Beam Deflection Calculator
This calculator is designed for engineers and students to compute the deflection of beams under various conditions. It solves the problem of determining how much a beam will bend under a specific load using standard engineering formulas.
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Data Source and Methodology
All calculations are based on the standards provided by the American Institute of Steel Construction (AISC). The formulas for beam deflection are derived from principles outlined in this authoritative resource. Visit AISC
The Formula Explained
The deflection \( \delta \) of a simply supported beam with a central load is given by:
\[ \delta = \frac{F \cdot L^3}{48 \cdot E \cdot I} \]
Where \( F \) is the force in Newtons, \( L \) is the length in meters, \( E \) is Young's Modulus in Pascals, and \( I \) is the moment of inertia in meters to the fourth power.
Glossary of Variables
- Beam Length (L): The length of the beam in meters.
- Load (F): The force applied to the beam in kilonewtons.
- Young's Modulus (E): The material's stiffness measure in gigapascals.
- Moment of Inertia (I): The beam's resistance to bending in cm4.
Example Application
Consider a steel beam 5 meters long with a central load of 10 kN. If the Young's Modulus is 210 GPa and the moment of inertia is 400 cm4, the deflection is calculated as follows:
Using the formula \(\delta = \frac{F \cdot L^3}{48 \cdot E \cdot I}\), we find that the deflection is approximately 3.2 mm.
Frequently Asked Questions (FAQ)
What is beam deflection?
Beam deflection refers to the deformation of a beam under load, typically expressed in millimeters or inches.
Why is understanding deflection important?
Deflection affects the structural integrity and functionality of beams in construction and mechanical applications.
How does Young's Modulus affect deflection?
Young's Modulus is a measure of material stiffness; higher values mean less deflection.
What is the moment of inertia?
The moment of inertia is a geometric property that affects the beam’s resistance to bending.
How can I reduce beam deflection?
Increasing the beam's moment of inertia or using materials with a higher Young's Modulus can reduce deflection.