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

✖Axial load on screw is the instantaneous load applied to the screw along its axis.ⓘ Axial load on screw [W_a]			+10% -10%
✖Nominal diameter of screw is defined as the diameter of the cylinder touching the external threads of the screw.ⓘ Nominal diameter of screw [d]			+10% -10%
✖Transverse shear stress in nut is the resistance force developed per unit cross-sectional area by the nut to avoid transverse deformation.ⓘ Transverse shear stress in nut [t_n]			+10% -10%
✖Thread Thickness is defined as the thickness of a single thread.ⓘ Thread Thickness [t]			+10% -10%

✖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.ⓘ Number of Threads in Engagement with Nut given Transverse Shear Stress at Root of Nut [z]

⎘ Copy

👎

Formula

✖

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

Formula

`"z" = "W"_{"a"}/(pi*"d"*"t"_{"n"}*"t")`

Example

`"8.948196"="131000N"/(pi*"50mm"*"23.3N/mm²"*"4mm")`

Calculator

LaTeX

Reset

👍

Download Mechanical Formula PDF

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

STEP 0: Pre-Calculation Summary

Formula Used

Number of Engaged Threads = Axial load on screw/(pi*Nominal diameter of screw*Transverse shear stress in nut*Thread Thickness)
z = W_a/(pi*d*t_n*t)
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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.
Axial load on screw - (Measured in Newton) - Axial load on screw is the instantaneous load applied to the screw along its axis.
Nominal diameter of screw - (Measured in Meter) - Nominal diameter of screw is defined as the diameter of the cylinder touching the external threads of the screw.
Transverse shear stress in nut - (Measured in Pascal) - Transverse shear stress in nut is the resistance force developed per unit cross-sectional area by the nut to avoid transverse deformation.
Thread Thickness - (Measured in Meter) - Thread Thickness is defined as the thickness of a single thread.

STEP 1: Convert Input(s) to Base Unit

Axial load on screw: 131000 Newton --> 131000 Newton No Conversion Required
Nominal diameter of screw: 50 Millimeter --> 0.05 Meter (Check conversion here)
Transverse shear stress in nut: 23.3 Newton per Square Millimeter --> 23300000 Pascal (Check conversion here)
Thread Thickness: 4 Millimeter --> 0.004 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

z = W_a/(pi*d*t_n*t) --> 131000/(pi*0.05*23300000*0.004)

Evaluating ... ...

z = 8.94819637126107

STEP 3: Convert Result to Output's Unit

8.94819637126107 --> No Conversion Required

FINAL ANSWER

8.94819637126107 ≈ 8.948196 <-- Number of Engaged Threads

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Mechanical » Machine Design » Power Screws » Design of Screw and Nut » Number of Threads in Engagement with Nut given Transverse Shear Stress at Root of Nut

Credits

Created by Kumar Siddhant

Indian Institute of Information Technology, Design and Manufacturing (IIITDM), Jabalpur

Kumar Siddhant has created this Calculator and 400+ more calculators!

Verified by Kethavath Srinath

Osmania University (OU), Hyderabad

Kethavath Srinath has verified this Calculator and 1200+ more calculators!

< 25 Design of Screw and Nut Calculators

Nominal Diameter of Screw given Transverse Shear Stress at Root of Nut

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

Transverse Shear Stress at Root of Nut

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

Thread Thickness at Core Diameter of Screw given Transverse Shear Stress

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

Number of Threads in Engagement with Nut given Transverse Shear Stress

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

Core Diameter of Screw given Transverse Shear Stress in Screw

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

Axial Load on Screw given Transverse Shear Stress

Go Axial load on screw = (Transverse Shear Stress in Screw*pi*Core diameter of screw*Thread Thickness*Number of Engaged Threads)

Transverse Shear Stress in Screw

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

Axial Load on Screw given Transverse Shear Stress at Root of Nut

Go Axial load on screw = pi*Transverse shear stress in nut*Thread Thickness*Nominal diameter of screw*Number of Engaged Threads

Overall Efficiency of Power Screw

Go Efficiency of power screw = Axial load on screw*Lead of Power Screw/(2*pi*Torsional Moment on Screw)

Lead of Screw given Overall Efficiency

Go Lead of Power Screw = 2*pi*Efficiency of power screw*Torsional Moment on Screw/Axial load on screw

Core Diameter of Screw given Direct Compressive Stress

Go Core diameter of screw = sqrt((4*Axial load on screw)/(pi*Compressive stress in screw))

Helix Angle of Thread

Go Helix angle of screw = atan(Lead of Power Screw/(pi*Mean Diameter of Power Screw))

Mean diameter of Screw given Helix Angle

Go Mean Diameter of Power Screw = Lead of Power Screw/(pi*tan(Helix angle of screw))

Lead of Screw given Helix angle

Go Lead of Power Screw = tan(Helix angle of screw)*pi*Mean Diameter of Power Screw

Core Diameter of Screw given Torsional Shear Stress

Go Core diameter of screw = (16*Torsional Moment on Screw/(pi*Torsional shear stress in screw))^(1/3)

Torsional Shear Stress of Screw

Go Torsional shear stress in screw = 16*Torsional Moment on Screw/(pi*(Core diameter of screw^3))

Torsional Moment in Screw given Torsional Shear Stress

Go Torsional Moment on Screw = Torsional shear stress in screw*pi*(Core diameter of screw^3)/16

Direct Compressive Stress in Screw

Go Compressive stress in screw = (Axial load on screw*4)/(pi*Core diameter of screw^2)

Axial Load on Screw given Direct Compressive Stress

Go Axial load on screw = (Compressive stress in screw*pi*Core diameter of screw^2)/4

Nominal Diameter of Power Screw given Mean Diameter

Go Nominal diameter of screw = Mean Diameter of Power Screw+(0.5*Pitch of power screw thread)

Pitch of Screw given Mean Diameter

Go Pitch of power screw thread = (Nominal diameter of screw-Mean Diameter of Power Screw)/0.5

Mean Diameter of Power Screw

Go Mean Diameter of Power Screw = Nominal diameter of screw-0.5*Pitch of power screw thread

Nominal Diameter of Power Screw

Go Nominal diameter of screw = Core diameter of screw+Pitch of power screw thread

Core Diameter of Power Screw

Go Core diameter of screw = Nominal diameter of screw-Pitch of power screw thread

Pitch of Power Screw

Go Pitch of power screw thread = Nominal diameter of screw-Core diameter of screw

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

Number of Engaged Threads = Axial load on screw/(pi*Nominal diameter of screw*Transverse shear stress in nut*Thread Thickness)
z = W_a/(pi*d*t_n*t)

Length and Depth of Thread Engagement

The axial distance through which the fully formed threads of Nut are in contact is called the Length of Thread Engagement. The Depth of Thread Engagement is the distance the threads overlap in a radial direction.

How to Calculate Number of Threads in Engagement with Nut given Transverse Shear Stress at Root of Nut?

Number of Threads in Engagement with Nut given Transverse Shear Stress at Root of Nut calculator uses Number of Engaged Threads = Axial load on screw/(pi*Nominal diameter of screw*Transverse shear stress in nut*Thread Thickness) to calculate the Number of Engaged Threads, The Number of Threads in Engagement with Nut given Transverse Shear Stress at Root of Nut, is a way to determine the minimum number of Threads of Nut required to be in engagement with the Screw, in order to support the applied load. Number of Engaged Threads is denoted by z symbol.

How to calculate Number of Threads in Engagement with Nut given Transverse Shear Stress at Root of Nut using this online calculator? To use this online calculator for Number of Threads in Engagement with Nut given Transverse Shear Stress at Root of Nut, enter Axial load on screw (W_a), Nominal diameter of screw (d), Transverse shear stress in nut (t_n) & Thread Thickness (t) and hit the calculate button. Here is how the Number of Threads in Engagement with Nut given Transverse Shear Stress at Root of Nut calculation can be explained with given input values -> 8.948196 = 131000/(pi*0.05*23300000*0.004).

FAQ

What is Number of Threads in Engagement with Nut given Transverse Shear Stress at Root of Nut?

The Number of Threads in Engagement with Nut given Transverse Shear Stress at Root of Nut, is a way to determine the minimum number of Threads of Nut required to be in engagement with the Screw, in order to support the applied load and is represented as z = W_a/(pi*d*t_n*t) or Number of Engaged Threads = Axial load on screw/(pi*Nominal diameter of screw*Transverse shear stress in nut*Thread Thickness). Axial load on screw is the instantaneous load applied to the screw along its axis, Nominal diameter of screw is defined as the diameter of the cylinder touching the external threads of the screw, Transverse shear stress in nut is the resistance force developed per unit cross-sectional area by the nut to avoid transverse deformation & Thread Thickness is defined as the thickness of a single thread.

How to calculate Number of Threads in Engagement with Nut given Transverse Shear Stress at Root of Nut?

The Number of Threads in Engagement with Nut given Transverse Shear Stress at Root of Nut, is a way to determine the minimum number of Threads of Nut required to be in engagement with the Screw, in order to support the applied load is calculated using Number of Engaged Threads = Axial load on screw/(pi*Nominal diameter of screw*Transverse shear stress in nut*Thread Thickness). To calculate Number of Threads in Engagement with Nut given Transverse Shear Stress at Root of Nut, you need Axial load on screw (W_a), Nominal diameter of screw (d), Transverse shear stress in nut (t_n) & Thread Thickness (t). With our tool, you need to enter the respective value for Axial load on screw, Nominal diameter of screw, Transverse shear stress in nut & Thread Thickness and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Number of Engaged Threads?

In this formula, Number of Engaged Threads uses Axial load on screw, Nominal diameter of screw, Transverse shear stress in nut & Thread Thickness. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

Home

FREE PDFs

🔍 Search