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

✖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.ⓘ Bending Moment [M]			+10% -10%
✖Stress at the cross section of curved beam.ⓘ Stress [S]			+10% -10%
✖Radius of Centroidal Axis is defined as the radius of the axis that passes through the centroid of the cross section.ⓘ Radius of Centroidal Axis [R]			+10% -10%
✖Distance from Neutral Axis is the measured between N.A and to the extreme point.ⓘ Distance from Neutral Axis [y]			+10% -10%
✖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.ⓘ Cross-Section Property [Z]			+10% -10%

✖The Cross Sectional Area is the breadth times the depth of the structure.ⓘ Cross-Sectional Area when Stress is Applied at Point in Curved Beam [A]

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Formula

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

Formula

`"A" = ("M"/("S"*"R"))*(1+("y"/("Z"*("R"+"y"))))`

Example

`"0.04m²"=("57kN*m"/("33.25MPa"*"50mm"))*(1+("25mm"/("2.0"*("50mm"+"25mm"))))`

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

STEP 0: Pre-Calculation Summary

Formula Used

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))))
A = (M/(S*R))*(1+(y/(Z*(R+y))))
This formula uses 6 Variables

Variables Used

Cross Sectional Area - (Measured in Square Meter) - The Cross Sectional Area is the breadth times the depth of the structure.
Bending Moment - (Measured in Newton Meter) - 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.
Stress - (Measured in Pascal) - Stress at the cross section of curved beam.
Radius of Centroidal Axis - (Measured in Meter) - Radius of Centroidal Axis is defined as the radius of the axis that passes through the centroid of the cross section.
Distance from Neutral Axis - (Measured in Meter) - Distance from Neutral Axis is the measured between N.A and to the extreme point.
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.

STEP 1: Convert Input(s) to Base Unit

Bending Moment: 57 Kilonewton Meter --> 57000 Newton Meter (Check conversion here)
Stress: 33.25 Megapascal --> 33250000 Pascal (Check conversion here)
Radius of Centroidal Axis: 50 Millimeter --> 0.05 Meter (Check conversion here)
Distance from Neutral Axis: 25 Millimeter --> 0.025 Meter (Check conversion here)
Cross-Section Property: 2 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = (M/(S*R))*(1+(y/(Z*(R+y)))) --> (57000/(33250000*0.05))*(1+(0.025/(2*(0.05+0.025))))

Evaluating ... ...

A = 0.04

STEP 3: Convert Result to Output's Unit

0.04 Square Meter --> No Conversion Required

FINAL ANSWER

0.04 Square Meter <-- Cross Sectional Area

(Calculation completed in 00.020 seconds)

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Don Bosco College of Engineering (DBCE), Goa

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< 3 Curved Beams Calculators

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

Go Stress = ((Bending Moment)/(Cross Sectional Area*Radius of Centroidal Axis))*(1+((Distance from Neutral Axis)/(Cross-Section Property*(Radius of Centroidal Axis+Distance from Neutral Axis))))

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

Go 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))))

Bending Moment when Stress is Applied at Point in Curved Beam

Go Bending Moment = ((Stress*Cross Sectional Area*Radius of Centroidal Axis)/(1+(Distance from Neutral Axis/(Cross-Section Property*(Radius of Centroidal Axis+Distance from Neutral Axis)))))

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

What is Cross-Sectional Area When Stress is Applied at Point y in a Curved Beam?

The cross-sectional area of a curved beam is the area of a two-dimensional shape that is obtained when the curved beam is sliced perpendicular to the centroidal axis at a point y where stress at the point is known.

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

Cross-Sectional Area when Stress is Applied at Point in Curved Beam calculator 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 calculate 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 calculate Cross-Sectional Area when Stress is Applied at Point in Curved Beam using this online calculator? To use this online calculator 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. Here is how the Cross-Sectional Area when Stress is Applied at Point in Curved Beam calculation can be explained with given input values -> 0.04 = (57000/(33250000*0.05))*(1+(0.025/(2*(0.05+0.025)))).

FAQ

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

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)))) and is represented as A = (M/(S*R))*(1+(y/(Z*(R+y)))) or 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)))). 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, Stress at the cross section of curved beam, Radius of Centroidal Axis is defined as the radius of the axis that passes through the centroid of the cross section, Distance from Neutral Axis is the measured between N.A and to the extreme point & 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.

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

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)))) is calculated using 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 calculate Cross-Sectional Area when Stress is Applied at Point in Curved Beam, you need Bending Moment (M), Stress (S), Radius of Centroidal Axis (R), Distance from Neutral Axis (y) & Cross-Section Property (Z). With our tool, you need to enter the respective value for Bending Moment, Stress, Radius of Centroidal Axis, Distance from Neutral Axis & Cross-Section Property and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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