Engineering Mechanics (Statics, Dynamics, Strength of Materials)
Engineering mechanics on the Nezam paper mixes three habits of thought: free-body equilibrium, kinematics and kinetics of moving bodies, and stress–strain reasoning inside members. The exam rarely asks for a full mechanism analysis; it asks whether you can set up the diagram correctly and carry one clean calculation to the end.
Statics
- Draw the free-body diagram first: pin = 2 reaction unknowns, roller = 1, fixed support = 3.
- ΣF = 0 and ΣM = 0; take moments about the point that eliminates the most unknowns.
- Trusses: method of joints for member forces, method of sections for a single member; zero-force members occur at unsupported L-joints.
Dynamics
- Choose fixed versus rotating frames, then use v = ωr, a_t = αr, a_n = ω²r.
- Work–energy (T₁ + V₁ + U₁₋₂ = T₂ + V₂) beats force analysis when only speeds are requested.
Strength of materials
- Axial: σ = P/A and δ = PL/AE. Bending: σ = Mc/I. Shear in a rectangle: τ_max = 3V/2A.
Worked example
A cantilever 1 m long, 20 mm × 40 mm rectangular section, loaded by P = 500 N at the free end, E = 200 GPa. I = bh³/12 = 20 × 40³/12 = 106,667 mm⁴ = 1.0667×10⁻⁷ m⁴. δ = PL³/(3EI) = 500 × 1/(3 × 200×10⁹ × 1.0667×10⁻⁷) = 500/64,000 = 7.81×10⁻³ m ≈ 7.8 mm. σ_max = Mc/I with M = 500 N·m and c = 0.020 m: σ = 10/1.0667×10⁻⁷ = 93.8 MPa. Check it against the allowable before accepting the section.
Traps
- Using the full depth instead of half-depth for c.
- Forgetting that I scales with h³, so doubling depth cuts deflection eightfold.
- Ignoring self-weight in long members where it is comparable to the applied load.