Stress at Point for Curved Beam as defined in Winkler-Bach Theory 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%
✖The Cross Sectional Area is the breadth times the depth of the structure.ⓘ Cross Sectional Area [A]			+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%

✖Stress at the cross section of curved beam.ⓘ Stress at Point for Curved Beam as defined in Winkler-Bach Theory [S]

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

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

Stress - (Measured in Pascal) - Stress at the cross section of curved beam.
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.
Cross Sectional Area - (Measured in Square Meter) - The Cross Sectional Area is the breadth times the depth of the structure.
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)
Cross Sectional Area: 0.04 Square Meter --> 0.04 Square Meter No Conversion Required
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

S = ((M)/(A*R))*(1+((y)/(Z*(R+y)))) --> ((57000)/(0.04*0.05))*(1+((0.025)/(2*(0.05+0.025))))

Evaluating ... ...

S = 33250000

STEP 3: Convert Result to Output's Unit

33250000 Pascal -->33.25 Megapascal (Check conversion here)

FINAL ANSWER

33.25 Megapascal <-- Stress

(Calculation completed in 00.004 seconds)

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< Curved Beams Calculators

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

LaTeX 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

LaTeX 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

LaTeX 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)))))

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

LaTeX Go

What is Stress at Point y for a Curved Beam?

The distribution of stress in a curved flexural member is determined by using the following assumptions. 1 The cross section has an axis of symmetry in a plane along the length of the beam. 2 Plane cross sections remain plane after bending. 3 The modulus of elasticity is the same in tension as in compression.

How to Calculate Stress at Point for Curved Beam as defined in Winkler-Bach Theory?

Stress at Point for Curved Beam as defined in Winkler-Bach Theory calculator uses 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)))) to calculate the Stress, The Stress at Point for Curved Beam as defined in Winkler-Bach Theory calculator formulated here is applicable when all “fibres” of a member have the same centre of curvature, resulting in the concentric or common type of curved beam. Such a beam is defined by the Winkler-Bach theory. Stress is denoted by S symbol.

How to calculate Stress at Point for Curved Beam as defined in Winkler-Bach Theory using this online calculator? To use this online calculator for Stress at Point for Curved Beam as defined in Winkler-Bach Theory, enter Bending Moment (M), Cross Sectional Area (A), Radius of Centroidal Axis (R), Distance from Neutral Axis (y) & Cross-Section Property (Z) and hit the calculate button. Here is how the Stress at Point for Curved Beam as defined in Winkler-Bach Theory calculation can be explained with given input values -> 3.3E-5 = ((57000)/(0.04*0.05))*(1+((0.025)/(2*(0.05+0.025)))).

FAQ

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

The Stress at Point for Curved Beam as defined in Winkler-Bach Theory calculator formulated here is applicable when all “fibres” of a member have the same centre of curvature, resulting in the concentric or common type of curved beam. Such a beam is defined by the Winkler-Bach theory and is represented as S = ((M)/(A*R))*(1+((y)/(Z*(R+y)))) or 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)))). 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, The Cross Sectional Area is the breadth times the depth of the structure, 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 Stress at Point for Curved Beam as defined in Winkler-Bach Theory?

The Stress at Point for Curved Beam as defined in Winkler-Bach Theory calculator formulated here is applicable when all “fibres” of a member have the same centre of curvature, resulting in the concentric or common type of curved beam. Such a beam is defined by the Winkler-Bach theory is calculated using 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)))). To calculate Stress at Point for Curved Beam as defined in Winkler-Bach Theory, you need Bending Moment (M), Cross Sectional Area (A), 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, Cross Sectional Area, 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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