Radius of Curvature given Bending Moment Calculator

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Bending of Beams

Residual Stresses

Torsion of Bars

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Nonlinear Behavior of Beams

Plastic Bending of Beams

Shear Stress Distribution in Beams

Yield Criteria

✖Elastoplastic Modulus is the constant used when the material yields plastically.ⓘ Elastoplastic Modulus [H]			+10% -10%
✖Nth Moment of Inertia is the integral arising from non-linear behavior of material.ⓘ Nth Moment of Inertia [I_n]			+10% -10%
✖Maximum Bending Moment is the moment at which the entire cross-section has reached its yield stress.ⓘ Maximum Bending Moment [M]			+10% -10%
✖Material Constant is the constant used when the beam yielded plastically.ⓘ Material Constant [n]			+10% -10%

✖Radius of curvature the minimum radius one can bend a pipe, tube, sheet, cable or hose without kinking it, damaging it, or shortening its life.ⓘ Radius of Curvature given Bending Moment [R]

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Formula

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Radius of Curvature given Bending Moment

Formula

`"R" = (("H"*"I"_{"n"})/"M")^(1/"n")`

Example

`"1.5E^-10mm"=(("700Pa"*"42.12mm⁴")/"1500e3N*mm")^(1/"0.25")`

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Radius of Curvature given Bending Moment Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of curvature = ((Elastoplastic Modulus*Nth Moment of Inertia)/Maximum Bending Moment)^(1/Material Constant)
R = ((H*I_n)/M)^(1/n)
This formula uses 5 Variables

Variables Used

Radius of curvature - (Measured in Centimeter) - Radius of curvature the minimum radius one can bend a pipe, tube, sheet, cable or hose without kinking it, damaging it, or shortening its life.
Elastoplastic Modulus - (Measured in Pascal) - Elastoplastic Modulus is the constant used when the material yields plastically.
Nth Moment of Inertia - (Measured in Centimeter⁴) - Nth Moment of Inertia is the integral arising from non-linear behavior of material.
Maximum Bending Moment - (Measured in Newton Meter) - Maximum Bending Moment is the moment at which the entire cross-section has reached its yield stress.
Material Constant - Material Constant is the constant used when the beam yielded plastically.

STEP 1: Convert Input(s) to Base Unit

Elastoplastic Modulus: 700 Pascal --> 700 Pascal No Conversion Required
Nth Moment of Inertia: 42.12 Millimeter⁴ --> 0.004212 Centimeter⁴ (Check conversion here)
Maximum Bending Moment: 1500000 Newton Millimeter --> 1500 Newton Meter (Check conversion here)
Material Constant: 0.25 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R = ((H*I_n)/M)^(1/n) --> ((700*0.004212)/1500)^(1/0.25)

Evaluating ... ...

R = 1.49272763796689E-11

STEP 3: Convert Result to Output's Unit

1.49272763796689E-13 Meter -->1.49272763796689E-10 Millimeter (Check conversion here)

FINAL ANSWER

1.49272763796689E-10 ≈ 1.5E-10 Millimeter <-- Radius of curvature

(Calculation completed in 00.004 seconds)

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< 4 Nonlinear Behavior of Beams Calculators

Radius of Curvature given Bending Stress

Go Radius of curvature = ((Elastoplastic Modulus*Depth Yielded Plastically^Material Constant)/Maximum Bending Stress in Plastic State)^(1/Material Constant)

Nth Moment of Inertia

Go Nth Moment of Inertia = (Breadth of rectangular beam*Depth of rectangular beam^(Material Constant+2))/((Material Constant+2)*2^(Material Constant+1))

Maximum Bending Stress in Plastic State

Go Maximum Bending Stress in Plastic State = (Maximum Bending Moment*Depth Yielded Plastically^Material Constant)/Nth Moment of Inertia

Radius of Curvature given Bending Moment

Go Radius of curvature = ((Elastoplastic Modulus*Nth Moment of Inertia)/Maximum Bending Moment)^(1/Material Constant)

Radius of Curvature given Bending Moment Formula

Radius of curvature = ((Elastoplastic Modulus*Nth Moment of Inertia)/Maximum Bending Moment)^(1/Material Constant)
R = ((H*I_n)/M)^(1/n)

What is radius of curvature in bending?

Bend radius, which is measured to the inside curvature, is the minimum radius one can bend a pipe, tube, sheet, cable or hose without kinking it, damaging it, or shortening its life. The smaller the bend radius, the greater is the material flexibility (as the radius of curvature decreases, the curvature increases).

How to Calculate Radius of Curvature given Bending Moment?

Radius of Curvature given Bending Moment calculator uses Radius of curvature = ((Elastoplastic Modulus*Nth Moment of Inertia)/Maximum Bending Moment)^(1/Material Constant) to calculate the Radius of curvature, Radius of Curvature given Bending Moment is defined as the minimum radius one can bend a pipe, tube, sheet, cable or hose without kinking it, damaging it, or shortening its life. Radius of curvature is denoted by R symbol.

How to calculate Radius of Curvature given Bending Moment using this online calculator? To use this online calculator for Radius of Curvature given Bending Moment, enter Elastoplastic Modulus (H), Nth Moment of Inertia (I_n), Maximum Bending Moment (M) & Material Constant (n) and hit the calculate button. Here is how the Radius of Curvature given Bending Moment calculation can be explained with given input values -> 0.122218 = ((700*4.212E-11)/1500)^(1/0.25).

FAQ

What is Radius of Curvature given Bending Moment?

Radius of Curvature given Bending Moment is defined as the minimum radius one can bend a pipe, tube, sheet, cable or hose without kinking it, damaging it, or shortening its life and is represented as R = ((H*I_n)/M)^(1/n) or Radius of curvature = ((Elastoplastic Modulus*Nth Moment of Inertia)/Maximum Bending Moment)^(1/Material Constant). Elastoplastic Modulus is the constant used when the material yields plastically, Nth Moment of Inertia is the integral arising from non-linear behavior of material, Maximum Bending Moment is the moment at which the entire cross-section has reached its yield stress & Material Constant is the constant used when the beam yielded plastically.

How to calculate Radius of Curvature given Bending Moment?

Radius of Curvature given Bending Moment is defined as the minimum radius one can bend a pipe, tube, sheet, cable or hose without kinking it, damaging it, or shortening its life is calculated using Radius of curvature = ((Elastoplastic Modulus*Nth Moment of Inertia)/Maximum Bending Moment)^(1/Material Constant). To calculate Radius of Curvature given Bending Moment, you need Elastoplastic Modulus (H), Nth Moment of Inertia (I_n), Maximum Bending Moment (M) & Material Constant (n). With our tool, you need to enter the respective value for Elastoplastic Modulus, Nth Moment of Inertia, Maximum Bending Moment & Material Constant 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 Radius of curvature?

In this formula, Radius of curvature uses Elastoplastic Modulus, Nth Moment of Inertia, Maximum Bending Moment & Material Constant. We can use 1 other way(s) to calculate the same, which is/are as follows -

Radius of curvature = ((Elastoplastic Modulus*Depth Yielded Plastically^Material Constant)/Maximum Bending Stress in Plastic State)^(1/Material Constant)

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