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Number of Threads in Engagement with Nut given Unit Bearing Pressure Formula

GoNumber of Threads in Engagement with Nut given Transverse Shear Stress Formula

GoNumber of Threads in Engagement with Nut given Transverse Shear Stress at Root of Nut Formula

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A number of Engaged Threads of a screw/bolt are the count of threads of the screw/bolt that are currently in engagement with the nut. Check FAQs

z = 4 \cdot \frac{W a}{(π \cdot S b \cdot ((d^{2}) - ({d c}^{2})))}

z - Number of Engaged Threads?W_a - Axial load on screw?S_b - Unit bearing pressure for nut?d - Nominal diameter of screw?d_c - Core diameter of screw?π - Archimedes' constant?

Number of Threads in Engagement with Nut given Unit Bearing Pressure Example

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With units

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Here is how the Number of Threads in Engagement with Nut given Unit Bearing Pressure equation looks like with Values.

Here is how the Number of Threads in Engagement with Nut given Unit Bearing Pressure equation looks like with Units.

Here is how the Number of Threads in Engagement with Nut given Unit Bearing Pressure equation looks like.

9.1013 = 4 \cdot \frac{131000}{(3.1416 \cdot 24.9 \cdot ((50^{2}) - (42^{2})))}

9.1013 = 4 \cdot \frac{131000N}{(3.1416 \cdot 24.9N/mm² \cdot (({50mm}^{2}) - ({42mm}^{2})))}

9.1013 = 4 \cdot \frac{131000}{(3.1416 \cdot 24.9 \cdot ((50^{2}) - (42^{2})))}

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Number of Threads in Engagement with Nut given Unit Bearing Pressure Solution

Follow our step by step solution on how to calculate Number of Threads in Engagement with Nut given Unit Bearing Pressure?

FIRST Step Consider the formula

z = 4 \cdot \frac{W a}{(π \cdot S b \cdot ((d^{2}) - ({d c}^{2})))}

Next Step Substitute values of Variables

∴

z = 4 \cdot \frac{131000N}{(π \cdot 24.9N/mm² \cdot (({50mm}^{2}) - ({42mm}^{2})))}

Next Step Substitute values of Constants

∴

z = 4 \cdot \frac{131000N}{(3.1416 \cdot 24.9N/mm² \cdot (({50mm}^{2}) - ({42mm}^{2})))}

Next Step Convert Units

∴

z = 4 \cdot \frac{131000N}{(3.1416 \cdot 2.5E+7Pa \cdot (({0.05m}^{2}) - ({0.042m}^{2})))}

Next Step Prepare to Evaluate

∴

z = 4 \cdot \frac{131000}{(3.1416 \cdot 2.5E+7 \cdot (({0.05}^{2}) - ({0.042}^{2})))}

Next Step Evaluate

∴

z = 9.10131724508394

LAST Step Rounding Answer

∴

z = 9.1013

Number of Threads in Engagement with Nut given Unit Bearing Pressure Formula Elements

Variables

Constants

Number of Engaged Threads

A number of Engaged Threads of a screw/bolt are the count of threads of the screw/bolt that are currently in engagement with the nut.

Symbol: z

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Engaged Threads

Axial load on screw

Axial load on screw is the instantaneous load applied to the screw along its axis.

Symbol: W_a

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Axial load on screw

Unit bearing pressure for nut

Unit bearing pressure for nut is the average pressure acting on the contact surface of the thread in a Screw-Nut pair.

Symbol: S_b

Measurement: PressureUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Unit bearing pressure for nut

Nominal diameter of screw

Nominal diameter of screw is defined as the diameter of the cylinder touching the external threads of the screw.

Symbol: d

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Nominal diameter of screw

Core diameter of screw

Core diameter of screw is defined as the smallest diameter of the thread of the screw or nut. The term “minor diameter” replaces the term “core diameter” as applied to the thread of a screw.

Symbol: d_c

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Core diameter of screw

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 Number of Engaged Threads

Go Number of Threads in Engagement with Nut given Transverse Shear Stress

z = \frac{W a}{π \cdot t \cdot τ s \cdot d c}

Go Number of Threads in Engagement with Nut given Transverse Shear Stress at Root of Nut

z = \frac{W a}{π \cdot d \cdot t n \cdot t}

Other formulas in Design of Screw and Nut category

Go Core Diameter of Power Screw

d c = d - p

Go Nominal Diameter of Power Screw

d = d c + p

Go Pitch of Power Screw

p = d - d c

Go Mean Diameter of Power Screw

d m = d - 0.5 \cdot p

How to Evaluate Number of Threads in Engagement with Nut given Unit Bearing Pressure?

Number of Threads in Engagement with Nut given Unit Bearing Pressure evaluator uses Number of Engaged Threads = 4*Axial load on screw/((pi*Unit bearing pressure for nut*((Nominal diameter of screw^2)-(Core diameter of screw^2)))) to evaluate the Number of Engaged Threads, The Number of Threads in Engagement with Nut given Unit Bearing Pressure refers to the minimum number of engaged threads required to support the Axial Load when the specification and properties of the material are known. Number of Engaged Threads is denoted by z symbol.

How to evaluate Number of Threads in Engagement with Nut given Unit Bearing Pressure using this online evaluator? To use this online evaluator for Number of Threads in Engagement with Nut given Unit Bearing Pressure, enter Axial load on screw (W_a), Unit bearing pressure for nut (S_b), Nominal diameter of screw (d) & Core diameter of screw (d_c) and hit the calculate button.

FAQs on Number of Threads in Engagement with Nut given Unit Bearing Pressure

What is the formula to find Number of Threads in Engagement with Nut given Unit Bearing Pressure?

The formula of Number of Threads in Engagement with Nut given Unit Bearing Pressure is expressed as Number of Engaged Threads = 4*Axial load on screw/((pi*Unit bearing pressure for nut*((Nominal diameter of screw^2)-(Core diameter of screw^2)))). Here is an example- 9.101317 = 4*131000/((pi*24900000*((0.05^2)-(0.042^2)))).

How to calculate Number of Threads in Engagement with Nut given Unit Bearing Pressure?

With Axial load on screw (W_a), Unit bearing pressure for nut (S_b), Nominal diameter of screw (d) & Core diameter of screw (d_c) we can find Number of Threads in Engagement with Nut given Unit Bearing Pressure using the formula - Number of Engaged Threads = 4*Axial load on screw/((pi*Unit bearing pressure for nut*((Nominal diameter of screw^2)-(Core diameter of screw^2)))). This formula also uses Archimedes' constant .

What are the other ways to Calculate Number of Engaged Threads?

Here are the different ways to Calculate Number of Engaged Threads-

Number of Engaged Threads=Axial load on screw/(pi*Thread Thickness*Transverse Shear Stress in Screw*Core diameter of screw)
Number of Engaged Threads=Axial load on screw/(pi*Nominal diameter of screw*Transverse shear stress in nut*Thread Thickness)

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Number of Threads in Engagement with Nut given Unit Bearing Pressure Formula

​GoNumber of Threads in Engagement with Nut given Transverse Shear Stress Formula

​GoNumber of Threads in Engagement with Nut given Transverse Shear Stress at Root of Nut Formula

Number of Threads in Engagement with Nut given Unit Bearing Pressure Example

Number of Threads in Engagement with Nut given Unit Bearing Pressure Solution

Number of Threads in Engagement with Nut given Unit Bearing Pressure Formula Elements

Other Formulas to find Number of Engaged Threads

Other formulas in Design of Screw and Nut category

How to Evaluate Number of Threads in Engagement with Nut given Unit Bearing Pressure?

FAQs on Number of Threads in Engagement with Nut given Unit Bearing Pressure

Variable Name

GoNumber of Threads in Engagement with Nut given Transverse Shear Stress Formula

GoNumber of Threads in Engagement with Nut given Transverse Shear Stress at Root of Nut Formula