Analysis of Frames

Key Concepts: Frame structures differ from trusses in that they can resist shear and

bending in addition to tension and compression due to applied loads. Analysis of frames

must account for the possibility of shear and bending when constructing free body

diagrams of frame elements.

In a Nut Shell: Common examples of structural members containing frame elements are

beam structures, and tools such as a wrench and a vise-grip. Apply the conditions of

equilibrium to analyze frames.

Note: Even if a structural element is supported by pins on both ends, it may have a load

acting between the ends of the element. This structural member then will resist shear and

bending in addition to tension and/or compression.

Strategy to Analyze Frames

1.	Draw a FBD of the entire structure to determine the support reactions and write the equations of equilibrium. For a structure in a plane there are three equations of equilibrium including Σ Fx = 0 Σ Fy = 0 Σ M = 0 The moment equation can be taken about any convenient point.
2.	Isolate individual members of the structure, as needed, and construct a FBD of these members noting that connections of members experience equal and opposite forces and moments. Then write the equations of equilibrium for these members.
3.	Check the equations of equilibrium to identify the unknowns. The total number of unknowns must equal the total number of equations of equilibrium in order to obtain a solution.
4.	Solve the system of equations for the desired unknown forces or moments.

Click here for an example.

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