A design team is designing a bag made of plastic for carrying a load of $20Kg.$ The material

has a tensile strength of $200$MPa, a compressive strength of $150$MPa and a shear strength

is $100$MPa.

Calculate the principal stresses and maximum in$-$plane shear stresses when the

following stresses are given in an element.

State that if the bag will fail or not in compression or tensile.

Determine the factor of safety in the case of compression and tension

${}_{1,2}=\frac{{}_x+{}_y}{2}+-\sqrt[\phantom{2}]{(\frac{{}_x-{}_y}{2}{)}^2+{}_{xy}^2}$

${}_{\text{m}\text{a}\text{x}}=\sqrt[\phantom{2}]{(\frac{{}_x-{}_y}{2}{)}^2+{}^{2}xy}$