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Beam Deflection Formula:
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Beam deflection refers to the displacement of a beam under load. The formula δ = FL³/(3EI) calculates the maximum deflection of a cantilever beam with a point load at the free end, where δ is deflection, F is force, L is length, E is elastic modulus, and I is moment of inertia.
The calculator uses the beam deflection formula:
Where:
Explanation: This formula applies to cantilever beams with a concentrated load at the free end. The deflection increases with the cube of the beam length and linearly with the applied force.
Details: Calculating beam deflection is crucial for structural design to ensure that beams don't deflect excessively under load, which could lead to structural failure or serviceability issues in buildings and mechanical systems.
Tips: Enter force in newtons, length in meters, elastic modulus in pascals, and moment of inertia in meters to the fourth power. All values must be positive numbers.
Q1: What types of beams does this formula apply to?
A: This specific formula applies to cantilever beams with a point load at the free end. Different support conditions and load distributions require different formulas.
Q2: What is elastic modulus (E)?
A: Elastic modulus is a material property that measures stiffness. Steel has E ≈ 200 GPa, aluminum ≈ 70 GPa, and wood varies by species.
Q3: How do I find moment of inertia (I)?
A: Moment of inertia depends on the cross-sectional shape. For common shapes like rectangles and circles, standard formulas are available in engineering handbooks.
Q4: What are typical deflection limits?
A: Building codes often limit deflection to L/360 for live loads and L/240 for total loads, where L is the span length.
Q5: Does this account for shear deflection?
A: No, this formula only considers bending deflection. For short, deep beams, shear deflection may be significant and should be calculated separately.