Problem Statement:

The cantilever beam shown in the figure is subjected to two$-$plane bending. It is loaded by $P_1=4800$ and $P_2=2880N$ at distances $a=100$ and $b=150$ mm$,$

respectively, as shown in the figure. The cross section is a rectangular tube, having width $w=50,$ height $h=75,$ and thickness $t=5$ mm$.$ Assume the corners are sharp,

not rounded.

Calculate the reaction$-$forces $R_y,R_z$ and reaction$-$moments $R{M}_y,R{M}_z,$ with sign convention shown in the adjacent figure $($z downward$).$

Next draw the shear$-$force and bending$-$moment diagrams $($on paper$)$ for both planes $(x-y$ and $x-z)$ using the orientations shown in the adjacent figure $(z$ downward$).$

Finally, calculate the maximum bending stress ${}_{\text{m}\text{a}\text{x}}$ at the critical point. You will have to check both at $x=0$ and $x=a$ to see which one gives the highest value.

Answer tolerance $=2\%.$ Be sure to include units and the correct sign with your answers. The sign of the bending$-$moment $M$ and the shear$-$force $V$ are determined by the sign

convention in the textbook. All quantities shown with arrows $($in the figures$)$ are considered positive in the directions shown.