ENGINEERING – TRUCTURAL ENGINEERING β BEAM & FRAME CALCULATOR
Beam Deflection
A precise tool.
What is the Beam Deflection & How does it work?
Beam deflection describes the displacement of a structural element under load. For a simply supported beam, the maximum vertical deflection occurs at the midpoint when a point load is applied there.
The relationship between load, geometry, and material stiffness is captured by the classic elasticβdeflection formula.
\delta_{max} = \frac{P L^{3}}{48 E I}
delta_{max} = maximum deflection, P = point load, L = span length, E = modulus of elasticity, I = second moment of area
In practice, engineers convert the computed deflection to millimetres and compare it with serviceability limits to ensure comfort and safety.
Parameters
Result
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Frequently Asked Questions
What is the formula for calculating beam deflection?
The formula is Ξ΄_max = (P * L^3) / (48 * E * I), where P is the point load, L is the span length, E is the modulus of elasticity, and I is the second moment of area.
Where does maximum deflection occur in a simply supported beam?
Maximum deflection occurs at the midpoint of the beam when a point load is applied there.
How do I find the modulus of elasticity for a material?
The modulus of elasticity (E) can typically be found in engineering materials tables or by consulting with a materials engineer.
What does the second moment of area (I) represent?
The second moment of area represents the distribution of a cross-section’s area around its centroidal axis and is crucial for calculating deflection.
Can this formula be used for beams with different supports?
No, this specific formula is for simply supported beams. Different support conditions require different formulas.
What units should I use when inputting values into the calculator?
Ensure consistent units: typically, P in Newtons (N), L in meters (m), E in Pascals (Pa) or GigaPascals (GPa), and I in cubic meters (m^3).
How does material stiffness affect beam deflection?
Higher material stiffness (higher E value) results in less deflection under the same load.
Results are for informational purposes only and do not constitute professional advice.