Structural Analysis
Structural Analysis examines how determinate and indeterminate structures respond to loads: trusses, frames, arches, cables, influence lines, and displacement methods. The exam expects both conceptual checks and short calculations.
Core rules
- For a plane frame, static indeterminacy D_s = 3m + r − 3j; for a plane truss, D_s = m + r − 2j.
- A roller provides one reaction, a pin two, and a fixed support three.
- Force methods use compatibility of displacements; stiffness methods use equilibrium of joint displacements.
- Muller-Breslau's principle gives influence-line ordinates by introducing a unit displacement at the coordinate of interest.
- A three-hinged arch is statically determinate and develops no bending moment at the hinges.
Worked example
A propped cantilever of span L = 4 m carries a UDL w = 10 kN/m; the fixed end has three reactions and the prop one, so D_s = 3(1) + 4 − 3(2) = 1. For a propped cantilever with a UDL over the full span, the prop reaction is 3wL/8 = 3 × 10 × 4/8 = 15 kN. The fixed-end moment is wL²/8 = 20 kN·m, and the fixed-end reaction is 5wL/8 = 25 kN. Check vertical equilibrium: 25 + 15 = 40 kN = 10 × 4.
Traps that cost marks
- Miscounting internal hinges or releases, which changes D_s.
- Treating a fixed support as two reactions instead of three.
- Using the wrong standard result for a propped cantilever or fixed beam.
- Forgetting that influence lines are for moving unit loads, not fixed loads.
Exam focus
Be ready to classify a structure, compute D_s, sketch qualitative deflected shapes, and apply standard fixed-end moments.