NivaarExam PrepOfficial exam papers ↗

07-Str-A4: December 2016

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

  1. Question 1 Schematic Shear and Bending Moment Diagrams for Three Structures
  2. Question 2 Influence Lines for the Shear Immediately Left of Support C
  3. Question 3 Midspan Deflection by Castigliano’s Second Theorem
  4. Question 4 Least Work Analysis of a Tied Trapezoidal Frame
  5. Question 5 Slope-Deflection Analysis of a Gable Frame with a Fabrication Error
  6. Question 6 Stiffness Matrix of a Straight Non-Prismatic Beam
  7. Question 7 Slope-Deflection Analysis with a Jacked Support and a Span Load
  8. Question 8 Anti-Symmetric Analysis of a Portal Frame
  9. Question 9 Derivation of the Stiffness Matrix and Load Vector for an L-Frame

Start with Question 1 →

Paper format. National Examinations, December 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 (12 and 8 marks); the candidate then answers TWO of Questions 3–5 (18 marks each) and TWO of Questions 6–9 (22 marks each), so six questions constitute a complete paper worth 100 marks. All nine questions are solved here, because the set is intended as a study resource rather than as an exam script.

Reference texts. R. C. Hibbeler, Structural Analysis, 10th ed. (Ch. 6 influence lines, Ch. 9 virtual work and Castigliano's theorems, 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.

Sign convention used throughout. Member-end moments follow the counter-clockwise-positive slope-deflection form $M_{ij}=\dfrac{2EI}{L}\left(2\theta_i+\theta_j-3\psi_{ij}\right)+\mathrm{FEM}_{ij}$, with the chord rotation $\psi_{ij}=\left[(\mathbf{D}_j-\mathbf{D}_i)\cdot \mathbf{e}_2\right]/L$ and $\mathbf{e}_2$ the member axis turned $+90^\circ$. For a downward uniformly distributed load on a horizontal member, $\mathrm{FEM}_{ij}=+wL^{2}/12$ and $\mathrm{FEM}_{ji}=-wL^{2}/12$. Sagging moments are recovered as $M_{\text{sag}}(i)=-M_{ij}$ and $M_{\text{sag}}(j)=+M_{ji}$, and every bending-moment diagram is plotted on the tension side of the member.