Questions
8–12 questions in major PSU papers
Difficulty
Medium-Hard
Importance
Core — never skip
Overview
Structural Analysis is a core civil engineering discipline that focuses on determining the internal forces, deflections, and stability of structures. Mastering this topic is essential for PSU exams as it forms the foundation for solving complex mechanics problems and predicting structural behavior under various loading conditions.
Static and Kinematic Indeterminacy
Understanding the degree of indeterminacy is the first step in classifying structures as determinate or indeterminate. Exam questions frequently test the ability to calculate both external and internal degrees of freedom for beams, frames, and trusses.
- Ds = r - 3 (for 2D frames)
- Di = 3C (for closed loops)
- Dk = 3j - r (for 2D frames ignoring axial deformation)
- Static Indeterminacy Ds = Dse + Dsi
- Kinematic Indeterminacy Dk = Dkext + Dkint
Slope Deflection and Moment Distribution
These displacement-based methods are standard for analyzing statically indeterminate structures. PSU exams prioritize conceptual understanding of carry-over factors and stiffness coefficients for fixed and hinged supports.
- Slope Deflection Equation: M_AB = (2EI/L)*(2θA + θB - 3δ/L) + MF_AB
- Stiffness of beam (far end fixed): 4EI/L
- Stiffness of beam (far end hinged): 3EI/L
- Carry over factor for fixed beam: 0.5
- Distribution Factor (DF) = (k_i / Σk)
Influence Line Diagrams (ILD)
ILDs graphically represent the variation of a reaction, shear, or moment at a specific point due to a moving unit load. These are highly predictable topics in PSU papers that rely on the Muller-Breslau Principle.
- Muller-Breslau Principle for influence lines
- Max shear force at a section due to UDL shorter than span
- Max bending moment at a section under a series of point loads
- Betti's Law and Maxwell's Reciprocal Theorem
- Absolute maximum bending moment in a simply supported beam
Matrix Methods
Matrix structural analysis provides a systematic approach for computer-aided structural calculations. Candidates should be familiar with the conversion of stiffness and flexibility matrices for simple elements.
- Force Method uses Flexibility Matrix [F]
- Displacement Method uses Stiffness Matrix [K]
- Relation: [P] = [K][Δ]
- Relation: [Δ] = [F][P]
- Stiffness matrix is symmetric and singular
Formula Sheet
Ds = r - 3 (for 2D frames)
Dk = 3j - r (for 2D frames)
M_AB = (2EI/L)(2θA + θB) + MF_AB
DF = k_i / Σk
Stiffness = 4EI/L or 3EI/L
Carry-over factor = 0.5
[P] = [K][Δ]
[Δ] = [F][P]
Exam Tip
Always verify if the structure is 2D or 3D before applying indeterminacy formulas, as the equilibrium equation count changes from 3 to 6.
Common Mistakes
- Forgetting to include internal releases (like internal hinges) when calculating static indeterminacy.
- Neglecting the axial deformation assumption which drastically changes the value of kinematic indeterminacy.
- Swapping the stiffness values for far-end-fixed (4EI/L) versus far-end-hinged (3EI/L) members.
More Revision Notes
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