The Distribution of Shear Stress in a Rectangular Beam

The nature of the distribution of shear stress in a rectangular beam can be represented by a parabolic curve. This distribution can be explained based on the theory of pure bending and the concept of shear flow.

Pure Bending and Shear Flow
In pure bending, a beam is subjected to a bending moment that causes it to deform into a curved shape. This bending moment induces both tensile and compressive stresses in the beam, resulting in a distribution of stress along its cross-section. However, the shear stress in the beam is not uniformly distributed and varies across its depth.

Shear flow refers to the distribution of shear stress across the cross-section of the beam. It is given by the formula Q/A, where Q is the shear force and A is the area over which the shear force is distributed. In a rectangular beam, the shear flow is constant across the depth of the beam.

Shear Stress Distribution
The shear stress distribution in a rectangular beam can be derived using the concept of shear flow. As mentioned earlier, the shear flow is constant across the depth of the beam. Since the shear flow is equal to the shear stress multiplied by the thickness of the beam, the shear stress distribution will be linear with respect to the depth of the beam.

However, the shear stress distribution is not uniform along the width of the beam. The maximum shear stress occurs at the neutral axis of the beam, which is located at the centroid of the cross-section. The shear stress gradually decreases from the neutral axis towards the top and bottom surfaces of the beam, resulting in a parabolic distribution.

Conclusion
In conclusion, the nature of the distribution of shear stress in a rectangular beam is parabolic. This distribution arises from the concept of shear flow, which is constant across the depth of the beam. The shear stress distribution is linear along the depth of the beam but varies parabolically along its width. Understanding the distribution of shear stress is essential for designing and analyzing the behavior of rectangular beams under different loading conditions.