Elasto Plastic Bending Moment of Rectangular Beam Calculator

✖Yield Stress is the stress at which a material begins to deform plastically, typically measured in bending beams under external loads.ⓘ Yield Stress [σ₀]			+10% -10%
✖Breadth of Rectangular Beam is the horizontal distance of a rectangular beam's cross-section, perpendicular to its length, in bending beam applications.ⓘ Breadth of Rectangular Beam [b]			+10% -10%
✖Depth of Rectangular Beam is the vertical distance from the neutral axis to the bottom of the beam, used to calculate bending stresses and moments.ⓘ Depth of Rectangular Beam [d]			+10% -10%
✖Depth of Outermost Shell Yields is the maximum distance from the neutral axis to the outermost fiber of a beam under bending stress.ⓘ Depth of Outermost Shell Yields [η]			+10% -10%

✖Elasto Plastic Bending Moment is the maximum moment a beam can withstand before it deforms plastically due to bending stress, affecting its structural integrity.ⓘ Elasto Plastic Bending Moment of Rectangular Beam [M_ep]

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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 is the maximum moment a beam can withstand before it deforms plastically due to bending stress, affecting its structural integrity.
Yield Stress - (Measured in Pascal) - Yield Stress is the stress at which a material begins to deform plastically, typically measured in bending beams under external loads.
Breadth of Rectangular Beam - (Measured in Meter) - Breadth of Rectangular Beam is the horizontal distance of a rectangular beam's cross-section, perpendicular to its length, in bending beam applications.
Depth of Rectangular Beam - (Measured in Meter) - Depth of Rectangular Beam is the vertical distance from the neutral axis to the bottom of the beam, used to calculate bending stresses and moments.
Depth of Outermost Shell Yields - (Measured in Meter) - Depth of Outermost Shell Yields is the maximum distance from the neutral axis to the outermost fiber of a beam under bending stress.

STEP 1: Convert Input(s) to Base Unit

Yield Stress: 230 Newton per Square Millimeter --> 230000000 Pascal (Check conversion here)
Breadth of Rectangular Beam: 80 Millimeter --> 0.08 Meter (Check conversion here)
Depth of Rectangular Beam: 20 Millimeter --> 0.02 Meter (Check conversion here)
Depth of Outermost Shell Yields: 1.1 Millimeter --> 0.0011 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M_ep = (σ₀*b*(3*d^2-4*η^2))/12 --> (230000000*0.08*(3*0.02^2-4*0.0011^2))/12

Evaluating ... ...

M_ep = 1832.57866666667

STEP 3: Convert Result to Output's Unit

1832.57866666667 Newton Meter -->1832578.66666667 Newton Millimeter (Check conversion here)

FINAL ANSWER

1832578.66666667 ≈ 1.8E+6 Newton Millimeter <-- Elasto Plastic Bending Moment

(Calculation completed in 00.020 seconds)

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< Plastic Bending of Beams Calculators

Elasto Plastic Bending Moment of Rectangular Beam

LaTeX 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

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

Incipient Bending Moment of Rectangular Beam

LaTeX Go Incipient Bending Moment = (Breadth of Rectangular Beam*Depth of Rectangular Beam^2*Yield Stress)/6

Elasto Plastic Bending Moment of Rectangular Beam Formula

LaTeX 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
M_ep = (σ₀*b*(3*d^2-4*η^2))/12

What is Elasto Plastic Bending Moment?

The Elasto-Plastic Bending Moment refers to the bending moment at which a material transitions from elastic behavior, where it deforms but can return to its original shape, to plastic behavior, where it undergoes permanent deformation. When a material is subjected to bending, it initially deforms elastically, following Hooke’s Law. However, as the load increases and reaches a critical point, the material yields and enters the plastic region, meaning any further deformation will be permanent. The elasto-plastic bending moment marks the boundary between these two stages and is crucial in structural design, as it indicates the maximum bending moment a material can withstand before permanent deformation begins, ensuring safety and durability in engineering applications.

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 formula is defined as a measure of the maximum bending moment that a rectangular beam can withstand before it starts to deform plastically, considering the yield strength, beam dimensions, and the extent of plastic deformation. 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 -> 1.8E+9 = (230000000*0.08*(3*0.02^2-4*0.0011^2))/12.

FAQ

What is Elasto Plastic Bending Moment of Rectangular Beam?

Elasto Plastic Bending Moment of Rectangular Beam formula is defined as a measure of the maximum bending moment that a rectangular beam can withstand before it starts to deform plastically, considering the yield strength, beam dimensions, and the extent of plastic deformation 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. Yield Stress is the stress at which a material begins to deform plastically, typically measured in bending beams under external loads, Breadth of Rectangular Beam is the horizontal distance of a rectangular beam's cross-section, perpendicular to its length, in bending beam applications, Depth of Rectangular Beam is the vertical distance from the neutral axis to the bottom of the beam, used to calculate bending stresses and moments & Depth of Outermost Shell Yields is the maximum distance from the neutral axis to the outermost fiber of a beam under bending stress.

How to calculate Elasto Plastic Bending Moment of Rectangular Beam?

Elasto Plastic Bending Moment of Rectangular Beam formula is defined as a measure of the maximum bending moment that a rectangular beam can withstand before it starts to deform plastically, considering the yield strength, beam dimensions, and the extent of plastic deformation 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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