Radius of Curvature given Bending Moment 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%
✖Nth Moment of Inertia is a measure of the distribution of the beam's mass around its axis of rotation, used in bending beam analysis.ⓘ Nth Moment of Inertia [I_n]			+10% -10%
✖Maximum Bending Moment is the maximum amount of stress a beam can withstand before it starts to bend or deform under external loads.ⓘ Maximum Bending Moment [M]			+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%

✖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 Moment [R]

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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 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 Pascal) - Elastoplastic Modulus is the measure of a material's tendency to deform plastically in bending, beyond the elastic limit, in beams under external loads.
Nth Moment of Inertia - (Measured in Kilogram Square Meter) - Nth Moment of Inertia is a measure of the distribution of the beam's mass around its axis of rotation, used in bending beam analysis.
Maximum Bending Moment - (Measured in Newton Meter) - Maximum Bending Moment is the maximum amount of stress a beam can withstand before it starts to bend or deform under external loads.
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.

STEP 1: Convert Input(s) to Base Unit

Elastoplastic Modulus: 700 Newton per Square Millimeter --> 700000000 Pascal (Check conversion here)
Nth Moment of Inertia: 12645542471 Kilogram Square Millimeter --> 12645.542471 Kilogram Square Meter (Check conversion here)
Maximum Bending Moment: 1500000000 Newton Millimeter --> 1500000 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) --> ((700000000*12645.542471)/1500000)^(1/0.25)

Evaluating ... ...

R = 1.21276591338816E+27

STEP 3: Convert Result to Output's Unit

1.21276591338816E+25 Meter -->1.21276591338816E+28 Millimeter (Check conversion here)

FINAL ANSWER

1.21276591338816E+28 ≈ 1.2E+28 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 Moment Formula

LaTeX Go

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?

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 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 formula is defined as a measure of the degree of curvature of a beam under bending stress, providing a way to quantify the amount of deformation that occurs when a beam is subjected to external forces, allowing engineers to design and analyze beams more accurately. 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 -> 1.2E+31 = ((700000000*12645.542471)/1500000)^(1/0.25).

FAQ

What is Radius of Curvature given Bending Moment?

Radius of Curvature given Bending Moment formula is defined as a measure of the degree of curvature of a beam under bending stress, providing a way to quantify the amount of deformation that occurs when a beam is subjected to external forces, allowing engineers to design and analyze beams more accurately 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 measure of a material's tendency to deform plastically in bending, beyond the elastic limit, in beams under external loads, Nth Moment of Inertia is a measure of the distribution of the beam's mass around its axis of rotation, used in bending beam analysis, Maximum Bending Moment is the maximum amount of stress a beam can withstand before it starts to bend or deform under external loads & Material Constant is a measure of the stiffness of a material, used to calculate the bending stress and deflection of beams under various loads.

How to calculate Radius of Curvature given Bending Moment?

Radius of Curvature given Bending Moment formula is defined as a measure of the degree of curvature of a beam under bending stress, providing a way to quantify the amount of deformation that occurs when a beam is subjected to external forces, allowing engineers to design and analyze beams more accurately 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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