The rectangular bar is connected to the support bracket with a $15-$mm$-$

diameter pin. The bar width is $w=70mm$ and the bar thickness is $20$ mm $.$

Each side of the bracket has the same dimensions as the bar. The average

shear stress in the pin cannot exceed $110$ MPa $,$ the bearing stress in the bar

cannot exceed $130$ MPa $,$ and the bearing stress in the bracket cannot

exceed $120$ MPa $.$ Determine the maximum value of $P_{\text{m}\text{a}\text{x}}$ that can be

supported by the structure.