Mechanical Systems
This domain tests statics, dynamics, stress analysis, torsion, beam deflection, friction, vibration and basic thermal and fluid effects. Questions usually combine a free-body diagram with a formula and demand correct SI units and boundary conditions.
Core rules
- Axial stress σ=F/A; normal strain ε=ΔL/L; elastic modulus E=σ/ε. Factor of safety SF=yield strength/working stress.
- A circular shaft under torque T has maximum shear τ=Tr/J; for a solid shaft J=πd⁴/32.
- Cantilever with end load P: δ=PL³/(3EI); simply supported centre load: δ=PL³/(48EI). EI must use consistent units.
- Natural frequency of a single mass-spring system f=(1/2π)√(k/m) in Hz; ω=√(k/m) in rad/s.
- Coulomb friction: impending slip uses F=μN; static μ is usually larger than kinetic μ.
Worked example
A 10 mm diameter steel rod carries a 5 kN tensile load. A=π(0.010)²/4=7.85×10⁻⁵ m². σ=5000/7.85×10⁻⁵=63.7 MPa. If yield strength is 250 MPa, SF=250/63.7=3.9. With E=200 GPa, strain ε=σ/E=3.18×10⁻⁴, so a 1 m rod stretches 0.318 mm.
Traps
- Using diameter instead of radius in area, or leaving mm² in a formula requiring m².
- Applying a cantilever formula to a simply supported beam.
- Mixing static and kinetic friction during motion.
- Forgetting that stress concentrations raise local stress without changing nominal stress.
- Confusing frequency in Hz with angular frequency in rad/s.