Engineering Mechanics: Statics and Dynamics
What the exam tests
Engineering Mechanics in this exam checks whether you can model a construction situation as a free-body diagram, apply equilibrium or Newton's laws, and interpret the result with correct units and sign conventions. Statics topics include reactions, moments, trusses, friction and centroids; dynamics covers kinematics, force-acceleration, work-energy and impulse-momentum.
Core rules
- Replace supports by reactions: pin = two components; roller = one normal reaction; fixed = two forces plus a moment.
- For a planar rigid body at rest: ΣFx = 0, ΣFy = 0, ΣM = 0.
- Take moments about a point that eliminates an unknown. A distributed load w over length L acts at its centroid with resultant wL.
- Trusses: method of joints for few members; method of sections cuts no more than three unknown members.
- Friction: limiting value F = μN; static friction can be less than μN until motion is impending.
- Dynamics: F = ma; for constant acceleration v = u + at, s = ut + ½at², v² = u² + 2as.
Worked example
A simply supported beam spans 6.0 m. A point load of 12 kN acts 2.0 m from the left support, and a uniform load of 4 kN/m acts over the full span. Find the reactions. Take moments about the left support A, positive anticlockwise: RB × 6 = 12 × 2 + (4 × 6) × 3 = 24 + 72 = 96 kN·m. RB = 16 kN. Vertical equilibrium: RA + RB = 12 + 24 = 36 kN, so RA = 20 kN. Check moments about B: RA × 6 = 20 × 6 = 120; clockwise loads give 12 × 4 + 24 × 3 = 48 + 72 = 120. Correct.
Traps
Using the UDL total but placing it at mid-span when the loaded length is not symmetric; forgetting a support reaction; mixing kN and N; omitting the moment of a force whose line of action does not pass through the moment centre; treating a roller as a pin; and reporting an internal force as an external reaction. In dynamics, sign errors from choosing a direction after writing equations are common.