What is the formula for flexural strength (Fr) under center point loading?

The formula for flexural strength under center point loading is indeed Fr = (3PL)/(BD^2). This equation arises from the basic principles of mechanics of materials, specifically in the analysis of beams subjected to bending.

In this context, P represents the load applied at the center of the beam, L is the length of the beam between supports, B is the width of the beam, and D is the depth of the beam. This formula derives from using the bending stress formula, which is based on the maximum bending moment created by the load P at the center of the beam.

For a simply supported beam with a central load, the maximum bending moment (M) at the center is given by M = (PL)/4. The bending stress (σ) is related to the moment by σ = (Mc)/I, where c is the distance from the neutral axis to the outermost fiber (which would be D/2 for a rectangular section), and I is the moment of inertia. For a rectangular cross-section, I can be expressed as (BD^3)/12.

By substituting in the maximum moment, and rearranging the terms, you can simplify the equation to arrive at the formula provided, which