0 of 15 units read in Engineering Sciences

Engineering Sciences • Statics

Method of Sections: One Cut, Three Forces

6 min read

A section cut through no more than three members whose forces are unknown leaves a free body with three equations. Pick each moment point where the other two unknown lines of action meet, and every force falls out of one equation.

Worked: a parallel-chord truss

A parallel-chord truss of four 20 ft panels, 80 ft long and 15 ft deep, pinned at A on the left and on a roller at E on the right. Bottom chord joints are A, B, C, D, E from left to right; top chord joints are F, G, H above B, C and D. Verticals BF, CG and DH; diagonals AF, FC, CH and HE. Loads of 12 kips hang from B, C and D. Bottom chord member BC is highlighted. Find the force in BC, and in the top chord and diagonal cut with it.

Symmetric loading: each reaction is 36/2 = 18 kips. Cut through FG, FC and BC, and keep the left piece.

  • BC: moments about F, where FG and FC meet. 18 × 20 = F_BC × 15, so F_BC = 24 kips tension. The load at B sits directly under F and drops out.
  • FG: moments about C. 18 × 40 − 12 × 20 = 480 = F_FG × 15, so F_FG = 32 kips compression.
  • FC: vertical equilibrium. The panel shear is 18 − 12 = 6 kips, and FC (25 ft long) has a vertical component of 15/25 = 0.6 per kip, so F_FC = 10 kips tension.

Check it stuck: a set from Statics, the knowledge area this unit teaches.

Quiz this area

0 of 15 units read in this chapter