Special cases of uncracked sections and calculation of displacements - Concrete Structures: Stresses and Deformations - page 80

Figure 3.3 Definition of symbols in Equations (3.15) to (3.23) for analysis of effects of
creep and shrinkage in a reinforced concrete uncracked section.

t 0 ; are the ratios of the area and moment of inertia of the concrete

section to the area and moment of inertia of the age-adjusted transformed
section (see Section 1.11.1); thus,

η and κ

η = A c / A (3.17)

κ = I c / I (3.18)

A c and A are areas of t he concrete section and of the age-adjusted trans-
formed section, I c and I are moments of inertia of the concrete area and of
the age-adjusted transformed section about an axis through O the centroid of
the age-adjusted transformed section.
The values

ect of the
reinforcement in reducing the absolute value of the change in axial strain and
in curvature due to creep and shrinkage or applied forces. For this reason,

η and κ , smaller than unity, represent the e ff

η

and κ will be referred to as axial strain and curvature reduction coe cients.

r c = I c / A c is the radius of gyration of the concrete area. y c is the y -

coordinate of the centroid c of the concrete area. y is measured in the down-
ward direction from the reference point O; thus in Fig. 3.3, y c is a negative
value.
The change in stress in concrete at any

fi bre during the period t 0 to t (see

Equations (2.45) and (2.46) ) is

∆ σ c = E c ( t , t 0 ){ − [ ε O ( t 0 ) + ψ ( t 0 ) y ] φ ( t , t 0 ) − ε cs ( t , t 0 ) + ∆ ε O + ∆ ψ y} (3.19)

where E c is the age-adjusted modulus of elasticity of concrete (see Equation
(1.31) ).
The change in steel stress may be calculated by Equation (2.47).