METHOD OF SECTIONS:
The method of joints is most suitable when the forces in all the members of truss are required. However, when the forces in few members alone are required, then this method becomes time consuming one and hence other method known as “method of sections” can be followed. For example, consider the truss shown in figure:
If the force in the members FH, GI is required the method of joints becomes a tedious process if we start from A or L. On the other hand, if we consider a portion of truss by passing a section through the members of truss whose forces are required, then using the three equations of equilibrium for any one portion, the forces in the members can be determined. But it should be noted that section must not intersect more than three members. The section divides the truss into two separate parts. The normal procedure for the method of section is as follows: STEPS IN METHOD OF SECTIONS:
Step 1: Identify the section 1-1 which passes through the members whose forces are required and note that the section is not passing through more than three members. For example, to find force in members FH and GI consider the section 1-1 as shown.
Using equations of equilibrium, find the reactions (VA, HA and VL) Step 2: Using this section 1-1, separate the truss into two parts. The free body diagram of both the parts is drawn.
One of the two parts of the truss obtained after the intersected members have b een cut may be used as free body
Step 3: Select the portion of free body bo dy where the member of forces are minimum. Hen ce the right part of free body is selected as it involves five forces only (PHF, PIF, PIG, VL and F4). But the left part involves eight forces (VA, HA,F1, F2, F3, PFH, PFI,PGI). Assume all the member forces are tensile.
Right part of free diagram Step 4: Use the equations of equilibrium ∑Fx = 0 : ∑Fy = 0 and ∑M = 0 and find forces in members HF, FI, and CI. If positive values are obtained, the members are in tension. If the force in member becomes negative, the nature of force assumed is not correct. Hence it is modified to be compression. These steps are illustrated in numerical examples. Example 1: Find the force in members HJ, CE, GH, DE for the truss shown in figure using method of section.
