Maximum Bending Stress in Plastic State Calculator

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Bending of Beams

Residual Stresses

Torsion of Bars

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Nonlinear Behavior of Beams

Plastic Bending of Beams

Shear Stress Distribution in Beams

Yield Criteria

✖Maximum Bending Moment is the moment at which the entire cross-section has reached its yield stress.ⓘ Maximum Bending Moment [M]			+10% -10%
✖Depth Yielded Plastically is the amount of depth of the beam yielded plastically from it's outermost fiber.ⓘ Depth Yielded Plastically [y]			+10% -10%
✖Material Constant is the constant used when the beam yielded plastically.ⓘ Material Constant [n]			+10% -10%
✖Nth Moment of Inertia is the integral arising from non-linear behavior of material.ⓘ Nth Moment of Inertia [I_n]			+10% -10%

✖Maximum Bending Stress in Plastic State is defined as the stresses within a beam exceed the elastic limit, then plastic deformation will occur.ⓘ Maximum Bending Stress in Plastic State [σ]

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Formula

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Maximum Bending Stress in Plastic State

Formula

`"σ" = ("M"*"y"^"n")/"I"_{"n"}`

Example

`"89.56079Pa"=("1500e3N*mm"*("40mm")^"0.25")/"42.12mm⁴"`

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Maximum Bending Stress in Plastic State Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Bending Stress in Plastic State = (Maximum Bending Moment*Depth Yielded Plastically^Material Constant)/Nth Moment of Inertia
σ = (M*y^n)/I_n
This formula uses 5 Variables

Variables Used

Maximum Bending Stress in Plastic State - (Measured in Pascal) - Maximum Bending Stress in Plastic State is defined as the stresses within a beam exceed the elastic limit, then plastic deformation will occur.
Maximum Bending Moment - (Measured in Newton Meter) - Maximum Bending Moment is the moment at which the entire cross-section has reached its yield stress.
Depth Yielded Plastically - (Measured in Millimeter) - Depth Yielded Plastically is the amount of depth of the beam yielded plastically from it's outermost fiber.
Material Constant - Material Constant is the constant used when the beam yielded plastically.
Nth Moment of Inertia - (Measured in Millimeter⁴) - Nth Moment of Inertia is the integral arising from non-linear behavior of material.

STEP 1: Convert Input(s) to Base Unit

Maximum Bending Moment: 1500000 Newton Millimeter --> 1500 Newton Meter (Check conversion here)
Depth Yielded Plastically: 40 Millimeter --> 40 Millimeter No Conversion Required
Material Constant: 0.25 --> No Conversion Required
Nth Moment of Inertia: 42.12 Millimeter⁴ --> 42.12 Millimeter⁴ No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ = (M*y^n)/I_n --> (1500*40^0.25)/42.12

Evaluating ... ...

σ = 89.5607855899527

STEP 3: Convert Result to Output's Unit

89.5607855899527 Pascal --> No Conversion Required

FINAL ANSWER

89.5607855899527 ≈ 89.56079 Pascal <-- Maximum Bending Stress in Plastic State

(Calculation completed in 00.004 seconds)

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< 4 Nonlinear Behavior of Beams Calculators

Radius of Curvature given Bending Stress

Go Radius of curvature = ((Elastoplastic Modulus*Depth Yielded Plastically^Material Constant)/Maximum Bending Stress in Plastic State)^(1/Material Constant)

Nth Moment of Inertia

Go Nth Moment of Inertia = (Breadth of rectangular beam*Depth of rectangular beam^(Material Constant+2))/((Material Constant+2)*2^(Material Constant+1))

Maximum Bending Stress in Plastic State

Go Maximum Bending Stress in Plastic State = (Maximum Bending Moment*Depth Yielded Plastically^Material Constant)/Nth Moment of Inertia

Radius of Curvature given Bending Moment

Go Radius of curvature = ((Elastoplastic Modulus*Nth Moment of Inertia)/Maximum Bending Moment)^(1/Material Constant)

Maximum Bending Stress in Plastic State Formula

Maximum Bending Stress in Plastic State = (Maximum Bending Moment*Depth Yielded Plastically^Material Constant)/Nth Moment of Inertia
σ = (M*y^n)/I_n

Importance of finding Maximum bending stress in plastic state.

If the stresses within a beam exceed the elastic limit, then plastic deformation will occur. This can dramatically change the behavior of the material and tends to failure of the material.

How to Calculate Maximum Bending Stress in Plastic State?

Maximum Bending Stress in Plastic State calculator uses Maximum Bending Stress in Plastic State = (Maximum Bending Moment*Depth Yielded Plastically^Material Constant)/Nth Moment of Inertia to calculate the Maximum Bending Stress in Plastic State, Maximum Bending Stress in Plastic State is defined as the stresses within a beam exceed the elastic limit, then plastic deformation will occur. Maximum Bending Stress in Plastic State is denoted by σ symbol.

How to calculate Maximum Bending Stress in Plastic State using this online calculator? To use this online calculator for Maximum Bending Stress in Plastic State, enter Maximum Bending Moment (M), Depth Yielded Plastically (y), Material Constant (n) & Nth Moment of Inertia (I_n) and hit the calculate button. Here is how the Maximum Bending Stress in Plastic State calculation can be explained with given input values -> 2.977348 = (1500*0.04^0.25)/4.212E-11.

FAQ

What is Maximum Bending Stress in Plastic State?

Maximum Bending Stress in Plastic State is defined as the stresses within a beam exceed the elastic limit, then plastic deformation will occur and is represented as σ = (M*y^n)/I_n or Maximum Bending Stress in Plastic State = (Maximum Bending Moment*Depth Yielded Plastically^Material Constant)/Nth Moment of Inertia. Maximum Bending Moment is the moment at which the entire cross-section has reached its yield stress, Depth Yielded Plastically is the amount of depth of the beam yielded plastically from it's outermost fiber, Material Constant is the constant used when the beam yielded plastically & Nth Moment of Inertia is the integral arising from non-linear behavior of material.

How to calculate Maximum Bending Stress in Plastic State?

Maximum Bending Stress in Plastic State is defined as the stresses within a beam exceed the elastic limit, then plastic deformation will occur is calculated using Maximum Bending Stress in Plastic State = (Maximum Bending Moment*Depth Yielded Plastically^Material Constant)/Nth Moment of Inertia. To calculate Maximum Bending Stress in Plastic State, you need Maximum Bending Moment (M), Depth Yielded Plastically (y), Material Constant (n) & Nth Moment of Inertia (I_n). With our tool, you need to enter the respective value for Maximum Bending Moment, Depth Yielded Plastically, Material Constant & Nth Moment of Inertia 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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