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Estimate maximum deflection, slope, flexural rigidity, and section properties for common Euler-Bernoulli beam cases.
Maximum deflection
1.66667 mm
Unit-normalization summary: 2 m; 2.00000e+11 Pa; 8.00000e-6 m^4
delta = C P L^3 / E I or C w L^4 / E I
Cantilever end load: PL^3/(3EI). Cantilever UDL: wL^4/(8EI). Simply supported center load: PL^3/(48EI). Simply supported UDL: 5wL^4/(384EI).
EI = 2.00000e+11 Pa x 8.00000e-6 m^4
Compare calculated deflection with project-specific serviceability limits. This tool does not choose an allowable deflection ratio.
Beam deflection is the displacement and rotation produced by transverse loading. Closed-form Euler-Bernoulli solutions combine load, span, elastic modulus, second moment of area, support condition, and load position for ideal slender beams with small deformation.
Beam Deflection Calculator applies this concept to its defined inputs and workflow. This beam deflection workflow complements bending stress, buckling, shaft alignment, and serviceability checks. Its governing relationship or workflow is stated as follows: Standard closed-form beam deflection and slope formulas for common support and load cases.
The calculator evaluates Calculation mode, Material preset, and Display precision and returns Beam Deflection, base-unit normalization, formula substitution, and calculation steps using the stated method. The selected units and sign or reference conventions must describe one consistent physical case. Users should interpret the output within the assumptions shown on the page and repeat the check with trusted reference values when the result affects engineering or research decisions. Only four standard single-load cases are included.
| Symbol | Meaning | Unit |
|---|---|---|
| P | Point load | N |
| w | Uniform distributed load | N/m |
| EI | Flexural rigidity | N*m^2 |
| delta | Maximum deflection | m |
| theta | Beam slope | rad |
The beam deflection workflow complements bending stress, buckling, shaft alignment, and serviceability checks.
Professional FEA, simulation setup, solid-mechanics calculations, mechanical-design review, technical documentation, and research support are available through the connected services website. These calculators remain free to use without purchasing services.
Visit ScholarEaseThis tool is intended for educational, estimation, and preliminary engineering use. It does not certify designs or replace applicable codes, standards, validated software, physical testing, or qualified professional engineering judgment.
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