What units should I use for the inputs?

The bending moment (M) must be in Newton-millimeters (N·mm), and all dimensional inputs must be in millimeters (mm).

What shapes are supported by this calculator?

It supports four standard cross-sections: Rectangle, Solid Circle, Hollow Circle (Tube), and I-Beam.

How is the section modulus (Z) calculated?

The section modulus is calculated as Z = I / c, where I is the area moment of inertia and c is the distance from the neutral axis to the outermost fiber.

Why is the output stress in MPa?

Using Newtons (N) for force and millimeters (mm) for dimensions yields stress in N/mm², which is equivalent to Megapascals (MPa).

Does this tool account for shear stress or axial loads?

No, this calculator specifically computes the maximum normal stress due to pure bending at the outermost fiber.

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Bending Stress Calculator

Calculate the maximum bending (flexural) stress σ_max = M·c/I = M/Z at the outermost fiber of a beam section. Supports solid circle, rectangle, hollow tube, and I-beam; computes I, section modulus Z, and distance c automatically. Stress in MPa.

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2 examples

Rectangle b=50, h=100 mm, M=5×10⁶ N·mm → σ_max = 60 MPa

I = b·h³/12 = 50·100³/12 = 4.1667×10⁶ mm⁴. c = h/2 = 50 mm. Z = I/c = 83333.33 mm³. σ_max = M/Z = 5×10⁶/83333.33 = 60 MPa.

{"result":"Rectangle b=50 mm, h=100 mm, M=5000000 N·mm. I = b·h³/12 = 4166666.6667 mm⁴, c = h/2 = 50 mm, Z = I/c = 83333.3333 mm³. σ_max = M/Z = 60 MPa.","metadata":{"input":{"shape":"rectangle","M":5000000,"b":50,"h":100},"result":{"shape":"rectangle","stress":60,"stressUnit":"MPa","inertia":4166666.6667,"sectionModulus":83333.3333,"c":50}}}

Solid circle D=100 mm, M=5×10⁶ N·mm → σ_max ≈ 50.93 MPa

I = π·D⁴/64 = π·100⁴/64 ≈ 4.9087×10⁶ mm⁴. c = D/2 = 50 mm. Z = I/c = π·D³/32 ≈ 98174.77 mm³. σ_max = M/Z ≈ 50.93 MPa.

{"result":"Solid circle D=100 mm, M=5000000 N·mm. I = π·D⁴/64 = 4908738.5212 mm⁴, c = D/2 = 50 mm, Z = π·D³/32 = 98174.7704 mm³. σ_max = M/Z = 50.9296 MPa.","metadata":{"input":{"shape":"circle","M":5000000,"D":100},"result":{"shape":"circle","stress":50.9296,"stressUnit":"MPa","inertia":4908738.5212,"sectionModulus":98174.7704,"c":50}}}

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12 options

SettingsAdjust formats, ranges, numbers, and modes.12

Cross-Section ShapeselectOptionalBending Moment M (N·mm)numberRequiredDiameter D (mm)numberOptionalRequired for Solid Circle.Width b (mm)numberOptionalSection width (horizontal). Required for Rectangle.Height h (mm)numberOptionalSection height (vertical). Required for Rectangle.Outer Diameter Do (mm)numberOptionalRequired for Hollow Circle.Inner Diameter Di (mm)numberOptionalRequired for Hollow Circle. Must be less than Do.Flange Width B (mm)numberOptionalRequired for I-Beam.Total Height H (mm)numberOptionalRequired for I-Beam.Web Thickness tw (mm)numberOptionalRequired for I-Beam.Flange Thickness tf (mm)numberOptionalRequired for I-Beam.Decimal PlacesnumberOptional

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Bending Stress Calculator

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1. Verifying a Rectangular Timber Beam

2. Analyzing a Solid Steel Shaft

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