instead of 3.0 and −

φ

and ε cs by a factor of 2 has some e ff ect, but the e ff ect is not as important

as the e ff ect of ignoring the non-prestressed steel.

3.10 General
The loss in tension in prestressed steel, P ps caused by creep, shrinkage and

relaxation is equal in absolute value to the loss in compression on the con-
crete,

∆

P c only in a cross-section without non-prestressed reinforcement. In
general the value of

∆

erence
depends on several variables one of which, of course, is the amount of non-
prestressed reinforcement (in Example 2.2,

∆ P c is greater in absolute value than ∆ P ps ; the di ff

=
451 kN; see Fig. 2.6). The presence of non-prestressed reinforcement may
substantially reduce the instantaneous strains and to a greater extent the
time-dependent strains. Thus, the non-prestressed steel must be taken into
consideration for accurate prediction of deformations of prestressed
structures.
Equation (3.4) gives the value of

∆ P ps = − 208 kN; and ∆ P c

P c when the prestressed steel and the
non-prestressed reinforcement are at one level, and the force

∆

∆ P c is situated at

this level. Once P c is known, it may be used to calculate the changes in

stresses and in strain variation over the section. The same procedure may also
be employed involving approximation, when the section has more than one
layer of reinforcement.
The methods discussed in Section 3.8 can be used to determine the dis-
placements when the axial strain

∆

ε O and the curvature ψ are known at all