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

CE-503-A Structural Analysis - II - Dec 2024 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 end moments of the member of the frame by moment distribution method. E is constant and relative I value are indicated on the frame.
    Rigid frame 1-2-3-4 with fixed bases at 1 and 4, 6 m span between 1 and 4. Beam 2-3 with 20 kN/m UDL over full span, I=6. Columns 1-2 and 3-4 with I=4. Horizontal 50 kN load acting on left column at mid-height.
    How to answer
    • Compute fixed-end moments for beam 2-3 under 20 kN/m UDL and for columns with lateral load.
    • Compute stiffness factors and distribution factors at joints 2 and 3 using relative I values.
    • Perform moment distribution cycles including sway correction for 50 kN lateral load.
    • Obtain final end moments for members 1-2, 2-3, 3-4 and equilibrium check.
  2. 14 Marks
    Determine the support moment for the continuous beam. Relative I value are indicated along the member in each span. E is constant. Use Kani's method.
    Continuous beam 1-2-3-4. Span 1-2 =3 m with 80 kN at 1 m from 1, I=1.5I. Span 2-3 =4 m with 50 kN/m UDL, I=2I. Span 3-4 =4 m with 40 kN at 2 m from 4, I=I. Supports at 2 and 3 shown as intermediate, 1 and 4 as ends.
    How to answer
    • Calculate fixed-end moments for spans 1-2 with 80 kN, 2-3 with 50 kN/m UDL, 3-4 with 40 kN.
    • Calculate rotation factors at joints 2 and 3 using relative I/L with E constant.
    • Perform Kani's iteration for rotation contributions and displacement if any.
    • Compute final support moments from fixed-end plus rotation contributions.
  3. 14 Marks
    Determine the collapse load $W_c$ for the frame shown in Fig.
    Rectangular portal A-B-C-D, A and D fixed bases, 4 m span, 3 m height. Horizontal load W at B to left, vertical load 2W on BC at 1 m from C. Column plastic capacity Mp, beam BC capacity 2Mp.
    How to answer
    • Identify possible collapse mechanisms: beam, sidesway and combined.
    • Compute virtual work equations with plastic moments Mp for columns and 2Mp for beam.
    • Solve for W in each mechanism from external work = internal plastic work.
    • Select minimum W as collapse load Wc.
  4. 14 Marks
    Analysis the frame by portal method as shown in Fig.
    Three-storey three-bay portal with fixed bases. Each storey 4 m high. Bays 8 m, 6 m, 4 m. Lateral loads 40 kN at roof, 80 kN at second and first floor levels from left.
    How to answer
    • Assume inflection points at mid-height of columns and mid-span of beams per portal method.
    • Distribute storey shear to interior and exterior columns.
    • Compute column shears and moments then beam moments by joint equilibrium.
    • Summarize axial, shear and moments for frame.
  5. 14 Marks
    Using the flexibility matrix method, analyse the continuous beam shown in Fig. The value of EI is as indicated.
    Continuous beam A-B-C each span 8 m. A is fixed, B is roller, C is roller. 100 kN at 4 m from A on AB, 60 kN at 4 m from B on BC.
    How to answer
    • Select redundants and release structure for flexibility method.
    • Compute flexibility coefficients by unit load and displacements by loads.
    • Solve compatibility equation for redundant reactions.
    • Draw shear force and bending moment diagrams.
  6. 14 Marks
    Analyse the continuous beam shown in Fig. By stiffness matrix method. EI is constant throughout.
    Continuous beam A-B-C. A fixed, B roller, C roller. AB=4 m with 60 kN/m UDL, BC=3 m with 100 kN at 1.5 m from C (midspan).
    How to answer
    • Discretize joints and degrees of freedom with EI constant.
    • Form element stiffness matrices for spans AB and BC.
    • Assemble global stiffness matrix and load vector for 60 kN/m UDL and 100 kN.
    • Solve for displacements and member end forces.
  7. 14 Marks
    Compute the ordinate of influence line for moment at mid span of BC for the beam showing in figure at 1 m interval and draw influence line diagram. Assume moment of inertia to be constant throughout.
    Beam A-B-C each 4 m. A hinged, B intermediate support, C roller. Points 1,2,3 marked on AB and 4,5,6 on BC at 1 m intervals. D is midspan of BC (2 m from B).
    How to answer
    • Use Muller-Breslau or consistent deformation to get ILD expression for moment at D.
    • Compute ordinates at 1 m intervals along 8 m beam A-B-C.
    • Tabulate ordinates at points 1-6 and supports.
    • Plot influence line diagram for moment at midspan of BC.
  8. 14 Marks
    Compute the ordinate of influence line for reaction $R_A$ for the beam showing in figure at 1 m interval and draw influence line diagram. Assume moment of inertia to be constant throughout.
    Continuous beam A-B-C. A hinged, B roller, C roller/hinged. Span AB=6 m, BC=5 m.
    How to answer
    • Apply Muller-Breslau for reaction RA by releasing vertical restraint at A.
    • Compute ILD ordinates at 1 m intervals over 11 m beam.
    • Tabulate values at A, B, C and intermediate points.
    • Draw influence line diagram for RA.
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