Equivalent Bending Moment given Torsional Moment Calculator

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Design of Shafts

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Maximum Shear Stress and Principal Stress Theory

ASME Code for Shaft Desgin

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Shaft Design on Strength Basis

Torsional Rigidity

✖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 in Shaft for MSST [Mt_t]			+10% -10%

✖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 given Torsional Moment [Mb_eq]

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Formula

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Equivalent Bending Moment given Torsional Moment

Formula

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

Example

`"2E^6N*mm"="9.8E5N*mm"+sqrt(("9.8E5N*mm")^2+("3.87E5N*mm")^2)`

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Download Design of Automobile Elements Formula PDF

Equivalent Bending Moment given Torsional Moment Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
Mb_eq = M_{b MSST}+sqrt(M_{b MSST}^2+Mt_t^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

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.
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.

STEP 1: Convert Input(s) to Base Unit

Bending Moment in Shaft for MSST: 980000 Newton Millimeter --> 980 Newton Meter (Check conversion here)
Torsional Moment in Shaft for MSST: 387000 Newton Millimeter --> 387 Newton Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Mb_eq = M_{b MSST}+sqrt(M_{b MSST}^2+Mt_t^2) --> 980+sqrt(980^2+387^2)

Evaluating ... ...

Mb_eq = 2033.64557608334

STEP 3: Convert Result to Output's Unit

2033.64557608334 Newton Meter -->2033645.57608334 Newton Millimeter (Check conversion here)

FINAL ANSWER

2033645.57608334 ≈ 2E+6 Newton Millimeter <-- Equivalent Bending Moment from 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

Equivalent Bending Moment given Torsional Moment Formula

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)
Mb_eq = M_{b MSST}+sqrt(M_{b MSST}^2+Mt_t^2)

Define Bending Moment

In solid mechanics, a bending moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend. The most common or simplest structural element subjected to bending moments is the beam.

How to Calculate Equivalent Bending Moment given Torsional Moment?

Equivalent Bending Moment given Torsional Moment calculator uses 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) to calculate the Equivalent Bending Moment from MSST, Equivalent Bending Moment given Torsional Moment formula is defined as the term used to describe the moment a member experiences when the loads on the said member are forces. Equivalent Bending Moment from MSST is denoted by Mb_eq symbol.

How to calculate Equivalent Bending Moment given Torsional Moment using this online calculator? To use this online calculator for Equivalent Bending Moment given Torsional Moment, enter Bending Moment in Shaft for MSST (M_{b MSST}) & Torsional Moment in Shaft for MSST (Mt_t) and hit the calculate button. Here is how the Equivalent Bending Moment given Torsional Moment calculation can be explained with given input values -> 2E+9 = 980+sqrt(980^2+387^2).

FAQ

What is Equivalent Bending Moment given Torsional Moment?

Equivalent Bending Moment given Torsional Moment formula is defined as the term used to describe the moment a member experiences when the loads on the said member are forces and is represented as Mb_eq = M_{b MSST}+sqrt(M_{b MSST}^2+Mt_t^2) or 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). 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 & 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.

How to calculate Equivalent Bending Moment given Torsional Moment?

Equivalent Bending Moment given Torsional Moment formula is defined as the term used to describe the moment a member experiences when the loads on the said member are forces is calculated using 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). To calculate Equivalent Bending Moment given Torsional Moment, you need Bending Moment in Shaft for MSST (M_{b MSST}) & Torsional Moment in Shaft for MSST (Mt_t). With our tool, you need to enter the respective value for Bending Moment in Shaft for MSST & Torsional 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.

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