Question $2$: Engineering Calculations

a$)$ Calculate the deflection of a beam under a uniform load.

Steps:

Use the Euler$-$Bernoulli beam theory:

$y(x)=\frac{}{24EI}{x}^2(L^2-x^2)$

where:

$=500\frac{N}{m}(load$ intensity$)$

$E=200$GPa $(Young\text{'}s$ modulus$)$

$I=1\mathrm{.}5{10}^{-6}{m}^4(momentof$ inertia$)$

$L=2m(length)$

Set up the Problem in MATLAB: Use the Symbolic Math Toolbox to define variables and the deflection equation.

syms $x$;

$w=500$;$E=200e9$;$I=1\mathrm{.}5e-6$;$L=2$

$y=(\frac{w}{{24}^{**}{E}^{**}\text{I}}{)}^{**}{x}^2**(L^2-x^2)$;

fplot $(y,[0,L])$;

title$(\text{'}$Beam Deflection'$)$;

xlabel$(\text{'}$Position along the beam $(m)\text{'})$;

ylabel$(\text{'}$Deflection $($m$)\text{'})$;

grid on;

$3.$ Give your interpretation of the results.