Explanation:
Shear stress is the force that acts parallel to the cross-sectional area of a material, causing it to deform. In the context of a beam, shear stress occurs due to the internal forces acting on the beam, such as bending moments.

Triangular Cross-Section:
A triangular cross-section refers to a beam that has a triangular shape when viewed from the side. This type of cross-section is commonly used in engineering applications because it allows for efficient use of material while maintaining structural integrity.

Maximum Shear Stress:
The maximum shear stress in a beam occurs at the mid-depth. This is because the shear force is distributed in a triangular manner across the cross-section of the beam.

Explanation:
When a beam is subjected to bending, the top fibers of the beam are in compression while the bottom fibers are in tension. This creates internal forces that cause the beam to bend.

At the extreme top fiber of the beam, the compression forces are at their maximum. However, there is no shear force acting at this location since the force is purely compressive. Therefore, the shear stress at the extreme top fiber is zero.

At the extreme bottom fiber of the beam, the tension forces are at their maximum. Similar to the top fiber, there is no shear force acting at this location since the force is purely tensile. Therefore, the shear stress at the extreme bottom fiber is also zero.

At the mid-depth of the beam, the shear force is at its maximum. This is because the shear force is distributed in a triangular manner across the cross-section of the beam. Since the shear force is at its maximum at the mid-depth, the shear stress is also at its maximum at this location.

Therefore, the correct answer is option 'B' - mid-depth.