A truss roof turns the sideways thrust of its rafters into tension in a tie beam, and the forces are plain statics: a 10 m span with a 2.5 m rise carrying 1.44 to 2.40 kPa of roof and snow load on trusses 3 m apart puts about 21.6 to 36 kN of tension in each tie beam and about 30.5 to 50.9 kN of compression at the foot of each rafter. Because bending moment in an unsupported rafter grows with the square of its span, adding a purlin at mid-span cuts the rafter moment to a quarter, which is why wider halls move from king-post to queen-post trusses.
Part of Community Gathering Hall
Large-span roof structures are the timber or steel frames that carry a roof across a hall without interior columns, sized from the loads they must resist.
A Truss Is A Machine For Turning Thrust Into Tension
The gathering-hall guide lists the options for the 8-12 m clear span. A cruck frame uses pairs of curved timbers leaning together as an arch and, the guide says, spans 8-10 m routinely. A king-post truss uses a horizontal tie beam with a vertical king post from its centre to the ridge and, the guide says, spans up to 8-10 m. A queen-post truss uses two posts and, the guide says, allows 10-14 m. Salvaged steel I-beams span far more, so even one or two beams as main rafters with timber secondary framing make a large hall straightforward. These span limits are the guide’s, drawn from historical carpentry; they are not verified here, and the forces below show why limits exist rather than where they are. For the triangle logic see Truss Structures and Truss Design.
Without a tie, a pitched roof spreads its walls apart. The tie beam holds the two feet of the rafters together, so the walls carry only vertical load. The tie is in tension; the rafters are in compression and also bend between their supports.
Worked Example: Forces In A King-Post Truss
Inputs: clear span L = 10 m; rise h = 2.5 m (so half-span 5 m and a slope of 26.6°); truss spacing s = 3 m (assumed), which suits a 12 m hall with trusses at each end and every 3 m, 5 trusses in all. Loads on the horizontal plan: dead load 8-10 lb/ft² for a tile roof on timber rafters = 0.38-0.48 kPa (Dead Loads; use the upper 0.48 kPa); snow 20-40 lb/ft² in a moderate snow zone = 0.96-1.92 kPa on the horizontal projection, no reduction below a 30° slope (Live Loads). Total w = 0.48 + 0.96 = 1.44 kPa to 0.48 + 1.92 = 2.40 kPa. The truss self-weight is not included.
- Total load on one truss: W = w × L × s = 1.44 × 10 × 3 = 43.2 kN to 2.40 × 10 × 3 = 72.0 kN.
- Reaction at each support: R = W ÷ 2 = 21.6 to 36.0 kN.
- Horizontal thrust, taking moments about the ridge for one half: H × h = R × (L ÷ 2) − (W ÷ 2) × (L ÷ 4), which gives H = W × L ÷ (8 × h) = 43.2 × 10 ÷ 20 = 21.6 kN up to 72.0 × 10 ÷ 20 = 36.0 kN.
- The tie beam carries H in tension: 21.6-36.0 kN. A force in kilonewtons is not a mass in kilograms: 36 kN is the weight of about 3,670 kg (36,000 ÷ 9.81), so 36 kN hanging on a tie beam is the weight of nearly four tonnes.
- Axial force at the rafter foot = √(R² + H²) = √(21.6² + 21.6²) = 30.5 kN up to √(36² + 36²) = 50.9 kN.
The tie beam’s end joints, where the rafter bears into it and the tension is passed on, are usually the critical points; a timber joint must carry H in shear along the grain and hold it for decades.
Worked Example: Why Spans Need Purlins
Inputs: a rafter 50 × 150 mm at 0.6 m spacing (assumed); the loads above, so a uniform load per horizontal metre of rafter q = w × 0.6 = 0.86 to 1.44 kN/m; the rafter simply supported over a horizontal length ℓ; M = q × ℓ² ÷ 8.
- Without a purlin, ℓ = 5 m (ridge to wall): M = 0.86 × 25 ÷ 8 = 2.7 kN·m up to 1.44 × 25 ÷ 8 = 4.5 kN·m.
- With a purlin at mid-rafter, ℓ = 2.5 m: M = 0.68 up to 1.12 kN·m. Halving ℓ divides M by 2² = 4.
- Section modulus Z = b × h² ÷ 6 = 0.05 × 0.15² ÷ 6 = 1.875 × 10⁻⁴ m³. Bending stress σ = M ÷ Z: 2,700 ÷ 1.875 × 10⁻⁴ = 14.4 MPa up to 4,500 ÷ 1.875 × 10⁻⁴ = 24 MPa without a purlin; 3.6 up to 6.0 MPa with one.
- Deflection grows as ℓ⁴ for the same load, so halving ℓ cuts deflection sixteenfold.
Whether 14-24 MPa is acceptable depends on the strength of the actual timber, which this corpus does not give; load-test samples of the wood in use (the corpus’s load-testing method covers rope, not timber) and apply a generous safety factor. The ratio of four holds whatever the timber.
Wider spans multiply these problems: a longer span lengthens the rafters (more bending), increases the tie’s tension (for a given rise and truss spacing, H grows with the square of the span, since W itself grows with L) and lengthens the tie beam, which sags under its own weight unless the king post holds it. The queen-post truss adds supports under the purlins and a central clear panel, and steel replaces tension timber where joints are the weakest link.
What You Need
- Sound, dry, straight timber of the section the loads need, or salvaged steel
- Joinery or bolts that carry the tie’s tension (Joinery Techniques)
- Wall plates or bond beams to spread the reactions (Bond Beam and Top Plate)
- A way to lift trusses safely, and bracing between trusses
Method
Step 1: Fix span, rise and spacing and compute W, R and H as above.
Step 2: Check the tie beam (tension, and the joints at its ends) and the rafters (compression and bending) against tested timber strength.
Step 3: Add purlins or queen posts where the rafter span between supports is large.
Step 4: Brace the trusses against each other and against wind (Wind Loads).
Step 5: Load-test a spare truss or a representative part before the roof goes on.
Common Mistakes
- Leaving out the tie and letting the walls carry the thrust; they spread and the roof falls.
- Reading kilonewtons as kilograms.
- Light joints on a heavy tie.
- Ignoring snow drifts next to a higher wall, which the live-loads guide puts at two to three times the normal load.
Safety
A roof truss failure drops a ridge onto a full hall
Roof failures are sudden, and this is the building where everyone gathers. Build to a higher standard than houses, keep to the lower end of the guide’s spans, assemble and lift on the ground with proper bracing, and never stand under a truss during lifting. Check every tie joint each year, and clear snow from the roof in heavy winters.
Sources And Honest Limits
The statics (reactions, thrust, bending moment, section modulus, deflection scaling) are exact for the stated idealisations: a pin-jointed symmetrical truss under a uniform load. Dead and snow loads come from the corpus; truss spacing, rafter section and spacing are assumed. The corpus’s snow-slope formula (dividing by cos² of the slope) is not used here because it appears to invert the usual reduction. The guide’s span limits (cruck 8-10 m, king-post 8-10 m, queen-post 10-14 m) are unverified, and the corpus disagrees with itself on the king post: Truss Design puts a king-post truss at up to about 6 m (20 ft), so treat 8-10 m as the upper end that needs good timber and joints. No allowable stress for timber is stated because none is sourced in this corpus.
What’s Next
- Learn next: Emergency Shelter Capability — the structure as a refuge
- Combine with: Sizing for Settlement Population — the floor it covers