Method of Members | Frames Containing Three-Force Members

A three-force member is in general a non-axial member that is not simply in tension or compression. A member of this kind has shear forces perpendicular to the member and subjected to bending loads. If forces are applied to more than two positions on the member, it is three-force member. Any beam is a three-force member according to the above definition.

Frames are pin-connected structures with some or all members are three-force members. To analyze a frame, we can disconnect the three-force member from the structure and draw the free-body diagram of the member. This approach is called the method of members.

In this method, three equilibrium equations can be written

$\Sigma F_H = 0$,   $\Sigma F_V = 0$,   and   $\Sigma M_O = 0$


Below is a figure that shows the difference between axial and non-axial (three-force) members.

Comparison of pure axial and three-force members