W$5$A: In class assignment $($MATLAB$)$

$(12$ points, $3$ points for each part$)$

a$.$ Calculate the deflection of a cantilevered beam as a function of $x$ and plot it$.$ For $x$ values, use an increment of $0\mathrm{.}05$ L $.$

b$.$ Calculate the maximum deflection and slope under given loading and state the corresponding $x$ values.

c$.$ Compute the values of $x$ when the deflection is zero and the slope is zero.

d$.$ Increase the applied load $P$ from $0$ to the given amount $(6000)$ in increment of $500$ pounds, calculate the deflection and show how beam $AB$ deflects in an animation.

Starting with Equation $1,$ and applying the boundary conditions to solve the differential equation resulted in:

$=\frac{P}{2EI}(L^2-x^2)$

$v=\frac{P}{6EI}(-x^3+3L^{2}x-2L^3)$

Data: $L=15$ feet; $P=6000$ pounds; For the beam A $36$ steel, $E=29{10}^6$ psi.

For the W $1226$ beam, $I=204$ in ${?}^4$