22-Mec-B9 Advanced Engineering Structures: May 2014

Paper format. National Exams, May 2014 — 07-Mec-B9 Advanced Engineering Structures. Three hours, open book, any non-communicating calculator permitted. Eight questions of equal total value (20 marks each); the rubric states that any five constitute a complete paper. All eight are solved here, because the complete set is the study resource.

Reference texts.

• T. H. G. Megson, Aircraft Structures for Engineering Students, 6th ed. — open and closed thin-walled sections, shear flow, shear centre, structural idealisation (Ch. 16, 17, 18, 20, 21, 23).
• A. C. Ugural and S. K. Fenster, Advanced Strength and Applied Elasticity, 5th ed. — yield and fracture criteria, torsion of thin-walled members, statically indeterminate axial members (Ch. 2, 4, 6).
• A. P. Boresi and R. J. Schmidt, Advanced Mechanics of Materials, 6th ed. — torsion of open and closed sections, multiply connected cells (Ch. 6).
• N. E. Dowling, Mechanical Behavior of Materials, 4th ed. — linear elastic fracture mechanics, the Paris law, strain-life and Miner’s rule (Ch. 8, 11, 14).
• R. C. Hibbeler, Mechanics of Materials, 10th ed. — thermal stress in restrained members and combined loading (Ch. 4, 8).

Axes and sign convention used throughout. For every thin-walled question a right-handed set is used: the span axis runs along the member, $Y$ is vertical (upward) in the cross-section, and $Z$ is horizontal. A vertical shear $S_y$ acting on a section whose product of inertia vanishes produces the open-section shear flow $q_s = -\dfrac{S_y}{I_{zz}}\displaystyle\int_0^s y\,t\,\mathrm{d}s$, measured positive in the direction of increasing $s$. Closed cells add the constant redundant flow $q_{s,0}$ fixed either by zero twist (shear-centre problems) or by moment equilibrium (a load of known line of action). All shear flows below are quoted with respect to a stated walking direction, and each question closes with the two statical checks — the resolved vertical force must return $S_y$ and the moment of the flows about a chosen origin must return the moment of the applied load.