Civil Engineering: Beams, Sections and Effective Stress
What this section tests
The Civil Engineering section applies statics to structures: shear and bending moment behaviour, simple beam design, properties of concrete and steel, soil mechanics fundamentals, and elementary fluid flow and surveying.
Core rules
- Simply supported beam with a uniformly distributed load w over span L: each reaction is wL/2; maximum moment wL²/8 at midspan; shear is linear and zero at midspan.
- Point load P at midspan: M_max = PL/4.
- Second moment of area for a rectangle: I = bd³/12; bending stress σ = My/I, maximal at the extreme fibre y = d/2.
- Effective stress in soil: σ′ = σ − u, with pore pressure u = γ_w h. Strength and settlement follow effective stress.
- Porosity and void ratio differ: n = e/(1+e).
- Discharge Q = Av; Manning's equation depends on slope and hydraulic radius.
Worked example
A simply supported beam spans 6 m under 10 kN/m (self-weight included). Reactions: R = wL/2 = 10 × 6/2 = 30 kN each. Midspan moment: M = wL²/8 = 10 × 36/8 = 45 kN·m. For a 200 mm × 400 mm section, I = 0.2 × 0.4³/12 = 1.067 × 10⁻³ m⁴, so σ_max = My/I = 45 000 × 0.2 / 1.067 × 10⁻³ ≈ 8.4 MPa - well inside normal concrete strength, which is why deflection often governs design instead.
Traps
Adding self-weight a second time when the given load already includes it; mixing kN/m with kN·m; using total rather than effective stress in soil; assuming concrete resists tension; taking I about the wrong axis.