Beam Deflection Calculator
Calculate maximum deflection, slope, and bending moment of beams under various loads. Step-by-step solutions with SI units included.
Beam deflection calculator:
This Beam Bending Stress Calculator is used to calculate the flexural stress in beams with different loads. Type of enter beam, span, cross-section, and applied load. Bending stress, maximum moment, and section modulus are represented through step-by-step formulas to perform structural or mechanical analysis.
Beam Bending Stress Tool Formula:
Formula:
Simply Supported Beam: Deflection (δ) = (F * L³) / (48 * E * I)
Cantilever Beam: Deflection (δ) = (F * L³) / (3 * E * I)
Moment of Inertia (I) for Rectangular Cross-Section = (b * h³) / 12
Moment of Inertia (I) for Circular Cross-Section = (π * d⁴) / 64
where δ = Deflection, F = Force, L = Length, E = Young's Modulus, I = Moment of inertia
The Beam Bending Stress Calculator is an aid that engineers and students use to study the flexural stress in beams under different loads. Bending stress comes as a result of bending forces on the cross-section of the beam and is computed with the help of the formula:
\[ \frac{d^{2}y}{dx^{2}} = \frac{M(x)}{EI} \]
Some of the inputs that users can make include applied load, beam type (simply supported, cantilever, overhanging), span length, beam cross-section dimensions, and material properties. The calculator determines maximum bending stress, bending moment, and section modulus, giving step-by-step solutions. SI units are accepted: N, m, mm, Pa, MPa. It has optional features to plot bending moment diagrams, compute deflection, and print results. The tool would be suitable for structural engineers, mechanical engineers, students, and educators who are analysing the beam strength, safety, and structural performance.
⚡ Work & Installation Input to Output:
Input:
- Beam type: simply supported, cantilever, overhanging
- Span length (L)
- Load: point load (P) or uniform distributed load (w)
- Cross-section: width (b), height (h) or I-section properties
- Material properties: Young’s modulus (E)
- Units: N, m, mm, Pa/MPa
Processing:
- Compute moment of inertia (I) for the cross-section
- Compute bending moment (M) based on beam type and loading
- Solve d²y/dx² = M(x)/EI using integration and boundary conditions
- Compute maximum deflection (y_max)
- Compute slope (θ) at supports or free ends
- Optional: generate deflection curve along the beam
Output:
- Maximum deflection (y_max)
- Slope at supports or free ends
- Bending moment distribution (M(x))
- Step-by-step formulas
- Optional deflection curve plot and printable results
Testing and Final Adjustments
Test common scenarios:
- Simply supported beam, P = 1000 N at midspan, L = 2 m, rectangular section b = 0.1 m, h = 0.2 m, E = 200 GPa → compute y_max and slope
- Cantilever beam with w = 500 N/m, L = 1.5 m → validate formulas for free end deflection
- I-section beam: check moment of inertia, slope, and maximum deflection
- Edge cases: zero load, very long span, thin cross-section → validate computation
- Verify units (Pa ↔ MPa, N·m for bending moment, meters/mm for deflection)
- Ensure mobile/desktop UX: numeric keypad, clear labels, error messages
- Include preset examples for education and professional use
- Optimize SEO metadata: "Beam Deflection Calculator," "Maximum Deflection," "Slope," "Bending Moment," schema markup
Frequently Asked Questions - Beam Deflection Calculator:
What is beam deflection?
Beam deflection is the displacement of a beam under loads due to bending moments.
How do I calculate beam deflection?
Use the moment-curvature relation: d²y/dx² = M(x)/EI, integrating with boundary conditions.
Which units are supported?
Lengths in meters or mm, forces in N, modulus E in Pa or MPa, angles in radians.
Can I calculate maximum deflection?
Yes, the calculator computes y_max at midspan or free end depending on beam type.
Can I calculate slope at supports?
Yes, slope θ can be calculated at supports or free ends based on boundary conditions.
Does it support different beam types?
Yes, simply supported, cantilever, and overhanging beams are supported.
Can it handle point and distributed loads?
Yes, both point loads and uniform distributed loads can be analyzed.
Is step-by-step solution available?
Yes, all formulas and integration steps are displayed clearly.
Who should use this calculator?
Civil and mechanical engineers, students, educators, and designers analyzing beams.
Can it plot deflection curves?
Yes, optional plotting of deflection along the beam length is available.
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