Shear - XY

Shear in the Y direction along the face perpendicular to the X axis is a combination of forces and moments. This can be seen in Figure 1.

Figure 1. XY Shear Forces and Moments

There are two mechanisms that can cause shear. The first is the beam double bending as shown in Figure 1. The second is shear generated by node displacement, as shown in Figure 2, where node 2 is displaced.

Figure 2. Shear Due to Node Displacement

Where,

$u_y=u_{y2}-u_{y1}-l\left(\frac{{\theta }_{z2}+{\theta }_{z1}}{2}\right)$

$f_y\left(u_y\right)$ is the function defining the force-displacement relationship.