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Recovery Bending Moment for Non Linear Relation Formula

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Non Linear Recovery Bending Moment is the bending moment that remains in a material after unloading, causing residual stresses and deformation. Check FAQs

M rec = - σ y \cdot d \cdot (\frac{d^{2}}{4} - \frac{n \cdot η^{2}}{n + 2})

M_rec - Non Linear Recovery Bending Moment?σ_y - Yield stress(non-linear)?d - Depth of Rectangular Beam?n - Material Constant?η - Depth of Outermost Shell Yields?

Recovery Bending Moment for Non Linear Relation Example

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Here is how the Recovery Bending Moment for Non Linear Relation equation looks like with Values.

Here is how the Recovery Bending Moment for Non Linear Relation equation looks like with Units.

Here is how the Recovery Bending Moment for Non Linear Relation equation looks like.

-49162500 = - 240 \cdot 95 \cdot (\frac{95^{2}}{4} - \frac{0.25 \cdot 30^{2}}{0.25 + 2})

-49162500N*mm = - 240MPa \cdot 95mm \cdot (\frac{{95mm}^{2}}{4} - \frac{0.25 \cdot {30mm}^{2}}{0.25 + 2})

-49162500 = - 240 \cdot 95 \cdot (\frac{95^{2}}{4} - \frac{0.25 \cdot 30^{2}}{0.25 + 2})

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Recovery Bending Moment for Non Linear Relation Solution

Follow our step by step solution on how to calculate Recovery Bending Moment for Non Linear Relation?

FIRST Step Consider the formula

M rec = - σ y \cdot d \cdot (\frac{d^{2}}{4} - \frac{n \cdot η^{2}}{n + 2})

Next Step Substitute values of Variables

∴

M rec = - 240MPa \cdot 95mm \cdot (\frac{{95mm}^{2}}{4} - \frac{0.25 \cdot {30mm}^{2}}{0.25 + 2})

Next Step Convert Units

∴

M rec = - 2.4E+8Pa \cdot 0.095m \cdot (\frac{{0.095m}^{2}}{4} - \frac{0.25 \cdot {0.03m}^{2}}{0.25 + 2})

Next Step Prepare to Evaluate

∴

M rec = - 2.4E+8 \cdot 0.095 \cdot (\frac{{0.095}^{2}}{4} - \frac{0.25 \cdot {0.03}^{2}}{0.25 + 2})

Next Step Evaluate

∴

M rec = -49162.5N*m

LAST Step Convert to Output's Unit

∴

M rec = -49162500N*mm

Recovery Bending Moment for Non Linear Relation Formula Elements

Variables

Non Linear Recovery Bending Moment

Non Linear Recovery Bending Moment is the bending moment that remains in a material after unloading, causing residual stresses and deformation.

Symbol: M_rec

Measurement: Moment of ForceUnit: N*mm

Note: Value can be positive or negative.

Formulas to find Non Linear Recovery Bending Moment

Yield stress(non-linear)

The yield stress(non-linear) is a material property and is the stress corresponding to the yield point at which the material begins to deform plastically.

Symbol: σ_y

Measurement: StressUnit: MPa

Note: Value can be positive or negative.

Formulas to find Yield stress(non-linear)

Depth of Rectangular Beam

Depth of Rectangular Beam is the vertical distance from the neutral axis to the extreme fibre of a rectangular beam under residual stresses.

Symbol: d

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Depth of Rectangular Beam

Material Constant

Material Constant is a measure of the internal stresses that remain within a material after the original cause of the stress has been removed.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Material Constant

Depth of Outermost Shell Yields

Depth of Outermost Shell Yields is the distance from the surface of a material to the outermost shell where residual stresses are present.

Symbol: η

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Depth of Outermost Shell Yields

Other formulas in Residual Stresses for Non Linear Stress Strain Relations category

Go Elasto Plastic Bending Moment for Non-Linear Relation

M EP = σ y \cdot d \cdot (\frac{d^{2}}{4} - \frac{n \cdot η^{2}}{n + 2})

Go Recovery Stress in Beams for Non Linear Relation

σ rc = \frac{M rec \cdot y}{J}

Go Residual Stress in Beams for Non Linear Relation when Y Lies between 0 and n

σ non_linear = - (σ y \cdot {(\frac{y d}{η})}^{n} + \frac{M rec \cdot y}{\frac{d \cdot d^{3}}{12}})

Go Residual Stress in Beams for Non Linear Relation when Whole Depth of Beam Yields

σ beam = - (σ y + \frac{M rec \cdot y}{\frac{d \cdot d^{3}}{12}})

How to Evaluate Recovery Bending Moment for Non Linear Relation?

Recovery Bending Moment for Non Linear Relation evaluator uses Non Linear Recovery Bending Moment = -Yield stress(non-linear)*Depth of Rectangular Beam*(Depth of Rectangular Beam^2/4-(Material Constant*Depth of Outermost Shell Yields^2)/(Material Constant+2)) to evaluate the Non Linear Recovery Bending Moment, Recovery Bending Moment for Non Linear Relation formula is defined as a measure of the bending moment required to recover the residual stresses in a material, which is essential in understanding the material's behavior under different loads and stresses, particularly in the context of residual stresses. Non Linear Recovery Bending Moment is denoted by M_rec symbol.

How to evaluate Recovery Bending Moment for Non Linear Relation using this online evaluator? To use this online evaluator for Recovery Bending Moment for Non Linear Relation, enter Yield stress(non-linear) (σ_y), Depth of Rectangular Beam (d), Material Constant (n) & Depth of Outermost Shell Yields (η) and hit the calculate button.

FAQs on Recovery Bending Moment for Non Linear Relation

What is the formula to find Recovery Bending Moment for Non Linear Relation?

The formula of Recovery Bending Moment for Non Linear Relation is expressed as Non Linear Recovery Bending Moment = -Yield stress(non-linear)*Depth of Rectangular Beam*(Depth of Rectangular Beam^2/4-(Material Constant*Depth of Outermost Shell Yields^2)/(Material Constant+2)). Here is an example- -49162500000 = -240000000*0.095*(0.095^2/4-(0.25*0.03^2)/(0.25+2)).

How to calculate Recovery Bending Moment for Non Linear Relation?

With Yield stress(non-linear) (σ_y), Depth of Rectangular Beam (d), Material Constant (n) & Depth of Outermost Shell Yields (η) we can find Recovery Bending Moment for Non Linear Relation using the formula - Non Linear Recovery Bending Moment = -Yield stress(non-linear)*Depth of Rectangular Beam*(Depth of Rectangular Beam^2/4-(Material Constant*Depth of Outermost Shell Yields^2)/(Material Constant+2)).

Can the Recovery Bending Moment for Non Linear Relation be negative?

Yes, the Recovery Bending Moment for Non Linear Relation, measured in Moment of Force can be negative.

Which unit is used to measure Recovery Bending Moment for Non Linear Relation?

Recovery Bending Moment for Non Linear Relation is usually measured using the Newton Millimeter[N*mm] for Moment of Force. Newton Meter[N*mm], Kilonewton Meter[N*mm], Millinewton Meter[N*mm] are the few other units in which Recovery Bending Moment for Non Linear Relation can be measured.

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Recovery Bending Moment for Non Linear Relation Formula

Recovery Bending Moment for Non Linear Relation Example

Recovery Bending Moment for Non Linear Relation Solution

Recovery Bending Moment for Non Linear Relation Formula Elements

Other formulas in Residual Stresses for Non Linear Stress Strain Relations category

How to Evaluate Recovery Bending Moment for Non Linear Relation?

FAQs on Recovery Bending Moment for Non Linear Relation

Variable Name