07-Str-B3: May 2015

Paper format. Professional Engineers Ontario / Engineers Canada national examination 07-Str-B3 — Applications of the Finite Element Method, May 2015. Three hours; four pages. Closed book, with two 8½ × 11 in pages of handwritten notes permitted and one approved non-communicating calculator. Three problems, all of equal value; candidates are instructed to attempt all three. Problem 1 is a ten-part concept paper, Problems 2 and 3 are calculations.

07-Str-B3 is a finite element methods paper rather than a member-design paper: bar and beam elements, isoparametric quadrilaterals, the constant-strain triangle, numerical integration and structural dynamics. The reference list below is therefore the finite-element literature.

Reference texts.

• Logan, D. L., A First Course in the Finite Element Method, 6th ed. — Ch. 3 (bar element), Ch. 4 and 5 (beam element, work-equivalent loads), Ch. 6 (constant-strain triangle, plane stress), Ch. 10 (isoparametric elements, Gauss quadrature), Ch. 16 (structural dynamics, mass matrices).
• Cook, R. D., Malkus, D. S., Plesha, M. E. and Witt, R. J., Concepts and Applications of Finite Element Analysis, 4th ed. — Ch. 3–4 (formulation and convergence), Ch. 6 (isoparametric elements and numerical integration), Ch. 7 (element quality, the patch test, mesh transitions), Ch. 11 (dynamics), Ch. 15 (mixed and hybrid formulations).
• Bathe, K.-J., Finite Element Procedures, 2nd ed. — Ch. 4 (variational basis and convergence), Ch. 5 (numerical integration, reduced and selective integration), Ch. 9 (time integration).
• Chandrupatla, T. R. and Belegundu, A. D., Introduction to Finite Elements in Engineering, 4th ed. — Ch. 5 (CST, plane stress and plane strain), Ch. 6 (beams and frames).
• Zienkiewicz, O. C., Taylor, R. L. and Zhu, J. Z., The Finite Element Method: Its Basis and Fundamentals, 7th ed. — Ch. 6 (the patch test), Ch. 11 (mixed and hybrid forms).
• Hughes, T. J. R., The Finite Element Method: Linear Static and Dynamic Finite Element Analysis — Ch. 4 (mixed methods and reduced integration), Ch. 5 (beam and plate elements), Ch. 7 (consistent and lumped mass matrices).
• CSA A23.3:19 Design of Concrete Structures and CSA S806:12 Design and Construction of Building Structures with Fibre-Reinforced Polymers — the Canadian code frame behind the strengthened-beam modelling question (1.9).