Maximum Bending Stress Calculator

✖The Bending Moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend.ⓘ Bending Moment [M_b]			+10% -10%
✖Distance from Neutral Axis to Extreme Point is the distance between the neutral axis and the extreme point.ⓘ Distance from Neutral Axis to Extreme Point [c]			+10% -10%
✖The Polar moment of Inertia is a shaft or beam's resistance to being distorted by torsion, as a function of its shape.ⓘ Polar Moment of Inertia [J]			+10% -10%

✖Maximum bending stress is the normal stress that is induced at a point in a body subjected to loads that cause it to bend.ⓘ Maximum Bending Stress [σ_max]

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Formula

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Maximum Bending Stress

Formula

`"σ"_{"max"} = ("M"_{"b"}*"c")/("J")`

Example

`"9.8E^-9N/mm²"=("53N*m"*"10mm")/("54.2m⁴")`

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Maximum Bending Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Bending Stress = (Bending Moment*Distance from Neutral Axis to Extreme Point)/(Polar Moment of Inertia)
σ_max = (M_b*c)/(J)
This formula uses 4 Variables

Variables Used

Maximum Bending Stress - (Measured in Pascal) - Maximum bending stress is the normal stress that is induced at a point in a body subjected to loads that cause it to bend.
Bending Moment - (Measured in Newton Meter) - The Bending Moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend.
Distance from Neutral Axis to Extreme Point - (Measured in Meter) - Distance from Neutral Axis to Extreme Point is the distance between the neutral axis and the extreme point.
Polar Moment of Inertia - (Measured in Meter⁴) - The Polar moment of Inertia is a shaft or beam's resistance to being distorted by torsion, as a function of its shape.

STEP 1: Convert Input(s) to Base Unit

Bending Moment: 53 Newton Meter --> 53 Newton Meter No Conversion Required
Distance from Neutral Axis to Extreme Point: 10 Millimeter --> 0.01 Meter (Check conversion here)
Polar Moment of Inertia: 54.2 Meter⁴ --> 54.2 Meter⁴ No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_max = (M_b*c)/(J) --> (53*0.01)/(54.2)

Evaluating ... ...

σ_max = 0.00977859778597786

STEP 3: Convert Result to Output's Unit

0.00977859778597786 Pascal -->9.77859778597786E-09 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

9.77859778597786E-09 ≈ 9.8E-9 Newton per Square Millimeter <-- Maximum Bending Stress

(Calculation completed in 00.020 seconds)

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Created by Nishan Poojary

Shri Madhwa Vadiraja Institute of Technology and Management (SMVITM), Udupi

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< 9 Stress in Design Calculators

Shear Stress on Circular Fillet Weld Subjected to Torsion

Go Torsional Shear Stress = Torsional Moment in Welded Shaft/(pi*Throat Thickness of Weld*Radius of Welded Shaft^2)

Torsional Shear Stress in Bar

Go Torsional Shear Stress = (8*Force*Mean Diameter of Coil)/(pi*Diameter of Spring Wire^3)

Maximum Bending Stress

Go Maximum Bending Stress = (Bending Moment*Distance from Neutral Axis to Extreme Point)/(Polar Moment of Inertia)

Shear Stress for Long Fillet Weld Subjected to Torsion

Go Torsional Shear Stress = (3*Torsional Moment in Welded Shaft)/(Throat Thickness of Weld*Length of Weld^2)

Shear Stress in Parallel Fillet Weld

Go Shear stress in parallel fillet weld = Load on Parallel Fillet Weld/(0.707*Length of Weld*Leg of Weld)

Shear Stress in Double Parallel Fillet Weld

Go Shearing Stress = Load on Double Parallel Fillet Weld/(0.707*Length of Weld*Leg of Weld)

Bolt Stress

Go Shear Stress in Bolt = pi/(4*(Nominal Bolt Diameter-0.9743*Pitch Diameter)^2)

Bending Stress in Shaft

Go Bending Stress = (32*Bending Moment)/(pi*Diameter of Shaft^3)

Maximum Bending Stress given Rectangular Section Modulus

Go Maximum Bending Stress = Bending Moment/Rectangular Section Modulus

Maximum Bending Stress Formula

Maximum Bending Stress = (Bending Moment*Distance from Neutral Axis to Extreme Point)/(Polar Moment of Inertia)
σ_max = (M_b*c)/(J)

What is stress?

Stress is defined as the force across a small boundary per unit area of that boundary, for all orientations of the boundary. Being derived from a fundamental physical quantity and a purely geometrical quantity, stress is also a fundamental quantity

How to Calculate Maximum Bending Stress?

Maximum Bending Stress calculator uses Maximum Bending Stress = (Bending Moment*Distance from Neutral Axis to Extreme Point)/(Polar Moment of Inertia) to calculate the Maximum Bending Stress, Maximum bending stress is the normal stress that is induced at a point in a body subjected to loads that cause it to bend. Maximum Bending Stress is denoted by σ_max symbol.

How to calculate Maximum Bending Stress using this online calculator? To use this online calculator for Maximum Bending Stress, enter Bending Moment (M_b), Distance from Neutral Axis to Extreme Point (c) & Polar Moment of Inertia (J) and hit the calculate button. Here is how the Maximum Bending Stress calculation can be explained with given input values -> 9.8E-15 = (53*0.01)/(54.2).

FAQ

What is Maximum Bending Stress?

Maximum bending stress is the normal stress that is induced at a point in a body subjected to loads that cause it to bend and is represented as σ_max = (M_b*c)/(J) or Maximum Bending Stress = (Bending Moment*Distance from Neutral Axis to Extreme Point)/(Polar Moment of Inertia). The Bending Moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend, Distance from Neutral Axis to Extreme Point is the distance between the neutral axis and the extreme point & The Polar moment of Inertia is a shaft or beam's resistance to being distorted by torsion, as a function of its shape.

How to calculate Maximum Bending Stress?

Maximum bending stress is the normal stress that is induced at a point in a body subjected to loads that cause it to bend is calculated using Maximum Bending Stress = (Bending Moment*Distance from Neutral Axis to Extreme Point)/(Polar Moment of Inertia). To calculate Maximum Bending Stress, you need Bending Moment (M_b), Distance from Neutral Axis to Extreme Point (c) & Polar Moment of Inertia (J). With our tool, you need to enter the respective value for Bending Moment, Distance from Neutral Axis to Extreme Point & Polar Moment of Inertia and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Maximum Bending Stress?

In this formula, Maximum Bending Stress uses Bending Moment, Distance from Neutral Axis to Extreme Point & Polar Moment of Inertia. We can use 1 other way(s) to calculate the same, which is/are as follows -

Maximum Bending Stress = Bending Moment/Rectangular Section Modulus

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