Problem $2$:

For the $2$D$,$ inextensible $($ pure bending $)$ beam, show that the stiffness coefficient, $k_{22}$

is given by

$k_{22}=\frac{4EI}{L}$

where L is the length of the beam, E is Young's modulus, and, I is the second moment of

area $($the area inertia$)$ about the axis of bending. Use the method of superposition

presented in class.

For the $2$D$,$ inextensible $($ pure bending $)$ beam, show that the stiffness coefficient, $k_{22}$

is given by

$k_{22}=\frac{4EI}{L}$

where L is the length of the beam, E is Young's modulus, and, I is the second moment of

area $($the area inertia$)$ about the axis of bending. Use the method of superposition

presented in class.