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Doubly reinforced rectangular concrete beams
This graduate paper deals with the subject of doubly reinforced rectangular concrete beams in bending. Their principle applications for today's engineers are listed in the early pages of the paper. Both the Working Stress theory and the Ultimate Strength theory for the design and analysis of doubly reinforced beams are thoroughly presented. The assumptions that these two theories are based upon are listed and discussed one by one. The formulas used in the design and analysis of these beams are developed and all the applicable ACI Codes for Reinforced Concrete are mentioned and explained. Although the inaccuracies of the Working Stress method are becoming more apparent with each additional piece of test data, it was included for historical interest since ultimate strength design is now being used almost exclusively. Due to the use of highly stressed steels and the designing of doubly reinforced beams by the ultimate strength method, the control of deflections becomes an absolute necessity. The prediction of instantaneous deflection is presented in this report as well as longtime deflection caused by shrinkage and by creep. Finally, the inelastic behavior of simply supported doubly reinforced concrete beams under cyclically repeated and reversed loads is also presented. Their response is predicted on the basis of technical beam theory and stress-strain relations of steel and concrete under cyclic loading. This theory is then compared to a series of tests conducted at the University of Colorado on doubly reinforced concrete beams subjected to variable repeated and reversed loadings.