Mohr's Circle

For Problems $10-56$ through $10-83,$ determine the principal stresses and the maximum shear stress using Mohr's circle. The following data sets give the stresses on the initial stress element. Perform the following operations:

a$)$ Draw the complete Mohr's circle, labeling critical points including ${}_1,{}_2,{}_{\text{m}\text{a}\text{x}},$ and ${}_{\text{a}\text{v}\text{g}}.$

b$)$ On Mohr's circle, indicate which line represents the $x-$axis on the initial stress element.

c$)$ On Mohr's circle, indicate the angles from the line representing the $x-$axis to the ${}_1-$axis and to the ${}_{\text{m}\text{a}\text{x}}-$axis.

d$)$ Draw the principal stress element and the maximum shear stress element in their proper orientation rela tive to the initial stress element.

$\backslash$table$[[$Problem$,{}_x,{}_y,{}_{xy},,],[10-56,300$ MPa,$-100$MPa,$80$ MPa CW$,,],[10-62,55$ ksi,$15$ ksi,$40$ ksi CCW$,,],[10-65,-580$kPa,$130$ kPa,$75$ kPa CCW$,,],[10-70,-4250$ psi,$3250$ psi,$2800$ psi CW$,$Final Answer$],[\backslash$table$[[$Problem$],[$Number$]],{}_1,{}_2,[],[(deg)],{}_{\text{M}\text{A}\text{X}},{}_{\text{A}\text{V}\text{G}},{}^{\text{'}}$

$(deg)$