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Analysis of truss using the method of section

The analysis of truss using the method of the section is suitable when the forces of a few members are required to be determined. The method of section provides a practical and direct way. In this method, an imaginary cut is made at an appropriate location. We cut the truss into two parts. The original truss is in equilibrium. This means the two portion of the truss also in equilibrium. The location of cutting should be appropriate, and the number of unknowns should not be more than 3 unknowns, given that there are only three equilibrium equations, calculate reaction before cutting the truss into two parts. 





Procedure for Analysis


  • Determine the location of section or cut. And you should decide how to cut the truss through the member's needs for analysis.
  • Determine the external force if it is necessary to reduce the number of unknowns. Remember, we have three equilibrium equation. So the number of the unknown should not be more than 3.
  • Draw the free body-diagram, assume the force in tension and if the numerical solution is positive, that means the assumption is ok and member in tension and if negative that means the member is in compression.
  • Use the equilibrium equation to determine the unknown forces.

Determine the force of GJ and CO

To determine at member GJ, we make cut a-a at the truss, free body diagram shown in figure 2. the number of unknown force is 3 only, the reaction at support are given. If the reaction at support not given we need to determine it before sectioning the truss, otherwise we will have more than 3 unknown forces, and we can find the force in member GJ.
Figure 1


  Σm at i=0
We select this equilibrium equation because it eliminates FKJ and FGH. So we find the force for FGJ without finding the forces for other members.
FGJ*6*sin(30)+300*3.464=0
FGJ=-346lb

Figure 2

  Σm at A=0

-300*3.464+FCO*6=0
FCO=173 lb

Figure 3






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