22-Mec-B9 Advanced Engineering Structures: December 2017

Paper format. National Exams, December 2017 — 16-Mec-B9 Advanced Engineering Structures. Three hours, open book, any non-communicating calculator permitted. The paper prints eight questions of equal value (20 marks each) and states that any five constitute a complete exam paper. All eight are solved below, because the set is a study resource rather than a sitting.

Reference texts.

• T. H. G. Megson, Aircraft Structures for Engineering Students, 6th ed. — unsymmetrical bending, shear flow in open and closed thin-walled sections, shear centre, structural idealisation, single- and multi-cell torsion (Ch. 15, 16, 17, 20, 23).
• A. C. Ugural and S. K. Fenster, Advanced Strength and Applied Elasticity, 5th ed. — three-dimensional states of stress, principal stresses, the Tresca and von Mises yield criteria (Ch. 1, 4).
• A. P. Boresi and R. J. Schmidt, Advanced Mechanics of Materials, 6th ed. — shear centre, torsion of multiply connected cells, column stability (Ch. 6, 12).
• N. E. Dowling, Mechanical Behavior of Materials, 4th ed. — strain-life fatigue, the Coffin–Manson relation, the Palmgren–Miner rule and Paris-law crack growth (Ch. 9, 11, 14).
• R. C. Hibbeler, Mechanics of Materials, 10th ed. — Euler buckling of pin-ended columns, slenderness ratio and the transition slenderness (Ch. 13).

Sign convention used throughout. A single right-handed frame is used for every thin-walled question: x runs along the span from the root to the free end, Y is vertically upward and Z horizontally to the right, both measured from the section centroid. Direct stress is written $\sigma_x = aZ + bY$, and the two coefficients follow from $aI_{ZZ} + bI_{YZ} = M_Y$ and $aI_{YZ} + bI_{YY} = M_Z$, in which $I_{ZZ}=\int Z^{2}\,dA$, $I_{YY}=\int Y^{2}\,dA$, $I_{YZ}=\int ZY\,dA$, $M_Y \equiv \int \sigma_x Z\,dA$ and $M_Z \equiv \int \sigma_x Y\,dA$. This one pair of equations replaces the memorised unsymmetrical-bending fraction and is self-checking: for a cantilever carrying a tip load, the fibres on the side the load points toward must go into compression.