[ANSWERED] 1. Derive the stiffness matrix for a beam element with a nodal linkage—that is, the shear is 0 at…

1. Derive the stiffness matrix for a beam element with a
nodal linkage—that is, the shear is 0 at node i, but the usual shear and moment
resistance are present at node j (see Figure P4–43).
2. Develop the stiffness matrix for a fictitious pure shear
panel element (Figure P4–44) in terms of the shear modulus, G, the shear web
area, AW , and the length, L. Notice that Y and v are the shear force and
transverse displacement at each node, respectively.