The Method of Sections

Learning Goal:

To apply the method of sections to a truss and determine the unknown forces in

specified members.

If a truss is in equilibrium then every member in the truss must also be in

equilibrium. This principle is used in analyzing a truss using the method of

sections. To apply the method of sections, we use an imaginary cut through

members of the truss to expose the forces in those members as external forces.

$($Figure $1)$

If the free$-$body diagram of the joint on either side of the cut is known, we can

apply the equations of equilibrium to that part of the member to determine the

forces at the cut section. Since only three equilibrium equations $({\displaystyle \underset{?}{\overset{?}{}}}{F}_x=0,$

${\displaystyle \underset{?}{\overset{?}{}}}{F}_y=0,$ and ${\displaystyle \underset{?}{\overset{?}{}}}{M}_O=0)$ can be applied to the free$-$body diagram of any

segment, we should try to select a cut that passes through no more than three

members of the truss in which the forces are unknown.

For the Howe bridge truss shown, $d=2\mathrm{.}75m,F_1=3150N,F_2=1850N,$

$F_3=2450N,$ and $F_4=3750N.$

$($Figure $2)$

Figure

Part A $-$ Determining the forces in three members on the right$-$hand side of the truss

Determine the forces in members $HD,CD,$ and $GD.$

Express the magnitudes of the forces in newtons to three significant figures. Separate your answers with commas.

View Available Hint$($s$)$

Hint $1.$ How to set up the solution

Hint $2.$ Determine the vertical support reaction at $E$

Hint $3.$ Considering the layout

Hint $4.$ Draw the external forces in the three cut members

Hint $5.$ Draw the free$-$body diagram for joint $D$

Incorrect; Try Again; $4$ attempts remaining

Part B $-$ The Sense of the Forces

State if the members considered in part A are in tension or compression.

Complete each sentence by dragging the appropriate word into the blank. The words can be used more than once.