16-Civ-B9 The Finite Element Method: May 2013

Paper format. 98-Civ-B9 Applications of the Finite Element Method, National Examinations, May 2013. Three hours, closed book, one two-sided aid sheet, any Casio or Sharp approved calculator. Four problems are set and the candidate answers any three; all problems are of equal value. All four are solved here, because the set is a study resource rather than a sitting.

Reference texts for this subject.

• Logan, D. L., A First Course in the Finite Element Method, 6th ed., Cengage — bar, beam and frame elements, the CST, and isoparametric quadrilaterals.
• Cook, R. D., Malkus, D. S., Plesha, M. E. and Witt, R. J., Concepts and Applications of Finite Element Analysis, 4th ed., Wiley — element quality, integration order and spurious modes.
• Bathe, K.-J., Finite Element Procedures, 2nd ed. — formulation and convergence.
• Zienkiewicz, O. C., Taylor, R. L. and Zhu, J. Z., The Finite Element Method: Its Basis and Fundamentals, 7th ed., Butterworth-Heinemann.
• McCormac, J. C., Structural Analysis: Using Classical and Matrix Methods, 5th ed., Wiley — the direct stiffness method for plane frames.
• Hibbeler, R. C., Structural Analysis, 10th ed., Pearson — shear and moment diagrams, symmetry arguments.

Canadian practice note: the numerical work below follows the units printed on each question (US customary in Problem 1, SI in Problems 3 and 4), as the exam intends. Where a design decision would follow, CSA S16 / CSA A23.3 and the NBCC govern in Canada; the element mechanics themselves are code-independent.