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Elasto Plastic Bending Moment for Non-Linear Relation Formula

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Non Linear Elasto Plastic Bending Moment can be defined as it occurs when the beam fibers beyond y=η have yielded. Check FAQs

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

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

Elasto Plastic Bending Moment for Non-Linear Relation Example

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

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

Here is how the Elasto Plastic Bending Moment for Non-Linear Relation equation looks like.

4.9E+7 = 240 \cdot 95 \cdot (\frac{95^{2}}{4} - \frac{0.25 \cdot 30^{2}}{0.25 + 2})

4.9E+7N*mm = 240MPa \cdot 95mm \cdot (\frac{{95mm}^{2}}{4} - \frac{0.25 \cdot {30mm}^{2}}{0.25 + 2})

4.9E+7 = 240 \cdot 95 \cdot (\frac{95^{2}}{4} - \frac{0.25 \cdot 30^{2}}{0.25 + 2})

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Elasto Plastic Bending Moment for Non-Linear Relation Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

M EP = 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 EP = 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 EP = 49162.5N*m

Next Step Convert to Output's Unit

∴

M EP = 49162500N*mm

LAST Step Rounding Answer

∴

M EP = 4.9E+7N*mm

Elasto Plastic Bending Moment for Non-Linear Relation Formula Elements

Variables

Non Linear Elasto Plastic Bending Moment

Non Linear Elasto Plastic Bending Moment can be defined as it occurs when the beam fibers beyond y=η have yielded.

Symbol: M_EP

Measurement: Moment of ForceUnit: N*mm

Note: Value can be positive or negative.

Formulas to find Non Linear Elasto Plastic 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 height of the beam.

Symbol: d

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Depth of Rectangular Beam

Material Constant

Material Constant is the constant used when the beam yielded plastically.

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 amount of yielding of outermost fiber of a beam when it is in Elasto-plastic state.

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 Recovery Bending Moment for Non Linear Relation

M rec = - 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 Elasto Plastic Bending Moment for Non-Linear Relation?

Elasto Plastic Bending Moment for Non-Linear Relation evaluator uses Non Linear Elasto Plastic 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 Elasto Plastic Bending Moment, Elasto Plastic Bending Moment for Non-Linear Relation is defined as it occurs when the beam fibres beyond y=η have yielded. Non Linear Elasto Plastic Bending Moment is denoted by M_EP symbol.

How to evaluate Elasto Plastic Bending Moment for Non-Linear Relation using this online evaluator? To use this online evaluator for Elasto Plastic 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 Elasto Plastic Bending Moment for Non-Linear Relation

What is the formula to find Elasto Plastic Bending Moment for Non-Linear Relation?

The formula of Elasto Plastic Bending Moment for Non-Linear Relation is expressed as Non Linear Elasto Plastic 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- 4.9E+10 = 240000000*0.095*(0.095^2/4-(0.25*0.03^2)/(0.25+2)).

How to calculate Elasto Plastic 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 Elasto Plastic Bending Moment for Non-Linear Relation using the formula - Non Linear Elasto Plastic 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 Elasto Plastic Bending Moment for Non-Linear Relation be negative?

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

Which unit is used to measure Elasto Plastic Bending Moment for Non-Linear Relation?

Elasto Plastic 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 Elasto Plastic Bending Moment for Non-Linear Relation can be measured.

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Elasto Plastic Bending Moment for Non-Linear Relation Formula

Elasto Plastic Bending Moment for Non-Linear Relation Example

Elasto Plastic Bending Moment for Non-Linear Relation Solution

Elasto Plastic Bending Moment for Non-Linear Relation Formula Elements

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

How to Evaluate Elasto Plastic Bending Moment for Non-Linear Relation?

FAQs on Elasto Plastic Bending Moment for Non-Linear Relation

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