22-Mec-B9 Advanced Engineering Structures: May 2013

Paper format. National Exams, May 2013 — 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, structural idealisation, shear centre (Ch. 16, 17, 20, 21, 23).
• A. C. Ugural and S. K. Fenster, Advanced Strength and Applied Elasticity, 5th ed. — unsymmetrical bending, yield criteria, torsion of non-circular bars (Ch. 4, 5, 6).
• A. P. Boresi and R. J. Schmidt, Advanced Mechanics of Materials, 6th ed. — torsion of rectangular sections, columns and elastic stability (Ch. 6, 12).
• 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. — Euler buckling and combined loading (Ch. 8, 13).

Axes and sign convention used throughout. A right-handed set $(X, Y, Z)$ is used for every thin-walled question: $X$ runs along the span from the free end toward the root, $Y$ is vertical (upward) in the cross-section, and $Z$ is horizontal, positive to the right when the section is viewed looking along $+X$. Direct stress is written $\sigma = aZ + bY$ with $Z$ and $Y$ measured from the section centroid, so that the two constants follow from the stress resultants the section must carry, $M_{Y} = \int \sigma Z\,\mathrm{d}A$ and $M_{Z} = \int \sigma Y\,\mathrm{d}A$:

$$a I_{ZZ} + b I_{YZ} = M_{Y}, \qquad a I_{YZ} + b I_{YY} = M_{Z}$$

This form is used in preference to the memorised unsymmetrical-bending fraction because it is self-checking: the physical sign of every answer can be confirmed from the simple rule that, for a cantilever carrying a tip load, the fibres on the side the load points toward go into compression.