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Cross-Sectional Area when Stress is Applied at Point in Curved Beam Formula

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The Cross Sectional Area is the breadth times the depth of the structure. Check FAQs

A = (\frac{M}{S \cdot R}) \cdot (1 + (\frac{y}{Z \cdot (R + y)}))

A - Cross Sectional Area?M - Bending Moment?S - Stress?R - Radius of Centroidal Axis?y - Distance from Neutral Axis?Z - Cross-Section Property?

Cross-Sectional Area when Stress is Applied at Point in Curved Beam Example

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Here is how the Cross-Sectional Area when Stress is Applied at Point in Curved Beam equation looks like with Values.

Here is how the Cross-Sectional Area when Stress is Applied at Point in Curved Beam equation looks like with Units.

Here is how the Cross-Sectional Area when Stress is Applied at Point in Curved Beam equation looks like.

0.04 = (\frac{57}{33.25 \cdot 50}) \cdot (1 + (\frac{25}{2 \cdot (50 + 25)}))

0.04m² = (\frac{57kN*m}{33.25MPa \cdot 50mm}) \cdot (1 + (\frac{25mm}{2 \cdot (50mm + 25mm)}))

0.04 = (\frac{57}{33.25 \cdot 50}) \cdot (1 + (\frac{25}{2 \cdot (50 + 25)}))

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Cross-Sectional Area when Stress is Applied at Point in Curved Beam Solution

Follow our step by step solution on how to calculate Cross-Sectional Area when Stress is Applied at Point in Curved Beam?

FIRST Step Consider the formula

A = (\frac{M}{S \cdot R}) \cdot (1 + (\frac{y}{Z \cdot (R + y)}))

Next Step Substitute values of Variables

∴

A = (\frac{57kN*m}{33.25MPa \cdot 50mm}) \cdot (1 + (\frac{25mm}{2 \cdot (50mm + 25mm)}))

Next Step Convert Units

∴

A = (\frac{57000N*m}{3.3E+7Pa \cdot 0.05m}) \cdot (1 + (\frac{0.025m}{2 \cdot (0.05m + 0.025m)}))

Next Step Prepare to Evaluate

∴

A = (\frac{57000}{3.3E+7 \cdot 0.05}) \cdot (1 + (\frac{0.025}{2 \cdot (0.05 + 0.025)}))

LAST Step Evaluate

∴

A = 0.04m²

Cross-Sectional Area when Stress is Applied at Point in Curved Beam Formula Elements

Variables

Cross Sectional Area

The Cross Sectional Area is the breadth times the depth of the structure.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Cross Sectional Area

Bending Moment

Bending Moment 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

Measurement: Moment of ForceUnit: kN*m

Note: Value can be positive or negative.

Formulas to find Bending Moment

Stress

Stress at the cross section of curved beam.

Symbol: S

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Stress

Radius of Centroidal Axis

Radius of Centroidal Axis is defined as the radius of the axis that passes through the centroid of the cross section.

Symbol: R

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Centroidal Axis

Distance from Neutral Axis

Distance from Neutral Axis is the measured between N.A and to the extreme point.

Symbol: y

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance from Neutral Axis

Cross-Section Property

Cross-Section Property can be found using analytical expressions or geometric integration and determines the stresses that exist in the member under a given load.

Symbol: Z

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Cross-Section Property

Other formulas in Curved Beams category

Go Stress at Point for Curved Beam as defined in Winkler-Bach Theory

S = (\frac{M}{A \cdot R}) \cdot (1 + (\frac{y}{Z \cdot (R + y)}))

Go Bending Moment when Stress is Applied at Point in Curved Beam

M = (\frac{S \cdot A \cdot R}{1 + (\frac{y}{Z \cdot (R + y)})})

How to Evaluate Cross-Sectional Area when Stress is Applied at Point in Curved Beam?

Cross-Sectional Area when Stress is Applied at Point in Curved Beam evaluator uses Cross Sectional Area = (Bending Moment/(Stress*Radius of Centroidal Axis))*(1+(Distance from Neutral Axis/(Cross-Section Property*(Radius of Centroidal Axis+Distance from Neutral Axis)))) to evaluate the Cross Sectional Area, The Cross-Sectional Area when Stress is Applied at Point in Curved Beam formula is defined as (Bending Moment of Beam/(Stress of Curved Beam*Radius_of Centroidal Axis))*(1+(Distance of Point from Centroidal Axis/(Cross Section Property*(Radius of Centroidal Axis+Distance of Point from Centroidal Axis)))). Cross Sectional Area is denoted by A symbol.

How to evaluate Cross-Sectional Area when Stress is Applied at Point in Curved Beam using this online evaluator? To use this online evaluator for Cross-Sectional Area when Stress is Applied at Point in Curved Beam, enter Bending Moment (M), Stress (S), Radius of Centroidal Axis (R), Distance from Neutral Axis (y) & Cross-Section Property (Z) and hit the calculate button.

FAQs on Cross-Sectional Area when Stress is Applied at Point in Curved Beam

What is the formula to find Cross-Sectional Area when Stress is Applied at Point in Curved Beam?

The formula of Cross-Sectional Area when Stress is Applied at Point in Curved Beam is expressed as Cross Sectional Area = (Bending Moment/(Stress*Radius of Centroidal Axis))*(1+(Distance from Neutral Axis/(Cross-Section Property*(Radius of Centroidal Axis+Distance from Neutral Axis)))). Here is an example- 0.04 = (57000/(33250000*0.05))*(1+(0.025/(2*(0.05+0.025)))).

How to calculate Cross-Sectional Area when Stress is Applied at Point in Curved Beam?

With Bending Moment (M), Stress (S), Radius of Centroidal Axis (R), Distance from Neutral Axis (y) & Cross-Section Property (Z) we can find Cross-Sectional Area when Stress is Applied at Point in Curved Beam using the formula - Cross Sectional Area = (Bending Moment/(Stress*Radius of Centroidal Axis))*(1+(Distance from Neutral Axis/(Cross-Section Property*(Radius of Centroidal Axis+Distance from Neutral Axis)))).

Can the Cross-Sectional Area when Stress is Applied at Point in Curved Beam be negative?

No, the Cross-Sectional Area when Stress is Applied at Point in Curved Beam, measured in Area cannot be negative.

Which unit is used to measure Cross-Sectional Area when Stress is Applied at Point in Curved Beam?

Cross-Sectional Area when Stress is Applied at Point in Curved Beam is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Cross-Sectional Area when Stress is Applied at Point in Curved Beam can be measured.

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Cross-Sectional Area when Stress is Applied at Point in Curved Beam Formula

Cross-Sectional Area when Stress is Applied at Point in Curved Beam Example

Cross-Sectional Area when Stress is Applied at Point in Curved Beam Solution

Cross-Sectional Area when Stress is Applied at Point in Curved Beam Formula Elements

Other formulas in Curved Beams category

How to Evaluate Cross-Sectional Area when Stress is Applied at Point in Curved Beam?

FAQs on Cross-Sectional Area when Stress is Applied at Point in Curved Beam

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