Incipient Yielding Torque in Work Hardening Solid Shaft Calculator

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Torsion of Bars

Bending of Beams

Residual Stresses

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Elastic Work Hardening Material

Elastic Perfectly Plastic Materials

Residual Stresses for Non-Linear stress strain Law

✖Yield Shear Stress(non-linear) is the shear stress above the yield point.ⓘ Yield Shear Stress(non-linear) [𝞽_nonlinear]			+10% -10%
✖Nth Polar Moment of Inertia can be defined as Integral arising from nonlinear behaviour of material.ⓘ Nth Polar Moment of Inertia [J_n]			+10% -10%
✖Outer Radius of Shaft is the external radius of shaft.ⓘ Outer Radius of Shaft [r₂]			+10% -10%
✖Material Constant is the constant used when the beam yielded plastically.ⓘ Material Constant [n]			+10% -10%

✖Incipient Yielding Torque, In this stage, the shaft regains its original configuration upon the removal of torque. The stresses are assumed to be fully recovered.ⓘ Incipient Yielding Torque in Work Hardening Solid Shaft [T_i]

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Formula

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Incipient Yielding Torque in Work Hardening Solid Shaft

Formula

`"T"_{"i"} = ("𝞽"_{"nonlinear"}*"J"_{"n"})/"r"_{"2"}^"n"`

Example

`"1804.954N*mm"=("175MPa"*"5800mm⁴")/("100mm")^"0.25"`

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Incipient Yielding Torque in Work Hardening Solid Shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

Incipient Yielding Torque = (Yield Shear Stress(non-linear)*Nth Polar Moment of Inertia)/Outer Radius of Shaft^Material Constant
T_i = (𝞽_nonlinear*J_n)/r₂^n
This formula uses 5 Variables

Variables Used

Incipient Yielding Torque - (Measured in Newton Meter) - Incipient Yielding Torque, In this stage, the shaft regains its original configuration upon the removal of torque. The stresses are assumed to be fully recovered.
Yield Shear Stress(non-linear) - (Measured in Pascal) - Yield Shear Stress(non-linear) is the shear stress above the yield point.
Nth Polar Moment of Inertia - (Measured in Meter⁴) - Nth Polar Moment of Inertia can be defined as Integral arising from nonlinear behaviour of material.
Outer Radius of Shaft - (Measured in Meter) - Outer Radius of Shaft is the external radius of shaft.
Material Constant - Material Constant is the constant used when the beam yielded plastically.

STEP 1: Convert Input(s) to Base Unit

Yield Shear Stress(non-linear): 175 Megapascal --> 175000000 Pascal (Check conversion here)
Nth Polar Moment of Inertia: 5800 Millimeter⁴ --> 5.8E-09 Meter⁴ (Check conversion here)
Outer Radius of Shaft: 100 Millimeter --> 0.1 Meter (Check conversion here)
Material Constant: 0.25 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_i = (𝞽_nonlinear*J_n)/r₂^n --> (175000000*5.8E-09)/0.1^0.25

Evaluating ... ...

T_i = 1.80495360118951

STEP 3: Convert Result to Output's Unit

1.80495360118951 Newton Meter -->1804.95360118951 Newton Millimeter (Check conversion here)

FINAL ANSWER

1804.95360118951 ≈ 1804.954 Newton Millimeter <-- Incipient Yielding Torque

(Calculation completed in 00.004 seconds)

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< 7 Elastic Work Hardening Material Calculators

Elasto Plastic Yielding Torque in Work Hardening for Hollow Shaft

Go Elasto Plastic Yielding Torque = (2*pi*Yield Shear Stress(non-linear)*Outer Radius of Shaft^3)/3*((3*Radius of Plastic Front^3)/(Outer Radius of Shaft^3*(Material Constant+3))-(3/(Material Constant+3))*(Inner Radius of Shaft/Radius of Plastic Front)^Material Constant*(Inner Radius of Shaft/Outer Radius of Shaft)^3+1-(Radius of Plastic Front/Outer Radius of Shaft)^3)

Elasto Plastic Yielding Torque in Work Hardening for Solid Shaft

Go Elasto Plastic Yielding Torque = (2*pi*Yield Shear Stress(non-linear)*Outer Radius of Shaft^3)/3*(1-(Material Constant/(Material Constant+3))*(Radius of Plastic Front/Outer Radius of Shaft)^3)

Nth Polar Moment of Inertia

Go Nth Polar Moment of Inertia = ((2*pi)/(Material Constant+3))*(Outer Radius of Shaft^(Material Constant+3)-Inner Radius of Shaft^(Material Constant+3))

Full Yielding Torque in Work Hardening for Hollow Shaft

Go Full Yielding Torque = (2*pi*Yield Shear Stress(non-linear)*Outer Radius of Shaft^3)/3*(1-(Inner Radius of Shaft/Outer Radius of Shaft)^3)

Incipient Yielding Torque in Work Hardening for Hollow Shaft

Go Incipient Yielding Torque = (Yield Shear Stress(non-linear)*Nth Polar Moment of Inertia)/Outer Radius of Shaft^Material Constant

Incipient Yielding Torque in Work Hardening Solid Shaft

Go Incipient Yielding Torque = (Yield Shear Stress(non-linear)*Nth Polar Moment of Inertia)/Outer Radius of Shaft^Material Constant

Full Yielding Torque in Work Hardening for Solid Shaft

Go Full Yielding Torque = (2*pi*Yield Shear Stress(non-linear)*Outer Radius of Shaft^3)/3

Incipient Yielding Torque in Work Hardening Solid Shaft Formula

Incipient Yielding Torque = (Yield Shear Stress(non-linear)*Nth Polar Moment of Inertia)/Outer Radius of Shaft^Material Constant
T_i = (𝞽_nonlinear*J_n)/r₂^n

What is Incipient Yielding in shafts?

In this stage, the shaft regains its original configuration upon the removal of torque. The stresses are assumed to be fully recovered. Shear stress follows a linear law with zero stress at the neutral axis, and maximum stress at the outermost fibre.

How to Calculate Incipient Yielding Torque in Work Hardening Solid Shaft?

Incipient Yielding Torque in Work Hardening Solid Shaft calculator uses Incipient Yielding Torque = (Yield Shear Stress(non-linear)*Nth Polar Moment of Inertia)/Outer Radius of Shaft^Material Constant to calculate the Incipient Yielding Torque, The Incipient Yielding Torque in work hardening solid shaft formula is defined as In this stage, the shaft regains its original configuration upon the removal of torque. The stresses are assumed to be fully recovered. Incipient Yielding Torque is denoted by T_i symbol.

How to calculate Incipient Yielding Torque in Work Hardening Solid Shaft using this online calculator? To use this online calculator for Incipient Yielding Torque in Work Hardening Solid Shaft, enter Yield Shear Stress(non-linear) (𝞽_nonlinear), Nth Polar Moment of Inertia (J_n), Outer Radius of Shaft (r₂) & Material Constant (n) and hit the calculate button. Here is how the Incipient Yielding Torque in Work Hardening Solid Shaft calculation can be explained with given input values -> 1.8E+9 = (175000000*5.8E-09)/0.1^0.25.

FAQ

What is Incipient Yielding Torque in Work Hardening Solid Shaft?

The Incipient Yielding Torque in work hardening solid shaft formula is defined as In this stage, the shaft regains its original configuration upon the removal of torque. The stresses are assumed to be fully recovered and is represented as T_i = (𝞽_nonlinear*J_n)/r₂^n or Incipient Yielding Torque = (Yield Shear Stress(non-linear)*Nth Polar Moment of Inertia)/Outer Radius of Shaft^Material Constant. Yield Shear Stress(non-linear) is the shear stress above the yield point, Nth Polar Moment of Inertia can be defined as Integral arising from nonlinear behaviour of material, Outer Radius of Shaft is the external radius of shaft & Material Constant is the constant used when the beam yielded plastically.

How to calculate Incipient Yielding Torque in Work Hardening Solid Shaft?

The Incipient Yielding Torque in work hardening solid shaft formula is defined as In this stage, the shaft regains its original configuration upon the removal of torque. The stresses are assumed to be fully recovered is calculated using Incipient Yielding Torque = (Yield Shear Stress(non-linear)*Nth Polar Moment of Inertia)/Outer Radius of Shaft^Material Constant. To calculate Incipient Yielding Torque in Work Hardening Solid Shaft, you need Yield Shear Stress(non-linear) (𝞽_nonlinear), Nth Polar Moment of Inertia (J_n), Outer Radius of Shaft (r₂) & Material Constant (n). With our tool, you need to enter the respective value for Yield Shear Stress(non-linear), Nth Polar Moment of Inertia, Outer Radius of Shaft & Material Constant and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Incipient Yielding Torque?

In this formula, Incipient Yielding Torque uses Yield Shear Stress(non-linear), Nth Polar Moment of Inertia, Outer Radius of Shaft & Material Constant. We can use 1 other way(s) to calculate the same, which is/are as follows -

Incipient Yielding Torque = (Yield Shear Stress(non-linear)*Nth Polar Moment of Inertia)/Outer Radius of Shaft^Material Constant

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