Structural Analysis
Structural Analysis tests how loads travel through determinate and indeterminate beams, frames, trusses, arches and cables. The WBPSC AE paper favours degree of indeterminacy, influence lines, slope-deflection and moment-distribution, and qualitative deflected shapes.
Core rules
- Plane frame static indeterminacy D_s=3m+r−3j; truss D_s=m+r−2j.
- Kinematic indeterminacy counts independent joint translations and rotations.
- Muller-Breslau gives influence-line ordinates from released deflected shapes.
- Moment distribution: stiffness 4EI/L for far end fixed, 3EI/L for far end pinned; carry-over 0.5.
- A three-hinged arch has four reactions; two equilibrium equations plus hinge moment zero solve it.
Worked example
A propped cantilever of span L carries UDL w. Let the prop reaction be R. Deflection at the prop due to UDL is wL⁴/(8EI); upward deflection due to R is RL³/(3EI). Compatibility gives RL³/(3EI)=wL⁴/(8EI), so R=3wL/8. The fixed-end moment is wL²/8 and the prop moment is zero. This is a classic compatibility check.
Traps
- Sign convention changes between slope-deflection and moment distribution.
- Counting releases twice.
- Assuming a roller provides horizontal reaction.
- Using 4EI/L when the far end is actually pinned.
- Ignoring axial deformation in a frame where it matters.