Quickly calculate maximum bending moment, deflection, and bending stress for common beam types.
Our free Beam Bending Calculator is ideal for engineers, students, and builders. Enter your beam length, load, material, and section details to get instant, accurate results.
Beam Bending Calculator
How it works
Formulas used:
- Simply Supported, Center Load: Mmax=P·L/4, δmax=P·L³/(48·E·I)
- Simply Supported, UDL: Mmax=w·L²/8, δmax=5·w·L⁴/(384·E·I)
- Cantilever, End Load: Mmax=P·L, δmax=P·L³/(3·E·I)
Section properties:
- Rectangular: I=b·h³/12, c=h/2
- Circular: I=π·d⁴/64, c=d/2
Bending stress is σmax = Mmax·c / I.
Beam Bending Calculator
Compute beam deflection and stress fast — supports simply supported and cantilever beams with point or uniform loads.
Beam Type • Length • Load • Young’s Modulus • Section Type
Rectangular | Circular | Custom I & c
Demo Clear
How It Works
The calculator uses standard structural formulas based on the beam type and loading condition:
| Beam Type | Max Moment (Mₘₐₓ) | Max Deflection (δₘₐₓ) |
|---|---|---|
| Simply Supported – Point Load at Center | P L / 4 | P L³ / (48 E I) |
| Simply Supported – UDL | w L² / 8 | 5 w L⁴ / (384 E I) |
| Cantilever – End Point Load | P L | P L³ / (3 E I) |
Then, bending stress is computed as:
σₘₐₓ = (Mₘₐₓ × c) / I
Example
Example – Simply Supported Beam:
- Length = 4 m
- Point Load = 20 kN
- Material E = 200 GPa (Steel)
- Section = 100 mm × 200 mm Rectangular
Results:
- Mₘₐₓ = 20 × 4 / 4 = 20 kN·m
- δₘₐₓ ≈ 1.0 mm
- σₘₐₓ ≈ 100 MPa
(Approximate, for educational use.)
Why Use This Calculator
✔ Handles multiple beam types & load cases
✔ Accepts custom section properties (I and c)
✔ Supports Rectangular & Circular sections
✔ Shows deflection and bending stress instantly
✔ Fast and mobile-friendly tool
How to Use the Beam Bending Calculator
1️⃣ Select beam type (Simply Supported or Cantilever)
2️⃣ Enter length (L) in meters
3️⃣ Input load (P or w) in kN
4️⃣ Choose Young’s Modulus (E) for material (steel, aluminum, wood)
5️⃣ Pick section shape (Rectangular, Circular, or Custom I & c)
6️⃣ Click Calculate to get:
• Maximum Moment (Mₘₐₓ)
• Deflection (δₘₐₓ)
• Bending Stress (σₘₐₓ)
FAQ
Q: What does the beam bending calculator do?
It computes moment, deflection, and bending stress for common beam scenarios.
Q: Which materials can I use?
Any material — just enter its Young’s Modulus (E) in GPa.
Q: What units are used?
Input in meters and kN; outputs in kN·m, mm, and MPa.
Q: Can I enter my own I and c values?
Yes — use the Custom I & c option for complex sections.
Q: Is this for structural design?
It’s for learning and estimation. Consult a qualified engineer for final design.