Method of joints practice problems

Find the reactions and every member force, with T or C, on an invented truss.

Educational practice only. Not for designing or checking real structures.

Method of sectionsZero-force members

Set

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      How the method of joints works

      1. Find the reactions from the whole truss: moments about the pin give the roller’s reaction, then ΣFy = 0 and ΣFx = 0 give the pin’s.
      2. Start at a joint with no more than two unknown members, usually a support.
      3. Draw each unknown member force pulling away from the joint, as tension.
      4. Resolve inclined members by their slope: on a 3-4-5 member the components are 3/5 and 4/5 of the force.
      5. ΣFx = 0 and ΣFy = 0 give the two unknowns. A negative answer means compression.
      6. Move to the next joint with the forces you found, until every member is known. The joints left over are a check.

      An example from set EXR52K

      A Pratt truss of four 3 m panels, 4 m high, has a pin at A, a roller at E, 8 kN down at B and 24 kN down at D. Moments about A: Ey × 12 − 8 × 3 − 24 × 9 = 0, so Ey = 20 kN, and ΣFy = 0 gives Ay = 12 kN. At joint A, ΣFy = 0 reads (4/5)FAF + 12 = 0, so FAF = −15 kN, which is 15 kN C; then ΣFx = 0 gives FAB = 9 kN T. At joint B the vertical BF holds up the 8 kN load: 8 kN T. Joint G at the top has no load, so the vertical CG carries no force. Open set EXR52K to work the rest.

      Questions

      How do you tell if a truss member is in tension or compression?

      Draw every unknown member force pulling away from the joint, which is tension. A positive answer means the member is in tension (T); a negative one means it pushes on the joint, in compression (C). Here you can type 12.5 C or −12.5.

      Which joint do you start with in the method of joints?

      One with no more than two unknown member forces, usually a support once the reactions are known. ΣFx = 0 and ΣFy = 0 can only find two unknowns. The key solves the joints in an order that always works.

      How do you resolve a diagonal member force?

      Use the slope, not the length. A member that rises 4 for every 3 across (a 3-4-5 triangle) has a vertical component of 4/5 of its force and a horizontal one of 3/5. Using a length in metres in place of these ratios is a common slip.

      Why does a member come out as zero?

      At a joint with no load, where two members are in line and a third is not, the third carries nothing under that loading. The zero-force members page practises spotting these before you start.

      Can I check my own truss here?

      No. Every truss here is invented for exam practice, and there is no way to enter your own. Educational practice only: not for designing or checking real structures.

      How do I give my class the same problems?

      Press Share with class and send the link: everyone gets the same set code and trusses. Print makes up to 30 different copies, each with its own answer key.

      Sources, checked 2 November 2026: Baker and Haynes, Engineering Statics: Open and Interactive, 6.3 Trusses (simple trusses, 2j = m + r, zero-force members), 6.4 Method of Joints (unknowns drawn as tension, so a negative answer is compression) and 6.5 Method of Sections.