Final answer:
The max shear stress theory of failure states that the relationship between yield strength in shear (σsy) and tensile yield strength (σyt) is σsy = σyt/√2, reflecting the different response of materials to tensile and shear stresses.
Step-by-step explanation:
According to the max shear stress theory of failure, also known as the Tresca criterion, the relationship between yield strength in shear (σsy) and tensile yield strength (σyt) is given by the equation σsy = σyt/√2. This suggests that the shear yield strength is less than the tensile yield strength due to the different nature of the stresses in each case. The derivation of this formula is based on the assumption that yielding begins when the maximum shear stress in a material reaches a value equal to the shear stress at yielding in a tensile test.
This ratio is closely related to the properties of materials, such as Young's modulus and the shear modulus, which define the relationship between stress and strain in materials subject to tensile and shear stresses, respectively. Materials data tables often list these properties for engineering and construction purposes.