22-Mec-B9 Advanced Engineering Structures: May 2016

Paper format. National Exams, May 2016 — 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, multi-cell torsion (Ch. 16, 17, 18, 20, 21, 23).
• A. C. Ugural and S. K. Fenster, Advanced Strength and Applied Elasticity, 5th ed. — yield criteria, torsion of thin-walled members, unsymmetrical bending (Ch. 2, 4, 6).
• A. P. Boresi and R. J. Schmidt, Advanced Mechanics of Materials, 6th ed. — torsion of multiply connected cells, columns and stability (Ch. 6, 12).
• N. E. Dowling, Mechanical Behavior of Materials, 4th ed. — linear elastic fracture mechanics, the Paris law, strain-life fatigue and Miner’s rule (Ch. 8, 11, 14).
• R. C. Hibbeler, Mechanics of Materials, 10th ed. — Euler buckling of pin-ended struts and combined loading (Ch. 8, 13).

Axes and sign convention used throughout. A right-handed set is used for every thin-walled question: the span axis runs along the member, $Y$ is vertical (upward) in the cross-section and $Z$ is horizontal (to the right). Section constants are written $I_{ZZ}=\int Z^{2}\,dA$, $I_{YY}=\int Y^{2}\,dA$ and $I_{YZ}=\int ZY\,dA$ about the centroid, and the bending stress is carried as the linear field $\sigma = aZ + bY$, whose coefficients follow from the pair

$$\begin{aligned} a\,I_{ZZ} + b\,I_{YZ} &= M_{Y}, \\ a\,I_{YZ} + b\,I_{YY} &= M_{Z} \end{aligned}$$

with $M_{Y}\equiv\int\sigma Z\,dA$ and $M_{Z}\equiv\int\sigma Y\,dA$. This one pair replaces the Megson fraction and handles symmetric and unsymmetrical sections alike. Shear flows are counted positive in the direction of the walk stated with each figure; a negative answer simply means the flow runs the other way round the circuit. Moments and torques are anticlockwise-positive in the $Z$–$Y$ plane.