Axial Load on Screw given Unit Bearing Pressure Calculator

✖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 Engaged Threads [z]			+10% -10%
✖Unit bearing pressure for nut is the average pressure acting on the contact surface of the thread in a Screw-Nut pair.ⓘ Unit bearing pressure for nut [S_b]			+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%
✖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.ⓘ Core diameter of screw [d_c]			+10% -10%

✖Axial load on screw is the instantaneous load applied to the screw along its axis.ⓘ Axial Load on Screw given Unit Bearing Pressure [W_a]

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Formula

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Axial Load on Screw given Unit Bearing Pressure

Formula

`"W"_{"a"} = pi*"z"*"S"_{"b"}*(("d"^2)-("d"_{"c"}^2))/4`

Example

`"129541.7N"=pi*"9"*"24.9N/mm²"*((("50mm")^2)-(("42mm")^2))/4`

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Axial Load on Screw given Unit Bearing Pressure Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
W_a = pi*z*S_b*((d^2)-(d_c^2))/4
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Axial load on screw - (Measured in Newton) - Axial load on screw is the instantaneous load applied to the screw along its axis.
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.
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

Number of Engaged Threads: 9 --> 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

W_a = pi*z*S_b*((d^2)-(d_c^2))/4 --> pi*9*24900000*((0.05^2)-(0.042^2))/4

Evaluating ... ...

W_a = 129541.688115183

STEP 3: Convert Result to Output's Unit

129541.688115183 Newton --> No Conversion Required

FINAL ANSWER

129541.688115183 ≈ 129541.7 Newton <-- Axial load on screw

(Calculation completed in 00.004 seconds)

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Home » Engineering » Mechanical » Machine Design » Power Screws » Design of Screw and Nut » Axial Load on Screw given Unit Bearing Pressure

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Created by Kumar Siddhant

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

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< 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

Axial Load on Screw given Unit Bearing Pressure Formula

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
W_a = pi*z*S_b*((d^2)-(d_c^2))/4

What is the Bearing Area for the Axial Load ?

The Bearing Area is the net effective area on which the Axial Load bears on. It's the projection of the Thread Contact Area in the Screw-Nut pair onto the head of the screw.Mathematically, it's defined as the difference between the Nominal and Core Area of the Screw.

How to Calculate Axial Load on Screw given Unit Bearing Pressure?

Axial Load on Screw given Unit Bearing Pressure calculator uses 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 to calculate the Axial load on screw, Axial Load on Screw given Unit Bearing Pressure is defined as any interaction that, when unopposed, will change the motion of a screw. It is a method to determine the maximum Axial Load a single engaged thread of Screw-Nut pair can support without failure. Axial load on screw is denoted by W_a symbol.

How to calculate Axial Load on Screw given Unit Bearing Pressure using this online calculator? To use this online calculator for Axial Load on Screw given Unit Bearing Pressure, enter Number of Engaged Threads (z), Unit bearing pressure for nut (S_b), Nominal diameter of screw (d) & Core diameter of screw (d_c) and hit the calculate button. Here is how the Axial Load on Screw given Unit Bearing Pressure calculation can be explained with given input values -> 129541.7 = pi*9*24900000*((0.05^2)-(0.042^2))/4.

FAQ

What is Axial Load on Screw given Unit Bearing Pressure?

Axial Load on Screw given Unit Bearing Pressure is defined as any interaction that, when unopposed, will change the motion of a screw. It is a method to determine the maximum Axial Load a single engaged thread of Screw-Nut pair can support without failure and is represented as W_a = pi*z*S_b*((d^2)-(d_c^2))/4 or 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. 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, 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 Axial Load on Screw given Unit Bearing Pressure?

Axial Load on Screw given Unit Bearing Pressure is defined as any interaction that, when unopposed, will change the motion of a screw. It is a method to determine the maximum Axial Load a single engaged thread of Screw-Nut pair can support without failure is calculated using 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. To calculate Axial Load on Screw given Unit Bearing Pressure, you need Number of Engaged Threads (z), Unit bearing pressure for nut (S_b), Nominal diameter of screw (d) & Core diameter of screw (d_c). With our tool, you need to enter the respective value for Number of Engaged Threads, 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 Axial load on screw?

In this formula, Axial load on screw uses Number of Engaged Threads, Unit bearing pressure for nut, Nominal diameter of screw & Core diameter of screw. We can use 3 other way(s) to calculate the same, which is/are as follows -

Axial load on screw = (Compressive stress in screw*pi*Core diameter of screw^2)/4
Axial load on screw = (Transverse Shear Stress in Screw*pi*Core diameter of screw*Thread Thickness*Number of Engaged Threads)
Axial load on screw = pi*Transverse shear stress in nut*Thread Thickness*Nominal diameter of screw*Number of Engaged Threads

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