CE 201 - Statics Chapter 6 – Lecture 21

THE METHOD OF SECTIONS The method of sections is based on the fact that if a body is in equilibrium, the any part of the body is in equilibrium. This method can be applied by cutting the body into two parts and including all loadings acting on the body in the free-body diagrams. Tensile Forces Compressive Forces

The method of sections can also be applied to cut several members of an entire truss. 

F2 FBE  FFE FBC Ay F1 FBC FFE  FBE Dy After isolating both parts, the equilibrium equations (Fx=0; Fy=0; Mo=0) can be applied to both sections. Since we have only three equilibrium equations, one should choose a section that has at most three unknowns.

Notes The line of action of each member can be identified from the geometry of the truss the member forces acting on one part of the truss are equal but opposite to those on the other part.

The unknown member forces (FBE, FBC, and FFE) can be determined by applying the three euilibrium equations to the free-body diagram of one part. Support reactive forces can be found by applying equilibrium equation on the entire truss. One the main advantages of the method of section is the ability to determine directly the force in a particular member. The direction of member forces can either be assumed of found by inspection.

Procedure for Analysis Make decision on where to section or cut the truss Draw the free-body diagram of the part to be considered in analysis Before isolating the two parts, determine the support reactive forces Decide about the direction of the forces Apply equilibrium equations