NivaarExam PrepOfficial exam papers ↗

07-Str-B3: May 2017

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

  1. Question 1 Tapered bar element and a two-element bridge pier
  2. Question 2 Square frame under parting forces, bare and truss-braced
  3. Question 3 Q4 shape functions, plane-stress stiffness term, and a reinforced plate

Start with Question 1 →

Paper format. National Examinations, May 2017 — 07-Str-B3 Applications of Finite Elements. Three hours, CLOSED BOOK with one aid sheet written on both sides and an approved non-communicating calculator. Four pages; three problems, all of equal value; the printed rubric asks the candidate to answer only TWO of the three, the first two that appear in the answer book being the ones marked. All three problems are worked in full below, because the complete set is the study resource rather than a single sitting.

Reference texts. D. L. Logan, A First Course in the Finite Element Method, 6th ed. (Cengage) — Ch. 3 the bar element and work-equivalent loads, Ch. 4–5 beam and plane-frame elements, Ch. 6 the constant-strain triangle, Ch. 10 the isoparametric Q4; R. D. Cook, D. S. Malkus, M. E. Plesha and R. J. Witt, Concepts and Applications of Finite Element Analysis, 4th ed. (Wiley) — Ch. 3 the bilinear rectangle and its stiffness terms, Ch. 6 isoparametric elements and integration order, Ch. 9 convergence and stress sampling; T. R. Chandrupatla and A. D. Belegundu, Introduction to Finite Elements in Engineering, 4th ed. (Pearson) — Ch. 3 and Ch. 7 for the tapered bar and the quadrilateral; K.-J. Bathe, Finite Element Procedures, 2nd ed., Ch. 4 for the variational basis of the element matrices; J. S. Przemieniecki, Theory of Matrix Structural Analysis, for the closed-form tapered-member and frame stiffnesses. The design codes in citations/structural.json (CSA A23.3, CSA S16, CSA O86, NBCC 2020) govern the member sizing that would follow such an analysis in Canada but carry no finite-element theory, so the texts above are cited inline throughout.

Check: two readings taken from the figures rather than the text. (i) In Figure 1(b) the pier is a trapezoid in front elevation only — the side view is a plain 0.5 m × 2 m rectangle — so the out-of-plane thickness is constant at 0.5 m and the cross-sectional area varies linearly with depth. (ii) In Figure 3(b) the plate carries support hatching along its left, top and bottom edges, and the 6000 N arrow springs from the mid-height node on the free right edge; node 4 is therefore the only unrestrained node, which is exactly why part 3.3 asks for $u_4$.