Final answer:
The maximum shear stress on the element is 5 MPa, which is equal to the given shear stress as the element is under pure shear. This stress state can be represented on an element oriented at 45 degrees to the principal planes, illustrating zero normal stress and maximum shear stress on those planes.
Step-by-step explanation:
The state of stress on an element can be analyzed using Mohr's Circle for stress. Given a stress of 5 MPa s y (simple shear stress) and a normal stress of 2 MPa, we can calculate the maximum shear stress, which occurs at an angle of 45 degrees from the principal planes. The maximum shear stress is equal to the radius of Mohr's Circle, which for pure shear stress is equal to the applied shear stress value.
To calculate this, the maximum shear stress (τ_max) will be half of the difference between the principal stresses, σ_1 and σ_2. However, since only shear stress is given (5 MPa), this implies that the principal stresses are equal and opposite (σ_1 = -σ_2 = 5 MPa), resulting in τ_max = 5 MPa.
A properly oriented element under pure shear would be angled at 45 degrees to align one set of faces with the principal stress directions, where the faces parallel to the shear plane would experience zero normal stress and a shear stress of 5 MPa.