Solve all problems using the finite element stiffness method. Explicitly evaluate πp of...

Solve all problems using the finite element stiffness method.

Explicitly evaluate π_p of Eq. (4.7.15); then differentiate π_p with respect to v₁, Φ₁, v₂, and Φ₂ and set each of these equations to zero (that is, minimize π_p) to obtain the four element equations for the beam element. Then express these equations in matrix form.

Eq. (4.7.15);