The correct answer is c) Pure shear.

Explanation:
In order to understand why the state of stress can be termed as pure shear when the principal stresses and maximum shearing stresses are of equal numerical value, let's first define what these terms mean.

- Principal Stresses: Principal stresses refer to the maximum and minimum normal stresses that act on a point in a stressed body. These stresses are perpendicular to each other and are obtained by solving the stress equations of the body.

- Maximum Shearing Stresses: Shearing stresses refer to the stresses that act parallel to a given plane in a stressed body. The maximum shearing stress is the maximum value of these stresses.

Now, let's consider a point in a stressed body where the principal stresses and maximum shearing stresses are of equal numerical value. This means that the magnitude of the maximum shearing stress is equal to the magnitude of either the maximum or minimum principal stress.

In such a case, the state of stress at that point can be termed as pure shear. This is because pure shear stress occurs when the normal stresses acting on a point are equal in magnitude but opposite in sign. In other words, pure shear stress results in the deformation of a material without any change in its volume.

To visualize this, imagine a rectangular block of material being subjected to equal and opposite forces in two perpendicular directions. The resulting stress on the block will be pure shear stress because the normal stresses are equal in magnitude but opposite in sign.

In conclusion, when the principal stresses and maximum shearing stresses are of equal numerical value at a point in a stressed body, it indicates a state of pure shear stress. This means that the normal stresses acting on the point are equal in magnitude but opposite in sign, resulting in deformation without any change in volume.

Explanation:

In order to understand why the state of stress can be termed as pure shear when the principal stresses and maximum shearing stresses are of equal numerical value at a point in a stressed body, let's first define these terms:

1. Principal Stresses: Principal stresses are the maximum and minimum normal stresses at a point in a stressed body. They occur on the planes where the shear stress is zero. The principal stresses are denoted by σ1 and σ2, with σ1 being the maximum and σ2 being the minimum.

2. Maximum Shearing Stresses: The maximum shearing stress occurs on the planes where the normal stress is zero. It is denoted by τmax.

Now, let's consider the scenario where the principal stresses and maximum shearing stresses are of equal numerical value at a point in a stressed body. This implies that σ1 = σ2 = τmax.

Under this condition, the stress state can be defined as pure shear. Here's why:

1. Pure Shear: Pure shear is a state of stress where the deformations are due to the shearing forces only, without any change in volume. In pure shear, the deformation occurs in one direction while the body remains unchanged in the perpendicular direction.

2. Relationship between Principal Stresses and Shearing Stresses: In pure shear, the principal stresses are equal in magnitude but opposite in sign, i.e., σ1 = -σ2. This means that the maximum shearing stress τmax is equal to the magnitude of either principal stress, as τmax = |σ1| = |σ2|.

3. Equality of Principal Stresses and Shearing Stresses: When σ1 = σ2 = τmax, it satisfies the condition of pure shear, where the principal stresses are equal in magnitude and opposite in sign. This implies that the deformation occurring at the point is purely due to shearing forces, without any change in volume.

Therefore, when the principal stresses and maximum shearing stresses are of equal numerical value at a point in a stressed body, the state of stress can be termed as pure shear (option C).

To summarize, the equality of principal stresses and maximum shearing stresses indicates that the stress state is purely shearing, without any change in volume, which is characteristic of pure shear stress.