HSC Engineering Studies cheat sheet

Stress σ = F/A (Pa); strain ε = ΔL/L₀ (dimensionless); Young's modulus E = σ/ε in the linear-elastic region, given by the slope of the stress–strain graph.

Factor of safety = yield (or ultimate) stress ÷ allowable working stress; a value below 1 means the member is predicted to fail under the design load.

Shear stress τ = V/A acts parallel to the cross-section; for a lap joint the shear area is the cross-section of the fastener, not the plate.

Bending stress σ = My/I, with I = bd³/12 for a rectangle about its centroidal axis and maximum stress at the greatest distance y from the neutral axis.

Second moment of area resists bending, not axial load; a hollow section of the same mass as a solid one has the larger I and therefore the greater bending stiffness.

Thermal strain ε = αΔT; if expansion is restrained, σ = EαΔT. Typical α: steel ≈ 12×10⁻⁶/K, aluminium ≈ 23×10⁻⁶/K.

Tensile test curve: proportional limit → yield (0.2% proof stress for metals without a distinct yield) → ultimate tensile strength → fracture; ductility is measured by elongation or reduction in area.

Hardness, toughness and ductility are separate properties: toughness is energy absorbed to fracture (area under the stress–strain curve), not the same as hardness.

Ferrous alloys: low-carbon steel is ductile and weldable; increasing carbon raises hardness and tensile strength but lowers ductility and weldability.

Heat treatment: quenching forms martensite (hard, brittle); tempering after quenching restores toughness; annealing softens and relieves internal stress.

Non-ferrous: aluminium alloys give high strength-to-weight ratio and corrosion resistance; copper alloys give electrical and thermal conductivity and wear resistance.

Polymers: thermoplastics soften on reheating (recyclable, e.g. PE, PVC, ABS); thermosets cross-link permanently and char rather than melt (e.g. epoxy, phenolic).

Composites: a fibre–matrix composite gains stiffness and strength along the fibre direction; properties are anisotropic, so laminate orientation is a design variable.

Corrosion control: sacrificial anodes use a metal higher in the galvanic series (zinc protects steel); barrier coatings and cathodic protection are alternatives to alloy selection.

Mechanisms: velocity ratio = distance moved by effort ÷ distance moved by load; for gears VR = N_driven/N_driver; efficiency = (work output ÷ work input) × 100%.

Fluids and energy: pressure p = F/A = ρgh; flow continuity Q = Av; power = pressure × flow rate. Electrical power P = VI and energy = P × time.