Question

A plane element in a body experiences a tensile stress of 100 MPa and a shear stress of 25 MPa. Calculate:

The normal and shear stress on a plane inclined at an angle of 20° with the tensile stress.

a. Normal stress = 92.27 MPa, Shear stress = 28.64 MPa
b. Normal stress = 84.51 MPa, Shear stress = 23.45 MPa
c. Normal stress = 96.80 MPa, Shear stress = 25.50 MPa
d. Normal stress = 89.14 MPa, Shear stress = 21.89 MPa

Answer 1

The normal stress on the inclined plane is 92.27 MPa and the shear stress is 28.64 MPa.

Step-by-step explanation:

To calculate the normal and shear stress on a plane inclined at an angle of 20° with the tensile stress, we can use trigonometry. The normal stress is the component of the tensile stress perpendicular to the inclined plane, and can be calculated using the formula:

Normal stress = Tensile stress * cos(angle)

Substituting the values, we have:

Normal stress = 100 MPa * cos(20°) = 92.27 MPa

The shear stress is the component of the shear stress parallel to the inclined plane, and can be calculated using the formula:

Shear stress = Shear Stress * sin(angle)

Substituting the values, we have:

Shear stress = 25 MPa * sin(20°) = 28.64 MPa