Engineering Sciences and Mechanics
Scope
Engineering Sciences and Mechanics tests equilibrium, stress and strain, beam behavior, dynamics, fluid flow, and thermodynamics. Expect combined problems: a beam load that requires statics first, then a stress calculation.
Core rules
- Static equilibrium: ΣF = 0 and ΣM = 0 about any point.
- Axial stress σ = P/A; bending stress σ = Mc/I; shear stress τ = VQ/(Ib).
- Simply supported beam with a central point load P: M_max = PL/4 at midspan.
- Bernoulli (frictionless, steady, incompressible): p/γ + v²/(2g) + z = constant.
- First law for a steady-flow open system: q − w = Δh + Δke + Δpe.
Worked example
A simply supported beam spans 4.0 m and carries a 10 kN point load at midspan. The section is 100 mm wide by 200 mm deep. Find the maximum bending stress. M = PL/4 = (10 kN)(4.0 m)/4 = 10 kN·m. I = bh³/12 = (0.100 m)(0.200 m)³/12 = 6.667 × 10⁻⁵ m⁴. c = 0.100 m. σ = Mc/I = (10,000 N·m)(0.100 m)/(6.667 × 10⁻⁵ m⁴) = 15.0 × 10⁶ Pa = 15 MPa. Reasoning check: converting to metres before computing I avoids a factor-of-10⁹ error.
Traps
- Using millimetres in E or I while the moment is in N·m.
- Taking c as the full depth instead of half.
- Forgetting self-weight in a “uniform beam” problem.
- Applying Bernoulli across a pump or turbine without the work term.