Engineering Mechanics and Strength of Materials
Engineering Mechanics and Strength of Materials is the mechanics foundation of the WBPSC AE Civil paper: statics of rigid bodies, friction, centroid and moment of inertia, stress-strain behaviour, shear force and bending moment, flexure, shear, torsion, deflection and columns. Questions often combine a standard formula with a unit-sensitive numerical case.
Core rules
- Equilibrium: ΣF=0 and ΣM=0; draw the free-body diagram before writing equations.
- Hooke's law σ=Eε within the elastic limit; Poisson ratio ν relates lateral and axial strain.
- Flexure: σ/y=M/I=E/R; section modulus Z=I/y.
- Shear: τ=VQ/(Ib); for a rectangle, maximum τ=1.5V/(bd).
- Torsion: τ=Tr/J; angle of twist θ=TL/(GJ).
- Euler buckling: P_cr=π²EI/(kL)²; k depends on end conditions.
Worked example
A simply supported beam of span 4 m carries a UDL of 10 kN/m. The section is 150 mm × 300 mm. Maximum BM M=wL²/8=10×4²/8=20 kN m=20×10⁶ N mm. I=bd³/12=150×300³/12=337.5×10⁶ mm⁴. σ=My/I=20×10⁶×150/337.5×10⁶=8.89 N/mm². The section is safe only if the allowable stress exceeds this value.
Traps
- Mixing kN m and N mm.
- Using overall depth instead of effective depth in reinforced concrete.
- Forgetting self-weight.
- Taking y=d/2 incorrectly for a non-rectangular section.
- Applying Euler buckling at low slenderness.