Mechanical Design Failure Mode Cases

Name the part and the failure mode

Mechanical design questions are easiest when treated as failure-mode selection problems. A shaft, gear, spring, bearing, bolt, weld, key, pressure vessel, or bracket does not simply have one generic strength. It can yield, buckle, fatigue, wear, loosen, fracture, overheat, deflect too much, or fail by contact stress. The equation choice follows that failure mode.

Start with a two-part sentence: this is a component under this loading, so the likely limit is this failure mode. Example: a rotating shaft carrying a pulley is under torque plus bending, so fatigue and combined stress may govern. A slender column in compression is a buckling problem even if the material yield strength is high. A bolt group with eccentric load is a load-distribution problem before it is a simple shear calculation.

Power transmission cases

Many design items start with power and rotational speed. Convert rpm to angular speed, find torque from P = T omega, and then translate torque into shaft stress, gear tangential force, or coupling load. In gear cases, the tangential force at the pitch circle is related to torque and pitch radius. Speed ratio follows tooth count or pitch diameter for meshing gears. If answer choices differ by a factor of two, check whether you used radius or diameter.

Bearing-life cases require careful reading of the exponent and units. If life is proportional to (C/P)^3 for a ball bearing, a modest load increase causes a large life decrease. Do not average loads casually unless the problem gives an equivalent-load method. If speed is included, convert between revolutions and hours consistently.

Springs, bolts, and pressure parts

Spring rate formulas are geometry sensitive. Wire diameter often appears to the fourth power, while mean coil diameter and active coils reduce stiffness. The same spring may also require a shear-stress check, so do not stop after deflection if the prompt asks for safety.

Fasteners require load path. A direct shear connection with centered load may divide load among bolts. An eccentric bracket produces primary shear plus secondary shear from the moment. A preloaded joint behaves differently from an unpreloaded pin-type connection. For FE practice, learn to identify whether the question asks for bolt stress, member bearing stress, thread area, or joint separation risk.

Thin-walled pressure vessels are common integrated checks. Hoop stress and longitudinal stress are different, and hoop stress is often twice longitudinal stress for a closed-end cylinder under the same assumptions. Use absolute or gauge pressure as the formula context requires; for stress from pressure difference across a wall, the pressure difference is the driver.

Review like a designer

When you miss a mechanical design question, record the earliest wrong design assumption. Did you choose static yielding when fatigue governed? Did you ignore stress concentration? Did you calculate bearing life with the wrong equivalent load? Did you compare alternating stress to yield strength without an endurance concept? That review style builds exam speed because the next similar problem is recognized by failure mode before equation lookup.