711 Moment Curvature Relationship of Reinforced Concrete Members

Member curvature f can be defined as rotation per unit length. It is related to the applied moment M and the section stiffness by the relationship EI = M/f. A typical moment-curvature diagram of a reinforced concrete beam is shown in Figure 7.3. The reduction in slope of the curve (EI) is the result of concrete cracking and steel yielding. The moment-curvature relationship is a basic parameter of deformation. This information is needed for input if a nonlinear analysis is carried out. For an unconfined reinforced concrete beam section, the point of first cracking is usually

FIGURE 7.3 Typical moment-curvature diagram of a reinforced concrete beam.

neglected for input; the curvature points of first yield fy and ultimate fu are calculated from the following formulas:

At ultimate

The concrete strain at ultimate ec is usually assumed to be a value between 0.003 and 0.004 for unconfined concrete. Software is available to obtain more refined moment-curvature relationships and to include other variables. If the concrete is considered confined, then an enhanced concrete stress-strain relationship may be adopted. For column members, the strain compatibility analysis must consider the axial load.

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