## Minimum longitudinal reinforcement in beams

Although: Clauses

' earthquakes impose deformations on structures and their members, not forces, and 5.2.3.7(3)(b),

• under deformation-controlled conditions, concrete members fail in flexure when their 5A.3.I.2(5), ultimate deformation capacity is reached, regardless of their force capacity, 5.5.3.1.3(5), an underreinforced beam may fail abruptly in flexure in a force-controlled manner, if its cracking moment exceeds its yield moment. The reason is the inherently brittle nature of concrete cracking and the large deformation energy released when this happens, especially if the beam cross-sectional area is large and that of the longitudinal reinforcement is small. So, enough longitudinal reinforcement should be provided to ensure that the yield moment of the beam exceeds its cracking moment. Because the seismic bending moments in the beam are very uncertain, this requirement is imposed on all sections of a beam and for both signs of bending, irrespective of the moment from the analysis for the seismic design situation.

The minimum reinforcement area,As min, should be sufficient to sustain, through its yield force, Asminfy, the full tensile force released when concrete cracks. For a linear stress distribution in the cross-section, this force is equal to 0.5fcpht, where b and h are the width and depth of the tension zone, respectively, before cracking. Beams commonly have a T section, and the neutral axis of the uncracked section is very close to the compression flange (in the slab) for positive moments, so that it can be conservatively assumed that ht ~ 0.9h ~ d. For negative moments the tension zone normally extends over the effective flange (in the slab), and its depth and width are quite uncertain; however, it can be assumed again that bht ~ bd, where b and d are the width and effective depth of the rectangular web of the T section. Then, the minimum ratio of reinforcement with respect to bd is

bd bdfyi /yk where the mean value,/ctm, is used for the tensile strength of concrete, and the characteristic or nominal value,/yk, for the yield stress of the longitudinal reinforcement. It is noted that the real danger for the section is fracture of the minimum reinforcement and that the margin between its tensile strength,/t, and/yk, which is of the order of 25%, provides some safety against overstrength of the concrete in tension (the 95% fractile of fct exceeds/ctm by 30%).

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