Method of Joints

\sum F_{x} = 0 \sum F_{y} = 0 at every joint

Ideal truss members are two-force members. Cut a joint, assume tension (away from the joint), and write ΣFx = ΣFy = 0. Start at a joint with at most two unknowns. Positive result = tension.

$T$ (N): Member axial force (tension +)
$F_{x}, F_{y}$ (N): Components at the joint

Step-by-step solved example

Simple triangle: base 4 m, height 3 m. Top joint has 12 kN downward. Find the two equal rafter forces.

Ideal truss joint: two-force members, ΣFx = ΣFy = 0.

1. Geometry
Each rafter length 2.5 m if isosceles? Base 4, half 2, height 3 → length 3.61 m. Vertical component: (3/3.61)T each.
2. ΣFy
2 T (3/√13) = 12 → T = 12√13 / 6 = 7.21 kN tension.
$T = 7.21 t e x t k N$

Answer: Each rafter 7.21 kN tension

10 practice questions

0/10 correct

1.A two-force member carries

2.Zero-force member at a joint with no external load and two collinear members plus one extra is the

3.Assume tension; a negative answer means

4.Method of joints cannot start if a joint has

5.Method of sections is better when you need

6.A simple plane truss with m members and j joints is determinate if

7.At a pinned support the joint includes

8.Counters (crossing diagonals) indicate

9.ΣFx = 0 at a joint does not involve

10.A vertical 10 kN load at a joint with a horizontal member and a 45° member: the 45° force is