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Total Turning Moment on Hollow Circular Shaft given Diameter of Shaft Formula

GoTotal Turning Moment on Hollow Circular Shaft given Radius of Shaft Formula

GoTurning Moment on Elementary Ring Formula

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The Turning Moment is the measure of the rotational force transmitted by a hollow circular shaft, essential for understanding its performance in mechanical systems. Check FAQs

T = \frac{π \cdot 𝜏 m \cdot (({d o}^{4}) - ({d i}^{4}))}{16 \cdot d o}

T - Turning Moment?𝜏_m - Maximum Shear Stress on Shaft?d_o - Outer Diameter of Shaft?d_i - Inner Diameter of Shaft?π - Archimedes' constant?

Total Turning Moment on Hollow Circular Shaft given Diameter of Shaft Example

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Here is how the Total Turning Moment on Hollow Circular Shaft given Diameter of Shaft equation looks like with Values.

Here is how the Total Turning Moment on Hollow Circular Shaft given Diameter of Shaft equation looks like with Units.

Here is how the Total Turning Moment on Hollow Circular Shaft given Diameter of Shaft equation looks like.

-6.6E-6 = \frac{3.1416 \cdot 3.2E-7 \cdot ((14^{4}) - (35^{4}))}{16 \cdot 14}

-6.6E-6N*m = \frac{3.1416 \cdot 3.2E-7MPa \cdot (({14mm}^{4}) - ({35mm}^{4}))}{16 \cdot 14mm}

-6.6E-6 = \frac{3.1416 \cdot 3.2E-7 \cdot ((14^{4}) - (35^{4}))}{16 \cdot 14}

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Total Turning Moment on Hollow Circular Shaft given Diameter of Shaft Solution

Follow our step by step solution on how to calculate Total Turning Moment on Hollow Circular Shaft given Diameter of Shaft?

FIRST Step Consider the formula

T = \frac{π \cdot 𝜏 m \cdot (({d o}^{4}) - ({d i}^{4}))}{16 \cdot d o}

Next Step Substitute values of Variables

∴

T = \frac{π \cdot 3.2E-7MPa \cdot (({14mm}^{4}) - ({35mm}^{4}))}{16 \cdot 14mm}

Next Step Substitute values of Constants

∴

T = \frac{3.1416 \cdot 3.2E-7MPa \cdot (({14mm}^{4}) - ({35mm}^{4}))}{16 \cdot 14mm}

Next Step Convert Units

∴

T = \frac{3.1416 \cdot 0.32Pa \cdot (({0.014m}^{4}) - ({0.035m}^{4}))}{16 \cdot 0.014m}

Next Step Prepare to Evaluate

∴

T = \frac{3.1416 \cdot 0.32 \cdot (({0.014}^{4}) - ({0.035}^{4}))}{16 \cdot 0.014}

Next Step Evaluate

∴

T = -6.56237864630412E-06N*m

LAST Step Rounding Answer

∴

T = -6.6E-6N*m

Total Turning Moment on Hollow Circular Shaft given Diameter of Shaft Formula Elements

Variables

Constants

Turning Moment

The Turning Moment is the measure of the rotational force transmitted by a hollow circular shaft, essential for understanding its performance in mechanical systems.

Symbol: T

Measurement: TorqueUnit: N*m

Note: Value should be greater than 0.

Formulas to find Turning Moment

Maximum Shear Stress on Shaft

Maximum Shear Stress on Shaft that acts coplanar with a cross-section of material arises due to shear forces.

Symbol: 𝜏_m

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Maximum Shear Stress on Shaft

Outer Diameter of Shaft

The Outer Diameter of Shaft is the measurement across the widest part of a hollow circular shaft, influencing its strength and torque transmission capabilities.

Symbol: d_o

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Outer Diameter of Shaft

Inner Diameter of Shaft

The Inner Diameter of Shaft is the measurement of the internal width of a hollow shaft, crucial for determining its torque transmission capacity.

Symbol: d_i

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Inner Diameter of Shaft

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Turning Moment

Go Total Turning Moment on Hollow Circular Shaft given Radius of Shaft

T = \frac{π \cdot 𝜏 m \cdot (({r h}^{4}) - ({r i}^{4}))}{2 \cdot r h}

Go Turning Moment on Elementary Ring

T = \frac{4 \cdot π \cdot 𝜏 s \cdot (r^{3}) \cdot b r}{d o}

Other formulas in Torque Transmitted by a Hollow Circular Shaft category

Go Maximum Shear Stress at Outer Surface given Diameter of Shaft on Hollow Circular Shaft

𝜏 m = \frac{16 \cdot d o \cdot T}{π \cdot ({d o}^{4} - {d i}^{4})}

Go Maximum Shear Stress at Outer Surface given Total Turning Moment on Hollow Circular Shaft

𝜏 m = \frac{T \cdot 2 \cdot r h}{π \cdot ({r h}^{4} - {r i}^{4})}

Go Outer Radius of Shaft using Turning Force on Elementary Ring given Turning Moment

r o = \frac{2 \cdot π \cdot 𝜏 s \cdot (r^{2}) \cdot b r}{T}

Go Maximum Shear Stress Induced at Outer Surface given Turning Moment on Elementary Ring

𝜏 s = \frac{T \cdot d o}{4 \cdot π \cdot (r^{3}) \cdot b r}

How to Evaluate Total Turning Moment on Hollow Circular Shaft given Diameter of Shaft?

Total Turning Moment on Hollow Circular Shaft given Diameter of Shaft evaluator uses Turning Moment = (pi*Maximum Shear Stress on Shaft*((Outer Diameter of Shaft^4)-(Inner Diameter of Shaft^4)))/(16*Outer Diameter of Shaft) to evaluate the Turning Moment, Total Turning Moment on Hollow Circular Shaft given Diameter of Shaft formula is defined as a measure of the torque transmitted by a hollow circular shaft based on its outer and inner diameters. This formula helps in understanding the mechanical performance and strength of the shaft under load. Turning Moment is denoted by T symbol.

How to evaluate Total Turning Moment on Hollow Circular Shaft given Diameter of Shaft using this online evaluator? To use this online evaluator for Total Turning Moment on Hollow Circular Shaft given Diameter of Shaft, enter Maximum Shear Stress on Shaft (𝜏_m), Outer Diameter of Shaft (d_o) & Inner Diameter of Shaft (d_i) and hit the calculate button.

FAQs on Total Turning Moment on Hollow Circular Shaft given Diameter of Shaft

What is the formula to find Total Turning Moment on Hollow Circular Shaft given Diameter of Shaft?

The formula of Total Turning Moment on Hollow Circular Shaft given Diameter of Shaft is expressed as Turning Moment = (pi*Maximum Shear Stress on Shaft*((Outer Diameter of Shaft^4)-(Inner Diameter of Shaft^4)))/(16*Outer Diameter of Shaft). Here is an example- -6.6E-6 = (pi*0.32*((0.014^4)-(0.035^4)))/(16*0.014).

How to calculate Total Turning Moment on Hollow Circular Shaft given Diameter of Shaft?

With Maximum Shear Stress on Shaft (𝜏_m), Outer Diameter of Shaft (d_o) & Inner Diameter of Shaft (d_i) we can find Total Turning Moment on Hollow Circular Shaft given Diameter of Shaft using the formula - Turning Moment = (pi*Maximum Shear Stress on Shaft*((Outer Diameter of Shaft^4)-(Inner Diameter of Shaft^4)))/(16*Outer Diameter of Shaft). This formula also uses Archimedes' constant .

What are the other ways to Calculate Turning Moment?

Here are the different ways to Calculate Turning Moment-

Turning Moment=(pi*Maximum Shear Stress on Shaft*((Outer Radius Of Hollow circular Cylinder^4)-(Inner Radius Of Hollow Circular Cylinder^4)))/(2*Outer Radius Of Hollow circular Cylinder)
Turning Moment=(4*pi*Maximum Shear Stress*(Radius of Elementary Circular Ring^3)*Thickness of Ring)/Outer Diameter of Shaft

Can the Total Turning Moment on Hollow Circular Shaft given Diameter of Shaft be negative?

No, the Total Turning Moment on Hollow Circular Shaft given Diameter of Shaft, measured in Torque cannot be negative.

Which unit is used to measure Total Turning Moment on Hollow Circular Shaft given Diameter of Shaft?

Total Turning Moment on Hollow Circular Shaft given Diameter of Shaft is usually measured using the Newton Meter[N*m] for Torque. Newton Centimeter[N*m], Newton Millimeter[N*m], Kilonewton Meter[N*m] are the few other units in which Total Turning Moment on Hollow Circular Shaft given Diameter of Shaft can be measured.

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