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

CE-503-A Structural Analysis - II - Nov 2022 Question Paper

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  1. 14 Marks
    Analyse the Rigid frame shown in fig.(1) by Kani's method. Draw deflected shape and bending moment diagram.
    Given: Rigid frame Figure 1: left column 6m high with 60kN/m UDL over full height, fixed at base, moment of inertia I; top beam 5m span (3m + 2m point load position) with 2I, point load downward at 3m from left; right column 3m high with I, fixed at base. Left top joint rigid, right top joint rigid.
    How to answer
    • Rotation and displacement contributions by Kani's method and iteration to convergence
    • Final end moments at joints
    • Deflected shape sketch with sway direction
    • Bending moment diagram on tension side with values
  2. 14 Marks
    Analyse the Rigid frame shown in fig. (2) by moment distribution method. Draw the deflected shape and bending moment diagram.
    Given: Rigid frame Figure 2: A fixed at base, B rigid joint, C rigid joint, D fixed at base. AB is 6m (3m+3m) with 12kN horizontal load to right at mid-height (3m from A). BC is beam with inertia I. AB upper part inertia not labelled, lower 3m marked 2I. CD is 3m column with inertia I.
    How to answer
    • Fixed-end moments, stiffness factors and distribution factors at B and C
    • Moment distribution with sway correction for 12kN lateral load
    • Final moments and reactions
    • Deflected shape and bending moment diagram
  3. 14 Marks
    A propped cantilever beam is loaded with uniformly distributed load (UDL) of intensity 'w' per unit length over its whole span. If the beam has uniform moment capacity $\mu_p$, locate the plastic hinges and find the collapse load.
    How to answer
    • Degree of indeterminacy and possible hinge locations for propped cantilever under UDL
    • Equilibrium and virtual work / mechanism condition with uniform Mp
    • Location of interior plastic hinge from support
    • Collapse load wc in terms of Mp and span
  4. 14 Marks
    Using Muller Breslau principle, compute the influence line ordinates for: For the propped cantilever beam of 8m span and having uniform EI.
    1. i)Reaction at fixed end
    2. ii)Moment at mid span
    How to answer
    • Muller-Breslau principle statement for ILD
    • Released structure and displaced shape for fixed-end reaction
    • Released structure and displaced shape for mid-span moment
    • Influence ordinates for 8m propped cantilever with uniform EI
  5. 14 Marks
    Using Stiffness method analyse the beam shown in fig. (3). EI is constant.
    Given: Beam Figure 3: left pin support to interior roller 3m with 20kN/m UDL; overhang to fixed end total 4m from interior roller, with 40kN at 1m from interior roller and 60kN at 3m from interior roller (1m from fixed end).
    How to answer
    • Degree of indeterminacy, coordinates and stiffness matrix
    • Fixed-end forces for UDL and point loads
    • Equilibrium equations and joint displacements
    • Final moments and shear with BMD
  6. 14 Marks
    Analyse the continuous beam shown in fig. (4) using flexibility method.
    Given: Beam Figure 4: left fixed end to roller 6m with 60kN/m UDL; right overhang beyond roller: 100kN at 3m from roller, support symbol at 4m from roller (1m after 100kN?), 20kN at 6m from roller (2m after middle mark). Dimensions marked 6m, 3m, 1m, 2m.
    How to answer
    • Primary structure and redundants by flexibility method
    • Compatibility equations and flexibility coefficients with diagrams
    • Solution for redundants
    • Final BMD and SFD
  7. 14 Marks
    For the continuous beam shown in fig. (5) obtain the ordinates of influence line and draw ILD for
    1. i)Reaction at (A)
    2. ii)Shear force and bending moment at (B)
    Given: Continuous beam Figure 5: A is pin support, B is internal hinge (dot), C is roller, D is roller with inclined base. Spans: A to B 5m, B to C 1m, C to D 2m.
    How to answer
    • Muller-Breslau displaced shapes for reaction, shear and moment at B
    • Calculation of ordinates along spans A-B-C-D
    • ILD plots with values
    • Interpretation for moving load
  8. 7 Marks
    aExplain how the wind and earthquake loads are accounted for in the analysis of tall building frames?
    How to answer
    • Wind load calculation and distribution on tall frames
    • Earthquake load: seismic weight, base shear and distribution
    • Load combinations and analysis approach
    • Codal provisions as per BIS for lateral loads
  9. 7 Marks
    bState various codal provisions for lateral loads, as per BIS, for the analysis of tall building frames.
    How to answer
    • Applicable BIS codes IS 875, IS 1893, IS 4326 etc.
    • Provisions for wind and seismic lateral loads
    • Ductility, drift and load factor requirements
    • Analysis requirements for tall frames
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