Strength of Materials and Simple Machines
Strength of Materials and Simple Machines combines direct stress calculations with machine efficiency. Expect stress, strain, elastic modulus, and the vocabulary of levers, pulleys, screw jacks and geared systems.
Core rules
- Direct stress σ = P/A (N/mm² = MPa); strain ε = δ/L (no units); Young's modulus E = σ/ε; Poisson's ratio ν = lateral strain ÷ longitudinal strain (about 0.3 for steel).
- Shear stress τ = V/A; a rivet in single shear carries the full load on one plane.
- Simple machine: mechanical advantage MA = W/P; velocity ratio VR from geometry; efficiency η = MA/VR × 100 %, never above 100 % for a real machine.
- VR: lever = effort arm ÷ load arm; wheel and axle = R/r; screw jack = 2πr ÷ pitch; gear train = product of driven teeth ÷ product of driver teeth; pulley block with n rope falls = n.
- Law of machine: P = mW + C, where C represents friction and m reflects losses.
Worked example
A screw jack has a handle radius of 200 mm and a pitch of 5 mm. It lifts 15 kN with an effort of 150 N. VR = 2πr/pitch = (2 × 3.14 × 200) ÷ 5 = 251.2. MA = W/P = 15,000 ÷ 150 = 100. η = 100 ÷ 251.2 × 100 ≈ 39.8 %. The remaining 60 % of the effort goes into friction, which is why the jack self-locks.
Traps that cost marks
Using diameter instead of radius for a wheel, axle or handle; reporting efficiency above 100 %; forgetting to convert kN, or mm² to m² for stress in N/m²; treating MA as a fixed property when it changes with load; confusing pitch with lead on a multi-start thread.