Problem $2$

A $5-$m long cantilever beam is constructed as shown in below Figure $a.$ The section dimensions are given

in Figure $c$ and the corresponding area of moment are given as $I_1=68740c{m}^4$ and $I_2=2480c{m}^4.$ A load

$P=50kN$ acts in the vertical direction at the end of the beam as shown in Figure a and $b.$

$($a$)$ Determine the maximum bending stresses $($tensile and compressive$)$ in the beam if the $y$ axis of the

cross section is vertical and therefore aligned with the load $P.$

$($b$)$ Determine the maximum bending stresses $($tensile and compressive$)$ if the beam is inclined at a small

angle $=1\mathrm{.}5$ to the load $P($Figure $\{$:$b).$

$($c$)$ What can you conclude by comparing the results of $($a$)$ and $($b$)?$

ANSWERS

$($a$)$ Maximum tensile stress$=90\mathrm{.}92$ MPa. Maximum compressive stress$=-90\mathrm{.}92$ MPa

$($b$)$The maximum tensile stress $=115\mathrm{.}28$ MPa. the maximum compressive stress$=-115\mathrm{.}28$

MPa