PROBLEMS

$4\mathrm{.}1-4\mathrm{.}16.$ For the beam problems shown in Figs. P$4\mathrm{.}1-$P$4\mathrm{.}16,$ use the Euler$-$Bernoulli

beam element, and give:

$($a$)$ the assembled stiffness matrix and force vector;

$($b$)$ the specified global displacements and forces, and the equilibrium conditions;

$($c$)$ the condensed matrix equations for the primary unknowns $($i$.$e$.,$ generalized

displacements$)$ and the secondary unknowns $($i$.$e$.,$ generalized forces$)$

separately.

Solve for the unknown displacements if there are less than four unknown

displacements $($use Cramer's rule$),$ and evaluate the bending moment $M^c=$

EI $d^2\frac{w}{d}{x}^2$ at point $C$ using the finite element interpolation of $w($when the

condensed equations are not solved, express $M^c$ in terms of the nodal values of

FIGURE P$4\mathrm{.}2$