Modulus of Elasticity (E)

Modulus of elasticity (E, also Young's modulus) is the ratio of stress to strain in the elastic (recoverable-deformation) range of a material — a measure of stiffness. For steel, E = 2 × 10⁵ MPa (= 200 GPa) and is universal across all grades (Fe415, Fe500, Fe550, Fe-410 etc.) — not affected by yield strength. For concrete, E is grade-dependent: Ec = 5000√fck MPa per IS 456:2000 Cl. 6.2.3.1. So for M20: Ec ≈ 22,361 MPa; M25: 25,000 MPa; M30: 27,386 MPa; M40: 31,623 MPa; M50: 35,355 MPa; M60: 38,730 MPa.

The modular ratio m (= Es / Ec) is the ratio of steel to concrete moduli, used in elastic-section analysis (WSM) and serviceability calculations (cracked moment of inertia, deflection). For Fe500 in M25: m = 200,000 / 25,000 = 8. For M30: m = 7.30. For M40: m = 6.32. The modular ratio decreases with concrete grade because higher concrete strength has higher modulus, narrowing the relative ratio. Modular ratio is critical for transformed-section analysis where concrete and steel are converted to a single equivalent material for uncracked or cracked analysis.

Applications: (a) Deflection of beams and slabs — short-term elastic deflection from force methods; (b) Axial shortening of columns under service load; (c) Pre-stress losses in PSC due to elastic shortening of concrete and creep; (d) Tall-building analysis — relative axial shortening of columns vs shear walls (which have similar Ec but different cross-sections); (e) Cracked-section moment of inertia (Ieff) for IS 456 Annex C deflection check. Higher E means stiffer structure with smaller deflections under load. Concrete's E increases with curing age (about 30% gain from 7 days to 28 days), so structures hardened only briefly may have lower stiffness than design; over-stripping forms can cause significant short-term deflection that becomes permanent.