The state of plane strain on the yellow differential material element shown representatively on the plane in the figure is given as $$x$=0,$y$=225(106),$ and $\backslash$gamma xy$=120(106).$ a$)$ Show this strain condition on a differential element. b$)$ Calculate the strains on an element oriented $-40$ counterclockwise with respect to the differential element and show it on a differential element. c$)$ Determine the principal strains and planes and show them on a differential element. d$)$ Represent the maximum in$-$plane shear strains on a differential element by determining the relevant normal strains and their orientation. the corresponding average normal strain on the oriented element. e$)$ If the yield stress of the material is $\backslash$sigma A $=95\mathrm{.}0$ MPa, the maximum safety coefficient of the design

Determine it according to shear stress theory. Recall that n $=\backslash$sigma A$/\backslash$sigma $,$ where $\backslash$sigma is determined from maximum shear stress theory. f$)$ If the yield stress of the material is $\backslash$sigma A $=95\mathrm{.}0$ MPa, use the maximum deformation energy theory to determine the safety factor of the design.