Stress and strain of uncracked sections - Concrete Structures: Stresses and Deformations - page 31

Figure 2.4 Examples of cross-sections treated in Section 2.5.

Figure 2.5 Analysis of time-dependent stress and strain in a composite section. All
variables are shown in their positive directions: (a) cross-section; (b) strain at
t 0 ; (c) change in strain during the period t − t 0 .

any fi bre if it were free, the creep coe cient φ ( t , t 0 ) and the aging coe cient

χ ( t , t 0 ).

The intrinsic relaxation ∆ σ pr that occurs during th e period ( t − t 0 ) is also

assumed to be known. A reduced relaxation value ∆ σ pr = χ r ( ∆ σ pr ) will be used

in the analysis. The reduction factor χ r must be assumed at the start of the

analysis and adjusted later if necessary as will be furthe r discussed in Section
3.2; here we assume that the reduced relaxation value

∆ σ pr is known.

2.5.1 Instantaneous stress and strain at age t 0
Before we can apply Equation (2.19), we must combine N and M with the
prestressing forces into an equivalent normal force at O and a moment: