Engineering Sciences Sectional Paper (XE Section B)
Section B of XE is one sectional paper chosen at application stage: XE-A Materials Science, XE-B Solid Mechanics, XE-C Thermodynamics, XE-D Polymer Science and Engineering, XE-E Food Technology, or XE-F Atmospheric and Oceanic Sciences. All Section B questions come from that single paper, and they test numerical application of standard formulae rather than derivations.
Core rules by section
- Solid Mechanics: principal stresses σ₁,₂ = (σx+σy)/2 ± √[((σx−σy)/2)² + τxy²]; torsion τ = Tr/J; Euler buckling Pcr = π²EI/(KL)² holds only above the critical slenderness ratio.
- Thermodynamics: entropy balance on a control volume; Rankine pump work ≈ v(P₂−P₁); Brayton efficiency 1 − rp^(−(γ−1)/γ).
- Materials Science: Bragg nλ = 2d sinθ, with θ the Bragg angle and the reflection appearing at 2θ; diffusion D = D₀exp(−Q/RT); Schmid factor τ = σcosφcosλ, maximum 0.5.
- Polymers: number-average M̄n = ΣNᵢMᵢ/ΣNᵢ against weight-average M̄w = ΣNᵢMᵢ²/ΣNᵢMᵢ, so polydispersity M̄w/M̄n ≥ 1; Mark–Houwink [η] = KM^a.
- Food Technology: D-value is the time for a one-log reduction, z-value the temperature change giving a tenfold change in D, and F₀ = ∫10^((T−121)/z)dt.
- Atmospheric and Oceanic Sciences: hydrostatic balance, standard lapse rate 6.5 K/km, Coriolis parameter f = 2Ωsinφ, geostrophic balance of pressure-gradient and Coriolis forces.
Worked example
A plane-stress element has σx = 100 MPa, σy = 20 MPa, τxy = 40 MPa. Centre = (100+20)/2 = 60 MPa; radius R = √(40² + 40²) = 56.6 MPa. Hence σ₁ = 60 + 56.6 = 116.6 MPa, σ₂ = 3.4 MPa and τmax = R = 56.6 MPa.
Traps
Mixing sign conventions for shear on Mohr's circle; inserting 2θ where θ belongs in Bragg's law; feeding millimetres and metres into the same buckling expression; quoting a D-value without its associated z-value; forgetting that Coriolis reverses sign in the southern hemisphere.