Structural Analysis and Design
Core concepts
Candidates must be fluent in statics (equilibrium, determinacy, influence lines), classical methods (virtual work, moment distribution, slope-deflection), and matrix stiffness analysis. Understand how support conditions change a structure from determinate to indeterminate, and how to compute reactions, shear and moment diagrams, and deflections. Know the distinction between strength and serviceability limit states and the role of load combinations.
Common traps
- Degree of indeterminacy: miscounting reactions at internal hinges or rollers on inclined planes. Count independent reaction components, then subtract available equilibrium equations (3 per planar body, plus condition equations at internal hinges).
- Sign conventions: fixed-end moments and shear sign flips are a frequent source of error.
- Approximate vs. exact: questions often ask which method is appropriate, not just to compute.
- Influence lines: confusion between absolute maximum shear and maximum moment positions.
Worked rule of thumb
For a continuous beam, a quick check on a fixed-end moment for a uniformly distributed load w over span L is M = wL²/12 at each end. If the far end is pinned, the moment redistributes to roughly wL²/8 at the fixed support. Use these as sanity anchors before trusting a long calculation.
Always verify equilibrium: sum of vertical forces, sum of moments about any point, and check that the deflected shape matches the boundary conditions (zero slope at fixed supports, zero moment at pins).