FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Radius of Curvature given Bending Stress Formula

GoRadius of Curvature given Bending Moment Formula

Fx Copy

LaTeX Copy

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 y^{n}}{σ})}^{\frac{1}{n}}

R - Radius of Curvature?H - Elastoplastic Modulus?y - Depth Yielded Plastically?n - Material Constant?σ - Maximum Bending Stress in Plastic State?

Radius of Curvature given Bending Stress Example

With values

With units

Only example

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

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

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

1.2E+27 = {(\frac{700 \cdot {0.5}^{0.25}}{1E-4})}^{\frac{1}{0.25}}

1.2E+27mm = {(\frac{700N/mm² \cdot {0.5mm}^{0.25}}{1E-4N/mm²})}^{\frac{1}{0.25}}

1.2E+27 = {(\frac{700 \cdot {0.5}^{0.25}}{1E-4})}^{\frac{1}{0.25}}

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Physics » Category

Mechanical » Category

Theory of Plasticity » fx Radius of Curvature given Bending Stress

Radius of Curvature given Bending Stress Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

R = {(\frac{700N/mm² \cdot {0.5mm}^{0.25}}{1E-4N/mm²})}^{\frac{1}{0.25}}

Next Step Convert Units

∴

R = {(\frac{700MPa \cdot {0.5mm}^{0.25}}{1E-4MPa})}^{\frac{1}{0.25}}

Next Step Prepare to Evaluate

∴

R = {(\frac{700 \cdot {0.5}^{0.25}}{1E-4})}^{\frac{1}{0.25}}

Next Step Evaluate

∴

R = 1.21276591338816E+24m

Next Step Convert to Output's Unit

∴

R = 1.21276591338816E+27mm

LAST Step Rounding Answer

∴

R = 1.2E+27mm

Radius of Curvature given Bending Stress 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

Depth Yielded Plastically

Depth Yielded Plastically is the distance along the beam where the stress exceeds the yield strength of the material during bending.

Symbol: y

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Depth Yielded Plastically

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

Maximum Bending Stress in Plastic State

Maximum Bending Stress in Plastic State is the maximum stress a beam can withstand in its plastic state without undergoing deformation or breaking.

Symbol: σ

Measurement: StressUnit: N/mm²

Note: Value can be positive or negative.

Formulas to find Maximum Bending Stress in Plastic State

Other Formulas to find Radius of Curvature

Go Radius of Curvature given Bending Moment

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

Radius of Curvature given Bending Stress evaluator uses Radius of Curvature = ((Elastoplastic Modulus*Depth Yielded Plastically^Material Constant)/Maximum Bending Stress in Plastic State)^(1/Material Constant) to evaluate 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 evaluate Radius of Curvature given Bending Stress using this online evaluator? To use this online evaluator 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.

FAQs on Radius of Curvature given Bending Stress

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

The formula of Radius of Curvature given Bending Stress is expressed as Radius of Curvature = ((Elastoplastic Modulus*Depth Yielded Plastically^Material Constant)/Maximum Bending Stress in Plastic State)^(1/Material Constant). Here is an example- 1.2E+30 = ((700000000*0.0005^0.25)/99.7461853276134)^(1/0.25).

How to calculate Radius of Curvature given Bending Stress?

With Elastoplastic Modulus (H), Depth Yielded Plastically (y), Material Constant (n) & Maximum Bending Stress in Plastic State (σ) we can find Radius of Curvature given Bending Stress using the formula - Radius of Curvature = ((Elastoplastic Modulus*Depth Yielded Plastically^Material Constant)/Maximum Bending Stress in Plastic State)^(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*Nth Moment of Inertia)/Maximum Bending Moment)^(1/Material Constant)

Can the Radius of Curvature given Bending Stress be negative?

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

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

Radius of Curvature given Bending Stress 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 Stress can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

Radius of Curvature given Bending Stress Formula

​GoRadius of Curvature given Bending Moment Formula

Radius of Curvature given Bending Stress Example

Radius of Curvature given Bending Stress Solution

Radius of Curvature given Bending Stress 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 Stress?

FAQs on Radius of Curvature given Bending Stress

Variable Name

GoRadius of Curvature given Bending Moment Formula