In a beam of rectangular cross section, the maximum shear stress is how much higher than the average shear stress?

• A. 150% higher
• B. 50% higher
• C. 33% higher
• D. 50% lower

Answer: (B)

In a beam with a rectangular cross-section subjected to shear forces, the maximum shear stress is indeed higher than the average shear stress due to the distribution of shear stress across the cross-section.

To understand this, we can analyze how shear stress behaves in a beam. The average shear stress is calculated by dividing the total shear force by the area of the cross-section. However, shear stress does not remain constant across the entire cross-section of the beam; it varies and is higher at the neutral axis and decreases towards the outer surfaces.

For a rectangular cross-section, the maximum shear stress occurs at the neutral axis, which is at the midpoint of the depth of the beam. The average shear stress can be expressed as a proportion of the maximum shear stress. In the case of a rectangular beam, it has been determined through shear stress distribution theories that the maximum shear stress is approximately 1.5 times the average shear stress (i.e., 50% higher).

This calculation results from the trapezoidal distribution of shear stress, with maximum values at the centroid and diminishing values toward the top and bottom surfaces of the beam. Therefore, the answer to how much higher the maximum shear stress is compared to the average shear stress in a rectangular beam is