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

STEP 0: Pre-Calculation Summary
Formula Used
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))))
z = 4*Wa/((pi*Sb*((d^2)-(dc^2))))
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.
Unit bearing pressure for nut - (Measured in Pascal) - Unit bearing pressure for nut is the average pressure acting on the contact surface of the thread in a Screw-Nut pair.
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.
Core diameter of screw - (Measured in Meter) - 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.
STEP 1: Convert Input(s) to Base Unit
Axial load on screw: 131000 Newton --> 131000 Newton No Conversion Required
Unit bearing pressure for nut: 24.9 Newton per Square Millimeter --> 24900000 Pascal (Check conversion here)
Nominal diameter of screw: 50 Millimeter --> 0.05 Meter (Check conversion here)
Core diameter of screw: 42 Millimeter --> 0.042 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
z = 4*Wa/((pi*Sb*((d^2)-(dc^2)))) --> 4*131000/((pi*24900000*((0.05^2)-(0.042^2))))
Evaluating ... ...
z = 9.10131724508394
STEP 3: Convert Result to Output's Unit
9.10131724508394 --> No Conversion Required
FINAL ANSWER
9.10131724508394 9.101317 <-- Number of Engaged Threads
(Calculation completed in 00.020 seconds)

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25 Design of Screw and Nut Calculators

Nominal Diameter of Screw given Unit Bearing Pressure
Go Nominal diameter of screw = sqrt((4*Axial load on screw/(Unit bearing pressure for nut*pi*Number of Engaged Threads))+(Core diameter of screw)^2)
Core Diameter of Screw given Unit Bearing Pressure
Go Core diameter of screw = sqrt((Nominal diameter of screw)^2-(4*Axial load on screw/(Unit bearing pressure for nut*pi*Number of Engaged Threads)))
Number of Threads in Engagement with Nut given Unit Bearing Pressure
Go 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))))
Unit Bearing Pressure for Thread
Go Unit bearing pressure for nut = 4*Axial load on screw/(pi*Number of Engaged Threads*((Nominal diameter of screw^2)-(Core diameter of screw^2)))
Axial Load on Screw given Unit Bearing Pressure
Go Axial load on screw = pi*Number of Engaged Threads*Unit bearing pressure for nut*((Nominal diameter of screw^2)-(Core diameter of screw^2))/4
Number of Threads in Engagement with Nut given Transverse Shear Stress at Root of Nut
Go Number of Engaged Threads = Axial load on screw/(pi*Nominal diameter of screw*Transverse shear stress in nut*Thread Thickness)
Thread Thickness at Root of Nut given Transverse Shear Stress at Root of Nut
Go Thread Thickness = Axial load on screw/(pi*Nominal diameter of screw*Number of Engaged Threads*Transverse shear stress in nut)
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
Core Diameter of Screw given Direct Compressive Stress
Go Core diameter of screw = sqrt((4*Axial load on screw)/(pi*Compressive stress in screw))
Bearing Area between Screw and Nut for One Thread
Go Bearing area between screw and nut = pi*((Nominal diameter of screw^2)-(Core diameter of screw^2))/4
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
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 Unit Bearing Pressure 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))))
z = 4*Wa/((pi*Sb*((d^2)-(dc^2))))

Importance of Thread Engagement

Thread engagement is important because it directly relates to the integrity of the joint. For little engagement, the mode of failure may be the nut member stripping out or breaking of the externally threaded fastener (bolt or screw).
For high engagement, the torque needed to drive the screw rises leading to inadequate clamp load or even breaking fasteners during assembly.

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

Number of Threads in Engagement with Nut given Unit Bearing Pressure calculator 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 calculate 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 calculate Number of Threads in Engagement with Nut given Unit Bearing Pressure using this online calculator? To use this online calculator for Number of Threads in Engagement with Nut given Unit Bearing Pressure, enter Axial load on screw (Wa), Unit bearing pressure for nut (Sb), Nominal diameter of screw (d) & Core diameter of screw (dc) and hit the calculate button. Here is how the Number of Threads in Engagement with Nut given Unit Bearing Pressure calculation can be explained with given input values -> 9.101317 = 4*131000/((pi*24900000*((0.05^2)-(0.042^2)))).

FAQ

What is Number of Threads in Engagement with Nut given Unit Bearing Pressure?
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 and is represented as z = 4*Wa/((pi*Sb*((d^2)-(dc^2)))) or 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)))). Axial load on screw is the instantaneous load applied to the screw along its axis, Unit bearing pressure for nut is the average pressure acting on the contact surface of the thread in a Screw-Nut pair, Nominal diameter of screw is defined as the diameter of the cylinder touching the external threads of the 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.
How to calculate Number of Threads in Engagement with Nut given Unit Bearing Pressure?
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 is calculated using 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 calculate Number of Threads in Engagement with Nut given Unit Bearing Pressure, you need Axial load on screw (Wa), Unit bearing pressure for nut (Sb), Nominal diameter of screw (d) & Core diameter of screw (dc). With our tool, you need to enter the respective value for Axial load on screw, Unit bearing pressure for nut, Nominal diameter of screw & Core diameter of screw 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, Unit bearing pressure for nut, Nominal diameter of screw & Core diameter of screw. 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 = Axial load on screw/(pi*Nominal diameter of screw*Transverse shear stress in nut*Thread Thickness)
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