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07-Str-A1: December 2018

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

  1. Question 1 Stability and Determinacy of Six Structures
  2. Question 2 Reactions, Shear and Bending Moment Diagrams for Three Structures
  3. Question 3 Vertical Deflections at B and D of a Stepped Beam
  4. Question 4 Member Forces in Two Trusses
  5. Question 5 Influence Lines for a Two-Span Beam and for a Truss Member
  6. Question 6 Moment Distribution Analysis of a Frame
  7. Question 7 Vertical Deflection of a Truss Joint by Virtual Work
  8. Question 8 Three-Hinged Gabled Frame — Reactions and Diagrams

Start with Question 1 →

Paper format. National Exams, December 2018 — 07-Str-A1 Elementary Structural Analysis; 3 hours, CLOSED BOOK (an approved Casio or Sharp calculator is permitted). Six questions constitute a complete paper: answer all of Questions 1–5, then one only of Questions 6, 7 or 8. Marks are shown in the left margin (6, 18, 18, 18, 18, then 22 for the optional question). Every question is worked below, including all three alternatives, because the full set is the more useful study resource.

Reference texts. R. C. Hibbeler, Structural Analysis (Ch. 2 determinacy and stability; Ch. 4 influence lines; Ch. 6–9 deflections and virtual work; Ch. 12 moment distribution); A. Kassimali, Structural Analysis (Ch. 3, 6, 8, 13, 16); K. Leet, C.-M. Uang and A. Gilbert, Fundamentals of Structural Analysis; J. C. McCormac, Structural Analysis: Using Classical and Matrix Methods. For Canadian practice the companion documents are the National Building Code of Canada (Part 4 load combinations) and CSA S16 Design of Steel Structures; this paper is pure analysis, so no design code is invoked in the answers.

Check — two figure readings that the printed figures leave open, both stated where they are used. (i) In Question 2(c) the hatched plane under the upper roller is drawn parallel to the inclined member, so the reaction is taken normal to the member. That reading makes every result an integer (R = 28 kN, shears 32 / −4 / −28 kN, axial forces 25 / 10 / 0 kN), whereas a vertical-plane reading gives nothing round; and because the two readings differ only by a force acting along the member axis, the shear and moment diagrams are identical either way. (ii) In Question 7 both wall supports are drawn as triangles on hatching. The truss is analysable only if one of them releases a component; taking the pin at U₂ and the horizontal-only roller at L₃ gives δ = 29.0 mm, and the same value follows if the thin vertical line between the two wall joints is a dimension witness line rather than a member. The alternative (pin at L₃) would give 31.8 mm.