CE-503-A Structural Analysis - II - Nov 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
   Analyze the continuous beam shown in Fig.(a) below by the moment distribution method. Draw the bending moment diagram and shear force diagram, the beam is of uniform section.

   How to answer

   • Compute fixed-end moments for spans AB and BC with $w=16\,kN/m$.
   • Compute stiffness, distribution factors at joint B with far ends fixed.
   • Perform moment distribution to get final support and span moments.
   • Derive reactions and draw shear force diagram.
   • Draw bending moment diagram showing hogging and sagging values.
2. 14 Marks
   Define the following terms:

   1. i)Load Factor
   2. ii)Plastic Modulus
   3. iii)Plastic neutral axis
   4. iv)Relative stiffness
   5. v)Distribution Factor
   6. vi)Factor of Safety
   How to answer

   • Define load factor as ratio of collapse load to working load.
   • Define plastic modulus as first moment of area about plastic neutral axis.
   • Define plastic neutral axis, relative stiffness and distribution factor with formulas.
   • Define factor of safety with significance.
3. 14 Marks
   Explain influence line diagram for indeterminate structures and Muller Breslau Principle.
   How to answer

   • Define influence line diagram and its use for indeterminate structures.
   • State Muller-Breslau principle for qualitative influence lines.
   • Explain application to reactions, shear and moment with displaced shape.
   • Note difference from determinate structures.
4. 14 Marks
   For the double overhanging beam shown in Figure (a), construct the influence lines for the support reactions at B and C and the shearing force and the bending moment at section n.

   How to answer

   • Draw beam A-B-C-D with overhangs and section n mid-way between B and C.
   • Construct influence lines for reactions at B and C using equilibrium or Muller-Breslau.
   • Construct influence lines for shear force at n and bending moment at n.
   • Mark ordinates at A, B, n, C, D.
5. 14 Marks
   A beam of span 8 m is to be designed for an ultimate u.d.l. of 50 kN/m. The beam is simply supported at the ends. Design a suitable I section using plastic theory, assuming $\sigma_y = 250\, N/mm^2$.
   How to answer

   • Compute ultimate bending moment $M_u = w_u L^2/8$ for simply supported beam.
   • Equate $M_p = \sigma_y Z_p$ to required moment.
   • Calculate required plastic modulus $Z_p$.
   • Select suitable I-section with $Z_p$ greater than required.
6. 14 Marks
   Analysis the continuous beam shown in figure by flexibility matrix method.

   How to answer

   • Select redundant(s) and primary structure for propped continuous beam.
   • Formulate compatibility and flexibility coefficients.
   • Solve for redundant reaction.
   • Compute final moments, shear and draw diagrams if required.
7. 14 Marks
   Calculate the section modulus, plastic modulus and shape factor for a circular body of radius R.
   How to answer

   • Recall elastic section modulus $Z = I/y_{max}$ for solid circle.
   • Compute plastic modulus $Z_p = A/2 (\bar{y}_1+\bar{y}_2)$ for circle.
   • Derive shape factor $S = Z_p/Z = 16/(3\pi)$.
   • Substitute $R$ to give values in terms of $R^3$.
8. 14 Marks
   Analyze the given frame and draw the bending moment diagram:

   How to answer

   • Identify sway / non-sway, compute relative stiffness with 2I columns.
   • Compute distribution factors and fixed-end moments for 50 kN and 100 kN loads.
   • Perform slope-deflection or moment distribution analysis.
   • Draw bending moment diagram with values at joints.