CE-403 Structural Analysis-I - Jun 2022 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
   aWhat are the assumptions made in the analysis of a simple truss?
   How to answer

   • Members are two-force, straight, connected by frictionless hinges
   • Loads act only at joints, self-weight neglected or at joints
   • Small deformations, linear elastic behaviour
2. 7 Marks
   bExplain the principles of virtual work applied to deformable bodies.
   How to answer

   • Statement of virtual work for deformable bodies: external virtual work = internal virtual work
   • Expression $\delta U_e = \delta U_i = \int \sigma \delta \epsilon dV$
   • Application to displacements and equilibrium
3. 7 Marks
   aExplain clearly about strain energy and complementary energy methods.
   How to answer

   • Definition of strain energy $U = \int M^2dx/2EI + ...$
   • Definition of complementary energy $U^* = \int ...$
   • Methods based on each and conditions when they coincide
4. 7 Marks
   bWhat is the advantage of method of section over method of joints?
   How to answer

   • Direct analysis of single member vs whole structure
   • No need to solve all joints progressively
   • Useful for finding force in specific / interior member
5. 7 Marks
   aClassify the arches based on materials, shapes and structural systems.
   How to answer

   • Classification by material: timber, steel, concrete, masonry
   • Classification by shape: circular, parabolic, elliptical, etc.
   • Classification by structural system: three-hinged, two-hinged, fixed
6. 7 Marks
   bState Eddy's theorem in arches.
   How to answer

   • Statement: bending moment at section in arch equals beam moment minus H times rise
   • Relation $M = M_{beam} - H \cdot y$
   • Interpretation as inverted funicular polygon
7. 7 Marks
   aA portal frame ABCD has its end A is hinged, while the other end D is on rollers. All members have the same flexural rigidity 'EI', length 'L'. A horizontal force 'P' is applied on the roller end. Find the displacement of the roller end.
   How to answer

   • Define portal ABCD with supports and load P at D
   • Compute bending moment equations in terms of P with EI, L constant
   • Apply strain energy / Castigliano / virtual work to get $\Delta = \int M m dx/EI$
8. 7 Marks
   bFind the vertical deflection of the overhanging end 'C' of the beam, shown in Figure.

   

   How to answer

   • Draw beam A-B with span L and overhang B-C L/3
   • Write M equations for AB and BC
   • Apply unit load / Castigliano to compute vertical deflection at C
9. 14 Marks
   A continuous beam ABCD, 16.0m long is shown Figure. Find the support moments and reactions; Draw also SFD and BMD, using Slope deflection method.

   

   How to answer

   • Calculate fixed-end moments and distribution for spans AB, BC, CD
   • Apply slope-deflection equations and equilibrium at B, C
   • Find reactions and draw SFD and BMD
10. 14 Marks
    A three hinged parabolic arch of 22 meters span and 4m central rise carries a point load at 4 kN at 4m horizontally from the left hand hinge. Calculate the normal thrust and shear force at section under the load. Also calculate the maximum bending moment positive and negative.
    How to answer

    • Compute reactions and horizontal thrust for three-hinged arch
    • Find arch ordinate and slope at 4m from left
    • Resolve to normal thrust $N$ and shear $Q$ and locate max positive/negative BM
11. 14 Marks
    Explain the importance of influence line diagram. Explain with suitable examples.
    How to answer

    • Definition of influence line diagram for reactions, SF, BM
    • Uses for moving loads, placement for maxima
    • Illustrate with simply supported beam and truss examples with diagrams
12. 14 Marks
    Write short notes on the following.

    1. a)Rib shortening and temperature effects
    2. b)EUDL
    3. c)Castigliano's first and second theorem
    How to answer

    • Rib shortening and temperature effects in arches: causes and corrections
    • EUDL: definition and equivalent load concept
    • Castigliano's first and second theorems: statements and uses