Mechanical Engineering: Stress, Strain and Thermodynamic Cycles
What this section tests
The Mechanical Engineering section concentrates on the first-two-years syllabus: statics and trusses, friction, particle kinematics and kinetics, stress and strain in axially loaded members, torsion and bending basics, thermodynamic cycles (Carnot, Otto, Rankine), and simple machine elements such as gears and bearings.
Core rules
- Normal stress σ = F/A; engineering strain ε = ΔL/L; within the elastic limit σ = Eε.
- 1 MPa = 1 N/mm² - remembering this removes most unit conversions in stress problems.
- Area uses radius: A = πd²/4. Doubling the diameter quadruples area and quarters the stress.
- Poisson's ratio ν = −ε_lateral/ε_axial, typically 0.25–0.35 for metals.
- Thermal stress appears only when expansion is restrained: σ = EαΔT for full constraint.
- Carnot efficiency η = 1 − T_c/T_h in absolute temperatures; no real engine between the same reservoirs can beat it.
- Gear trains: ratio = N_driven/N_driver, with torque and speed trading inversely.
Worked example
A 20 kN tensile load acts on a rod of 200 mm² cross-section, E = 200 GPa, L = 1 m. σ = 20 000 N / 200 mm² = 100 N/mm² = 100 MPa. ε = σ/E = 100 × 10⁶ / 200 × 10⁹ = 5 × 10⁻⁴. ΔL = εL = 5 × 10⁻⁴ × 1000 mm = 0.5 mm. The load (20 kN) and the stress number (100) differ by exactly the area conversion - a common place to slip a factor of 1000.
Traps
Using diameter instead of radius in area; quoting efficiency above 100% after inverting a ratio; mixing °C and K in Carnot or ideal-gas relations; ignoring self-weight in beam reactions.