Torsional Moment given Equivalent Bending Moment Calculator

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Design of Shafts

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Maximum Shear Stress and Principal Stress Theory

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Torsional Rigidity

✖Equivalent Bending Moment from MSST is the bending moment that, acting alone, would produce in a circular shaft and is calculated from Max shear stress theory.ⓘ Equivalent Bending Moment from MSST [Mb_eq]			+10% -10%
✖Bending Moment in Shaft for MSST is the reaction induced in a structural shaft element when an external force or moment is applied to the element, causing the element to bend.ⓘ Bending Moment in Shaft for MSST [M_{b MSST}]			+10% -10%

✖Torsional Moment in Shaft for MSST is the reaction induced in a structural shaft element when an external force or moment is applied to the element, causing the element to twist.ⓘ Torsional Moment given Equivalent Bending Moment [Mt_t]

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Formula

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Torsional Moment given Equivalent Bending Moment

Formula

`"Mt"_{"t"} = sqrt(("Mb"_{"eq"}-"M"_{"b MSST"})^2-"M"_{"b MSST"}^2)`

Example

`"376961.5N*mm"=sqrt(("2.03E6N*mm"-"9.8E5N*mm")^2-("9.8E5N*mm")^2)`

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Torsional Moment given Equivalent Bending Moment Solution

STEP 0: Pre-Calculation Summary

Formula Used

Torsional Moment in Shaft for MSST = sqrt((Equivalent Bending Moment from MSST-Bending Moment in Shaft for MSST)^2-Bending Moment in Shaft for MSST^2)
Mt_t = sqrt((Mb_eq-M_{b MSST})^2-M_{b MSST}^2)
This formula uses 1 Functions, 3 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Torsional Moment in Shaft for MSST - (Measured in Newton Meter) - Torsional Moment in Shaft for MSST is the reaction induced in a structural shaft element when an external force or moment is applied to the element, causing the element to twist.
Equivalent Bending Moment from MSST - (Measured in Newton Meter) - Equivalent Bending Moment from MSST is the bending moment that, acting alone, would produce in a circular shaft and is calculated from Max shear stress theory.
Bending Moment in Shaft for MSST - (Measured in Newton Meter) - Bending Moment in Shaft for MSST is the reaction induced in a structural shaft element when an external force or moment is applied to the element, causing the element to bend.

STEP 1: Convert Input(s) to Base Unit

Equivalent Bending Moment from MSST: 2030000 Newton Millimeter --> 2030 Newton Meter (Check conversion here)
Bending Moment in Shaft for MSST: 980000 Newton Millimeter --> 980 Newton Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Mt_t = sqrt((Mb_eq-M_{b MSST})^2-M_{b MSST}^2) --> sqrt((2030-980)^2-980^2)

Evaluating ... ...

Mt_t = 376.961536499415

STEP 3: Convert Result to Output's Unit

376.961536499415 Newton Meter -->376961.536499415 Newton Millimeter (Check conversion here)

FINAL ANSWER

376961.536499415 ≈ 376961.5 Newton Millimeter <-- Torsional Moment in Shaft for MSST

(Calculation completed in 00.004 seconds)

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< 17 Maximum Shear Stress and Principal Stress Theory Calculators

Factor of Safety for Tri-axial State of Stress

Go Factor of Safety = Tensile Yield Strength/sqrt(1/2*((Normal Stress 1-Normal Stress 2)^2+(Normal Stress 2-Normal Stress 3)^2+(Normal Stress 3-Normal Stress 1)^2))

Diameter of Shaft given Permissible Value of Maximum Principle Stress

Go Diameter of Shaft from MPST = (16/(pi*Maximum Principle Stress in Shaft)*(Bending Moment in Shaft+sqrt(Bending Moment in Shaft^2+Torsional Moment in Shaft^2)))^(1/3)

Permissible Value of Maximum Principle Stress

Go Maximum Principle Stress in Shaft = 16/(pi*Diameter of Shaft from MPST^3)*(Bending Moment in Shaft+sqrt(Bending Moment in Shaft^2+Torsional Moment in Shaft^2))

Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory

Go Diameter of Shaft from MSST = (16/(pi*Maximum Shear Stress in Shaft from MSST)*sqrt(Bending Moment in Shaft for MSST^2+Torsional Moment in Shaft for MSST^2))^(1/3)

Bending Moment given Maximum Shear Stress

Go Bending Moment in Shaft for MSST = sqrt((Maximum Shear Stress in Shaft from MSST/(16/(pi*Diameter of Shaft from MSST^3)))^2-Torsional Moment in Shaft for MSST^2)

Torsional Moment given Maximum Shear Stress

Go Torsional Moment in Shaft for MSST = sqrt((pi*Diameter of Shaft from MSST^3*Maximum Shear Stress in Shaft from MSST/16)^2-Bending Moment in Shaft for MSST^2)

Maximum Shear Stress in Shafts

Go Maximum Shear Stress in Shaft from MSST = 16/(pi*Diameter of Shaft from MSST^3)*sqrt(Bending Moment in Shaft for MSST^2+Torsional Moment in Shaft for MSST^2)

Factor of Safety for Bi-Axial State of Stress

Go Factor of Safety = Tensile Yield Strength/(sqrt(Normal Stress 1^2+Normal Stress 2^2-Normal Stress 1*Normal Stress 2))

Torsional Moment given Equivalent Bending Moment

Go Torsional Moment in Shaft for MSST = sqrt((Equivalent Bending Moment from MSST-Bending Moment in Shaft for MSST)^2-Bending Moment in Shaft for MSST^2)

Equivalent Bending Moment given Torsional Moment

Go Equivalent Bending Moment from MSST = Bending Moment in Shaft for MSST+sqrt(Bending Moment in Shaft for MSST^2+Torsional Moment in Shaft for MSST^2)

Factor of Safety given Permissible Value of Maximum Shear Stress

Go Factor of Safety of Shaft = 0.5*Yield Strength in Shaft from MSST/Maximum Shear Stress in Shaft from MSST

Yield Strength in Shear Maximum Shear Stress Theory

Go Shear Yield Strength in Shaft from MSST = 0.5*Factor of Safety of Shaft*Maximum Principle Stress in Shaft

Permissible Value of Maximum Shear Stress

Go Maximum Shear Stress in Shaft from MSST = 0.5*Yield Strength in Shaft from MSST/Factor of Safety of Shaft

Yield Stress in Shear given Permissible Value of Maximum Principle Stress

Go Yield Strength in Shaft from MPST = Maximum Principle Stress in Shaft*Factor of Safety of Shaft

Permissible Value of Maximum Principle Stress using Factor of Safety

Go Maximum Principle Stress in Shaft = Yield Strength in Shaft from MPST/Factor of Safety of Shaft

Factor of Safety given Permissible Value of Maximum Principle Stress

Go Factor of Safety of Shaft = Yield Strength in Shaft from MPST/Maximum Principle Stress in Shaft

Factor of Safety given Ultimate Stress and Working Stress

Go Factor of Safety = Fracture Stress/Working Stress

Torsional Moment given Equivalent Bending Moment Formula

Torsional Moment in Shaft for MSST = sqrt((Equivalent Bending Moment from MSST-Bending Moment in Shaft for MSST)^2-Bending Moment in Shaft for MSST^2)
Mt_t = sqrt((Mb_eq-M_{b MSST})^2-M_{b MSST}^2)

Define Torsion

In the field of solid mechanics, torsion is the twisting of an object due to an applied torque. Torsion is expressed in either the Pascal (Pa), an SI unit for newtons per square metre, or in pounds per square inch (psi) while torque is expressed in newton metres (N·m) or foot-pound force (ft·lbf). In sections perpendicular to the torque axis, the resultant shear stress in this section is perpendicular to the radius.

How to Calculate Torsional Moment given Equivalent Bending Moment?

Torsional Moment given Equivalent Bending Moment calculator uses Torsional Moment in Shaft for MSST = sqrt((Equivalent Bending Moment from MSST-Bending Moment in Shaft for MSST)^2-Bending Moment in Shaft for MSST^2) to calculate the Torsional Moment in Shaft for MSST, The Torsional Moment given Equivalent Bending Moment formula is defined as the twisting of a part by application of equal and opposite torques. The condition of twist and shear stress produced by a torque on a part or component. Torsional Moment in Shaft for MSST is denoted by Mt_t symbol.

How to calculate Torsional Moment given Equivalent Bending Moment using this online calculator? To use this online calculator for Torsional Moment given Equivalent Bending Moment, enter Equivalent Bending Moment from MSST (Mb_eq) & Bending Moment in Shaft for MSST (M_{b MSST}) and hit the calculate button. Here is how the Torsional Moment given Equivalent Bending Moment calculation can be explained with given input values -> 3.8E+8 = sqrt((2030-980)^2-980^2).

FAQ

What is Torsional Moment given Equivalent Bending Moment?

The Torsional Moment given Equivalent Bending Moment formula is defined as the twisting of a part by application of equal and opposite torques. The condition of twist and shear stress produced by a torque on a part or component and is represented as Mt_t = sqrt((Mb_eq-M_{b MSST})^2-M_{b MSST}^2) or Torsional Moment in Shaft for MSST = sqrt((Equivalent Bending Moment from MSST-Bending Moment in Shaft for MSST)^2-Bending Moment in Shaft for MSST^2). Equivalent Bending Moment from MSST is the bending moment that, acting alone, would produce in a circular shaft and is calculated from Max shear stress theory & Bending Moment in Shaft for MSST is the reaction induced in a structural shaft element when an external force or moment is applied to the element, causing the element to bend.

How to calculate Torsional Moment given Equivalent Bending Moment?

The Torsional Moment given Equivalent Bending Moment formula is defined as the twisting of a part by application of equal and opposite torques. The condition of twist and shear stress produced by a torque on a part or component is calculated using Torsional Moment in Shaft for MSST = sqrt((Equivalent Bending Moment from MSST-Bending Moment in Shaft for MSST)^2-Bending Moment in Shaft for MSST^2). To calculate Torsional Moment given Equivalent Bending Moment, you need Equivalent Bending Moment from MSST (Mb_eq) & Bending Moment in Shaft for MSST (M_{b MSST}). With our tool, you need to enter the respective value for Equivalent Bending Moment from MSST & Bending Moment in Shaft for MSST 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 Torsional Moment in Shaft for MSST?

In this formula, Torsional Moment in Shaft for MSST uses Equivalent Bending Moment from MSST & Bending Moment in Shaft for MSST. We can use 1 other way(s) to calculate the same, which is/are as follows -

Torsional Moment in Shaft for MSST = sqrt((pi*Diameter of Shaft from MSST^3*Maximum Shear Stress in Shaft from MSST/16)^2-Bending Moment in Shaft for MSST^2)

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