Special cases of uncracked sections and calculation of displacements - Concrete Structures: Stresses and Deformations - page 71

Figure 3.1 Definition of symbols used in Equations (3.1) to (3.14).

reinforcement are assumed to be the same; thus, one symbol E st is used for the
modulus of elasticity of the total steel:

E st = E ns = E ps (3.2)

The prestress force P is applied at age t 0 at the same time as a bending
moment and an axial force. It is required to calculate the prestress loss and
calculate the changes in axial strain and curvature and in stresses in steel and
concrete due to creep, shrinkage and relaxation.
Creep, shrinkage and relaxation cause changes in the distribution of stress
in concrete and the two steel types, but any time the sum of the total changes
in the forces in the three materials must be zero; thus,

∆ P c =−∆ P ns − ∆ P ps (3.3)

where ∆ P c is the change in the resultant force on the concrete, ∆ P ps is the

change in the force in the prestress tendon, and ∆ P ns is the change in the force

in the non-prestressed reinforcement.
We recall, according to our sign convention (see Section 2.2), that a posi-
tive

∆ P means an increase in tension. Thus, generally ∆ P c is a positive value

while P ps is negative.

The loss in tension in the tendon is equal to the loss of the compressive
force on concrete (

∆

∆ P c = −∆ P ps ) only in the absence of non-prestressed

reinforcement.
The change of the resultant force on concrete due to creep, shrinkage and