22-Mec-B1 Advanced Machine Design · May 2018
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format: National Exams, 16-Mec-B1 Advanced Machine Design, May 2018. Open book, 3 hours, 100 marks. Part I (Problems 1 & 2) is compulsory; candidates answer only three of the four Part II problems (3–6). All six problems are solved here as a complete study resource.
Reference texts. Budynas & Nisbett, Shigley’s Mechanical Engineering Design (10th ed.) — shaft/fatigue §7, bolted joints §8, journal bearings §12, brakes §16, power screws §8–2; Juvinall & Marshek, Fundamentals of Machine Component Design; Norton, Machine Design: An Integrated Approach.
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
No — Tresca (maximum-shear-stress) is the more conservative theory; von Mises is the less conservative of the two. Plotted in principal-stress space for a common yield strength $S_y$, the Tresca yield locus is a hexagon that is inscribed within the von Mises ellipse and touches it at the six uniaxial/equibiaxial vertices. Everywhere else the hexagon lies inside the ellipse, so for a general biaxial state Tresca predicts yielding at the same or a lower load than von Mises. The gap is largest in pure shear: Tresca sets shear yield at $\tau_Y = S_y/2 = 0.500\,S_y$, whereas von Mises sets it at $\tau_Y = S_y/\sqrt{3} = 0.577\,S_y$.
Thus von Mises permits a factor of $2/\sqrt{3}=1.155$ more shear stress before predicting yield — it is the more permissive (less conservative) but also the more experimentally accurate criterion for ductile metals. Tresca is preferred when a guaranteed-safe, hand-calculable bound is wanted.
Fatigue damage is driven primarily by the alternating stress $\sigma_a$, but a superimposed mean stress $\sigma_m$ shifts the amount of alternating stress a part can tolerate for a given life. A tensile mean stress is detrimental: it holds micro-cracks open, accelerates crack propagation, and lowers the permissible $\sigma_a$. This is captured by the Goodman, Gerber and Soderberg lines, on which the safe alternating stress falls monotonically from the fully-reversed endurance limit $S_e$ (at $\sigma_m=0$) toward zero as $\sigma_m$ approaches $S_{ut}$ (Goodman) or $S_y$ (Soderberg). A compressive mean stress is benign or beneficial — it tends to keep cracks closed, which is exactly why shot-peening and surface rolling induce compressive residual stresses to extend fatigue life.
Solid-film lubricants (graphite, molybdenum disulphide MoS₂, PTFE, tungsten disulphide) are selected when a liquid film cannot survive or cannot be maintained. Two representative cases:
They are also favoured for very high contact pressures at low sliding speed, where a hydrodynamic film cannot form and boundary lubrication governs.
Fretting corrosion is the surface damage that occurs at the interface of two nominally clamped or press-fitted parts subjected to small-amplitude oscillatory relative motion (typically a few micrometres, from vibration or cyclic load). The tiny slip continually breaks the protective oxide film and abrades fresh metal, which immediately re-oxidises; the trapped, hard oxide debris (reddish on steel, “cocoa”) acts as an abrasive, pitting the surfaces and initiating fatigue cracks. It is common at shaft–hub press fits, bolted flange faces, splines and bearing seats, and is a frequent precursor to fretting-fatigue failure.
