Longitudinal Strain in Member
Embedded in Equations (4) and (5) is the strain term ex which represents the average longitudinal strain in the member at the mid-depth. Figure 5 shows that the crack spacing, sz, is calculated in the longitudinal direction of the member at mid-depth as well as it is appropriate to calculate behaviour based on coexisting strains and crack spacings. For reinforced concrete members subjected only to moment and shear, the equation to determine ex can be generated from a simple free body diagram such as that shown in Figure 4 and can be taken as:
In the use of this equation, the values of moment and shear are always taken as positive. The numerator of the equation estimates the force that must be resisted in the flexural reinforcement of a member including the shear-moment interaction mentioned above. The denominator converts this force to a strain in the tension reinforcement by dividing by the quantity and stiffness of flexural reinforcement. As a final simplification, the strain at mid-depth of the member, ex, is simply taken as one half of the value in the flexural tension reinforcement. For prestressed concrete or members subjected to axial loads, additional terms are added to the numerator of Equation (6) which are not shown here.