Elasto Plastic Bending Moment of Rectangular Beam Calculator

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Bending of Beams

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Plastic Bending of Beams

Nonlinear Behavior of Beams

Shear Stress Distribution in Beams

Yield Criteria

✖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%

✖Elasto plastic bending moment occurs when the beam fibres beyond y=η have yielded.ⓘ Elasto Plastic Bending Moment of Rectangular Beam [M_ep]

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Formula

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Elasto Plastic Bending Moment of Rectangular Beam

Formula

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

Example

`"4.2E^7N*mm"=("240MPa"*"80mm"*(3*("100mm")^2-4*("30mm")^2))/12`

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Elasto Plastic Bending Moment of Rectangular Beam Solution

STEP 0: Pre-Calculation Summary

Formula Used

Elasto plastic bending moment = (Yield Stress*Breadth of rectangular beam*(3*Depth of rectangular beam^2-4*Depth of outermost shell yields^2))/12
M_ep = (σ₀*b*(3*d^2-4*η^2))/12
This formula uses 5 Variables

Variables Used

Elasto plastic bending moment - (Measured in Newton Meter) - Elasto plastic bending moment occurs when the beam fibres beyond y=η have yielded.
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: 240 Megapascal --> 240000000 Pascal (Check conversion here)
Breadth of rectangular beam: 80 Millimeter --> 0.08 Meter (Check conversion here)
Depth of rectangular beam: 100 Millimeter --> 0.1 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_ep = (σ₀*b*(3*d^2-4*η^2))/12 --> (240000000*0.08*(3*0.1^2-4*0.03^2))/12

Evaluating ... ...

M_ep = 42240

STEP 3: Convert Result to Output's Unit

42240 Newton Meter -->42240000 Newton Millimeter (Check conversion here)

FINAL ANSWER

42240000 ≈ 4.2E+7 Newton Millimeter <-- Elasto plastic bending moment

(Calculation completed in 00.008 seconds)

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< 3 Plastic Bending of Beams Calculators

Elasto Plastic Bending Moment of Rectangular Beam

Go Elasto plastic bending moment = (Yield Stress*Breadth of rectangular beam*(3*Depth of rectangular beam^2-4*Depth of outermost shell yields^2))/12

Fully Plastic Bending Moment

Go Fully Plastic Bending Moment = (Breadth of rectangular beam*Depth of rectangular beam^2*Yield Stress)/4

Incipient Bending Moment of Rectangular Beam

Go Incipient Bending Moment = (Breadth of rectangular beam*Depth of rectangular beam^2*Yield Stress)/6

Elasto Plastic Bending Moment of Rectangular Beam Formula

Elasto plastic bending moment = (Yield Stress*Breadth of rectangular beam*(3*Depth of rectangular beam^2-4*Depth of outermost shell yields^2))/12
M_ep = (σ₀*b*(3*d^2-4*η^2))/12

Importance of Plastic Analysis of Beams or any other structures.

Plastic analysis is the method through which the actual failure load of a structure is calculated, and as will be seen, this failure load can be significantly greater than the elastic load capacity.

How to Calculate Elasto Plastic Bending Moment of Rectangular Beam?

Elasto Plastic Bending Moment of Rectangular Beam calculator uses Elasto plastic 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 Elasto plastic bending moment, Elasto Plastic Bending Moment of Rectangular Beam is defined as, Elasto plastic bending moment occurs when the beam fibres beyond y=η have yielded. Elasto plastic bending moment is denoted by M_ep symbol.

How to calculate Elasto Plastic Bending Moment of Rectangular Beam using this online calculator? To use this online calculator for Elasto Plastic Bending Moment of Rectangular Beam, 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 Elasto Plastic Bending Moment of Rectangular Beam calculation can be explained with given input values -> 2.2E+10 = (240000000*0.08*(3*0.1^2-4*0.03^2))/12.

FAQ

What is Elasto Plastic Bending Moment of Rectangular Beam?

Elasto Plastic Bending Moment of Rectangular Beam is defined as, Elasto plastic bending moment occurs when the beam fibres beyond y=η have yielded and is represented as M_ep = (σ₀*b*(3*d^2-4*η^2))/12 or Elasto plastic 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 Elasto Plastic Bending Moment of Rectangular Beam?

Elasto Plastic Bending Moment of Rectangular Beam is defined as, Elasto plastic bending moment occurs when the beam fibres beyond y=η have yielded is calculated using Elasto plastic bending moment = (Yield Stress*Breadth of rectangular beam*(3*Depth of rectangular beam^2-4*Depth of outermost shell yields^2))/12. To calculate Elasto Plastic Bending Moment of Rectangular Beam, 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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