BEM PCE Part B Mechanical flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Section modulus

Ratio Z = I/c of the second moment of area to the distance from the neutral axis to the extreme fibre; bending stress is σ = M/Z.

Parallel-axis theorem

Second moment of area about any parallel axis equals the centroidal value plus A·d², where d is the perpendicular distance between axes.

Euler buckling load

Critical axial load P_cr = π²EI/(KL)² at which a slender column becomes unstable; K depends on end restraint conditions.

Effective length factor K

Multiplier applied to column length for Euler buckling: 0.5 fixed-fixed, 0.7 fixed-pinned, 1.0 pinned-pinned, 2.0 fixed-free.

Torsion of circular shaft

Shear stress τ = T·r/J and twist angle θ = T·L/(G·J); polar second moment J = π·d⁴/32 for a solid shaft.

Hoop stress

Circumferential stress in a thin-walled cylinder under internal pressure, σ_h = p·r/t; it is twice the longitudinal stress.

Stress concentration factor

K_t is the ratio of peak local stress at a geometric discontinuity to the nominal stress; it amplifies fatigue damage at notches.

Von Mises stress

Equivalent stress √(σx² − σxσy + σy² + 3τxy²) for plane stress; yielding of ductile material is predicted when it reaches yield strength.

Mohr's circle

Graphical representation of plane stress transformation; its radius equals maximum shear stress and its intersections with the axis give principal stresses.

Thermal stress

Stress σ = −E·α·ΔT induced when thermal expansion is fully constrained; zero stress occurs if the member expands freely.

Paris law

Empirical fatigue crack growth relation da/dN = C·(ΔK)^m, linking crack growth per cycle to the stress intensity range.

Goodman diagram

Fatigue design plot of alternating versus mean stress; the line from endurance limit to ultimate strength gives the safe design boundary.

Steady-flow energy equation

For an open system, q − w = Δh + Δke + Δpe per unit mass; adiabatic turbine work equals the enthalpy drop.

Carnot efficiency

Maximum possible efficiency between two reservoirs, η = 1 − T_L/T_H, using absolute temperatures; no real cycle can exceed it.

Rankine cycle

Vapour power cycle of pump, boiler, turbine, and condenser; efficiency rises with higher boiler pressure and lower condenser pressure.

Otto cycle efficiency

Ideal spark-ignition cycle efficiency η = 1 − r^(1−k), depending only on compression ratio r and specific heat ratio k.

Log-mean temperature difference

Driving temperature difference for heat exchangers: ΔT_lm = (ΔT₁ − ΔT₂)/ln(ΔT₁/ΔT₂), multiplied by correction factor F for multipass units.

Reynolds number

Re = ρVD/μ characterizes flow regime; pipe flow is laminar below about 2300 and fully turbulent above about 4000.

Grashof condition

A four-bar linkage has at least one fully rotating link when shortest plus longest link length is less than or equal to the sum of the other two.

Gear ratio

Ratio of input to output speed equals the inverse ratio of tooth numbers; output torque scales up by the same speed reduction factor.

Belt friction equation

Ratio of tight-side to slack-side tension T₁/T₂ = e^(μθ) for a flat belt, where θ is the arc of contact in radians.

Sommerfeld number

Dimensionless bearing parameter S = (μN/P)(r/c)² that governs friction coefficient and film thickness in hydrodynamic journal bearings.

Flywheel speed fluctuation

Energy variation ΔE = I·ω_mean²·C_s, where C_s = (ω_max − ω_min)/ω_mean is the coefficient of speed fluctuation.

Worst-case tolerance stack

Total assembly variation equals the arithmetic sum of individual component tolerances; assumes every dimension at its extreme simultaneously.

Clearance fit

Fit in which the minimum hole size exceeds the maximum shaft size, guaranteeing a positive gap between mating parts in assembly.

Hole-basis system

Limits-and-fits approach where hole lower deviation is fixed at zero and shaft tolerance zones are varied to obtain the required fit.

Surface roughness Ra

Arithmetic mean deviation of the measured profile from its mean line over the sampling length; a common specification for machined surfaces.

Keyway shear stress

For a square key transmitting torque T on shaft diameter d, shear stress τ = 2T/(d·L·w) with key length L and width w.

Spring rate

Stiffness of a helical compression spring k = G·d⁴/(8·D³·N_a), with wire diameter d, mean coil diameter D, and active coils N_a.

Bearing rating life

L₁₀ = (C/P)^p in millions of revolutions, where C is dynamic capacity, P the equivalent load, and p is 3 for ball bearings.

Bolted joint preload

Initial clamping force in a bolt that must exceed the external load divided by the stiffness ratio to keep the joint closed.

Fillet weld throat

Minimum cross-section of a fillet weld, equal to 0.707 times the leg length; shear stress is calculated on the throat area.