Please show every step! The specimen has a cross-sectional area A and is subjected to the axial load P. Determine the maximum average shear stress in the material and associated angle theta of the plane over which it acts. Solution let maximum shear stress acts on angle theta with the specimen (as given in fig of question) ... shear stress is the stress acting along the plane area of plane which is cut in angle theta to cross section (as given in question figure) = A/sin(theta) force along this plance is Pcos(theta) hence maximum shear stress =Pcos(theta) /(A/sin(theta)) =P*cos(theta)*sin(theta) /A as 2*sin(theta) *cos(theta) =sin (2* theta) shear stress =p*SIN(2*THETA) /2A maximum vaue of sin of any angle is 1 hence sin(2*theta ) =1 hence 2*theta =90 theta =45 degrees also maximum shear stress =P/2A ...( as sin(2*theta) = 1) .

1. Please show every step!
The specimen has a cross-sectional area A and is subjected to the axial load P. Determine the
maximum average shear stress in the material and associated angle theta of the plane over which
it acts.
Solution
let maximum shear stress acts on angle theta with the specimen (as given in fig of question)
... shear stress is the stress acting along the plane
area of plane which is cut in angle theta to cross section (as given in question figure) =
A/sin(theta)
force along this plance is Pcos(theta)
hence maximum shear stress =Pcos(theta) /(A/sin(theta)) =P*cos(theta)*sin(theta) /A
as 2*sin(theta) *cos(theta) =sin (2* theta)
shear stress =p*SIN(2*THETA) /2A
maximum vaue of sin of any angle is 1
hence sin(2*theta ) =1
hence 2*theta =90
theta =45 degrees
also maximum shear stress =P/2A ...( as sin(2*theta) = 1)