Structures
Structures questions test three things: can you identify the forces in a member, can you calculate reactions and moments, and can you explain why a shape or material fails.
Forces and equilibrium
Members carry tension (pulled), compression (pushed), shear (slid), torsion (twisted) or bending. A body at rest satisfies ΣF = 0 and ΣM = 0. Moment = force × perpendicular distance (N m). Resolve inclined forces with sin/cos before summing.
Form and stability
Triangulation makes a frame rigid: a rectangular frame racks under shear, and one diagonal creates two triangles and fixes it. Identify members by imagining removal - if the joint springs apart, the member was a tie (tension); if it collapses together, a strut (compression). Beams are simply supported (both ends) or cantilevered (one fixed end); for a central point load, maximum bending moment = FL/4, and for a cantilever with an end load it is FL. Stability improves with a low centre of gravity and a wide base; a body topples when the weight's line of action falls outside the base.
Stress, strain and safety
σ = F/A (N/mm² = MPa); ε = ΔL/L; E = σ/ε. Factor of safety = failure stress ÷ working stress, always above 1. Slender compression members fail by buckling well below the yield stress, which is why trusses use triangulation and compression tubes use large diameters.
Worked example
A 4 m simply supported beam carries 600 N at 1 m from the left support. Moments about the left support: R_right × 4 = 600 × 1, so R_right = 150 N and R_left = 450 N. Maximum bending moment is under the load: 450 × 1 = 450 N m. With a section modulus Z = 3,000 mm³ = 3 × 10⁻⁶ m³, σ = M/Z = 450 ÷ 3 × 10⁻⁶ = 150 × 10⁶ Pa = 150 MPa. For a yield strength of 250 MPa the factor of safety is 250/150 ≈ 1.67 - sound for a static load, marginal if the load is cyclic and fatigue is possible.
Traps
- Using the sloping length instead of the perpendicular distance in a moment.
- Mixing N with kN, or mm² with m² - a factor of 10⁶ error.
- Calling every compression member a strut without applying the "remove it" test.
- Confusing stress (load per area) with force, and stiffness (E) with strength.
- Quoting a factor of safety with no calculation behind it.