Elasto Plastic Bending Moment for Non-Linear Relation Solution

STEP 0: Pre-Calculation Summary
Formula Used
Non Linear Elasto Plastic Bending Moment = Yield stress(non-linear)*Depth of Rectangular Beam*(Depth of Rectangular Beam^2/4-(Material Constant*Depth of Outermost Shell Yields^2)/(Material Constant+2))
MEP = σy*d*(d^2/4-(n*η^2)/(n+2))
This formula uses 5 Variables
Variables Used
Non Linear Elasto Plastic Bending Moment - (Measured in Newton Meter) - Non Linear Elasto Plastic Bending Moment can be defined as it occurs when the beam fibers beyond y=η have yielded.
Yield stress(non-linear) - (Measured in Pascal) - The yield stress(non-linear) is a material property and is the stress corresponding to the yield point at which the material begins to deform plastically.
Depth of Rectangular Beam - (Measured in Meter) - Depth of rectangular beam is the height of the beam.
Material Constant - Material Constant is the constant used when the beam yielded plastically.
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(non-linear): 240 Megapascal --> 240000000 Pascal (Check conversion here)
Depth of Rectangular Beam: 95 Millimeter --> 0.095 Meter (Check conversion here)
Material Constant: 0.25 --> No Conversion Required
Depth of Outermost Shell Yields: 30 Millimeter --> 0.03 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
MEP = σy*d*(d^2/4-(n*η^2)/(n+2)) --> 240000000*0.095*(0.095^2/4-(0.25*0.03^2)/(0.25+2))
Evaluating ... ...
MEP = 49162.5
STEP 3: Convert Result to Output's Unit
49162.5 Newton Meter -->49162500 Newton Millimeter (Check conversion here)
FINAL ANSWER
49162500 4.9E+7 Newton Millimeter <-- Non Linear Elasto Plastic Bending Moment
(Calculation completed in 00.020 seconds)

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7 Residual Stresses for Non-Linear Stress Strain Relations Calculators

Residual Stress in Beams for Non Linear Relation when Y Lies between 0 and n
Go Non Linear Residual Stresses(Y lies between 0&η) = -(Yield stress(non-linear)*(Depth Yielded Between 0 and η/Depth of Outermost Shell Yields)^Material Constant+(Non Linear Recovery Bending Moment*Depth Yielded Plastically)/((Depth of Rectangular Beam*Depth of Rectangular Beam^3)/12))
Elasto Plastic Bending Moment for Non-Linear Relation
Go Non Linear Elasto Plastic Bending Moment = Yield stress(non-linear)*Depth of Rectangular Beam*(Depth of Rectangular Beam^2/4-(Material Constant*Depth of Outermost Shell Yields^2)/(Material Constant+2))
Recovery Bending Moment for Non Linear Relation
Go Non Linear Recovery Bending Moment = -Yield stress(non-linear)*Depth of Rectangular Beam*(Depth of Rectangular Beam^2/4-(Material Constant*Depth of Outermost Shell Yields^2)/(Material Constant+2))
Residual Stress in Beams for Non Linear Relation (Y Lies between 0 and n) given Recovery Stress
Go Non Linear Residual Stresses(Y lies between 0&η) = -(Yield stress(non-linear)*(Depth Yielded Between 0 and η/Depth of Outermost Shell Yields)^Material Constant+(Recovery Stress in beams for non linear relation))
Residual Stress in Beams for Non Linear Relation when Whole Depth of Beam Yields
Go Residual Stress in Beams above Yielding Point = -(Yield stress(non-linear)+(Non Linear Recovery Bending Moment*Depth Yielded Plastically)/((Depth of Rectangular Beam*Depth of Rectangular Beam^3)/12))
Recovery Stress in Beams for Non Linear Relation
Go Recovery Stress in beams for non linear relation = (Non Linear Recovery Bending Moment*Depth Yielded Plastically)/(Polar Moment of Inertia)
Residual Stress in Beams for Non Linear Relation at Whole Depth of Beam Yields given Recovery Stress
Go Residual Stress in Beams above Yielding Point = -(Yield stress(non-linear)+(Recovery Stress in beams for non linear relation))

Elasto Plastic Bending Moment for Non-Linear Relation Formula

Non Linear Elasto Plastic Bending Moment = Yield stress(non-linear)*Depth of Rectangular Beam*(Depth of Rectangular Beam^2/4-(Material Constant*Depth of Outermost Shell Yields^2)/(Material Constant+2))
MEP = σy*d*(d^2/4-(n*η^2)/(n+2))

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 for Non-Linear Relation?

Elasto Plastic Bending Moment for Non-Linear Relation calculator uses Non Linear Elasto Plastic Bending Moment = Yield stress(non-linear)*Depth of Rectangular Beam*(Depth of Rectangular Beam^2/4-(Material Constant*Depth of Outermost Shell Yields^2)/(Material Constant+2)) to calculate the Non Linear Elasto Plastic Bending Moment, Elasto Plastic Bending Moment for Non-Linear Relation is defined as it occurs when the beam fibres beyond y=η have yielded. Non Linear Elasto Plastic Bending Moment is denoted by MEP symbol.

How to calculate Elasto Plastic Bending Moment for Non-Linear Relation using this online calculator? To use this online calculator for Elasto Plastic Bending Moment for Non-Linear Relation, enter Yield stress(non-linear) y), Depth of Rectangular Beam (d), Material Constant (n) & Depth of Outermost Shell Yields (η) and hit the calculate button. Here is how the Elasto Plastic Bending Moment for Non-Linear Relation calculation can be explained with given input values -> 4.9E+10 = 240000000*0.095*(0.095^2/4-(0.25*0.03^2)/(0.25+2)).

FAQ

What is Elasto Plastic Bending Moment for Non-Linear Relation?
Elasto Plastic Bending Moment for Non-Linear Relation is defined as it occurs when the beam fibres beyond y=η have yielded and is represented as MEP = σy*d*(d^2/4-(n*η^2)/(n+2)) or Non Linear Elasto Plastic Bending Moment = Yield stress(non-linear)*Depth of Rectangular Beam*(Depth of Rectangular Beam^2/4-(Material Constant*Depth of Outermost Shell Yields^2)/(Material Constant+2)). The yield stress(non-linear) is a material property and is the stress corresponding to the yield point at which the material begins to deform plastically, Depth of rectangular beam is the height of the beam, Material Constant is the constant used when the beam yielded plastically & 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 for Non-Linear Relation?
Elasto Plastic Bending Moment for Non-Linear Relation is defined as it occurs when the beam fibres beyond y=η have yielded is calculated using Non Linear Elasto Plastic Bending Moment = Yield stress(non-linear)*Depth of Rectangular Beam*(Depth of Rectangular Beam^2/4-(Material Constant*Depth of Outermost Shell Yields^2)/(Material Constant+2)). To calculate Elasto Plastic Bending Moment for Non-Linear Relation, you need Yield stress(non-linear) y), Depth of Rectangular Beam (d), Material Constant (n) & Depth of Outermost Shell Yields (η). With our tool, you need to enter the respective value for Yield stress(non-linear), Depth of Rectangular Beam, Material Constant & 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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