Fully Plastic Bending Moment Calculator

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Bending of Beams

Residual Stresses

Torsion of Bars

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Plastic Bending of Beams

Nonlinear Behavior of Beams

Shear Stress Distribution in Beams

Yield Criteria

✖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%
✖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%

✖Fully Plastic Bending Moment occurs in a beam which has yielded fully.ⓘ Fully Plastic Bending Moment [M_f]

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Formula

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Fully Plastic Bending Moment

Formula

`"M"_{"f"} = ("b"*"d"^2*"σ"_{"0"})/4`

Example

`"4.8E^7N*mm"=("80mm"*("100mm")^2*"240MPa")/4`

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Download Theory of Plasticity Formula PDF

Fully Plastic Bending Moment Solution

STEP 0: Pre-Calculation Summary

Formula Used

Fully Plastic Bending Moment = (Breadth of rectangular beam*Depth of rectangular beam^2*Yield Stress)/4
M_f = (b*d^2*σ₀)/4
This formula uses 4 Variables

Variables Used

Fully Plastic Bending Moment - (Measured in Newton Meter) - Fully Plastic Bending Moment occurs in a beam which has yielded fully.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Breadth of rectangular beam: 80 Millimeter --> 0.08 Meter (Check conversion here)
Depth of rectangular beam: 100 Millimeter --> 0.1 Meter (Check conversion here)
Yield Stress: 240 Megapascal --> 240000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M_f = (b*d^2*σ₀)/4 --> (0.08*0.1^2*240000000)/4

Evaluating ... ...

M_f = 48000

STEP 3: Convert Result to Output's Unit

48000 Newton Meter -->48000000 Newton Millimeter (Check conversion here)

FINAL ANSWER

48000000 ≈ 4.8E+7 Newton Millimeter <-- Fully Plastic Bending Moment

(Calculation completed in 00.004 seconds)

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BMS COLLEGE OF ENGINEERING (BMSCE), BANGALORE

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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

Fully Plastic Bending Moment Formula

Fully Plastic Bending Moment = (Breadth of rectangular beam*Depth of rectangular beam^2*Yield Stress)/4
M_f = (b*d^2*σ₀)/4

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 Fully Plastic Bending Moment?

Fully Plastic Bending Moment calculator uses Fully Plastic Bending Moment = (Breadth of rectangular beam*Depth of rectangular beam^2*Yield Stress)/4 to calculate the Fully Plastic Bending Moment, Fully Plastic Bending Moment is defined When the beam is fully Yielded and the moment is referred as Fully plastic bending moment. Fully Plastic Bending Moment is denoted by M_f symbol.

How to calculate Fully Plastic Bending Moment using this online calculator? To use this online calculator for Fully Plastic Bending Moment, enter Breadth of rectangular beam (b), Depth of rectangular beam (d) & Yield Stress (σ₀) and hit the calculate button. Here is how the Fully Plastic Bending Moment calculation can be explained with given input values -> 2.5E+10 = (0.08*0.1^2*240000000)/4.

FAQ

What is Fully Plastic Bending Moment?

Fully Plastic Bending Moment is defined When the beam is fully Yielded and the moment is referred as Fully plastic bending moment and is represented as M_f = (b*d^2*σ₀)/4 or Fully Plastic Bending Moment = (Breadth of rectangular beam*Depth of rectangular beam^2*Yield Stress)/4. Breadth of rectangular beam is the width of the beam, Depth of rectangular beam is the height of the beam & The Yield Stress is a material property and is the stress corresponding to the yield point at which the material begins to deform plastically.

How to calculate Fully Plastic Bending Moment?

Fully Plastic Bending Moment is defined When the beam is fully Yielded and the moment is referred as Fully plastic bending moment is calculated using Fully Plastic Bending Moment = (Breadth of rectangular beam*Depth of rectangular beam^2*Yield Stress)/4. To calculate Fully Plastic Bending Moment, you need Breadth of rectangular beam (b), Depth of rectangular beam (d) & Yield Stress (σ₀). With our tool, you need to enter the respective value for Breadth of rectangular beam, Depth of rectangular beam & Yield Stress 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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