Mechanics of Materials

The core stress-analysis area: axial, shear, bending, torsion, and how they combine, plus buckling, static and fatigue failure, and thermal/interference stresses. It's the heaviest area on the Machine Design & Materials depth — the one that decides the most points.

What the problems look like

Calculation-heavy and often multi-step — compute a stress or deflection, combine loads, then check against a failure criterion. Recurring shapes — axial/bending/torsion stresses and deflections; principal stresses and max shear (Mohr's circle); static failure (von Mises, Tresca) and fatigue (Goodman/Soderberg, endurance limit, stress concentration); column buckling (Euler); thermal/interference stresses. Exhibit-heavy (free-body and beam diagrams, Mohr's circle).

By exam day you should be able to —

• compute axial, shear, bending, and torsional stresses and deflections;
• find principal stresses and max shear via Mohr's circle;
• apply static failure theories (von Mises, Tresca) and fatigue (Goodman/Soderberg, endurance limit, Kf);
• size columns for buckling (Euler, slenderness, end conditions);
• handle thermal stress (constrained αEΔT) and interference/press fits.

Where people lose points

• Torsion uses the polar J, not I — solid shaft J = πd⁴/32 (vs. bending I = πd⁴/64); τ_max at the surface (r = d/2).
• Combined bending + torsion must be combined (principal / von Mises / max-shear), not added — the classic shaft-design slip.
• von Mises vs. Tresca — using the wrong criterion (Tresca is the more conservative).
• Sign / combination errors in principal stress (Mohr's circle).
• Buckling end-condition factor K (fixed/pinned/free) wrong → wrong critical load.
• Fatigue: skipping the stress-concentration / endurance-limit corrections or mishandling mean stress (Goodman).
• Bending stress with the wrong section modulus / neutral axis.
• Thermal stress: free expansion produces no stress — only constrained expansion does.

Have these at your fingertips

σ = Mc/I, τ = Tr/J, σ = P/A; Euler P_cr = π²EI/(KL)²; Mohr's circle; the von Mises expression; the Goodman line — and where they sit in the Handbook.

Going deeper

• Combined loading & stress analysis
• Fatigue & failure theories
• Columns & buckling

Part of the Machine Design & Materials depth. Practice this area with exam-real problems — the tutor walks any one you miss. → Start your 7-day free trial — no card. Or take the free practice exam first.