Method of Section (A method for evaluating internal forces and moments)

When a structural body is subjected to external load, it gets deform. Externally, the  structure remains static as the external load vectors gets counterbalanced by the support reaction vectors and maintain its state of equilibrium. The method of section is a very powerful method to understand that how does the external load vectors and support reaction vectors deforms the structure. The internal force can be axial force, shear force, bending moment and twisting moment.

General steps required to determine the variations of internal forces in the structural member are as follows:

1.       Determine the all of the support reactions.

2.       Draw the free body diagram.

3.       Establish the coordinate system in such a manner that entire structure occupies first quadrant.

4.       Cut a section on the structure at a variable distance from origin.

5.       Write expressions for internal loading in terms of variable distance with using sign conventions.

6.       Go back to step 4 and step 5 to cover entire structure for accounting variations of internal loading due to change in loading pattern.

7.       Plot the results graphically.

The knowledge of equations which gives relationships in between internal loading and their corresponding stresses gives facility to the designer to identify the variations of stresses in the structure. Since strength of the structure is the minimum value of stress up to which structure remains serviceable and hence the concept of method of section is very important to understand the behaviour of the structure.

Note: Reader should not be confused in method of section of finding internal forces with method of section of finding member forces for trusses.