Method of Sections (Truss)

\sum F_{x} = 0, \sum F_{y} = 0, \sum M = 0 (\leq 3 cut members)

Cut through at most three unknown members so the free-body of one side is solvable with three equilibrium equations. Take moments about a joint where two unknowns meet to isolate the third.

$F_{i}$ (kN): Member force

Step-by-step solved example

Simple triangular truss span 8 m, height 3 m, 12 kN down at the ridge. Find the bottom chord by a section through the three members.

Cut through three members; ΣM about a joint kills two unknowns.

1. Reactions
Each support 6 kN up.
2. Section
Cut vertical through mid; ΣM about the ridge: bottom chord T×3 m = 6 kN×4 m → T=8 kN (tension).
$T = 8 kN$

Answer: Bottom chord T = 8 kN (tension)

10 practice questions

0/10 correct

1.Cut at most how many unknowns?

2.Method of joints uses

3.A zero-force member at an unloaded joint with two collinear members is the

4.Tension pulls

5.If a section cuts four members

6.ΣM about a joint is useful to

7.Truss members are assumed

8.Compression pushes

9.A section through the midspan of a Pratt truss typically finds

10.If joints are actually rigid, extra moments mean