Question # $2$:

The bar shown in Figure $2$ is subjected to a linearly distributed axial line loading that varies from

zero at point B to a maximum of $200k\frac{N}{m}$ at point A acting in the negative direction of x $-$axis.

The bar has a constant cross$-$sectional area $A=1\mathrm{.}3{10}^{-3}{m}^2$ and a modulus of elasticity

$E=2{10}^5$MPa.

Apply the finite element method $($hand calculations$)$ to plot the axial displacement and axial

stress along the length of the bar using:

a$)$ One element

b$)$ Two elements

c$)$ Four elements

Compare these plots with the exact solution. Develop two figures: i$)$ Comparison of the exact

solution and the finite element solution $($parts $a,b,$ and c $)$ for axial displacement along the

length of the bar, ii$)$ Comparison of the exact solution and the finite element solution $($parts a$,$

b $,$ and c$)$ for axial stress along the length of the bar.

Model the same problem using the commercial software SAP$2000,$ compare SAP$2000$ results

to those obtained from $(1),$ and comment on the results.