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.

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.

The forces and moments are calculated by:(1)

F_{y 1} = f_{y} (u_{y}) + C_{y} {\dot{u}}_{y}

(2)

F_{y 2} = - F_{y 1}

(3)

M_{z 1} = - l F_{y 2}

(4)

M_{z 2} = M_{z 1}

Where,

$u_{y} = u_{y 2} - u_{y 1} - l (\frac{θ_{z 2} + θ_{z 1}}{2})$

$f_{y} (u_{y})$ is the function defining the force-displacement relationship.