The Chartership Forum
Lesson review: expert verification remains open

This lesson has received a full-context editorial review and a check of its technical explanations. Selected arithmetic has been checked separately. This is not independent engineering sign-off.

Checks needed for project use

  • An independent structural reviewer must check the illustrated models, prediction feedback, geometry and full interactive input ranges.
  • Independently verify every member-state diagram against the actual loaded joints. Cable shape depends on load distribution per horizontal projection versus arc length. Member-count equality alone does not prove stability or determinacy.
  • Remaining generic Howe/Pratt comparisons must not imply that all Pratt verticals are compression members: force signs depend on loaded joints. Member count is only a necessary determinacy test.

These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.

Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.

Read the lesson register and outstanding review notes

Module 8 · Course notes

Form: carrying load without bending

Some structures carry their load almost entirely in axial force — pure tension or compression — with little or no bending. Trusses, cables and arches all do this, each in its own way. The skill is to read the form: to see which members pull, which push, and when a shape is following the load rather than resisting it by bending.

A truss is a triangulated frame of pin-jointed bars. Because the joints are pins and loads are applied only at joints, every bar carries axial force alone — tension or compression, never bending. Reading a truss is reading which bars pull and which push.

In a simple roof truss the sloping rafters are squeezed (compression) and the bottom tie is stretched (tension) — the tie stops the supports from spreading apart.

tensioncompression
a roof truss under an apex load
The rafters are in compression (they carry the load down to the supports); the bottom tie is in tension (it holds the supports together against the outward thrust). The central post carries nothing here — a zero-force member.

Zero-force members are bars that, for a particular loading, carry no force at all. They are not useless — they brace the truss, hold its geometry and carry other load cases — but recognising them simplifies the reading. A common rule: at an unloaded joint where two members are collinear and a third branches off, the branch is a zero-force member.

Cables and arches take the idea further. A cable can only pull, so it takes up whatever shape lets it carry the load in pure tension — the funicular shape. Turn that shape upside down and you have an arch, which carries the same load in pure compression, provided its shape matches the load. Where the shape and the load do not match, bending appears.

a loaded cable finds its funicular shape
A cable cannot push or resist bending. Under a point load it hangs in straight segments meeting at the load, carrying everything in tension. Invert this shape and it becomes an arch that carries the same load in pure compression.

Worked example

Worked example — which way does each bar act?

Read a king-post roof truss under a load at its apex, one joint at a time.

  1. Step 1 — the rafters and tie

    The apex load pushes down the two rafters, which are therefore in compression. They thrust outward at the supports, and the bottom tie stretches to hold the supports together — the tie is in tension.

    tensioncompression

  2. Step 2 — the zero-force post

    At the bottom-middle joint, the two halves of the tie are collinear and the vertical post branches off. With no load at that joint, the post carries nothing — a zero-force member. Move the load down to that joint and the post springs into tension to carry it.

    tensioncompression

In the exercises, read which bars pull and which push, spot the zero-force members, and reason about how cables and arches carry load by shape.

How to read these problems

The three-step method

  1. 1Points of certainty. Match the displacement and rotation that each support prescribes, including any settlement. Infer the displacement direction from the whole structure and load case; it need not be downward at every loaded point.
  2. 2Deflected shape and reaction directions. Sketch the compatible deflected shape. To find a reaction's direction, imagine removing that support: the direction that pushes the structure back to its place is the reaction's sense (it may be a hold-down).
  3. 3Bending moment and contraflexure. Draw the bending-moment diagram on the tension side and check it against the shape: hogging where the curve is convex-up, sagging where convex-down, zero at pins and at every contraflexure.

Rules that must always hold

  • 1.Moment is zero at a genuine moment release and at an unloaded simple end. A continuous member can carry moment over a translational support.
  • 2.A bending-moment diagram crosses the baseline exactly at a point of contraflexure.
  • 3.Under a distributed load the bending-moment diagram is curved; under point loads alone it is straight lines.
  • 4.At a fully fixed support the deflected shape leaves the support with zero rotation (tangent along the member).
  • 5.For an initially straight elastic beam without imposed curvature, zero curvature implies zero bending moment.
  • 6.The moment is drawn on the tension side: sagging below the member, hogging above it.

Now predict for yourself

Trusses & structural-form exercises

34 exercises on tension and compression members, zero-force members, cantilever trusses, thrust and cables. Predict, then reveal an explanation.

Start the exercises →

This lesson is educational material. It uses simplified examples to teach principles, and must not be relied on for real design or safety-critical decisions.