Simply Supported Beam Calculator
Calculate bending stress, deflection, slope, and bending moment for simply supported beams under point or distributed loads. Step-by-step solutions included.
simply supported beam calculator:
Calculate bending stress, deflection, slope, and maximum bending moment for and-supported beams using this Supported Beam Calculator. Enter the span length, load, cross-section, and the material properties. Midspan deflection, support slop, and distribution of bending moment are demonstrated using step-by-step calculations.
supported beam Tool Formula:
For Point Load at Center::
- Maximum Deflection: \( (\delta) = \frac{F \times L^{3}}{48 \times E \times I} \)
- Maximum Bending Moment: \( (M) = \frac{F \times L}{4} \)
For Uniformly Distributed Load (UDL):
- Maximum Deflection: \( (\delta) = \frac{5 \times W \times L^{4}}{384 \times E \times I} \)
- Maximum Bending Moment: \( (M) = \frac{W \times L^{2}}{8} \)
- 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
Simple Supported Beam Calculator is a tool that assists engineers, students, and teachers in calculating the bending stress, deflection, slope, and the moment of bending of a beam that is supported on both sides. Types of beam. Simply supported beams are used in bridges, structural floors, and mechanical frames, where the beam is mounted on two load-bearing supports and is at liberty to rotate at the ends.
The users have the option of entering beam length, load type (point or uniform), cross-section dimensions, and the material properties (E). The calculator computes maximum bending moment, maximum bending stress, maximum deflection, and slope at support,s, with the steps being included.
SI units are acceptable: meters (m), mm, N, Pa/MPa. Additional options of features are bending moment diagrams, deflection curves, and printable results. The software is suitable for civil engineers, structural engineers, mechanical engineers, students, and teachers who analyze the beam strength, safety, and performance.
⚡ Work & Installation Input to Output:
Input:
- Beam type: simply supported
- Span length (L)
- Load: point load (P) at midspan or uniform distributed load (w)
- Cross-section: rectangular (b, h), 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. Midspan point load: M_max = P × L / 4 B. Uniform load: M_max = w × L² / 8
- Compute maximum bending stress: σ_max = M_max × y / I
- Compute maximum deflection (y_max): A. Point load: y_max = P × L³ / (48 × E × I) B. Uniform load: y_max = 5 × w × L⁴ / (384 × E × I)
- Compute slope at supports (θ_max): A. Point load: θ_max = P × L² / (16 × E × I) B. Uniform load: θ_max = w × L³ / (24 × E × I)
Output:
- Maximum bending moment (M_max)
- Maximum bending stress (σ_max)
- Maximum deflection (y_max)
- Slope at supports (θ_max)
- Step-by-step formulas
- Optional bending moment and deflection diagrams, printable results
Testing and Final Adjustments
Test common scenarios:
- Point load P = 1000 N at midspan, L = 2 m, rectangular section 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, very long span, thin cross-section → validate calculations
- Verify units (Pa ↔ MPa, N·m, m/mm for deflection)
- Step-by-step solution clarity
- Mobile/desktop UX: numeric keypad, labels, error messages
- Include preset examples for educational and professional structural analysis
- Optimize SEO metadata: "Simply Supported Beam Calculator," "Maximum Deflection," "Bending Stress," "Slope," schema markup
Frequently Asked Questions - Simply Supported Beam Calculator:
What is a simply supported beam?
A simply supported beam rests on two supports and is free to rotate at the ends, commonly used in bridges and floors.
How do I calculate maximum bending moment?
For point load at midspan: M_max = P × L / 4; for uniform load: M_max = w × L² / 8.
How do I calculate maximum bending stress?
σ_max = M_max × y / I, where y is distance from neutral axis, I is moment of inertia.
How do I calculate maximum deflection?
Point load: y_max = P × L³ / (48 × E × I); Uniform load: y_max = 5 × w × L⁴ / (384 × E × I).
How do I calculate slope at supports?
Point load: θ_max = P × L² / (16 × E × I); Uniform load: θ_max = w × L³ / (24 × E × I).
Which units are supported?
Lengths in meters 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 bending moment and deflection diagrams?
Yes, optional plotting along the beam length is available.
Who should use this calculator?
Structural and mechanical engineers, students, educators, and designers analyzing simply supported beams.
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