Radius of Curvature given Bending Stress Calculator

✖Elastoplastic Modulus is the measure of a material's tendency to deform plastically in bending, beyond the elastic limit, in beams under external loads.ⓘ Elastoplastic Modulus [H]			+10% -10%
✖Depth Yielded Plastically is the distance along the beam where the stress exceeds the yield strength of the material during bending.ⓘ Depth Yielded Plastically [y]			+10% -10%
✖Material Constant is a measure of the stiffness of a material, used to calculate the bending stress and deflection of beams under various loads.ⓘ Material Constant [n]			+10% -10%
✖Maximum Bending Stress in Plastic State is the maximum stress a beam can withstand in its plastic state without undergoing deformation or breaking.ⓘ Maximum Bending Stress in Plastic State [σ]			+10% -10%

✖Radius of Curvature is the radius of the circle at the center of which the beam is bent, defining the curvature of the beam.ⓘ Radius of Curvature given Bending Stress [R]

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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 is the radius of the circle at the center of which the beam is bent, defining the curvature of the beam.
Elastoplastic Modulus - (Measured in Megapascal) - Elastoplastic Modulus is the measure of a material's tendency to deform plastically in bending, beyond the elastic limit, in beams under external loads.
Depth Yielded Plastically - (Measured in Millimeter) - Depth Yielded Plastically is the distance along the beam where the stress exceeds the yield strength of the material during bending.
Material Constant - Material Constant is a measure of the stiffness of a material, used to calculate the bending stress and deflection of beams under various loads.
Maximum Bending Stress in Plastic State - (Measured in Megapascal) - Maximum Bending Stress in Plastic State is the maximum stress a beam can withstand in its plastic state without undergoing deformation or breaking.

STEP 1: Convert Input(s) to Base Unit

Elastoplastic Modulus: 700 Newton per Square Millimeter --> 700 Megapascal (Check conversion here)
Depth Yielded Plastically: 0.5 Millimeter --> 0.5 Millimeter No Conversion Required
Material Constant: 0.25 --> No Conversion Required
Maximum Bending Stress in Plastic State: 9.97461853276134E-05 Newton per Square Millimeter --> 9.97461853276134E-05 Megapascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R = ((H*y^n)/σ)^(1/n) --> ((700*0.5^0.25)/9.97461853276134E-05)^(1/0.25)

Evaluating ... ...

R = 1.21276591338816E+27

STEP 3: Convert Result to Output's Unit

1.21276591338816E+24 Meter -->1.21276591338816E+27 Millimeter (Check conversion here)

FINAL ANSWER

1.21276591338816E+27 ≈ 1.2E+27 Millimeter <-- Radius of Curvature

(Calculation completed in 00.020 seconds)

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< Nonlinear Behavior of Beams Calculators

Radius of Curvature given Bending Stress

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

Nth Moment of Inertia

LaTeX 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

LaTeX 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

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

Radius of Curvature given Bending Stress Formula

LaTeX Go

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?

The Radius of Curvature in Bending refers to the radius of the arc that a beam or structural element forms when it undergoes bending. It quantifies the degree of curvature, with a smaller radius indicating sharper bending and a larger radius indicating gentler bending. This radius is inversely related to the bending moment and material stiffness: higher bending moments or less stiff materials result in a smaller radius of curvature. In engineering, calculating the radius of curvature is essential for understanding deflection and ensuring that structural elements remain within safe deformation limits under load.

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 formula is defined as a measure of the curvature of a beam under bending stress, providing a way to quantify the degree of deformation in a beam due to external forces, which is essential in structural analysis and design of beams in various engineering applications. 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 -> 1.2E+30 = ((700000000*0.0005^0.25)/99.7461853276134)^(1/0.25).

FAQ

What is Radius of Curvature given Bending Stress?

Radius of Curvature given Bending Stress formula is defined as a measure of the curvature of a beam under bending stress, providing a way to quantify the degree of deformation in a beam due to external forces, which is essential in structural analysis and design of beams in various engineering applications 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 measure of a material's tendency to deform plastically in bending, beyond the elastic limit, in beams under external loads, Depth Yielded Plastically is the distance along the beam where the stress exceeds the yield strength of the material during bending, Material Constant is a measure of the stiffness of a material, used to calculate the bending stress and deflection of beams under various loads & Maximum Bending Stress in Plastic State is the maximum stress a beam can withstand in its plastic state without undergoing deformation or breaking.

How to calculate Radius of Curvature given Bending Stress?

Radius of Curvature given Bending Stress formula is defined as a measure of the curvature of a beam under bending stress, providing a way to quantify the degree of deformation in a beam due to external forces, which is essential in structural analysis and design of beams in various engineering applications 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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