Modular Ratio

The modular ratio m is the ratio of the modulus of elasticity of steel to that of concrete (Es/Ec). It lets a composite reinforced-concrete section be analysed as an equivalent all-concrete 'transformed section' by replacing steel area Ast with an equivalent concrete area m·Ast at the same level.

In the Working Stress Method, IS 456 Annex B defines m = 280 / (3·σcbc), where σcbc is the permissible concrete bending compressive stress — giving m ≈ 13.33 for M20, ≈ 10.98 for M25, ≈ 9.33 for M30 (the 280/3 form deliberately allows for the long-term effect of creep on the effective concrete modulus). Although modern design uses Limit State, the modular ratio is still essential for serviceability checks — cracked-section moment of inertia, crack width and deflection (IS 456 Annex C / F) — and for masonry + composite design.