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Radius of Curvature given Bending Moment Formula

GoRadius of Curvature given Bending Stress Formula

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Radius of Curvature is the radius of the circle at the center of which the beam is bent, defining the curvature of the beam. Check FAQs

R = {(\frac{H \cdot I n}{M})}^{\frac{1}{n}}

R - Radius of Curvature?H - Elastoplastic Modulus?I_n - Nth Moment of Inertia?M - Maximum Bending Moment?n - Material Constant?

Radius of Curvature given Bending Moment Example

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Here is how the Radius of Curvature given Bending Moment equation looks like with Values.

Here is how the Radius of Curvature given Bending Moment equation looks like with Units.

Here is how the Radius of Curvature given Bending Moment equation looks like.

1.2E+28 = {(\frac{700 \cdot 1.3E+10}{1.5E+9})}^{\frac{1}{0.25}}

1.2E+28mm = {(\frac{700N/mm² \cdot 1.3E+10kg*mm²}{1.5E+9N*mm})}^{\frac{1}{0.25}}

1.2E+28 = {(\frac{700 \cdot 1.3E+10}{1.5E+9})}^{\frac{1}{0.25}}

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Radius of Curvature given Bending Moment Solution

Follow our step by step solution on how to calculate Radius of Curvature given Bending Moment?

FIRST Step Consider the formula

R = {(\frac{H \cdot I n}{M})}^{\frac{1}{n}}

Next Step Substitute values of Variables

∴

R = {(\frac{700N/mm² \cdot 1.3E+10kg*mm²}{1.5E+9N*mm})}^{\frac{1}{0.25}}

Next Step Convert Units

∴

R = {(\frac{7E+8Pa \cdot 12645.5425kg·m²}{1.5E+6N*m})}^{\frac{1}{0.25}}

Next Step Prepare to Evaluate

∴

R = {(\frac{7E+8 \cdot 12645.5425}{1.5E+6})}^{\frac{1}{0.25}}

Next Step Evaluate

∴

R = 1.21276591338816E+25m

Next Step Convert to Output's Unit

∴

R = 1.21276591338816E+28mm

LAST Step Rounding Answer

∴

R = 1.2E+28mm

Radius of Curvature given Bending Moment Formula Elements

Variables

Radius of Curvature

Radius of Curvature is the radius of the circle at the center of which the beam is bent, defining the curvature of the beam.

Symbol: R

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Curvature

Elastoplastic Modulus

Elastoplastic Modulus is the measure of a material's tendency to deform plastically in bending, beyond the elastic limit, in beams under external loads.

Symbol: H

Measurement: StressUnit: N/mm²

Note: Value can be positive or negative.

Formulas to find Elastoplastic Modulus

Nth Moment of Inertia

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.

Symbol: I_n

Measurement: Moment of InertiaUnit: kg*mm²

Note: Value should be greater than 0.

Formulas to find Nth Moment of Inertia

Maximum Bending Moment

Maximum Bending Moment is the maximum amount of stress a beam can withstand before it starts to bend or deform under external loads.

Symbol: M

Measurement: Moment of ForceUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Maximum Bending Moment

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.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Material Constant

Other Formulas to find Radius of Curvature

Go Radius of Curvature given Bending Stress

R = {(\frac{H \cdot y^{n}}{σ})}^{\frac{1}{n}}

Other formulas in Nonlinear Behavior of Beams category

Go Maximum Bending Stress in Plastic State

σ = \frac{M \cdot y^{n}}{I n}

Go Nth Moment of Inertia

I n = \frac{b \cdot d^{n + 2}}{(n + 2) \cdot 2^{n + 1}}

How to Evaluate Radius of Curvature given Bending Moment?

Radius of Curvature given Bending Moment evaluator uses Radius of Curvature = ((Elastoplastic Modulus*Nth Moment of Inertia)/Maximum Bending Moment)^(1/Material Constant) to evaluate 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 evaluate Radius of Curvature given Bending Moment using this online evaluator? To use this online evaluator 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.

FAQs on Radius of Curvature given Bending Moment

What is the formula to find Radius of Curvature given Bending Moment?

The formula of Radius of Curvature given Bending Moment is expressed as Radius of Curvature = ((Elastoplastic Modulus*Nth Moment of Inertia)/Maximum Bending Moment)^(1/Material Constant). Here is an example- 1.2E+31 = ((700000000*12645.542471)/1500000)^(1/0.25).

How to calculate Radius of Curvature given Bending Moment?

With Elastoplastic Modulus (H), Nth Moment of Inertia (I_n), Maximum Bending Moment (M) & Material Constant (n) we can find Radius of Curvature given Bending Moment using the formula - Radius of Curvature = ((Elastoplastic Modulus*Nth Moment of Inertia)/Maximum Bending Moment)^(1/Material Constant).

What are the other ways to Calculate Radius of Curvature?

Here are the different ways to Calculate Radius of Curvature-

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

Can the Radius of Curvature given Bending Moment be negative?

No, the Radius of Curvature given Bending Moment, measured in Length cannot be negative.

Which unit is used to measure Radius of Curvature given Bending Moment?

Radius of Curvature given Bending Moment is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Radius of Curvature given Bending Moment can be measured.

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Radius of Curvature given Bending Moment Formula

​GoRadius of Curvature given Bending Stress Formula

Radius of Curvature given Bending Moment Example

Radius of Curvature given Bending Moment Solution

Radius of Curvature given Bending Moment Formula Elements

Other Formulas to find Radius of Curvature

Other formulas in Nonlinear Behavior of Beams category

How to Evaluate Radius of Curvature given Bending Moment?

FAQs on Radius of Curvature given Bending Moment

Variable Name

GoRadius of Curvature given Bending Stress Formula