Rotating Angle Shear Theories - Unified Theory of Concrete Structures - page 150

Figure 5.1 Stress state in reinforced concrete

Adding Equations (5.1) and (5.2) gives

σ r + σ d = σ + σ t − ( ρ f + ρ t f t ) (5.4)

σ r , is small and can be considered a given value, the
compressive stress in the concrete element

Since the tensile stress of concrete,

σ d can be calculated from the externally applied

stresses ρ t f t , according to Equation (5.4).

The three equilibrium equations (5.1)-(5.3), derived from the transformation, are convenient
for computer analysis. These equations can be expressed in two ways that are convenient for
calculation by hand and/or calculator. The first type given in Section 5.1.2 is convenient for
analysis, and the second type given in Section 5.1.3 is convenient for design.

σ and σ t , as well as the steel stresses ρ f and

5.1.2 First Type of Equilibrium Equations
In the three equilibrium equations, (5.1)-(5.3), the tensile stress of concrete σ r is smaller by

an order of magnitude when compared with the other internal stresses σ d , ρ f and ρ t f t .

Therefore, our focus will be on the relationships among the stresses ( σ − ρ f ), ( σ t − ρ t f t ),

τ t and σ r as a small value of secondary importance. With this in mind,

we can relate the three stresses (

σ d , while considering

σ − ρ f ), ( σ t − ρ t f t ) and τ t , to the compressive stress in

the concrete struts σ d .