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

CE-403 Structural Analysis-I - 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. 7 Marks
    aThe degree of static indeterminacy, $N_s$ and the degree of kinematic indeterminacy, $N_k$ for the plane frame shown below, assuming axial deformations to be negligible, are given by:
    Plane frame with three vertical columns connected rigidly at top by horizontal beam; left column base fixed (hatched), middle and right column bases hinged/pinned on ground (triangular pin supports). No dimensions given.
    How to answer
    • Define degree of static indeterminacy Ns and kinematic indeterminacy Nk for plane frame
    • Apply formulas with axial deformations negligible
    • Count external and internal indeterminacy from supports and closed loops
    • Obtain Ns and Nk values for given fixed and hinged supports
  2. 7 Marks
    bWhat do you understand by indeterminacy? Also explain static and kinematic indeterminacy.
    How to answer
    • Define indeterminacy in structural analysis
    • Explain static indeterminacy with external and internal components
    • Explain kinematic indeterminacy with joint displacements/rotations
    • Give examples/formulas for beams, frames and trusses
  3. 7 Marks
    aWhat do you understand by stability of structure?
    How to answer
    • Define stability of structure
    • Distinguish stable, unstable, externally and internally stable
    • Explain conditions for geometric stability and equilibrium
    • Give examples of stable and unstable arrangements
  4. 7 Marks
    bFor the fixed beam shown in the figure, the influence line diagram for the bending moment at the mid-span of the beam is best represented as
    Horizontal beam AC with A left fixed support (hatched) and C right fixed support (hatched); point B marked at mid-span; dimension L/2 from A to B and L/2 from B to C; sign convention with curved arrows + on top and - at bottom shown at right of C.
    How to answer
    • Identify fixed beam AC with mid-span point B
    • Recall Muller-Breslau principle for influence line for moment
    • Describe shape/sign of ILD for mid-span moment in fixed beam
    • Select best represented ILD curve
  5. 7 Marks
    aWhat is cable? Write assumptions in force analysis of cable.
    How to answer
    • Define cable as flexible tension-only member
    • List assumptions: inextensible/extensible, no bending/shear, load types
    • Explain funicular shape under concentrated and distributed loads
    • State equilibrium conditions for cable analysis
  6. 7 Marks
    bExplain the principles of virtual work applied to deformable bodies.
    How to answer
    • State principle of virtual work for deformable bodies
    • Distinguish virtual displacements and virtual forces
    • Write external virtual work equals internal virtual work
    • Mention application to deflections and equilibrium
  7. 7 Marks
    aWhat is Maxwell reciprocal deflection theorem?
    How to answer
    • State Maxwell reciprocal deflection theorem
    • Define two points and corresponding loads/displacements
    • Express symmetry of flexibility coefficients
    • Mention conditions and uses
  8. 7 Marks
    bDefine
    1. i)Distribution Factor
    2. ii)Stiffness Factor
    How to answer
    • Define distribution factor as ratio of member stiffness to joint stiffness
    • Define stiffness factor for members with far end conditions
    • Give formulas for prismatic members
    • Mention use in moment distribution method
  9. 7 Marks
    aThe horizontal thrust support A in a three hinged arch shown in the given figure is
    Curved arch ACB with A left support and B right support; C crown at top; UDL of 1 kN/m shown over left portion above arch; vertical arrow of 5 m from C downwards; A marked 1 m above base level; horizontal dimensions 8 m from A to C line and 10 m from C line to B.
    How to answer
    • Identify three-hinged arch geometry and UDL of 1 kN/m
    • Take moments about supports to find vertical reactions
    • Use moment zero at internal hinge to solve horizontal thrust at A
    • Compute thrust value with given spans 8 m and 10 m and rise 5 m
  10. 7 Marks
    bState Eddy's theorem in arches.
    How to answer
    • State Eddy's theorem in words
    • Relate bending moment in arch to beam moment and thrust
    • Write expression for moment due to horizontal thrust
    • Mention use for arch analysis
  11. 7 Marks
    aA three-hinged parabolic arch of span '$l$' and rise '$h$' is subjected to a u.d.l. of intensity '$w$'. Then the horizontal thrust at the supports is.
    How to answer
    • Recall three-hinged parabolic arch under full UDL
    • Use equilibrium and zero moment at crown
    • Derive horizontal thrust $H = w l^2 / (8h)$
    • State thrust at supports
  12. 7 Marks
    bIf the deflection at the free end of a uniformly loaded cantilever beam is $15$ mm and the slope of the deflection curve at the free end is $0.02$ radian, then the length of the beam is.
    How to answer
    • Recall deflection and slope formulas for uniformly loaded cantilever
    • Use $\delta = wL^4/(8EI)$ and $\theta = wL^3/(6EI)$
    • Eliminate load-stiffness to get $L = (4/3)(\delta/\theta)$
    • Substitute $\delta=15$ mm and $\theta=0.02$ rad to get length
  13. 7 Marks
    aA cantilever beam is shown in the figure. The moment to be applied at free end for zero vertical deflection at the point is.
    Horizontal cantilever beam 2 m long with fixed support at right end (hatched) and free end at left; downward arrow of 9 kN at free end; span dimension 2 m marked below.
    How to answer
    • Draw cantilever with point load 9 kN at free end
    • Write deflection at free end due to load and due to moment
    • Set total vertical deflection to zero for no deflection condition
    • Solve for required end moment
  14. 7 Marks
    bA uniformly distributed load of $50$ kN/m and $5$ m long crosses a girder of span $15$ m from left to right. What will be the maximum bending moment at a section $6$ m from left end?
    How to answer
    • Draw girder span 15 m and section 6 m from left
    • Place 5 m UDL to maximize moment using ILD ordinates
    • Compute maximum ordinate area for bending moment
    • Multiply by $w=50$ kN/m to get maximum bending moment
  15. 7 Marks
    aWhat are the assumptions made in the analysis of a simple truss?
    How to answer
    • Define simple truss as triangulated pin-jointed frame
    • List assumptions: pin joints, loads at joints, straight members
    • Assume members carry axial force only, neglect self-weight
    • Mention small deflections and static determinacy
  16. 7 Marks
    bIn the cantilever beam PQR shown in figure below, the segment PQ has flexural rigidity $EI$ and the segment QR has infinite flexural rigidity. The deflection and slope of the beam at '$Q$' are respectively.
    Cantilever beam PQR horizontal with P left fixed support (hatched); segment PQ length L with EI marked; segment QR length L marked as Rigid (thick bar); downward load W at R right end.
    How to answer
    • Identify cantilever PQR with PQ flexible EI length L and QR rigid length L
    • Consider load W at R transferred as point load plus moment at Q
    • Compute slope and deflection at Q using cantilever formulas
    • Obtain deflection $W(2L)^? $ and slope due to rigid rotation
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