Equivalent Bending Moment when Shaft is Subjected to Fluctuating Loads Calculator

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Design of Shafts

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ASME Code for Shaft Desgin

Design of Hollow Shaft

Maximum Shear Stress and Principal Stress Theory

Shaft Design on Strength Basis

Torsional Rigidity

✖Combined Shock Fatigue Factor of Bending Moment is a factor accounting for the combined shock and fatigue load applied with bending moment.ⓘ Combined Shock Fatigue Factor of Bending Moment [k_b]			+10% -10%
✖Bending Moment in Shaft 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 [M_b]			+10% -10%
✖Torsional Moment in Shaft 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 [Mt_shaft]			+10% -10%
✖Combined Shock Fatigue Factor of Torsion Moment is a factor accounting for the combined shock and fatigue load applied with torsion moment.ⓘ Combined Shock Fatigue Factor of Torsion Moment [k_t]			+10% -10%

✖Equivalent Bending Moment for Fluctuating Load is the torsional moment which, if acting alone in the fluctuating load manner, would produce in a circular shaft the shear stress.ⓘ Equivalent Bending Moment when Shaft is Subjected to Fluctuating Loads [Mb_feq]

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Formula

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Equivalent Bending Moment when Shaft is Subjected to Fluctuating Loads

Formula

`"Mb"_{"feq"} = "k"_{"b"}*"M"_{"b"}+sqrt(("Mt"_{"shaft"}*"k"_{"t"})^2+("k"_{"b"}*"M"_{"b"})^2)`

Example

`"6.5E^6N*mm"="1.8"*"1.8E6N*mm"+sqrt(("3.3E5N*mm"*"1.3")^2+("1.8"*"1.8E6N*mm")^2)`

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Equivalent Bending Moment when Shaft is Subjected to Fluctuating Loads Solution

STEP 0: Pre-Calculation Summary

Formula Used

Equivalent Bending Moment for Fluctuating Load = Combined Shock Fatigue Factor of Bending Moment*Bending Moment in Shaft+sqrt((Torsional Moment in Shaft*Combined Shock Fatigue Factor of Torsion Moment)^2+(Combined Shock Fatigue Factor of Bending Moment*Bending Moment in Shaft)^2)
Mb_feq = k_b*M_b+sqrt((Mt_shaft*k_t)^2+(k_b*M_b)^2)
This formula uses 1 Functions, 5 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 for Fluctuating Load - (Measured in Newton Meter) - Equivalent Bending Moment for Fluctuating Load is the torsional moment which, if acting alone in the fluctuating load manner, would produce in a circular shaft the shear stress.
Combined Shock Fatigue Factor of Bending Moment - Combined Shock Fatigue Factor of Bending Moment is a factor accounting for the combined shock and fatigue load applied with bending moment.
Bending Moment in Shaft - (Measured in Newton Meter) - Bending Moment in Shaft 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 - (Measured in Newton Meter) - Torsional Moment in Shaft 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.
Combined Shock Fatigue Factor of Torsion Moment - Combined Shock Fatigue Factor of Torsion Moment is a factor accounting for the combined shock and fatigue load applied with torsion moment.

STEP 1: Convert Input(s) to Base Unit

Combined Shock Fatigue Factor of Bending Moment: 1.8 --> No Conversion Required
Bending Moment in Shaft: 1800000 Newton Millimeter --> 1800 Newton Meter (Check conversion here)
Torsional Moment in Shaft: 330000 Newton Millimeter --> 330 Newton Meter (Check conversion here)
Combined Shock Fatigue Factor of Torsion Moment: 1.3 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Mb_feq = k_b*M_b+sqrt((Mt_shaft*k_t)^2+(k_b*M_b)^2) --> 1.8*1800+sqrt((330*1.3)^2+(1.8*1800)^2)

Evaluating ... ...

Mb_feq = 6508.27798695276

STEP 3: Convert Result to Output's Unit

6508.27798695276 Newton Meter -->6508277.98695276 Newton Millimeter (Check conversion here)

FINAL ANSWER

6508277.98695276 ≈ 6.5E+6 Newton Millimeter <-- Equivalent Bending Moment for Fluctuating Load

(Calculation completed in 00.004 seconds)

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< 5 ASME Code for Shaft Desgin Calculators

Equivalent Bending Moment when Shaft is Subjected to Fluctuating Loads

Go Equivalent Bending Moment for Fluctuating Load = Combined Shock Fatigue Factor of Bending Moment*Bending Moment in Shaft+sqrt((Torsional Moment in Shaft*Combined Shock Fatigue Factor of Torsion Moment)^2+(Combined Shock Fatigue Factor of Bending Moment*Bending Moment in Shaft)^2)

Diameter of Shaft given Principle Shear Stress

Go Diameter of Shaft from ASME = (16/(pi*Maximum Shear Stress in Shaft from ASME)*sqrt((Torsional Moment in Shaft*Combined Shock Fatigue Factor of Torsion Moment)^2+(Combined Shock Fatigue Factor of Bending Moment*Bending Moment in Shaft)^2))^(1/3)

Principle Shear Stress Maximum Shear Stress Theory of Failure

Go Maximum Shear Stress in Shaft from ASME = 16/(pi*Diameter of Shaft from ASME^3)*sqrt((Torsional Moment in Shaft*Combined Shock Fatigue Factor of Torsion Moment)^2+(Combined Shock Fatigue Factor of Bending Moment*Bending Moment in Shaft)^2)

Design of Shaft using ASME Code

Go Maximum Shearing Stress = (16*sqrt((Combined Shock and Fatigue Factor to Bending*Bending Moment)^2+(Combined Shock and Fatigue Factor to Torsion*Torsional Moment)^2))/(pi*Diameter of Shaft^3)

Equivalent Torsional Moment when Shaft is Subjected to Fluctuating Loads

Go Equivalent Torsion Moment for Fluctuating Load = sqrt((Torsional Moment in Shaft*Combined Shock Fatigue Factor of Torsion Moment)^2+(Combined Shock Fatigue Factor of Bending Moment*Bending Moment in Shaft)^2)

Equivalent Bending Moment when Shaft is Subjected to Fluctuating Loads Formula

Define Equivalent Bending Moment

A bending moment which, acting alone, would produce in a circular shaft a normal stress of the same magnitude as the maximum normal stress produced by a given bending moment and a given twisting moment acting simultaneously.

How to Calculate Equivalent Bending Moment when Shaft is Subjected to Fluctuating Loads?

Equivalent Bending Moment when Shaft is Subjected to Fluctuating Loads calculator uses Equivalent Bending Moment for Fluctuating Load = Combined Shock Fatigue Factor of Bending Moment*Bending Moment in Shaft+sqrt((Torsional Moment in Shaft*Combined Shock Fatigue Factor of Torsion Moment)^2+(Combined Shock Fatigue Factor of Bending Moment*Bending Moment in Shaft)^2) to calculate the Equivalent Bending Moment for Fluctuating Load, The Equivalent Bending Moment when Shaft is Subjected to Fluctuating Loads formula is defined as a bending moment which, acting alone, would produce in a circular shaft a normal stress of the same magnitude as the maximum normal stress produced by a given bending moment and a given twisting moment acting simultaneously. Equivalent Bending Moment for Fluctuating Load is denoted by Mb_feq symbol.

How to calculate Equivalent Bending Moment when Shaft is Subjected to Fluctuating Loads using this online calculator? To use this online calculator for Equivalent Bending Moment when Shaft is Subjected to Fluctuating Loads, enter Combined Shock Fatigue Factor of Bending Moment (k_b), Bending Moment in Shaft (M_b), Torsional Moment in Shaft (Mt_shaft) & Combined Shock Fatigue Factor of Torsion Moment (k_t) and hit the calculate button. Here is how the Equivalent Bending Moment when Shaft is Subjected to Fluctuating Loads calculation can be explained with given input values -> 6.5E+9 = 1.8*1800+sqrt((330*1.3)^2+(1.8*1800)^2).

FAQ

What is Equivalent Bending Moment when Shaft is Subjected to Fluctuating Loads?

The Equivalent Bending Moment when Shaft is Subjected to Fluctuating Loads formula is defined as a bending moment which, acting alone, would produce in a circular shaft a normal stress of the same magnitude as the maximum normal stress produced by a given bending moment and a given twisting moment acting simultaneously and is represented as Mb_feq = k_b*M_b+sqrt((Mt_shaft*k_t)^2+(k_b*M_b)^2) or Equivalent Bending Moment for Fluctuating Load = Combined Shock Fatigue Factor of Bending Moment*Bending Moment in Shaft+sqrt((Torsional Moment in Shaft*Combined Shock Fatigue Factor of Torsion Moment)^2+(Combined Shock Fatigue Factor of Bending Moment*Bending Moment in Shaft)^2). Combined Shock Fatigue Factor of Bending Moment is a factor accounting for the combined shock and fatigue load applied with bending moment, Bending Moment in Shaft 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 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 & Combined Shock Fatigue Factor of Torsion Moment is a factor accounting for the combined shock and fatigue load applied with torsion moment.

How to calculate Equivalent Bending Moment when Shaft is Subjected to Fluctuating Loads?

The Equivalent Bending Moment when Shaft is Subjected to Fluctuating Loads formula is defined as a bending moment which, acting alone, would produce in a circular shaft a normal stress of the same magnitude as the maximum normal stress produced by a given bending moment and a given twisting moment acting simultaneously is calculated using Equivalent Bending Moment for Fluctuating Load = Combined Shock Fatigue Factor of Bending Moment*Bending Moment in Shaft+sqrt((Torsional Moment in Shaft*Combined Shock Fatigue Factor of Torsion Moment)^2+(Combined Shock Fatigue Factor of Bending Moment*Bending Moment in Shaft)^2). To calculate Equivalent Bending Moment when Shaft is Subjected to Fluctuating Loads, you need Combined Shock Fatigue Factor of Bending Moment (k_b), Bending Moment in Shaft (M_b), Torsional Moment in Shaft (Mt_shaft) & Combined Shock Fatigue Factor of Torsion Moment (k_t). With our tool, you need to enter the respective value for Combined Shock Fatigue Factor of Bending Moment, Bending Moment in Shaft, Torsional Moment in Shaft & Combined Shock Fatigue Factor of Torsion Moment 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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