Structural Analysis and Mechanics
Domain overview
This section tests how loads travel through determinate and indeterminate structures and whether you can compute reactions, internal forces, deflections and stability without relying on software. It rewards clear free-body diagrams and consistent sign conventions.
Core rules
- Equilibrium: sum of forces and moments must vanish for every free body; draw all reactions before writing equations.
- Plane-frame static indeterminacy: DSI = 3m + r - 3j, adjusted for internal hinges and releases; for a plane truss use m + r - 2j.
- Virtual work: 1·Δ = Σ∫Mm/EI ds + ΣNn/EA ds; temperature and support settlement need corresponding terms.
- Stiffness method: form K, impose supports, solve KD=F; fixed-end forces come from member loads and settlement.
Worked example
A simply supported beam of span 6 m carries a 10 kN/m UDL and a 20 kN point load at midspan. By symmetry, each reaction is (10×6+20)/2 = 40 kN. At midspan, M = 40×3 − 10×3×1.5 = 120 − 45 = 75 kN·m. Check: PL/4 = 20×6/4 = 30 kN·m and wL²/8 = 10×36/8 = 45 kN·m; 30+45 = 75 kN·m.
Traps
Using a roller as a moment restraint, mixing kN and N, omitting a point-load term in the moment equation, and assuming a frame is determinate because it looks simple are common mark losers.