Structural Engineering: Mechanics of Solids, Structural Analysis, Concrete and Steel Design
Structural engineering carries the largest question share. Mechanics of solids tests stress–strain behaviour and beam theory; structural analysis tests determinate and indeterminate systems; design tests IS 456 for concrete and IS 800 for steel. Numerical answers dominate, so limit-state constants must be at your fingertips.
Core rules
- Bending: σ/y = M/I = E/R; maximum shear stress in a rectangular section is 1.5 V/bd, at the neutral axis.
- Deflection of a simply supported beam under a central point load is δ = WL³/48EI.
- For a propped cantilever with a central point load, the prop reaction is 5W/16.
- Singly reinforced limit state: Mu = 0.87 fy Ast d (1 − fy Ast/(fck b d)); the limiting moment coefficient is 0.138 for Fe 415 and 0.148 for Fe 250.
- IS 800 uses partial safety factors of 1.10 on yield stress and 1.25 on ultimate stress; design compressive stress depends on buckling class a to d.
- IS 456 load factors: 1.5 for dead plus live, 1.2 for dead plus wind or earthquake.
Worked example
A 230 mm × 450 mm beam, M25, Fe 415, clear cover 30 mm, 8 mm stirrups, 20 mm main bars. Effective depth d = 450 − 30 − 8 − 10 = 402 mm, take 400 mm. Mu,lim = 0.138 fck b d² = 0.138 × 25 × 230 × 400² = 127 × 10⁶ N·mm = 127 kN·m. An applied factored moment above this requires a doubly reinforced or flanged section.
Traps
Using overall depth instead of effective depth; applying 0.148 to an Fe 415 section; omitting minimum eccentricity in columns (0.05 times the least lateral dimension, capped at 20 mm); and mixing working-stress and limit-state factors in one calculation.