<Dd> R = (1 2 (σ x − σ y)) 2 + τ x y 2 = (1 2 (− 10 − 50)) 2 + 40 2 = 50 MPa (\ displaystyle (\ begin (aligned) R& = (\ sqrt (\ left ((\ tfrac (1) (2)) (\ sigma _ (x) - \ sigma _ (y)) \ right) ^ (2) + \ tau _ (xy) ^ (2))) \ \ & = (\ sqrt (\ left ((\ tfrac (1) (2)) (- 10 - 50) \ right) ^ (2) + 40 ^ (2))) \ \ & = 50 (\ textrm (MPa)) \ \ \ end (aligned))) </Dd> <Dl> <Dd> σ a v g = 1 2 (σ x + σ y) = 1 2 (− 10 + 50) = 20 MPa (\ displaystyle (\ begin (aligned) \ sigma _ (\ mathrm (avg)) & = (\ tfrac (1) (2)) (\ sigma _ (x) + \ sigma _ (y)) \ \ & = (\ tfrac (1) (2)) (- 10 + 50) \ \ & = 20 (\ textrm (MPa)) \ \ \ end (aligned))) </Dd> </Dl> <Dd> σ a v g = 1 2 (σ x + σ y) = 1 2 (− 10 + 50) = 20 MPa (\ displaystyle (\ begin (aligned) \ sigma _ (\ mathrm (avg)) & = (\ tfrac (1) (2)) (\ sigma _ (x) + \ sigma _ (y)) \ \ & = (\ tfrac (1) (2)) (- 10 + 50) \ \ & = 20 (\ textrm (MPa)) \ \ \ end (aligned))) </Dd> <P> and the principal stresses are </P>

Given that yx is a diameter of circle v