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

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Stress at the cross section of curved beam. Check FAQs

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

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

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

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Here is how the Stress at Point for Curved Beam as defined in Winkler-Bach Theory equation looks like with Values.

Here is how the Stress at Point for Curved Beam as defined in Winkler-Bach Theory equation looks like with Units.

Here is how the Stress at Point for Curved Beam as defined in Winkler-Bach Theory equation looks like.

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

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

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

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

Follow our step by step solution on how to calculate Stress at Point for Curved Beam as defined in Winkler-Bach Theory?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

S = (\frac{57000N*m}{0.04m² \cdot 0.05m}) \cdot (1 + (\frac{0.025m}{2 \cdot (0.05m + 0.025m)}))

Next Step Prepare to Evaluate

∴

S = (\frac{57000}{0.04 \cdot 0.05}) \cdot (1 + (\frac{0.025}{2 \cdot (0.05 + 0.025)}))

Next Step Evaluate

∴

S = 33250000Pa

LAST Step Convert to Output's Unit

∴

S = 33.25MPa

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

Variables

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

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

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

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

A = (\frac{M}{S \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 Stress at Point for Curved Beam as defined in Winkler-Bach Theory?

Stress at Point for Curved Beam as defined in Winkler-Bach Theory evaluator 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 evaluate 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 evaluate Stress at Point for Curved Beam as defined in Winkler-Bach Theory using this online evaluator? To use this online evaluator 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.

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

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

The formula of Stress at Point for Curved Beam as defined in Winkler-Bach Theory is expressed as 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)))). Here is an example- 3.3E-5 = ((57000)/(0.04*0.05))*(1+((0.025)/(2*(0.05+0.025)))).

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

With Bending Moment (M), Cross Sectional Area (A), Radius of Centroidal Axis (R), Distance from Neutral Axis (y) & Cross-Section Property (Z) we can find Stress at Point for Curved Beam as defined in Winkler-Bach Theory using the formula - 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)))).

Can the Stress at Point for Curved Beam as defined in Winkler-Bach Theory be negative?

No, the Stress at Point for Curved Beam as defined in Winkler-Bach Theory, measured in Stress cannot be negative.

Which unit is used to measure Stress at Point for Curved Beam as defined in Winkler-Bach Theory?

Stress at Point for Curved Beam as defined in Winkler-Bach Theory is usually measured using the Megapascal[MPa] for Stress. Pascal[MPa], Newton per Square Meter[MPa], Newton per Square Millimeter[MPa] are the few other units in which Stress at Point for Curved Beam as defined in Winkler-Bach Theory can be measured.

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

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

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

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

Other formulas in Curved Beams category

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

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

Variable Name