Hollow Rectangular Beams Deflection Calculator

The Hollow Rectangular Beams Deflection Calculator is an invaluable tool for engineers and construction professionals. It computes the deflection and bending stress of hollow rectangular beams under a specified force, considering the beam's dimensions and the material's modulus of elasticity.

Historical Background

The engineering principles behind beam deflection calculation have evolved over centuries, with significant contributions from renowned mathematicians and engineers. The study of beam behavior under load is fundamental to structural engineering, ensuring safety and stability in construction projects.

Calculation Formula

The moment of inertia (MI) for hollow rectangular beams and the formulas for deflection and bending stress are derived from classical beam theory. The deflection \(\delta\) of a beam subjected to a uniform load can be calculated as follows:

\[ \delta = \frac{F \cdot L^3}{3 \cdot E \cdot I} \]

And the bending stress \(\sigma\) in the beam can be calculated using:

\[ \sigma = \frac{M \cdot c}{I} \]

Where:

• \(F\) = Applied force
• \(L\) = Length of the beam
• \(E\) = Modulus of Elasticity of the material
• \(I\) = Moment of Inertia of the beam's cross-section
• \(M\) = Moment at the point of interest on the beam
• \(c\) = Distance from the neutral axis to the outermost fiber