Truss Structures

Part of Structural Engineering

How to design and build triangulated frameworks that span long distances with minimal material.

Why This Matters

A truss is one of the most powerful tools in a rebuilder’s structural repertoire. By arranging members in triangles, you convert bending forces — which are difficult for most materials to resist — into pure tension and compression, which wood and iron handle extremely well. A simple truss can span ten meters with lumber that would sag and break if used as a solid beam.

Trusses appear everywhere in reconstruction: roof systems, bridges, scaffolding, crane booms, and workshop floors. Understanding how they work means you can design structures to fit available materials rather than waiting for ideal timber sizes. A forest of small-diameter poles becomes structurally useful when you know how to triangulate them.

The underlying geometry is ancient. Roman builders used timber trusses. Medieval cathedral roofs survived centuries on truss principles. You do not need engineering software — you need to understand forces, triangles, and how to connect members so joints behave as intended.

The Triangle Principle

The triangle is the only polygon that cannot change shape without changing the length of its sides. A rectangle made of four hinged sticks collapses into a parallelogram under load. A triangle cannot deform. Every truss is a collection of triangles sharing sides.

Member types in a truss:

• Top chord — the upper member, usually in compression
• Bottom chord — the lower member, usually in tension
• Verticals — transmit loads between chords
• Diagonals — carry shear forces, alternating tension/compression by position

When a load pushes down at the center of a simply supported truss, the top chord is squeezed (compression) and the bottom chord is stretched (tension). Diagonals near the supports carry the highest shear. This pattern lets you assign materials by what they resist best: use iron rods for tension members, stout timber for compression members.

Rule of thumb for depth: A truss should be approximately 1/6 to 1/8 of its span in depth. A 9-meter bridge truss should be roughly 1.1 to 1.5 meters deep. Shallower trusses are lighter but have higher chord forces; deeper trusses are heavier but lower-stressed.

Common Truss Types

King Post Truss

The simplest truss. Two rafters meet at a peak, joined by a horizontal tie beam, with a single vertical “king post” connecting the apex to the tie beam center. The tie beam is in tension — it prevents the rafters from spreading. Use for spans up to 6 meters.

Components:

• Two rafters (top chords) — in compression
• One tie beam (bottom chord) — in tension
• One king post — in tension, suspending the tie beam midpoint

Queen Post Truss

Two verticals instead of one, creating a flat central panel. Allows a wider span (up to 10 meters) and creates usable headroom in the central bay. The queen posts are in tension.

Pratt Truss

Verticals in compression, diagonals in tension. Since tension members can be slender (iron rods, rope, thin timber), this design is efficient when you have strong material for diagonals. Diagonals slope toward the center from each support.

Howe Truss

Reverse of Pratt — verticals in tension, diagonals in compression. Better when vertical iron rods are available but diagonal compression members (stout timber) are easy to source.

Warren Truss

No verticals — only diagonals alternating direction, creating a zigzag pattern. Equal load distribution, good for uniform loads. Simpler to build since all members are identical length.

Truss Type	Max Span	Best For	Key Material Need
King Post	6 m	Simple roofs	Straight timber
Queen Post	10 m	Wider roofs	Straight timber
Pratt	15 m	Bridges, floors	Iron for diagonals
Howe	15 m	Bridges	Iron for verticals
Warren	20 m	Long spans	Uniform members

Calculating Member Forces: Method of Joints

You do not need calculus. The method of joints uses simple equilibrium — at any pin joint in a loaded truss, the forces must balance horizontally and vertically.

Step-by-step for a symmetric king post truss under uniform load W:

1. Total load = W (distributed across top chord panel points)
2. Each support reaction = W/2 (symmetric loading)
3. At each rafter foot joint, two forces meet: the rafter (angled) and the tie beam (horizontal). Draw the force triangle.
4. If the rafter rises at angle θ from horizontal, rafter force = (W/2) / sin(θ)
5. Tie beam tension = rafter force × cos(θ) = (W/2) × cos(θ)/sin(θ) = (W/2) / tan(θ)
6. King post tension = W/2 (it carries the midpoint load)

Example: Span 8 m, rise 2 m, total load 20 kN (2,000 kg).

• Each reaction = 10 kN
• Rafter angle θ = arctan(2/4) = 26.6°
• Rafter compression = 10 / sin(26.6°) = 22.4 kN
• Tie beam tension = 10 / tan(26.6°) = 20 kN
• King post tension = 10 kN

Now size each member: timber in compression at 22.4 kN needs cross-section ≥ 22,400 N ÷ 8 N/mm² (green softwood) = 2,800 mm² → a 60×60 mm post is borderline; use 75×75 mm minimum. Tie beam in tension at 20 kN: 20,000 ÷ 10 N/mm² = 2,000 mm² → 50×50 mm adequate in tension, but use 75×100 mm for practical stiffness.

Always add a safety factor of 3× for timber in primary structural use. Multiply calculated forces by 3 before sizing members.

Joint Design

The joint is usually the weakest link in a timber truss. Forces cannot be transferred unless the connection is solid.

Traditional timber joints:

• Mortise and tenon — for compression joints at rafter feet
• Notched halvings — two members crossing, each notched half-depth
• Bridle joint — a fork receiving a tenon, good for king post to tie beam
• Hardwood pegs (treenails) — 20–30 mm diameter oak or locust pegs through overlapping members

Iron connectors (when available):

• Wrought iron straps bent around joints and spiked through
• Square-headed bolts through overlapping members with washers
• Flat iron plates on both faces of a joint, bolted through

Critical rule: Tension joints must be positive connections. Compression joints can simply bear against each other (a rafter sitting in a notch is fine in compression). But if the king post is in tension, it must be bolted or strapped to the tie beam — it cannot just sit on top.

Layout rule: Always draw the joint full-size on a flat floor before cutting. Mark the centerlines of all members. The member centerlines should meet at a single point at each joint; if they do not, eccentric loading creates bending moments that the joint was not designed to handle.

Building a Roof Truss: Practical Sequence

1. Lay out the floor plan — mark the full span on a flat floor with chalk and string lines
2. Cut the tie beam first — length equals clear span plus bearing on each wall (minimum 150 mm each side)
3. Mark the apex — use a plumb line from the midpoint, rise as designed
4. Cut rafters to length — birdsmouth notch at the foot to sit on the wall plate; plumb cut at the apex
5. Assemble flat on the floor — nail or bolt temporarily, check geometry
6. Cut and fit the king post — measure the actual gap between apex and tie beam center (always measure from the built assembly, not the drawings)
7. Install iron straps or bolts at all tension joints
8. Check diagonals — the assembly should be square if diagonals are equal
9. Lift into position — for trusses over 4 m, you need at least four people and a temporary prop at midspan
10. Brace immediately — a truss on edge wants to fall sideways; fix temporary diagonal bracing before releasing

Common Failures and How to Avoid Them

Tie beam sag: Tie beams in tension do not sag — if yours is sagging, it is NOT in tension. Check that the king post is actually attached. A sagging tie beam means the whole roof is spreading at the eaves.

Rafter buckling: Long rafters in compression can buckle sideways. Add purlins (horizontal members spanning between trusses) at the third points to brace the top chord.

Joint splitting: Treenails too close to the end split the timber. Keep treenails at least 7 times their diameter from the end and 3 times diameter from the edge.

Asymmetric loading: If snow or equipment loads one side of a roof more than the other, forces in the diagonals can reverse. Design for worst-case asymmetric load, or add cross-bracing.

The truss is not a complicated device. It is geometry in the service of forces. Build the triangle, connect it honestly, and size the members for what they actually carry.