Radius of Curvature given Bending Stress 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%
✖Depth Yielded Plastically is the amount of depth of the beam yielded plastically from it's outermost fiber.ⓘ Depth Yielded Plastically [y]			+10% -10%
✖Material Constant is the constant used when the beam yielded plastically.ⓘ Material Constant [n]			+10% -10%
✖Maximum Bending Stress in Plastic State is defined as the stresses within a beam exceed the elastic limit, then plastic deformation will occur.ⓘ Maximum Bending Stress in Plastic State [σ]			+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 Stress [R]

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Formula

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Radius of Curvature given Bending Stress

Formula

`"R" = (("H"*"y"^"n")/"σ")^(1/"n")`

Example

`"693637.9mm"=(("700Pa"*("40mm")^"0.25")/"61Pa")^(1/"0.25")`

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Radius of Curvature given Bending Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of curvature = ((Elastoplastic Modulus*Depth Yielded Plastically^Material Constant)/Maximum Bending Stress in Plastic State)^(1/Material Constant)
R = ((H*y^n)/σ)^(1/n)
This formula uses 5 Variables

Variables Used

Radius of curvature - (Measured in Millimeter) - 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 Megapascal) - Elastoplastic Modulus is the constant used when the material yields plastically.
Depth Yielded Plastically - (Measured in Millimeter) - Depth Yielded Plastically is the amount of depth of the beam yielded plastically from it's outermost fiber.
Material Constant - Material Constant is the constant used when the beam yielded plastically.
Maximum Bending Stress in Plastic State - (Measured in Megapascal) - Maximum Bending Stress in Plastic State is defined as the stresses within a beam exceed the elastic limit, then plastic deformation will occur.

STEP 1: Convert Input(s) to Base Unit

Elastoplastic Modulus: 700 Pascal --> 0.0007 Megapascal (Check conversion here)
Depth Yielded Plastically: 40 Millimeter --> 40 Millimeter No Conversion Required
Material Constant: 0.25 --> No Conversion Required
Maximum Bending Stress in Plastic State: 61 Pascal --> 6.1E-05 Megapascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R = ((H*y^n)/σ)^(1/n) --> ((0.0007*40^0.25)/6.1E-05)^(1/0.25)

Evaluating ... ...

R = 693637.894585096

STEP 3: Convert Result to Output's Unit

693.637894585096 Meter -->693637.894585096 Millimeter (Check conversion here)

FINAL ANSWER

693637.894585096 ≈ 693637.9 Millimeter <-- Radius of curvature

(Calculation completed in 00.020 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 Stress Formula

Radius of curvature = ((Elastoplastic Modulus*Depth Yielded Plastically^Material Constant)/Maximum Bending Stress in Plastic State)^(1/Material Constant)
R = ((H*y^n)/σ)^(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 Stress?

Radius of Curvature given Bending Stress calculator uses Radius of curvature = ((Elastoplastic Modulus*Depth Yielded Plastically^Material Constant)/Maximum Bending Stress in Plastic State)^(1/Material Constant) to calculate the Radius of curvature, Radius of Curvature given Bending Stress 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 Stress using this online calculator? To use this online calculator for Radius of Curvature given Bending Stress, enter Elastoplastic Modulus (H), Depth Yielded Plastically (y), Material Constant (n) & Maximum Bending Stress in Plastic State (σ) and hit the calculate button. Here is how the Radius of Curvature given Bending Stress calculation can be explained with given input values -> 6.9E+8 = ((700*0.04^0.25)/61000000)^(1/0.25).

FAQ

What is Radius of Curvature given Bending Stress?

Radius of Curvature given Bending Stress 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*y^n)/σ)^(1/n) or Radius of curvature = ((Elastoplastic Modulus*Depth Yielded Plastically^Material Constant)/Maximum Bending Stress in Plastic State)^(1/Material Constant). Elastoplastic Modulus is the constant used when the material yields plastically, Depth Yielded Plastically is the amount of depth of the beam yielded plastically from it's outermost fiber, Material Constant is the constant used when the beam yielded plastically & Maximum Bending Stress in Plastic State is defined as the stresses within a beam exceed the elastic limit, then plastic deformation will occur.

How to calculate Radius of Curvature given Bending Stress?

Radius of Curvature given Bending Stress 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*Depth Yielded Plastically^Material Constant)/Maximum Bending Stress in Plastic State)^(1/Material Constant). To calculate Radius of Curvature given Bending Stress, you need Elastoplastic Modulus (H), Depth Yielded Plastically (y), Material Constant (n) & Maximum Bending Stress in Plastic State (σ). With our tool, you need to enter the respective value for Elastoplastic Modulus, Depth Yielded Plastically, Material Constant & Maximum Bending Stress in Plastic State 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, Depth Yielded Plastically, Material Constant & Maximum Bending Stress in Plastic State. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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