# For the given stale of stress, determine (a) the orientation of the planes of maximum in-plane shearing stress, (b) the maximum in-plane shearing stress, (c) the corresponding normal stress.

Question-AnswerCategory: Strength of MaterialsFor the given stale of stress, determine (a) the orientation of the planes of maximum in-plane shearing stress, (b) the maximum in-plane shearing stress, (c) the corresponding normal stress.

For the given stale of stress, determine (a) the orientation of the planes of maximum in-plane shearing stress, (b) the maximum in-plane shearing stress, (c) the corresponding normal stress. Step: 1

(a)
Calculate the orientation of the planes of the maximum in-plane shearing stress using the following formula: Here, normal stress in the x-direction is , normal stress in the y-direction is , and the shear stress is .
Substitute , , and in the above equation.  Calculate the second shear plane angle by using the following relation: Therefore, the orientation of the planes of the maximum in-plane shearing stress are .

Step: 2

(b)
Calculate the maximum in plane shearing stress using the following formula: Therefore, the maximum in-plane shearing stress is .

Step: 3

(c)
Calculate the normal stress on the maximum shear stress plane:
Note: the normal stress on the maximum shear stress plane is equal to the average of the two normal stresses. Therefore, the normal stress on the maximum shear stress plane is .