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Area of cross section of curved beam given bending stress at inner fiber Formula

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GoArea of cross section of curved beam given bending stress at outer fiber Formula

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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. Check FAQs

A = \frac{M b \cdot h i}{(e) \cdot σ b i \cdot (R i)}

A - Cross sectional area of curved beam?M_b - Bending moment in curved beam?h_i - Distance of Inner Fibre from Neutral Axis?e - Eccentricity Between Centroidal and Neutral Axis?σ_bi - Bending Stress at Inner Fibre?R_i - Radius of Inner Fibre?

Area of cross section of curved beam given bending stress at inner fiber Example

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Here is how the Area of cross section of curved beam given bending stress at inner fiber equation looks like with Values.

Here is how the Area of cross section of curved beam given bending stress at inner fiber equation looks like with Units.

Here is how the Area of cross section of curved beam given bending stress at inner fiber equation looks like.

275.7752 = \frac{985000 \cdot 10}{(6.5) \cdot 78.5 \cdot (70)}

275.7752mm² = \frac{985000N*mm \cdot 10mm}{(6.5mm) \cdot 78.5N/mm² \cdot (70mm)}

275.7752 = \frac{985000 \cdot 10}{(6.5) \cdot 78.5 \cdot (70)}

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Area of cross section of curved beam given bending stress at inner fiber Solution

Follow our step by step solution on how to calculate Area of cross section of curved beam given bending stress at inner fiber?

FIRST Step Consider the formula

A = \frac{M b \cdot h i}{(e) \cdot σ b i \cdot (R i)}

Next Step Substitute values of Variables

∴

A = \frac{985000N*mm \cdot 10mm}{(6.5mm) \cdot 78.5N/mm² \cdot (70mm)}

Next Step Convert Units

∴

A = \frac{985N*m \cdot 0.01m}{(0.0065m) \cdot 7.9E+7Pa \cdot (0.07m)}

Next Step Prepare to Evaluate

∴

A = \frac{985 \cdot 0.01}{(0.0065) \cdot 7.9E+7 \cdot (0.07)}

Next Step Evaluate

∴

A = 0.000275775180233779m²

Next Step Convert to Output's Unit

∴

A = 275.775180233779mm²

LAST Step Rounding Answer

∴

A = 275.7752mm²

Area of cross section of curved beam given bending stress at inner fiber Formula Elements

Variables

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.

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.

Distance of Inner Fibre from Neutral Axis

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

Symbol: h_i

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

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.

Bending Stress at Inner Fibre

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

Symbol: σ_bi

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Radius of Inner Fibre

Radius of Inner Fibre is the radius of the inner fiber of a curved structural element.

Symbol: R_i

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Credits

Creator Image

Created by Saurabh Patil

Shri Govindram Seksaria Institute of Technology and Science (SGSITS ), Indore

Saurabh Patil has created this Formula and 700+ more formulas!

Verifier Image

Verified by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has verified this Formula and 2500+ more formulas!

Other Formulas to find Cross sectional area of curved beam

Go Area of cross section of curved beam given bending stress at outer fiber

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

Other formulas in Design of Curved Beams category

Go Eccentricity between central and neutral axis of curved beam

e = R - R N

Go Bending stress in fiber of curved beam

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

Go Eccentricity between centroidal and neutral axis of curved beam given radius of both axis

e = R - R N

Go Bending stress in fibre of curved beam given eccentricity

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

See More

How to Evaluate Area of cross section of curved beam given bending stress at inner fiber?

Area of cross section of curved beam given bending stress at inner fiber evaluator uses Cross sectional area of curved beam = (Bending moment in curved beam*Distance of Inner Fibre from Neutral Axis)/((Eccentricity Between Centroidal and Neutral Axis)*Bending Stress at Inner Fibre*(Radius of Inner Fibre)) to evaluate the Cross sectional area of curved beam, Area of cross section of curved beam given bending stress at inner fiber is the cross-sectional area of the transverse section of a curved beam. Cross sectional area of curved beam is denoted by A symbol.

How to evaluate Area of cross section of curved beam given bending stress at inner fiber using this online evaluator? To use this online evaluator for Area of cross section of curved beam given bending stress at inner fiber, enter Bending moment in curved beam (M_b), Distance of Inner Fibre from Neutral Axis (h_i), Eccentricity Between Centroidal and Neutral Axis (e), Bending Stress at Inner Fibre (σ_bi) & Radius of Inner Fibre (R_i) and hit the calculate button.

FAQs on Area of cross section of curved beam given bending stress at inner fiber

What is the formula to find Area of cross section of curved beam given bending stress at inner fiber?

The formula of Area of cross section of curved beam given bending stress at inner fiber is expressed as Cross sectional area of curved beam = (Bending moment in curved beam*Distance of Inner Fibre from Neutral Axis)/((Eccentricity Between Centroidal and Neutral Axis)*Bending Stress at Inner Fibre*(Radius of Inner Fibre)). Here is an example- 2.8E+8 = (985*0.01)/((0.0065)*78500000*(0.07)).

How to calculate Area of cross section of curved beam given bending stress at inner fiber?

With Bending moment in curved beam (M_b), Distance of Inner Fibre from Neutral Axis (h_i), Eccentricity Between Centroidal and Neutral Axis (e), Bending Stress at Inner Fibre (σ_bi) & Radius of Inner Fibre (R_i) we can find Area of cross section of curved beam given bending stress at inner fiber using the formula - Cross sectional area of curved beam = (Bending moment in curved beam*Distance of Inner Fibre from Neutral Axis)/((Eccentricity Between Centroidal and Neutral Axis)*Bending Stress at Inner Fibre*(Radius of Inner Fibre)).

What are the other ways to Calculate Cross sectional area of curved beam?

Here are the different ways to Calculate Cross sectional area of curved beam-

Cross sectional area of curved beam=(Bending moment in curved beam*Distance of Outer Fibre from Neutral Axis)/((Eccentricity Between Centroidal and Neutral Axis)*Bending Stress at Outer Fibre*(Radius of Outer Fibre))

Can the Area of cross section of curved beam given bending stress at inner fiber be negative?

No, the Area of cross section of curved beam given bending stress at inner fiber, measured in Area cannot be negative.

Which unit is used to measure Area of cross section of curved beam given bending stress at inner fiber?

Area of cross section of curved beam given bending stress at inner fiber is usually measured using the Square Millimeter[mm²] for Area. Square Meter[mm²], Square Kilometer[mm²], Square Centimeter[mm²] are the few other units in which Area of cross section of curved beam given bending stress at inner fiber can be measured.

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