Cantilever Beam Calculator
Calculate deflection, bending stress, slope, and bending moment for cantilever beams under point or distributed loads. Step-by-step solutions included.
cantilever beam calculator:
This Cantilever Beam Calculator is used to find the deflection, slope, bending stress, and bending moment of cantilever beams when there is a point or uniform load. Load, cross-section, material properties, and enter length. Calculations have been performed step-by-step to show how the values of stress and deflection change through the beam.
cantilever beam Tool Formula:
For Point Load at Free End:
- Maximum Deflection: \( (\delta) = \frac{F \times L^{3}}{3 \times E \times I} \)
- Maximum Bending Moment: \( (M) = F \times L \)
For Uniformly Distributed Load (UDL):
- Maximum Deflection: \( (\delta) = \frac{W \times L^{4}}{8 \times E \times I} \)
- Maximum Bending Moment: \( (M) = \frac{W \times L^{2}}{2} \)
- Moment of Inertia (I) for Rectangular Cross-Section: \( \frac{b \times h^{3}}{12} \)
- Moment of Inertia (I) for Circular Cross-Section: \( \frac{\pi \times d^{4}}{64} \)
where δ = Deflection, F = Force, w = UDL, L = Length, E = Young's Modulus, I = Moment of inertia
Cantilever Beam Calculator is a software application that allows engineers and students to study cantilever beams under the influence of point loads or uniformly distributed loads (UDL) or non-uniform loads. Cantilever beams are mounted at one end and at the free end, and they are known to have the highest bending moment and deflection at the fixed end.
The users can enter beam length, type and size of load, cross-section size, and material properties (E). The calculator solves maximum deflection, slope at the fixed end, maximum bending moment, and bending stress step-wise wise giving solutions to each.
The calculator has SI units: meters (m), mm, N, Pa/MPa. Other optional features are plotting the deflection curve along the beam, stress distribution, and printable results. The tool applies to structural engineers, mechanical engineers, students, and teachers of structural safety and material behavior of beams.
⚡ Work & Installation Input to Output:
Input:
- Beam length (L)
- Load: point load (P) at free end or uniform distributed load (w)
- Cross-section: rectangular (b, h) or circular (d) or I-section
- Material properties: Young’s modulus (E)
- Units: N, m, mm, Pa/MPa
Processing:
- Compute moment of inertia (I): A. Rectangular: I = b × h³ / 12 B. Circular: I = π × d⁴ / 64
- Compute maximum bending moment (M_max): A. Point load at free end: M_max = P × L B. Uniform load: M_max = w × L² / 2
- Compute maximum bending stress: σ_max = M_max × y / I
- Compute maximum deflection (y_max): A. Point load: y_max = P × L³ / (3 × E × I) B. Uniform load: y_max = w × L⁴ / (8 × E × I)
- Compute slope at fixed end (θ_max): A. Point load: θ_max = P × L² / (2 × E × I) B. Uniform load: θ_max = w × L³ / (6 × E × I)
Output:
- Maximum bending moment (M_max)
- Maximum bending stress (σ_max)
- Maximum deflection (y_max)
- Maximum slope (θ_max)
- Step-by-step formulas
- Optional deflection/stress curve plots and printable results
Testing and Final Adjustments
Test common scenarios:
- Point load P = 1000 N at free end, L = 2 m, rectangular beam b = 0.1 m, h = 0.2 m, E = 200 GPa → compute M_max, σ_max, y_max, θ_max
- Uniform distributed load w = 500 N/m, L = 1.5 m → validate formulas for deflection and slope
- Circular beam: d = 0.1 m → check I, σ_max, y_max
- Edge cases: zero load, extremely long span, thin cross-section → validate calculations
- Verify units (Pa ↔ MPa, N·m, m/mm for deflection)
- Ensure mobile/desktop UX: numeric keypad, labels, error messages
- Include preset examples for education and professional structural analysis
- Optimize SEO metadata: "Cantilever Beam Calculator," "Maximum Deflection," "Bending Stress," "Slope," schema markup
Frequently Asked Questions - Cantilever Beam Calculator:
What is a cantilever beam?
A cantilever beam is fixed at one end and free at the other, supporting loads along its length or at the free end.
How do I calculate maximum bending moment?
For a point load at free end: M_max = P × L; for uniform load: M_max = w × L² / 2.
How do I calculate maximum bending stress?
σ_max = M_max × y / I, where M_max is maximum bending moment, y is distance from neutral axis, and I is moment of inertia.
How do I calculate maximum deflection?
For point load: y_max = P × L³ / (3 × E × I); for UDL: y_max = w × L⁴ / (8 × E × I).
How do I calculate slope at fixed end?
For point load: θ_max = P × L² / (2 × E × I); for UDL: θ_max = w × L³ / (6 × E × I).
Which units are supported?
Lengths in m or mm, forces in N, modulus E in Pa/MPa, stress in Pa/MPa.
Can it handle rectangular and circular beams?
Yes, it supports rectangular, circular, and I-section beams.
Is step-by-step solution available?
Yes, formulas and calculations are displayed step-by-step.
Can it plot deflection and stress curves?
Yes, optional plotting of deflection and bending stress along the beam is available.
Who should use this calculator?
Structural and mechanical engineers, students, educators, and designers analyzing cantilever beams.
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