Timber structures
Timber is renewable and light (about 6 kN/m³). Strong along the grain, weak across it; strength drops with knots, cracks and damp. Used for roof trusses, floor joists, posts and beams, and modern engineered wood (glulam, CLT) for larger buildings.
- Design: find the bending moment, choose a size with Z = M / allowable stress, check sag ≤ span/250, check shear and bearing.
- Joints are the weak point: nails, bolts, metal plates, or carved wooden joints.
- Durability: keep it dry, treat against termites and rot. Thick timber chars slowly in fire (about 0.65 mm per minute) and keeps its core.
Reinforced concrete structures
Concrete (cement, sand, stone, water) is strong in compression (typically 20–40 MPa) but only about one tenth as strong in tension. Reinforced concrete puts steel bars (yield about 500 MPa) where tension acts: at the bottom of a sagging beam, at the top over supports.
- Bars and concrete grip each other (bond) and expand almost equally with heat.
- Cover (concrete outside the bars, 20–40 mm) protects steel from rust and fire.
- Stirrups (rings) resist shear; columns have vertical bars with ties; slabs have a mesh of bars.
- Curing (keeping it wet for days) gives full strength at about 28 days.
Fine hairline cracks at the bottom of an RC beam are normal: they show that the steel is working.
Steel structures
Steel has high strength (yield 250–355 MPa), is ductile and stiff (E = 200 GPa), and is equally good in tension and compression. Rolled shapes: I, H, channel, angle, pipe. The I-shape puts material far from the neutral axis where it is most useful.
- Buckling: a slender column bends sideways and fails early. Euler load: P_cr = π²·E·I / L² (pinned ends).
- Connections: bolts and welds; they decide the strength of the frame.
- Weaknesses: rust (paint, galvanising) and fire (loses much of its strength near 550 °C; cover with fire boards, paint or concrete).
- Advantages: factory made, fast to erect, long spans, light for its strength, recyclable.
Choosing a material
Weight per cubic metre: timber about 6 kN, concrete 25 kN, steel 78.5 kN. Steel is heavy per volume but needs very little volume, so a steel frame is light overall. Pick by span, load, fire rules, cost, speed, local supply and look. Whatever the material, check the load path: slab, beam, column, foundation, soil.
Key formulas and definitions
- Required bar area A_s = T / allowable stress
- Timber beam: Z = M / σ_allow (rectangle Z = b·h²/6)
- Euler buckling (pinned): P_cr = π²·E·I / L²
- Safe load = capacity / factor of safety
- Unit weights: timber about 6, concrete 25, steel 78.5 kN/m³
- Timber char depth = rate × time (about 0.65 mm/min)
Worked examples
1. The tension at the bottom of an RC beam is 60 kN. Allowable steel stress is 150 MPa. How many 12 mm bars (113 mm² each)?
A_s = 60 000 / 150 = 400 mm². 400 / 113 = 3.5, so use 4 bars (452 mm²).
2. A timber joist must carry M = 2 kN·m with allowable stress 10 MPa. The joist is 50 mm wide. Find the depth.
M = 2 × 10⁶ N·mm. Z = 2 × 10⁶ / 10 = 0.2 × 10⁶ mm³. Z = bh²/6, so h² = 6 × 0.2 × 10⁶ / 50 = 24 000 and h = 155 mm. Use 50 × 160 mm.
3. A steel column, pinned both ends, L = 3 m, I = 2 × 10⁶ mm⁴, E = 200 000 N/mm². Find the Euler load.
P_cr = π² E I / L² = 9.87 × 200 000 × 2 × 10⁶ / 3000² = 4.39 × 10⁵ N = 439 kN.
4. Compare the weights of 0.1 m³ of timber, concrete and steel.
Timber 6 × 0.1 = 0.6 kN; concrete 25 × 0.1 = 2.5 kN; steel 78.5 × 0.1 = 7.85 kN.
5. A 100 × 100 mm timber post is exposed to fire on all four sides for 30 minutes (char rate 0.65 mm/min). What section is left?
Char depth = 0.65 × 30 = 19.5 mm per side. Left: 100 − 2 × 19.5 = 61 mm. So 61 × 61 mm.
6. A 20 mm steel bar (314 mm²) has yield stress 250 MPa. Find the yield load and the safe load with a safety factor of 1.5.
Yield load = 250 × 314 = 78 500 N = 78.5 kN. Safe load = 78.5 / 1.5 = 52.3 kN.
Common mistakes
- Placing rebar in the middle or the top of a sagging beam. It must sit in the tension zone, near the bottom, with proper cover.
- Saying concrete is "weak". It is strong in compression; it is weak only in tension.
- Forgetting that slender steel columns fail by buckling long before the steel yields.
- Thinking steel does not need fire protection because it does not burn. It loses strength when hot.