Mechanics of Materials and Machine Design
Mechanics of Materials and Machine Design tests whether you can size and check load-carrying components: shafts, beams, columns, bolted and welded joints, bearings, and fatigue-prone parts. Expect combined loading, stress concentration, and design-factor reasoning rather than derivation.
Core rules
- Axial stress σ = P/A; elastic strain ε = δ/L = σ/E.
- Bending stress σ = My/I, with maximum at the outer fibre; transverse shear τ = VQ/(It).
- Torsion: τ = Tr/J and twist θ = TL/(GJ); for a solid circle J = πd⁴/32.
- Euler buckling: Pcr = π²EI/(KL)²; K depends on end conditions.
- Fatigue design uses S–N data, endurance limit, stress concentration Kt, and a mean-stress correction such as Goodman.
- Design factor n is applied to strength, not to the load, unless the problem states otherwise.
Worked example
A solid shaft transmits 15 kW at 300 rpm. Allowable shear stress is 40 MPa. Find the minimum diameter. Torque T = P/ω = 15,000/(2π × 300/60) = 477.5 N·m. For a solid shaft, τ = 16T/(πd³), so d = [16T/(πτ)]^(1/3). Substitute: d = [16 × 477.5/(π × 40 × 10⁶)]^(1/3) = (6.08 × 10⁻⁵)^(1/3) = 0.0393 m, about 39.3 mm. Select the next standard size above this.
Traps
- Using radius where the formula expects diameter.
- Forgetting to convert rpm to rad/s.
- Applying yield strength directly as allowable stress without a design factor.
- Using J for a hollow shaft when the shaft is solid.
- Ignoring stress concentration at keyways and shoulders in fatigue checks.