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Civil EngineeringWBPSC AE · SSC JE · RRB JE

Structural Analysis— Important Topics, Formulas & MCQs

Structural Analysis (Theory of Structures) deals with determining internal forces and deformations in structures — determinate and indeterminate beams, frames, trusses and arches. It is conceptually demanding but high-yield for AE-level papers.

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Important topics in Structural Analysis

Static & kinematic indeterminacy
Determinate beams, frames, trusses
Slope-deflection & moment-distribution methods
Force (flexibility) & displacement (stiffness) methods
Influence lines
Rolling loads
Arches & cables
Plastic analysis — collapse load, plastic hinge
Deflection — unit load, Castigliano's theorems
Approximate methods for frames
Must-know

Key concepts & formulas — Structural Analysis

Static indeterminacy

Ds = (3m + r) − 3j for plane frames; internal hinges reduce it by the releases they introduce.

Plastic hinge

Forms at Mp where curvature becomes very large while moment stays constant.

Collapse load (propped cantilever, central load)

Pc = 6Mp/L from the plastic mechanism (hinges at fixed end and under load).

Indeterminate solution

Requires equilibrium, compatibility AND constitutive (force-displacement) relations together.

Exam relevance

6–9 questions in AE papers — one of the most important technical subjects for higher posts.

Study tip

Get comfortable with indeterminacy counting and moment distribution; they anchor most structural MCQs.

Worked example

Sample Structural Analysis MCQ

The static indeterminacy of a propped cantilever (fixed at one end, simple support at the other) is:

A. 0
B. 1
C. 2
D. 3
Answer: B. Total reactions = 3 (fixed) + 1 (prop) = 4; equilibrium equations = 3; Ds = 4 − 3 = 1 (one redundant reaction).

Common mistakes to avoid

Static indeterminacy Ds = (3m + r) − 3j for plane frames; each internal hinge adds a release.
A plastic hinge forms at Mp with very large rotation, not infinite moment.
Collapse load of a propped cantilever with a central point load = 6Mp/L.
Solving an indeterminate structure needs equilibrium, compatibility AND constitutive relations together.
Keep going

Related Civil Engineering subjects

Strength of Materials
RCC
Steel Structures
Soil Mechanics
Foundation Engineering
Surveying
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