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CE-403 · Structural Analysis-I/Unsolved PYQ Paper

CE-403 Structural Analysis-I - Jun 2023 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
    Determine the forces in the members of the pin-jointed truss shown in figure 1.
    Truss with joint C at top left, D vertically below C 8m, A 6m right of D, B 6m right of A. Horizontal 10 kN at C to right, vertical 20 kN at B downward. Members: C-D vertical (dashed reference), C-A, C-B, A-B. Reactions V_A, H_A at A, V_B at B.
    How to answer
    • Calculate support reactions at A and B from equilibrium
    • Analyse joints D/C/A/B using equilibrium $\sum F_x=0, \sum F_y=0$
    • Determine magnitude in each member (CA, CB, AB)
    • Identify tensile vs compressive nature
  2. 14 Marks
    Determine the forces in all the members of the truss shown in figure 2 by using method of joints.
    Symmetric truss span 8m with 4 panels of 2m each. Left pin support, right roller support. Apex 3m high at centre. Vertical loads 5 kN, 10 kN, 5 kN at top joints. Members include bottom chord, top chord rafters and central verticals/diagonals.
    How to answer
    • Find reactions at pin and roller supports
    • Apply method of joints joint by joint
    • Compute forces in top chord, bottom chord and vertical/diagonal members
    • State tension/compression for all members
  3. 14 Marks
    A mild steel bar 100 mm diameter is bent as shown in figure 3. It is fixed horizontally at A and a load of 500 N hangs at D. Draw the bending moment diagram for the parts AB, BC and CD, indicating the maximum values. Find the maximum bending stress. also find the deflection at D. Take $E = 2\times10^5$ $N/mm^2$.
    Bent bar: A fixed horizontal, AB 3m to B, BC 1m down to C, CD 2m left to D. 500 N downward at D. Forms crank shape in plan/elevation.
    How to answer
    • Draw bending moment diagram for AB, BC, CD with maximum values
    • Calculate maximum bending moment and section modulus for 100 mm diameter
    • Compute maximum bending stress $\sigma = M/Z$
    • Compute deflection at D by strain energy / Castigliano considering bending and torsion
  4. 14 Marks
    A three hinged arch has span 20 m and a rise 4 m. The arch carries a uniformly distributed load of 20 kN/m on the left half of the span. Find the horizontal thrust at each support and location and magnitude of the maximum bending moment of the arch.
    How to answer
    • Calculate reactions and horizontal thrust for UDL on left half
    • Write bending moment equation for arch vs beam moment
    • Locate zero shear / maximum moment position
    • Compute maximum bending moment magnitude
  5. 14 Marks
    Determine the prop reaction and the deflection at mid-span of a propped cantilever beam shown in figure 4. The prop sinks by 30 mm. Take EI = 15,000 $kNm^2$.
    Propped cantilever A fixed left, B propped right with settlement downward. Total span 6m (3m+3m). 100 kN downward at mid-span (3m from A). Prop settlement shown as downward displacement.
    How to answer
    • Treat prop reaction as redundant with settlement 30 mm downward
    • Use compatibility: upward deflection due to R minus downward due to 100 kN equals settlement
    • Solve for prop reaction R using $EI = 15000$ $kNm^2$
    • Find mid-span deflection from superposition
  6. 7 Marks
    aDetermine the fixed end moments for the loaded beam shown in figure 5. Also draw BMD for the beam of span 'l'.
    Fixed beam A to B with span l divided into quarters. Downward loads W at C (l/4), D (l/2), E (3l/4). Both ends fixed.
    How to answer
    • Calculate fixed end moments due to W at l/4, l/2, 3l/4 using superposition
    • Apply equilibrium and symmetry to get FEM at A and B
    • Draw free and fixed BMD and combine
  7. 7 Marks
    bA beam 10 m long fixed at both ends carries a uniformly distributed load of 4500 N/m over the entire span. Find the maximum bending and maximum bending deflection. Take E = 200 $kN/m^2$, I = $5\times10^7$ $mm^4$.
    How to answer
    • Recall fixed beam with full UDL: $M_{end}=wL^2/12$, $M_{mid}=wL^2/24$
    • Compute maximum bending moment value
    • Compute maximum deflection $wL^4/(384EI)$
    • Substitute $E, I, w, L$ with unit conversion
  8. 14 Marks
    The support B of a continuous beam shown in figure 6 has settled by 12 mm. Find out the moments at supports.
    Continuous beam: A fixed left, B interior roller settled 12 mm, C roller right. AB 4m with 7 kN/m UDL. BC 4m (2m+2m) with 15 kN at 2m from B.
    How to answer
    • Model AB as propped/fixed with UDL and BC with point load plus 12 mm settlement at B
    • Apply slope-deflection / moment distribution with settlement term $6EI\Delta/L^2$
    • Solve for moments at A, B, C
    • Check equilibrium at joint B
  9. 14 Marks
    Construct the influence line for a diagonal member $U_5L_4$ of a Warren truss with verticals shown in figure 7.
    Warren truss with verticals: bottom joints L0 to L6 at 2.5m spacing (total 15m), top joints U1 to U5. Height 3m. Diagonal and vertical members as shown. Target diagonal member U5L4 connecting top U5 to bottom L4.
    How to answer
    • Identify panel and section cutting U5L4
    • Place unit load at successive lower joints and compute force in U5L4
    • Plot ordinates to get influence line diagram
    • Mark maximum positive and negative ordinates
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