Applied Mechanics and Statics
This domain tests whether you can replace a real machine part with a free-body diagram and solve it. Expect vector resolution, equilibrium of concurrent and non-concurrent forces, moments, friction, and the basic stress and factor-of-safety relationships that link statics to design.
Core rules
- Equilibrium: ΣFx = 0, ΣFy = 0, ΣM = 0 about any point.
- Moment = force × perpendicular distance from the pivot. A couple is two equal, opposite, parallel forces; its moment is F × the perpendicular gap.
- Resolve inclined forces: Fx = F cos θ, Fy = F sin θ, measuring θ from the horizontal.
- Friction at the point of slipping: F = μN.
- Stress σ = F/A; factor of safety = failure stress / working stress.
Method
Draw the free-body diagram first: isolate the body, replace supports with reaction forces (roller = one perpendicular reaction, pin = two components, fixed = two forces plus a moment), and show the load directions and units. Take moments about the support that eliminates the most unknowns.
Worked example. A simply supported beam spans 4 m with a 12 kN point load 1 m from the left support. Moment about B: R_A × 4 = 12 × 3, so R_A = 9 kN. Then ΣFy = 0 gives R_B = 12 − 9 = 3 kN. Check by taking moments about A: R_B × 4 = 12 × 1, giving R_B = 3 kN. Consistent.
Traps. Using the sloping length instead of the perpendicular distance for a moment; mixing kilograms and newtons; ignoring self-weight when told the beam is uniform; forgetting that stress in N/mm² is numerically the same as MPa but not the same as N/m².