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 図 1.
図 1. XY Shear Forces and Moments


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


The forces and moments are calculated by:
図 3.
F y 1 = f y ( u y ) + C y u ˙ y
図 4.
F y 2 = − F y 1
図 5.
M z 1 = − l F y 2
図 6.
M z 2 = M z 1

Where,

u y = u y 2 − u y 1 − l ( θ z 2 + θ z 1 2 )

f y ( u y ) is the function defining the force-displacement relationship.