Problem $\backslash$# $5$

A lever loaded safety valve is mounted on the boiler to blow off at a pressure of $1\mathrm{.}5$ MPa gauge. The effective diameter of the opening of the valve is $50$ mm $.$ The distance between the fulcrum and the pin connecting the valve spindle to the lever is $100$ mm $.$ The lever and the pin are made of plain carbon steel $\backslash (30\backslash$mathrm$\{$C$8\}\backslash$left$($S$\_\{$y t$\}=400\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$mm$\}^\{2\}\backslash$right$)\backslash )$ and the factor of safety is $5.$ The permissible bearing pressure at the pins in the lever is $\backslash (25\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$mm$\}^\{2\}\backslash ).$ The lever has a rectangular cross$-$section and the ratio of width to thickness is $3$:$1.$ Design a suitable lever for the safety valve. Note: Show all steps clearly, draw diagrams, show stress elements, etc.