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16-Civ-B1 Advanced Structural Analysis: December 2019

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

  1. Question 1 Statical indeterminacy and the minimum number of structural degrees of freedom
  2. Question 2 Schematic shear force and bending moment diagrams
  3. Question 3 Least work applied to two cantilevers joined by a tension member
  4. Question 4 Castigliano's theorem — vertical deflection of an overhang tip
  5. Question 5 Influence lines for a three-span continuous beam
  6. Question 6 Slope-deflection analysis of a three-member beam with support settlement
  7. Question 7 Flexibility analysis of a non-prismatic fixed-ended beam
  8. Question 8 Slope-deflection analysis of a sway portal with free stubs
  9. Question 9 Deriving the stiffness matrix and load vector for a three-member frame

Start with Question 1 →

Paper format. National Examination, December 2019 — 16-Civ-B1 Advanced Structural Analysis, 3 hours, CLOSED BOOK (an approved Casio or Sharp calculator only). Nine questions on seven pages: Questions 1 and 2 are compulsory (8 and 12 marks); the candidate then answers TWO of Questions 3, 4 or 5 (18 marks each) and TWO of Questions 6, 7, 8 or 9 (22 marks each), so six questions make a complete paper of 100 marks. Because this set is a study resource, all nine questions are solved here.

Reference texts. R. C. Hibbeler, Structural Analysis, 10th ed. (Pearson) — Ch. 6 influence lines, Ch. 8–9 deflections and virtual work, Ch. 10 force (flexibility) method, Ch. 11 slope-deflection, Ch. 12 moment distribution, Ch. 15–16 matrix stiffness. A. Kassimali, Structural Analysis, 6th ed. (Cengage) — Ch. 7 Castigliano and least work, Ch. 8 influence lines, Ch. 13 slope-deflection, Ch. 17–18 matrix stiffness. A. Ghali, A. M. Neville and T. G. Brown, Structural Analysis: A Unified Classical and Matrix Approach, 7th ed. (CRC). Canadian context for the settlement question: NBC 2020 Part 4 and CSA S6:19 treat differential support settlement as an imposed deformation to be combined with the permanent loads, so the self-equilibrating moment set computed in Question 6 is a real design action, not a curiosity.

Sign convention used throughout. End moments are written counter-clockwise-positive on the member, which is the convention that matches the standard six-degree-of-freedom element stiffness matrix; the slope-deflection equation is then $M_{ij} = \dfrac{2EI}{L}\left(2\theta_i + \theta_j - 3\psi_{ij}\right) + \mathrm{FEM}_{ij}$ with $\psi$ the counter-clockwise chord rotation and, for a downward UDL, $\mathrm{FEM}_{ij} = +wL^2/12$, $\mathrm{FEM}_{ji} = -wL^2/12$. Ordinary sagging bending moments, which is what every diagram below plots, are recovered as $M_{\text{sag}}(i) = -M_{ij}$ and $M_{\text{sag}}(j) = +M_{ji}$. Mixing this with the clockwise-positive convention of some textbooks produces clean-looking integers that are wrong.