Problem n$1.40$ pts

An overhanging W$760$ x $257$ rolled$-$steel beam supports a load $P_1=400kN$ and $P_2=600$ kN as shown.

Knowing that $a=5m,b=2\mathrm{.}5m,{}_{\text{a}\text{l}\text{l}}=3F0$MPa and ${}_{\text{a}\text{l}\text{l}}=170$MPa. Determine:

The maximum value of the normal stress ${}_m$ in the beam,

the maximum value of the principal stress ${}_{\text{m}\text{a}\text{x}}$ and the maximum value of the shearing stress ${}_{\text{m}\text{a}\text{x}}$ at the junction of the flange and web,

State if the specified shape is weather acceptable or not? as far as these two. stresses ${}_{\text{m}\text{a}\text{x}}$ and ${}_{\text{m}\text{a}\text{x}}$ are concerned.

Then determine the angles ${}_P$ and ${}_S$ and draw the principle planes stress and the maximum in$-$plane shearing stress.

Draw Mohr's circle showing all characteristic points:

${}_{\text{a}\text{v}\text{e}},{}_{\text{m}\text{i}\text{n}},{}_{\text{m}\text{a}\text{x}},{}_{\text{m}\text{a}\text{x}}.$

Show ${}_b,{}_b,{}_p,{}_s$ in Mohr's circle