Reflecting on Principal Stresses and Maximum Shear Stress in Materials

What are the three principal stresses and the max shear stress?

a) Tensile, Compressive, Shear - Tensile

b) Normal, Shear, Tensile - Compressive

c) Tensile, Compressive, Shear - Compressive

d) Normal, Shear, Tensile - Shear

Answer:

The three principal stresses are normal stress (tensile or compressive), shear stress, and the maximum shear stress generally occurs at 45 degrees to the principal normal stresses. The correct answer is Normal, Shear, Tensile - Compressive.

The question relates to the principal stresses and the maximum shear stress in materials, which is a typical concern in the field of materials science and engineering. In mechanical and structural engineering, the three principal stresses are generally considered to be normal stress (tensile or compressive) and shear stress.

Normal stress is the stress component perpendicular to a given surface, which can be either tensile, when forces act to stretch the material, or compressive, when forces act to compress the material. Shear stress is the stress component parallel to the surface, typically caused by forces that act in opposite directions along the same plane.

The maximum shear stress occurs when the shear stress reaches its highest value. It occurs typically in a plane that is oriented 45 degrees to the principal normal stresses. This kind of stress is significant for understanding failure modes in materials and structures.

Therefore, the correct answer to the student's problem 2a regarding the principal stresses and the maximum shear stress is option b) Normal, Shear, Tensile - Compressive.