Deformation of progressively cracking reinforced concrete beams

A consistent theory for the analysis of curvature and deflections of reinforced concrete beams in the cracking stage is presented. The theory assumes concrete to have a nonzero tensile carrying capacity, characterized by a uniaxial stress-strain diagram which characterizes progressive microcracking due to strain softening. The tensile stressstrain properties are the same as those which are obtained in direct tensile tests and those which have recently been used with success in modeling fracture test results for concrete. The theory agrees well with the simpler formula of Branson within the range for which his formula is intended. The value of the proposed theory is its much broader applicability. Aside from demonstrating a good agreement with available test data for short-time deformations up to the ultimate load, it is shown that the theory also correctly predicts the longtime creep deformations of cracked beams. To this end, the average creep coefficient for tensile response including peak stress and strain softening needs to be taken about three times larger than that for compression states. The theory also predicts the reduction of creep deflections achieved by the use of compression reinforcement, and a comparison of modeling this effect is made with an ACI formula. As a simplified version of the model, it is proposed to replace the tensile strain-softening behavior by the use of an equivalent tensile area of concrete at the level of tensile steel, behaving linearly. Assuming this area to be a constant, realistic predictions for shorttime as well as longtime deformations in the service stress range can still be obtained.

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