Engineering Mechanics and Strength of Materials
This domain tests statics, dynamics, and the mechanics of deformable bodies: equilibrium, shear force and bending moment, stress and strain, bending and shear in beams, torsion, deflection, and column buckling. Expect numerical problems with SI units and section properties.
Core rules
- Equilibrium requires ΣF = 0 and ΣM = 0; draw the free-body diagram before writing equations.
- Bending stress is σ = My/I, with section modulus Z = I/y_max; shear stress is τ = VQ/(Ib).
- Torsion in a circular shaft gives τ = Tr/J; angle of twist θ = TL/GJ.
- Euler buckling load is P_cr = π²EI/L_e², where L_e depends on end conditions.
Worked example
A simply supported beam of span 4 m carries a UDL of 5 kN/m. Reactions are 10 kN each. Maximum BM = wL²/8 = 5 × 16/8 = 10 kN·m. For a 100 mm × 200 mm rectangular section, I = 100 × 200³/12 = 66.67 × 10⁶ mm⁴ and y = 100 mm. Then σ = M y/I = (10 × 10⁶ N·mm × 100 mm)/(66.67 × 10⁶ mm⁴) = 15 N/mm². Check units: convert kN·m to N·mm before substituting.
Traps that cost marks
- Using total UDL instead of intensity, or mixing kN with N and m with mm.
- Taking maximum shear at mid-span rather than at supports.
- Using overall depth instead of extreme-fibre distance in σ = My/I.
- Forgetting that a UDL gives a parabolic BMD and a linear SFD.
Exam focus
Practise SFD/BMD for point loads, UDLs, and overhangs; compute centroid and moment of inertia for T- and I-sections; and check buckling with the correct effective length.