Problem $3(10$ points$)$

A beam is subjected to triangular distributed load $\backslash ($ w$\_\{0\}\backslash ).$ Given the yield stress $\backslash (\backslash$sigma$\_\{$y$\}\backslash ),$ beam cross$-$section thickness $\backslash ($ t $\backslash ),$ beam cross$-$section height $\backslash ($ h $\backslash ),$ and the beam length $\backslash ($ L $\backslash ),$ calculate the plastic load$-$carrying capacity of the beam. How many plastic hinges will be formed under the load? Assume different failure deformation modes if you can.