Module 2 (2)

If σₓ= 35 MPa, σ_y = 28 MPa, and τ _{x y} = 18 MPa, find the stresses σₓ', σ_y ', and τ _x' _y' after rotating the coordinate system 90° clockwise.

• σₓ' = 28, σy'= 35,

  τxy' =-18

• σₓ' = 35, σy' = 18,

  τxy' = 28

• σₓ' = 18, σy' = 35,

  τxy' = 28

• σₓ' = 28, σy' = 30,

  τxy' = 18

Given σₓ= 25 MPa, σ_y = 20 MPa, and τ _{x y} = 12 MPa, find the stresses σₓ' after rotating the coordinate system 60° counterclockwise

• σₓ' = 25 MPa

• σₓ' = 35 MPa

• σₓ'=32 Mpa

• σₓ' = 30 MPa

  How do principal stresses change when the material is subjected to hydrostatic stress?

• Principal stresses increase uniformly by the amount of hydrostatic pressure.
• Principle stesses will be same as hydrostatic stress and equal normal stress in all directions.

• Principal stresses remain unchanged under hydrostatic stress.
• Principal stresses decrease uniformly with hydrostatic pressure.

.   If the stress transformation results in no change in the stress components, what can be concluded about the angle of rotation?

• The angle of rotation is 270 degrees.
• The angle of rotation is 0 degrees or 180 degrees.

• The angle of rotation is 45 degrees.
• The angle of rotation is 90 degrees.

What is the significance of the transformation angle (θ) in plane stress transformation?

• The transformation angle (θ) is used to determine the material properties of a structure.
• It has no effect on the shear stresses acting on the material.

• It specifies the temperature distribution in the material.

• It influences the magnitudes of principal stresses and their orientation.

What is the relationship between the angle of rotation and the maximum shear stress in a material?

• The angle of rotation has no impact on maximum shear stress.

• The angle of rotation determines the orientation of maximum shear stress.

• The angle of rotation is always 45 degrees for maximum shear stress.

• The angle of rotation is irrelevant in determining shear stress.

    Which of the following statements best describes the relationship between principal stresses and maximum shear stress in a material?

• The maximum shear stress occurs at the same angle as the maximum principal stress.

• Maximum shear stress is independent of the difference between the principal stresses.

• The maximum shear stress is maximum when the difference between the principal stresses is max.

• Maximum shear stress is always equal to the sum of the principal stresses.

.     If the principal stresses are equal (σ₁ = σ₂), what can be concluded about the state of stress?

• The state of stress is purely shear.
• The state of stress is triaxial.
• The state of stress is hydrostatic.
• The state of stress is uniaxial.

If the principal stresses in a plane stress problem, are σ₁ = 100 MPa, σ₂ = 40 MPa, the magnitude of the maximum shear stress (in MPa) will be

• 20 MPa
• 10 MPa
• 50 MPa
• 30 MPa

Shear stress on mutually perpendicular planes are

• Equal in magnitude but not perpendicular.
• Equal in magnitude and opposite in direction.
• Unequal in magnitude and opposite in direction.
• Equal in magnitude and same in direction.