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Radius of outer fibre of curved beam given bending stress at fiber Formula

GoRadius of outer fiber of rectangular curved beam given radius of neutral axis and inner fiber Formula

GoRadius of outer fiber of circular curved beam given radius of neutral axis and inner fiber Formula

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Radius of Outer Fibre is the radius of the outer fiber of a curved structural element. Check FAQs

R o = \frac{M b \cdot h o}{A \cdot e \cdot σ b o}

R_o - Radius of Outer Fibre?M_b - Bending Moment in Curved Beam?h_o - Distance of Outer Fibre from Neutral Axis?A - Cross Sectional Area of Curved Beam?e - Eccentricity Between Centroidal and Neutral Axis?σ_bo - Bending Stress at Outer Fibre?

Radius of outer fibre of curved beam given bending stress at fiber Example

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Here is how the Radius of outer fibre of curved beam given bending stress at fiber equation looks like with Values.

Here is how the Radius of outer fibre of curved beam given bending stress at fiber equation looks like with Units.

Here is how the Radius of outer fibre of curved beam given bending stress at fiber equation looks like.

88.6878 = \frac{245000 \cdot 48}{240 \cdot 6.5 \cdot 85}

88.6878mm = \frac{245000N*mm \cdot 48mm}{240mm² \cdot 6.5mm \cdot 85N/mm²}

88.6878 = \frac{245000 \cdot 48}{240 \cdot 6.5 \cdot 85}

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Radius of outer fibre of curved beam given bending stress at fiber Solution

Follow our step by step solution on how to calculate Radius of outer fibre of curved beam given bending stress at fiber?

FIRST Step Consider the formula

R o = \frac{M b \cdot h o}{A \cdot e \cdot σ b o}

Next Step Substitute values of Variables

∴

R o = \frac{245000N*mm \cdot 48mm}{240mm² \cdot 6.5mm \cdot 85N/mm²}

Next Step Convert Units

∴

R o = \frac{245N*m \cdot 0.048m}{0.0002m² \cdot 0.0065m \cdot 8.5E+7Pa}

Next Step Prepare to Evaluate

∴

R o = \frac{245 \cdot 0.048}{0.0002 \cdot 0.0065 \cdot 8.5E+7}

Next Step Evaluate

∴

R o = 0.0886877828054299m

Next Step Convert to Output's Unit

∴

R o = 88.6877828054299mm

LAST Step Rounding Answer

∴

R o = 88.6878mm

Radius of outer fibre of curved beam given bending stress at fiber Formula Elements

Variables

Radius of Outer Fibre

Radius of Outer Fibre is the radius of the outer fiber of a curved structural element.

Symbol: R_o

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Outer Fibre

Bending Moment in Curved Beam

Bending moment in curved beam is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend.

Symbol: M_b

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Bending Moment in Curved Beam

Distance of Outer Fibre from Neutral Axis

Distance of Outer Fibre from Neutral Axis is the point where the fibers of a material undergoing bending are stretched maximum.

Symbol: h_o

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance of Outer Fibre from Neutral Axis

Cross Sectional Area of Curved Beam

Cross sectional area of curved beam is the area of a two-dimensional section that is obtained when a beam is sliced perpendicular to some specified axis at a point.

Symbol: A

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Formulas to find Cross Sectional Area of Curved Beam

Eccentricity Between Centroidal and Neutral Axis

Eccentricity Between Centroidal and Neutral Axis is the distance between the centroidal and the neutral axis of a curved structural element.

Symbol: e

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Eccentricity Between Centroidal and Neutral Axis

Bending Stress at Outer Fibre

Bending Stress at Outer Fibre is the amount of bending moment at the outer fiber of a curved structural element.

Symbol: σ_bo

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Bending Stress at Outer Fibre

Other Formulas to find Radius of Outer Fibre

Go Radius of outer fiber of rectangular curved beam given radius of neutral axis and inner fiber

R o = R i \cdot e^{\frac{y}{R N}}

Go Radius of outer fiber of circular curved beam given radius of neutral axis and inner fiber

R o = {(\sqrt{4 \cdot R N} - \sqrt{R i})}^{2}

Other formulas in Radius of Fiber and Axis category

Go Radius of centroidal axis of curved beam given eccentricity between axis

R = R N + e

Go Radius of neutral axis of curved beam given eccentricity between axis

R N = R - e

Go Radius of neutral axis of curved beam given bending stress

R N = (\frac{M b \cdot y}{A \cdot σ b \cdot e}) + y

Go Radius of centroidal axis of curved beam given bending stress

R = (\frac{M b \cdot y}{A \cdot σ b \cdot (R N - y)}) + R N

How to Evaluate Radius of outer fibre of curved beam given bending stress at fiber?

Radius of outer fibre of curved beam given bending stress at fiber evaluator uses Radius of Outer Fibre = (Bending Moment in Curved Beam*Distance of Outer Fibre from Neutral Axis)/(Cross Sectional Area of Curved Beam*Eccentricity Between Centroidal and Neutral Axis*Bending Stress at Outer Fibre) to evaluate the Radius of Outer Fibre, Radius of outer fibre of curved beam given bending stress at fiber is the radius of the outermost fiber of a curved beam and is the radius of curvature of the outer surface of the beam. Radius of Outer Fibre is denoted by R_o symbol.

How to evaluate Radius of outer fibre of curved beam given bending stress at fiber using this online evaluator? To use this online evaluator for Radius of outer fibre of curved beam given bending stress at fiber, enter Bending Moment in Curved Beam (M_b), Distance of Outer Fibre from Neutral Axis (h_o), Cross Sectional Area of Curved Beam (A), Eccentricity Between Centroidal and Neutral Axis (e) & Bending Stress at Outer Fibre (σ_bo) and hit the calculate button.

FAQs on Radius of outer fibre of curved beam given bending stress at fiber

What is the formula to find Radius of outer fibre of curved beam given bending stress at fiber?

The formula of Radius of outer fibre of curved beam given bending stress at fiber is expressed as Radius of Outer Fibre = (Bending Moment in Curved Beam*Distance of Outer Fibre from Neutral Axis)/(Cross Sectional Area of Curved Beam*Eccentricity Between Centroidal and Neutral Axis*Bending Stress at Outer Fibre). Here is an example- 88687.78 = (245*0.048)/(0.00024*0.0065*85000000).

How to calculate Radius of outer fibre of curved beam given bending stress at fiber?

With Bending Moment in Curved Beam (M_b), Distance of Outer Fibre from Neutral Axis (h_o), Cross Sectional Area of Curved Beam (A), Eccentricity Between Centroidal and Neutral Axis (e) & Bending Stress at Outer Fibre (σ_bo) we can find Radius of outer fibre of curved beam given bending stress at fiber using the formula - Radius of Outer Fibre = (Bending Moment in Curved Beam*Distance of Outer Fibre from Neutral Axis)/(Cross Sectional Area of Curved Beam*Eccentricity Between Centroidal and Neutral Axis*Bending Stress at Outer Fibre).

What are the other ways to Calculate Radius of Outer Fibre?

Here are the different ways to Calculate Radius of Outer Fibre-

Radius of Outer Fibre=Radius of Inner Fibre*e^(Distance from Neutral Axis of Curved Beam/Radius of Neutral Axis)
Radius of Outer Fibre=(sqrt(4*Radius of Neutral Axis)-sqrt(Radius of Inner Fibre))^2

Can the Radius of outer fibre of curved beam given bending stress at fiber be negative?

No, the Radius of outer fibre of curved beam given bending stress at fiber, measured in Length cannot be negative.

Which unit is used to measure Radius of outer fibre of curved beam given bending stress at fiber?

Radius of outer fibre of curved beam given bending stress at fiber is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Radius of outer fibre of curved beam given bending stress at fiber can be measured.

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Radius of outer fibre of curved beam given bending stress at fiber Formula

​GoRadius of outer fiber of rectangular curved beam given radius of neutral axis and inner fiber Formula

​GoRadius of outer fiber of circular curved beam given radius of neutral axis and inner fiber Formula

Radius of outer fibre of curved beam given bending stress at fiber Example

Radius of outer fibre of curved beam given bending stress at fiber Solution

Radius of outer fibre of curved beam given bending stress at fiber Formula Elements

Other Formulas to find Radius of Outer Fibre

Other formulas in Radius of Fiber and Axis category

How to Evaluate Radius of outer fibre of curved beam given bending stress at fiber?

FAQs on Radius of outer fibre of curved beam given bending stress at fiber

Variable Name

GoRadius of outer fiber of rectangular curved beam given radius of neutral axis and inner fiber Formula

GoRadius of outer fiber of circular curved beam given radius of neutral axis and inner fiber Formula