How the method of sections works
- Find the reactions from the whole truss.
- Cut through the members you want, three at most, and keep one side. Every outside force on that side goes in, including its support reaction.
- Draw each cut member force pulling out of the part you keep, as tension.
- Take moments about the point where two of the cut members meet: the third is then the only unknown. Its arm is the perpendicular distance to its line.
- When the other two cut members are parallel chords, ΣFy = 0 gives the third instead.
An example from set EXDE2K
A Pratt truss of six 4.5 m panels, 6 m high, with a pin at A and a roller at G, carries 20 kN at C and 8 kN at E, so Gy = 12 kN and Ay = 16 kN. Cut through CD, DI and IJ and keep the left part. Moments about I, where DI and IJ meet: FCD × 6 − 16 × 9 = 0, so FCD = 24 kN T. The chords are parallel, so ΣFy = 0 gives the diagonal: −20 + 16 − (4/5)FDI = 0, so FDI = −5 kN, which is 5 kN C. Moments about D: −FIJ × 6 + 20 × 4.5 − 16 × 13.5 = 0, so FIJ = −21 kN, which is 21 kN C. Open set EXDE2K.
Questions
Where do you take moments in the method of sections?
About the point where two of the cut members meet. Their forces pass through it, so the equation has only the third member as an unknown. When two cut members are parallel chords, use ΣFy = 0 for the third instead.
Which side of the cut should you keep?
Either side gives the same answers. The side with fewer loads and supports is quicker, and the key keeps that one. Leaving out the support reaction on your side is a common slip.
How many members can you cut?
Three at most, and not all meeting at one point, because one free body gives only three equations.
What is the moment arm of an inclined member?
Its perpendicular distance from the moment centre. You can also slide the force along its line to a joint and take the moments of its two components there; both give the same moment.
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.