Recovery Bending Moment Calculator

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Residual Stresses in Plastic Bending

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Residual Stresses for Non-Linear Stress Strain Relations

✖The Yield Stress is a material property and is the stress corresponding to the yield point at which the material begins to deform plastically.ⓘ Yield Stress [σ₀]			+10% -10%
✖Breadth of rectangular beam is the width of the beam.ⓘ Breadth of Rectangular Beam [b]			+10% -10%
✖Depth of rectangular beam is the height of the beam.ⓘ Depth of Rectangular Beam [d]			+10% -10%
✖Depth of outermost shell yields is the amount of yielding of outermost fiber of a beam when it is in Elasto-plastic state.ⓘ Depth of Outermost Shell Yields [η]			+10% -10%

✖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.ⓘ Recovery Bending Moment [M_Rec]

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Formula

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Recovery Bending Moment

Formula

`"M"_{"Rec"} = -(("σ"_{"0"}*"b"* (3*"d"^2-4*"η"^2))/12)`

Example

`"-36679687.5N*mm"=-(("250MPa"*"75mm"* (3*("95mm")^2-4*("30mm")^2))/12)`

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Recovery Bending Moment Solution

STEP 0: Pre-Calculation Summary

Formula Used

Recovery Bending Moment = -((Yield Stress*Breadth of Rectangular Beam* (3*Depth of Rectangular Beam^2-4*Depth of Outermost Shell Yields^2))/12)
M_Rec = -((σ₀*b* (3*d^2-4*η^2))/12)
This formula uses 5 Variables

Variables Used

Recovery Bending Moment - (Measured in Newton Meter) - 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.
Yield Stress - (Measured in Pascal) - The Yield Stress is a material property and is the stress corresponding to the yield point at which the material begins to deform plastically.
Breadth of Rectangular Beam - (Measured in Meter) - Breadth of rectangular beam is the width of the beam.
Depth of Rectangular Beam - (Measured in Meter) - Depth of rectangular beam is the height of the beam.
Depth of Outermost Shell Yields - (Measured in Meter) - Depth of outermost shell yields is the amount of yielding of outermost fiber of a beam when it is in Elasto-plastic state.

STEP 1: Convert Input(s) to Base Unit

Yield Stress: 250 Megapascal --> 250000000 Pascal (Check conversion here)
Breadth of Rectangular Beam: 75 Millimeter --> 0.075 Meter (Check conversion here)
Depth of Rectangular Beam: 95 Millimeter --> 0.095 Meter (Check conversion here)
Depth of Outermost Shell Yields: 30 Millimeter --> 0.03 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M_Rec = -((σ₀*b* (3*d^2-4*η^2))/12) --> -((250000000*0.075* (3*0.095^2-4*0.03^2))/12)

Evaluating ... ...

M_Rec = -36679.6875

STEP 3: Convert Result to Output's Unit

-36679.6875 Newton Meter -->-36679687.5 Newton Millimeter (Check conversion here)

FINAL ANSWER

-36679687.5 Newton Millimeter <-- Recovery Bending Moment

(Calculation completed in 00.004 seconds)

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< 8 Residual Stresses in Plastic Bending Calculators

Residual Stress in Beam in Fully Plastic State

Go Residual stress in beam in plastic state = -(Yield Stress+(Fully Plastic Recovery Bending Moment*Depth Yielded Plastically)/((Breadth of Rectangular Beam*Depth of Rectangular Beam^3)/12))

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

Go Residual Stress in Beams above Yielding Point = -(Yield Stress+(Recovery Bending Moment*Depth Yielded Plastically)/((Breadth of Rectangular Beam*Depth of Rectangular Beam^3)/12))

Residual Stress in Beams when Y Lies between 0 and n

Go Residual Stress in beams (Y lies between 0 and η) = (Recovery Bending Moment* Depth Yielded Between 0 and η)/((Depth of Rectangular Beam*Depth of Rectangular Beam^3)/12)

Fully Plastic Recovery Stress in Beams

Go Fully plastic Recovery stress in beams = (Fully Plastic Recovery Bending Moment*Depth Yielded Plastically)/((Breadth of Rectangular Beam*Depth of Rectangular Beam^3)/12)

Recovery Bending Moment

Go Recovery Bending Moment = -((Yield Stress*Breadth of Rectangular Beam* (3*Depth of Rectangular Beam^2-4*Depth of Outermost Shell Yields^2))/12)

Recovery Stress in Beams

Go Recovery Stress in Beams = (Recovery Bending Moment*Depth Yielded Plastically)/((Breadth of Rectangular Beam*Depth of Rectangular Beam^3)/12)

Fully Plastic Recovery Bending Moment

Go Fully Plastic Recovery Bending Moment = -(Breadth of Rectangular Beam*Depth of Rectangular Beam^2*Yield Stress)/4

Residual Stress in Beam in Fully Plastic State given Recovery Stress

Go Residual stress in beam in plastic state = -(Yield Stress+(Fully plastic Recovery stress in beams))

Recovery Bending Moment Formula

Recovery Bending Moment = -((Yield Stress*Breadth of Rectangular Beam* (3*Depth of Rectangular Beam^2-4*Depth of Outermost Shell Yields^2))/12)
M_Rec = -((σ₀*b* (3*d^2-4*η^2))/12)

What is recovery bending moment?

when a beam so bent is applied with a moment of same magnitude in the opposite direction, then the recovery of stress takes place and the opposite moment is called Recovery bending moment.

How to Calculate Recovery Bending Moment?

Recovery Bending Moment calculator 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 calculate 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 calculate Recovery Bending Moment using this online calculator? To use this online calculator 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. Here is how the Recovery Bending Moment calculation can be explained with given input values -> -36679687500 = -((250000000*0.075* (3*0.095^2-4*0.03^2))/12).

FAQ

What is 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 and is represented as M_Rec = -((σ₀*b* (3*d^2-4*η^2))/12) or Recovery Bending Moment = -((Yield Stress*Breadth of Rectangular Beam* (3*Depth of Rectangular Beam^2-4*Depth of Outermost Shell Yields^2))/12). The Yield Stress is a material property and is the stress corresponding to the yield point at which the material begins to deform plastically, Breadth of rectangular beam is the width of the beam, Depth of rectangular beam is the height of the beam & Depth of outermost shell yields is the amount of yielding of outermost fiber of a beam when it is in Elasto-plastic state.

How to calculate 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 is calculated using Recovery Bending Moment = -((Yield Stress*Breadth of Rectangular Beam* (3*Depth of Rectangular Beam^2-4*Depth of Outermost Shell Yields^2))/12). To calculate Recovery Bending Moment, you need Yield Stress (σ₀), Breadth of Rectangular Beam (b), Depth of Rectangular Beam (d) & Depth of Outermost Shell Yields (η). With our tool, you need to enter the respective value for Yield Stress, Breadth of Rectangular Beam, Depth of Rectangular Beam & Depth of Outermost Shell Yields 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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