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Equivalent Torsional Moment when Shaft is Subjected to Fluctuating Loads Formula

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Equivalent Torsion Moment For Fluctuating Load is the bending moment which, if acting alone in the fluctuating load manner, would produce in a circular shaft the shear stress. Check FAQs

M t = \sqrt{{(M' s \cdot k t')}^{2} + {(k b' \cdot M s)}^{2}}

M_t - Equivalent Torsion Moment For Fluctuating Load?M'_s - Torsional Moment in Shaft?k_t' - Combined Shock Fatigue Factor of Torsion Moment?k_b' - Combined Shock Fatigue Factor of Bending Moment?M_s - Bending Moment in Shaft?

Equivalent Torsional Moment when Shaft is Subjected to Fluctuating Loads Example

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Here is how the Equivalent Torsional Moment when Shaft is Subjected to Fluctuating Loads equation looks like with Values.

Here is how the Equivalent Torsional Moment when Shaft is Subjected to Fluctuating Loads equation looks like with Units.

Here is how the Equivalent Torsional Moment when Shaft is Subjected to Fluctuating Loads equation looks like.

3.3E+6 = \sqrt{{(330000 \cdot 1.3)}^{2} + {(1.8 \cdot 1.8E+6)}^{2}}

3.3E+6N*mm = \sqrt{{(330000N*mm \cdot 1.3)}^{2} + {(1.8 \cdot 1.8E+6N*mm)}^{2}}

3.3E+6 = \sqrt{{(330000 \cdot 1.3)}^{2} + {(1.8 \cdot 1.8E+6)}^{2}}

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Equivalent Torsional Moment when Shaft is Subjected to Fluctuating Loads Solution

Follow our step by step solution on how to calculate Equivalent Torsional Moment when Shaft is Subjected to Fluctuating Loads?

FIRST Step Consider the formula

M t = \sqrt{{(M' s \cdot k t')}^{2} + {(k b' \cdot M s)}^{2}}

Next Step Substitute values of Variables

∴

M t = \sqrt{{(330000N*mm \cdot 1.3)}^{2} + {(1.8 \cdot 1.8E+6N*mm)}^{2}}

Next Step Convert Units

∴

M t = \sqrt{{(330N*m \cdot 1.3)}^{2} + {(1.8 \cdot 1800N*m)}^{2}}

Next Step Prepare to Evaluate

∴

M t = \sqrt{{(330 \cdot 1.3)}^{2} + {(1.8 \cdot 1800)}^{2}}

Next Step Evaluate

∴

M t = 3268.27798695276N*m

Next Step Convert to Output's Unit

∴

M t = 3268277.98695276N*mm

LAST Step Rounding Answer

∴

M t = 3.3E+6N*mm

Equivalent Torsional Moment when Shaft is Subjected to Fluctuating Loads Formula Elements

Variables

Functions

Equivalent Torsion Moment For Fluctuating Load

Equivalent Torsion Moment For Fluctuating Load is the bending moment which, if acting alone in the fluctuating load manner, would produce in a circular shaft the shear stress.

Symbol: M_t

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Equivalent Torsion Moment For Fluctuating Load

Torsional Moment in Shaft

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.

Symbol: M'_s

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Torsional Moment in Shaft

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.

Symbol: k_t'

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Combined Shock Fatigue Factor of Torsion Moment

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.

Symbol: k_b'

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Combined Shock Fatigue Factor of Bending Moment

Bending Moment in Shaft

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.

Symbol: M_s

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Bending Moment in Shaft

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.

Syntax: sqrt(Number)

Other formulas in ASME Code for Shaft Desgin category

Go Principle Shear Stress Maximum Shear Stress Theory of Failure

𝜏' max = \frac{16}{π \cdot {d'}^{3}} \cdot \sqrt{{(M' s \cdot k t')}^{2} + {(k b' \cdot M s)}^{2}}

Go Diameter of Shaft given Principle Shear Stress

d' = {(\frac{16}{π \cdot 𝜏' max} \cdot \sqrt{{(M' s \cdot k t')}^{2} + {(k b' \cdot M s)}^{2}})}^{\frac{1}{3}}

Go Equivalent Bending Moment when Shaft is Subjected to Fluctuating Loads

M f = k b' \cdot M s + \sqrt{{(M' s \cdot k t')}^{2} + {(k b' \cdot M s)}^{2}}

Go Design of Shaft using ASME Code

𝜏 max = \frac{16 \cdot \sqrt{{(k b \cdot M b)}^{2} + {(k t \cdot M t')}^{2}}}{π \cdot {d s}^{3}}

How to Evaluate Equivalent Torsional Moment when Shaft is Subjected to Fluctuating Loads?

Equivalent Torsional Moment when Shaft is Subjected to Fluctuating Loads evaluator uses 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) to evaluate the Equivalent Torsion Moment For Fluctuating Load, Equivalent Torsional Moment when Shaft is Subjected to Fluctuating Loads formula is defined as a measure of the total torsional moment that a shaft is subjected to when it is under fluctuating loads, taking into account the shaft's torsional moment and the bending moment of the bearing. Equivalent Torsion Moment For Fluctuating Load is denoted by M_t symbol.

How to evaluate Equivalent Torsional Moment when Shaft is Subjected to Fluctuating Loads using this online evaluator? To use this online evaluator for Equivalent Torsional Moment when Shaft is Subjected to Fluctuating Loads, enter Torsional Moment in Shaft (M'_s), Combined Shock Fatigue Factor of Torsion Moment (k_t'), Combined Shock Fatigue Factor of Bending Moment (k_b') & Bending Moment in Shaft (M_s) and hit the calculate button.

FAQs on Equivalent Torsional Moment when Shaft is Subjected to Fluctuating Loads

What is the formula to find Equivalent Torsional Moment when Shaft is Subjected to Fluctuating Loads?

The formula of Equivalent Torsional Moment when Shaft is Subjected to Fluctuating Loads is expressed as 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). Here is an example- 3.3E+9 = sqrt((330*1.3)^2+(1.8*1800)^2).

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

With Torsional Moment in Shaft (M'_s), Combined Shock Fatigue Factor of Torsion Moment (k_t'), Combined Shock Fatigue Factor of Bending Moment (k_b') & Bending Moment in Shaft (M_s) we can find Equivalent Torsional Moment when Shaft is Subjected to Fluctuating Loads using the formula - 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). This formula also uses Square Root (sqrt) function(s).

Can the Equivalent Torsional Moment when Shaft is Subjected to Fluctuating Loads be negative?

No, the Equivalent Torsional Moment when Shaft is Subjected to Fluctuating Loads, measured in Torque cannot be negative.

Which unit is used to measure Equivalent Torsional Moment when Shaft is Subjected to Fluctuating Loads?

Equivalent Torsional Moment when Shaft is Subjected to Fluctuating Loads is usually measured using the Newton Millimeter[N*mm] for Torque. Newton Meter[N*mm], Newton Centimeter[N*mm], Kilonewton Meter[N*mm] are the few other units in which Equivalent Torsional Moment when Shaft is Subjected to Fluctuating Loads can be measured.

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Equivalent Torsional Moment when Shaft is Subjected to Fluctuating Loads Formula

Equivalent Torsional Moment when Shaft is Subjected to Fluctuating Loads Example

Equivalent Torsional Moment when Shaft is Subjected to Fluctuating Loads Solution

Equivalent Torsional Moment when Shaft is Subjected to Fluctuating Loads Formula Elements

Other formulas in ASME Code for Shaft Desgin category

How to Evaluate Equivalent Torsional Moment when Shaft is Subjected to Fluctuating Loads?

FAQs on Equivalent Torsional Moment when Shaft is Subjected to Fluctuating Loads

Variable Name