Elasto-plastic analysis of flexural stiffness in r.c. structures

The flexural stiffness of reinforced concrete members is studied herein with the intention to give an accurate, simple, and practical formulae which can be used for design offices tocalculate deformations.It is well-known that flexural stiffness is the product of two other factors, namely; the Young’s modulus, and the moment of inertia. To determine the moment of inertia of uncracked reinforced concrete members is an easy task, but problems emerge if cracked members are considered.The research theoretically investigates the empirical formula of Branson for effective moment of inertia, which wasadopted by many codes and pecifications including the 1990’s edition of the Egyptian code. A computer program is proposed to calculate accurate values of flexural rigidity of reinforced concrete sections. The program takes into account concrete in tension, stress-strain relationship for concrete, and tension stiffening effect.Thirty-six models are used to compare the results of the computer program with those calculated using Branson’sformula. All the models are rectangular sections having the same cross section dimensions and steel yield stress. Thevarying parameters are concrete compressive strength, andsteel ratio in tension and compression.Some amendments to the formula are proposed to make it more accurate. Consequently a method to calculate thedeflection of beams is presented together with an elaborate example.The research also investigates the possibility of extending the applicability of Branson’s formula to include reinforced concrete framed structures which have axial forcesin addition to bending moments. The study is exclusive to two hinged portal frames. Published test data of sixteen prototype portal frames are used to check the results of using theformula in calculating deformations.