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07-Str-A4: May 2016

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

  1. Question 1 Schematic Shear Force and Bending Moment Diagrams
  2. Question 2 Influence Lines for Two Bars of a Pin-Jointed Truss
  3. Question 3 Fixed-End Moment of a Non-Prismatic Beam by the Flexibility Method
  4. Question 4 Horizontal Deflection of a Hinged Portal by Castigliano’s Theorem
  5. Question 5 Lack of Fit — a Link Fabricated 0.06 m Too Long
  6. Question 6 Sway Frame with an Overhang by the Slope-Deflection Method
  7. Question 7 Frame with an Inclined Member and Two Built-in Bases at Different Levels
  8. Question 8 Deriving the Equilibrium Equations and the Stiffness Matrix for a Gable Frame

Start with Question 1 →

Paper format. National Examinations, May 2016 — 07-Str-A4 Advanced Structural Analysis, three hours, closed book (an approved Sharp or Casio calculator is permitted). Questions 1 and 2 are compulsory at 8 marks each; the candidate then answers two of Questions 3, 4 or 5 and two of Questions 6, 7 or 8 at 21 marks each, so six questions make a complete paper of 100 marks. All eight questions are worked here, because this set is a study resource rather than a sat examination.

Reference texts. R. C. Hibbeler, Structural Analysis, 10th ed. (Ch. 6 influence lines, Ch. 9 virtual work and Castigliano, Ch. 10 force method, Ch. 11 slope-deflection, Ch. 12 moment distribution, Ch. 16 stiffness method for frames); A. Kassimali, Structural Analysis, 6th ed.; A. Ghali, A. M. Neville & T. G. Brown, Structural Analysis: A Unified Classical and Matrix Approach, 7th ed.; J. C. McCormac, Structural Analysis: Using Classical and Matrix Methods, 4th ed. Canadian design context for the same structures: CSA S16, CSA A23.3 and the National Building Code of Canada 2020.

Check: sign conventions used throughout. Slope-deflection and moment-distribution end moments \(M_{ij}\) and joint rotations \(\theta\) are clockwise positive (Hibbeler), and the chord rotation \(\psi_{ij}\) is positive when the member chord rotates clockwise. Internal bending moments are plotted sagging positive, converted from the end moments by \(M_{\text{sag}}(i)=M_{ij}\) at the near end and \(M_{\text{sag}}(j)=-M_{ji}\) at the far end. Truss bar forces are tension positive.