Engineering Fundamentals and Applied Mechanics
Domain scope
Engineering Fundamentals and Applied Mechanics tests static equilibrium, free-body diagrams, friction, centroids and second moments, kinematics, work-energy, and impulse-momentum. Machine-framed questions usually reduce to a beam, bracket, or inclined plane once the supports are replaced correctly.
Core rules
- Replace supports with reactions: pin = two force components, roller = one normal, fixed = force plus moment.
- Apply ΣF=0 and ΣM=0 about a point chosen to eliminate unknowns.
- A distributed load w over length L becomes wL acting at its centroid.
- At impending slip, friction F=μN; once sliding, use μ_k.
- Work-energy: U=ΔT+ΔV; power P=Fv or P=Tω.
Worked example
A simply supported beam is 4 m long with a 10 kN point load 1 m from the left support. Taking moments about the left support: R_B×4 = 10×1, so R_B = 2.5 kN. Vertical equilibrium gives R_A = 10 − 2.5 = 7.5 kN. Check with moments about the right support: R_A×4 = 10×3, so R_A = 7.5 kN, which agrees.
Traps
- Treating a roller as a pin and adding a horizontal reaction that does not exist.
- Using the full beam length instead of the load-to-pivot distance.
- Mixing kN with N, or mm with m, in moment arms.
- Assuming F=μN at all times rather than only at impending slip.
- Forgetting that a fixed support carries a moment as well as forces.