How trusses work
Trusses are frameworks of slender members joined into triangles. They carry large loads with little material, which is why they appear in bridges, roofs, towers, and cranes.
What a truss is
A truss is a structure of straight members connected at their ends by joints. Because a triangle cannot change shape without changing a side's length, triangulated frameworks are rigid. Trusses use material efficiently, making them ideal for long spans such as bridges and roofs.
Standard assumptions
Truss analysis assumes members are connected by smooth pins, loads are applied only at joints, and members' own weights are small or shared between their end joints. Under these assumptions, every member is a two-force member, carrying pure tension or pure compression along its length.
Tension and compression
A member in tension is being pulled and tends to lengthen; slender steel rods and cables handle tension well. A member in compression is being pushed and tends to shorten; long compressed members can buckle sideways, so they are made thicker or braced. Knowing which is which drives the design.
Simple trusses
A simple truss starts with a basic triangle and grows by adding two members and one joint at a time. For a simple plane truss, the number of members m and joints j satisfy m = 2j - 3. A truss with 7 joints therefore has 11 members.
Determinacy
Each joint gives two equilibrium equations, so a truss with j joints has 2j equations. With m member forces and r support reactions, the truss is statically determinate when m + r = 2j and is stable. More members than that make it indeterminate; fewer make it unstable.
Famous truss types
Named truss patterns include the Howe truss (1840), the Pratt truss (1844), and the Warren truss (1848), differing in how diagonals are arranged. In a Pratt truss under typical loads, diagonals are in tension and verticals in compression; in a Howe truss, the opposite.
Space trusses
A space truss extends the idea to three dimensions using tetrahedra, the 3D equivalent of triangles. Transmission towers, stage lighting rigs, and the International Space Station's main truss are space trusses.
Worked example
A roof truss has 6 joints and rests on a pin (2 reactions) and a roller (1 reaction). For determinacy, m + 3 = 2 x 6 = 12, so it should have 9 members. If the builder adds a tenth member as an extra brace, the truss becomes statically indeterminate: stronger and more redundant, but requiring deformation analysis to find member forces.
Key takeaways
Trusses are triangulated frameworks of straight members joined at their ends, rigid because triangles cannot deform. Assuming pinned joints and loads only at joints makes every member a two-force member in tension or compression; compression members can buckle. Simple plane trusses satisfy m = 2j - 3, and a truss is statically determinate when m + r = 2j. Common patterns include Howe (1840), Pratt (1844), and Warren (1848) trusses, and space trusses use tetrahedra.
Flashcard
Framework of straight members in triangles
Check your understanding
A simple plane truss has 7 joints. How many members does it have?