Frame Members

Let us look at a typical member of a plane frame, which is lying the xy plane. It is convenient to draw a horizontal member - see Figure 4.1

Figure 4.1: Plane Frame Member

For the particular member, the $\bar x$ axis is taken along the beam axis. The $\bar z$ axis is towards the viewer and this defines the $\bar y$ axis. This constitutes the member axes. The convention is the same as for truss bars.

The joints at the end of a member may transmit an axial force, a transverse shear force and a couple onto the member. These forces are denoted by $\bar{P_1} \ldots \bar{P_6}$. The forces $\bar{P_1} \ldots \bar{P_3}$ act on the member at the end where $\bar x$ commences and the forces $\bar{P_4} \ldots \bar{P_6}$ - on the end where $\bar x$ terminates. These are forces external to the member and are positive if they are in the same direction as the member axes.

The member ends also undergo displacements. The end displacements which correspond to $\bar{P_1} \ldots \bar{P_6}$ are denoted by $\bar{u_1} \ldots \bar{u_6}$, each $\bar u$ taken in the same direction as the corresponding $\bar P$

The end forces give rise to axial force, shear force and bending moment, which usually varies along the member.