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Recovery Bending Moment Formula

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Recovery Bending Moment can be defined as when a beam so bent is applied with a moment of same magnitude in the opposite direction and the opposite moment is called Recovery bending moment. Check FAQs

M Rec = - (\frac{σ 0 \cdot b \cdot (3 \cdot d^{2} - 4 \cdot η^{2})}{12})

M_Rec - Recovery Bending Moment?σ₀ - Yield Stress?b - Breadth of Rectangular Beam?d - Depth of Rectangular Beam?η - Depth of Outermost Shell Yields?

Recovery Bending Moment Example

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Here is how the Recovery Bending Moment equation looks like with Values.

Here is how the Recovery Bending Moment equation looks like with Units.

Here is how the Recovery Bending Moment equation looks like.

-36679687.5 = - (\frac{250 \cdot 75 \cdot (3 \cdot 95^{2} - 4 \cdot 30^{2})}{12})

-36679687.5N*mm = - (\frac{250MPa \cdot 75mm \cdot (3 \cdot {95mm}^{2} - 4 \cdot {30mm}^{2})}{12})

-36679687.5 = - (\frac{250 \cdot 75 \cdot (3 \cdot 95^{2} - 4 \cdot 30^{2})}{12})

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Recovery Bending Moment Solution

Follow our step by step solution on how to calculate Recovery Bending Moment?

FIRST Step Consider the formula

M Rec = - (\frac{σ 0 \cdot b \cdot (3 \cdot d^{2} - 4 \cdot η^{2})}{12})

Next Step Substitute values of Variables

∴

M Rec = - (\frac{250MPa \cdot 75mm \cdot (3 \cdot {95mm}^{2} - 4 \cdot {30mm}^{2})}{12})

Next Step Convert Units

∴

M Rec = - (\frac{2.5E+8Pa \cdot 0.075m \cdot (3 \cdot {0.095m}^{2} - 4 \cdot {0.03m}^{2})}{12})

Next Step Prepare to Evaluate

∴

M Rec = - (\frac{2.5E+8 \cdot 0.075 \cdot (3 \cdot {0.095}^{2} - 4 \cdot {0.03}^{2})}{12})

Next Step Evaluate

∴

M Rec = -36679.6875N*m

LAST Step Convert to Output's Unit

∴

M Rec = -36679687.5N*mm

Recovery Bending Moment Formula Elements

Variables

Recovery Bending Moment

Recovery Bending Moment can be defined as when a beam so bent is applied with a moment of same magnitude in the opposite direction and the opposite moment is called Recovery bending moment.

Symbol: M_Rec

Measurement: Moment of ForceUnit: N*mm

Note: Value can be positive or negative.

Formulas to find Recovery Bending Moment

Yield Stress

The Yield Stress is a material property and is the stress corresponding to the yield point at which the material begins to deform plastically.

Symbol: σ₀

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Yield Stress

Breadth of Rectangular Beam

Breadth of rectangular beam is the width of the beam.

Symbol: b

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Breadth of Rectangular Beam

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

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 in Plastic Bending category

Go Recovery Stress in Beams

σ Rec = \frac{M Rec \cdot y}{\frac{b \cdot d^{3}}{12}}

Go Residual Stress in Beams when Y Lies between 0 and n

σ Res = \frac{M Rec \cdot y d}{\frac{d \cdot d^{3}}{12}}

Go Residual Stress in Beams when Bending Stress is Equal to Yield Stress

σ beam = - (σ 0 + \frac{M Rec \cdot y}{\frac{b \cdot d^{3}}{12}})

Go Fully Plastic Recovery Stress in Beams

σ rec_plastic = \frac{M rec_plastic \cdot y}{\frac{b \cdot d^{3}}{12}}

How to Evaluate Recovery Bending Moment?

Recovery Bending Moment evaluator uses Recovery Bending Moment = -((Yield Stress*Breadth of Rectangular Beam*(3*Depth of Rectangular Beam^2-4*Depth of Outermost Shell Yields^2))/12) to evaluate the Recovery Bending Moment, The Recovery Bending Moment formula is defined as when a beam so bent is applied with a moment of same magnitude in the opposite direction and the opposite moment is called Recovery bending moment. Recovery Bending Moment is denoted by M_Rec symbol.

How to evaluate Recovery Bending Moment using this online evaluator? To use this online evaluator for Recovery Bending Moment, enter Yield Stress (σ₀), Breadth of Rectangular Beam (b), Depth of Rectangular Beam (d) & Depth of Outermost Shell Yields (η) and hit the calculate button.

FAQs on Recovery Bending Moment

What is the formula to find Recovery Bending Moment?

The formula of Recovery Bending Moment is expressed as Recovery Bending Moment = -((Yield Stress*Breadth of Rectangular Beam*(3*Depth of Rectangular Beam^2-4*Depth of Outermost Shell Yields^2))/12). Here is an example- -36679687500 = -((250000000*0.075*(3*0.095^2-4*0.03^2))/12).

How to calculate Recovery Bending Moment?

With Yield Stress (σ₀), Breadth of Rectangular Beam (b), Depth of Rectangular Beam (d) & Depth of Outermost Shell Yields (η) we can find Recovery Bending Moment using the formula - Recovery Bending Moment = -((Yield Stress*Breadth of Rectangular Beam*(3*Depth of Rectangular Beam^2-4*Depth of Outermost Shell Yields^2))/12).

Can the Recovery Bending Moment be negative?

Yes, the Recovery Bending Moment, measured in Moment of Force can be negative.

Which unit is used to measure Recovery Bending Moment?

Recovery Bending Moment 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 can be measured.

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Recovery Bending Moment Formula

Recovery Bending Moment Example

Recovery Bending Moment Solution

Recovery Bending Moment Formula Elements

Other formulas in Residual Stresses in Plastic Bending category

How to Evaluate Recovery Bending Moment?

FAQs on Recovery Bending Moment

Variable Name