Reinforced Concrete Beam Sections: Over-Reinforced, Balanced, and Under-Reinforced (as per IS 456:2000).
Reinforced Concrete Beam Sections: Over-Reinforced, Balanced, and Under-Reinforced (as per IS 456:2000). 1. Under-Reinforced Section Definition : The steel reinforcement yields before the concrete crushes, leading to ductile failure with visible cracks and deflection. Preferred in design for safety. Formulas : Neutral axis depth: x u = 0.87 f y A s t 0.36 f c k b (Clause 38.1, IS 456) x u = 0.36 f c k b 0.87 f y A s t (Clause 38.1, IS 456) Moment of resistance: M u = 0.87 f y A s t ( d − 0.42 x u ) M u = 0.87 f y A s t ( d − 0.42 x u ) Condition : x u < x u , lim x u < x u , l i m For Fe 415: x u , lim = 0.48 d x u , l i m = 0.48 d . Example : A rectangular beam ( b = 230 mm , d = 450 mm b = 230 mm , d = 450 mm ) uses M20 concrete ( f c k = 20 MPa f c k = 20 MPa ) and Fe415 steel ( f y = 415 MPa f y = 415 MPa ) with A s t = 900 mm 2 A s t = 900 mm 2 . Calculate...