The existing method for flexural design of Reinforced Concrete (RC) members was developed from extensive experimental tests and is largely semi-empirical. This paper reports a new approach that was developed completely from mathematical derivation. Theorems governing the flexural strength as well as ultimate curvature of RC flexural members are derived. A critical status of potential instability of concrete compressive resistance was mathematically identified and defined as the onset point of ultimate curvature. Mathematical solutions of concrete strain at extreme compression fibre at onset of flexural strength and ultimate curvature were obtained for all types of RC flexural members, which can be conveniently applied in practice for accurate calculation of flexural strength as well as the corresponding deformation. In the meantime, concrete damage condition at the onset of flexural strength and ultimate curvature can also be conveniently identified.
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