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Truss Force Analysis

Method of joints reveals tension and compression in every member of a triangulated truss.

A free, animated truss force analysis you can read here or embed on any website, from Scrollchart.

Truss Force Analysis

Truss Force Analysis (Method of Joints)4-panel Pratt truss, simply supported, central load P applied at apex. Forces in multiples of P.R = PR = P2P-2P-P-P-2P+2P+P+P+2P+P+2P+P-2P√2-P√2-P√2-2P√2ABCDEFGHIJTension (+): bottom chord and inner verticals carry pullCompression (-): top chord and diagonals carry push. Zero-force members remain for stability.Joint equilibrium:ΣFx = 0, ΣFy = 0at every joint JMembers: m = 2j - 3Here: 17 = 2×10 - 3 ✓

A simple Pratt truss with applied load. Each member colored by tension (red) or compression (blue). Joint-method equilibrium equations annotated.

Good for

  • Statics coursework illustrating method of joints, member force sign conventions, and determinacy check
  • Structural analysis articles comparing Pratt and Howe truss force patterns under the same loading
  • Bridge and roof truss design content explaining why chord forces govern member sizing

Source & accuracy

This truss force analysis is an editorial illustration built to represent the concept accurately. Where it shows figures, they are typical or representative values chosen to make the relationship clear, not a single underlying dataset. The diagram and its explainer are reviewed and maintained centrally, and updated over time as understanding improves.

How the method of joints reveals internal forces

A truss is a frame of triangles pinned together with no moment resistance at joints. This simplification means each member carries only axial force: tension or compression. The method of joints isolates one pin joint at a time and applies equilibrium: the sum of all forces (known loads, reactions, and unknown member forces) must equal zero in both x and y directions. Starting at a joint with no more than two unknowns, the method solves for forces iteratively, moving from joint to joint until the entire truss is analyzed.

Tension, compression, and member sizing

Once member forces are known, designers size each member by material. A member in tension must resist the pull; a rod or cable works well. A member in compression must resist buckling, so a column or tube is chosen. The force magnitude determines the cross-sectional area needed. A bottom chord in tension under a big load needs a large bar; a top chord in compression over the same load also needs area, but for stiffness against buckling rather than pure strength. Symmetry in loading often creates symmetric internal force patterns, easing design.

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Reference

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