To understand the distribution of shearing stress across a rectangular cross section beam, let's delve into the principle of shearing stress in beams which is studied under the subject of Strength of Materials.

When a beam with a rectangular cross section is subjected to a bending moment and shear force, the distribution of shear stress is not uniform across the depth of the beam. The shear stress \(\tau\) at any given point of the cross section is given by the formula:

\(\tau = \frac{V \cdot Q}{I \cdot b}\)

Where:

• V = Shear force at the cross section
• Q = First moment of area about the neutral axis at the point where shear stress is calculated
• I = Moment of inertia of the entire cross section about the neutral axis
• b = Width of the section at the point where shear stress is calculated

In a rectangular cross section, the maximum shear stress occurs at the neutral axis, while it reduces to zero at the extreme fibers. The distribution from the bottom to the top of the rectangle forms a parabolic shape. This is due to the symmetrical nature of a rectangle about its neutral axis, causing the shear stress to peak at the center and taper off towards the edges.

Conclusion: The correct answer is Parabolic. This is because the shearing stress distribution is parabolic across the height of a rectangular cross section due to its symmetrical geometry and the properties of materials in response to shear forces.

Other options such as "Rectangular", "Triangular", or "Both Rectangular and parabolic shape" are incorrect as they do not accurately describe the gradual variation in shear stress from the neutral axis to the outer fibers.