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CE-503 (A) · Structural analysis-II/Unsolved PYQ Paper

CE-503-A Structural Analysis - II - Jun 2025 Question Paper

Under each question, How to answer lists the points an answer should cover, outlined by CampusPrep from the syllabus. Check the details against your textbook.

  1. 14 Marks
    Analyze the frame shown in the figure using Kani's method. Assume moment of inertia for the beams as $1.5I$. Draw bending moment and elastic curve.
    Two-storey two-bay? single-bay two-storey frame fixed at bases, span 6 m. Top beam with 10 kN/m UDL over full span. Middle beam with 15 kN point load at 3 m from left (midpoint). Upper columns height 3 m with I=2I, lower columns height 3.3 m with I=2I. Beams assumed 1.5I.
    How to answer
    • Compute fixed-end moments and rotation factors with beam I = 1.5I and column I = 2I
    • Perform Kani's iteration for rotation contributions and storey sway if any
    • Compute final end moments, reactions and draw BMD
    • Draw deflected / elastic curve consistent with moments and supports
  2. 7 Marks
    aDiscuss the limitations and assumptions in a plastic analysis of beams and frames.
    How to answer
    • Define plastic analysis and idealised elastic-perfectly plastic behaviour
    • List assumptions: plane sections, yield stress, small deflections, proportional loading
    • Discuss limitations: stability, buckling, fatigue, strain hardening, deflections ignored
  3. 7 Marks
    bDescribe the formation of a plastic hinge in a fixed beam under uniform loading.
    How to answer
    • State fixed beam with UDL and elastic BMD with support and mid moments
    • Explain first yield at supports then redistribution with load increase
    • Formation of third hinge at midspan to form mechanism / collapse
    • Sketch load-deflection and hinge sequence
  4. 14 Marks
    In a multistoried building the frames, as shown in the figure below, are spaced at $3.5\text{ m c/c}$. The dead and live loads carried by the slab are $1\text{ kN/m}^2$ and $2\text{ kN/m}^2$ respectively. Using substitute frame method, analyze an intermediate span of the first floor for maximum negative bending moment.
    Two-storey frame with 3 bays: spans 4 m, 5 m, 4 m. Ground storey height 4 m fixed at bases, upper storey height 3 m. Intermediate span is 5 m span on first floor.
    How to answer
    • Compute slab load per m: dead + live times spacing 3.5 m c/c
    • Select substitute frame for first floor intermediate span and loading for max negative moment
    • Compute distribution factors, FEMs and analyse by moment distribution / slope deflection
    • Report maximum negative bending moment at support
  5. 14 Marks
    Analyze the pin-jointed plane frame supported and loaded as shown in Figure below, Use stiffness method.
    Symmetric triangular truss with pin support left, roller support right, total span 3.0 m (1.5 m + 1.5 m). Apex joint at centre with vertical member to base centre and two inclined members to supports at 45 degrees. 60 kN downward load at apex.
    How to answer
    • Identify joints, members, degrees of freedom and coordinate system
    • Form element stiffness matrices in global coordinates for 45-degree members
    • Assemble structure stiffness matrix and apply 60 kN load at apex
    • Solve for displacements and compute member axial forces
  6. 14 Marks
    Using the Muller-Breslau principle, draw the influence line for shear force at mid span of a simply supported beam of length $4\text{ m}$.
    How to answer
    • State Muller-Breslau principle for influence lines
    • Release shear at midspan and apply relative unit displacement
    • Sketch deflected shape which is ILD for shear
    • Mark ordinates (+0.5 to -0.5) for 4 m beam
  7. 14 Marks
    Calculate section modulus, Plastic modulus and shape factor for a circular section of radius $r$.
    How to answer
    • Define elastic section modulus Z = I/y_max and compute I for circle
    • Define plastic modulus Zp as first moment about equal area axis
    • Compute Zp = 4r^3/3 for solid circle
    • Compute shape factor S = Zp/Z = 16/(3π) ≈ 1.698
  8. 7 Marks
    aExplain the matrix Force Method of structural analysis with a suitable example.
    How to answer
    • Define primary structure, redundants and compatibility
    • Explain flexibility coefficients and matrix equation Delta = F*P + Delta_L
    • Illustrate with simple propped cantilever / continuous beam example
  9. 7 Marks
    bDiscuss the steps involved and the formation of the flexibility matrix.
    How to answer
    • List steps: select redundants, release structure, compute displacements
    • Define flexibility influence coefficients f_ij by unit load
    • Show assembly and properties (symmetric) of flexibility matrix
    • Write compatibility equations in matrix form
  10. 2 Marks
    aExplain the following terms. a) Redundant structure
    How to answer
    • Define redundant / indeterminate structure with examples
    • Explain degree of redundancy and why analysis needs compatibility
  11. 4 Marks
    bExplain the following terms. b) Collapse load and plastic modulus
    How to answer
    • Define collapse load as load forming mechanism
    • Define plastic modulus Zp and relation Mp = fy*Zp
    • Give formula / example for beam
  12. 4 Marks
    cExplain the following terms. c) Shear wall and wind drift
    How to answer
    • Define shear wall function in lateral load resistance
    • Define wind drift / lateral sway limits
    • Explain importance in tall buildings
  13. 4 Marks
    dExplain the following terms. d) Compatibility equations and degree of Indeterminacy
    How to answer
    • Define compatibility as continuity / zero displacement conditions
    • Define degree of indeterminacy (static and kinematic) with formula
    • Give example counting indeterminacy
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