Core Diameter of Screw given Unit Bearing Pressure Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)))
dc = sqrt((d)^2-(4*Wa/(Sb*pi*z)))
This formula uses 1 Constants, 1 Functions, 5 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
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.
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.
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.
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.
STEP 1: Convert Input(s) to Base Unit
Nominal diameter of screw: 50 Millimeter --> 0.05 Meter (Check conversion here)
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)
Number of Engaged Threads: 9 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
dc = sqrt((d)^2-(4*Wa/(Sb*pi*z))) --> sqrt((0.05)^2-(4*131000/(24900000*pi*9)))
Evaluating ... ...
dc = 0.0419012470082511
STEP 3: Convert Result to Output's Unit
0.0419012470082511 Meter -->41.9012470082511 Millimeter (Check conversion here)
FINAL ANSWER
41.9012470082511 41.90125 Millimeter <-- Core diameter of screw
(Calculation completed in 00.020 seconds)

Credits

Created by Parul Keshav
National Institute of Technology (NIT), Srinagar
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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

Core Diameter of Screw given Unit Bearing Pressure Formula

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)))
dc = sqrt((d)^2-(4*Wa/(Sb*pi*z)))

Define core diameter?

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 and also the term “inside diameter” as applied to the thread of a nut.

How to Calculate Core Diameter of Screw given Unit Bearing Pressure?

Core Diameter of Screw given Unit Bearing Pressure calculator uses 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))) to calculate the Core diameter of screw, Core Diameter of Screw given Unit Bearing Pressure 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 is denoted by dc symbol.

How to calculate Core Diameter of Screw given Unit Bearing Pressure using this online calculator? To use this online calculator for Core Diameter of Screw given Unit Bearing Pressure, enter Nominal diameter of screw (d), Axial load on screw (Wa), Unit bearing pressure for nut (Sb) & Number of Engaged Threads (z) and hit the calculate button. Here is how the Core Diameter of Screw given Unit Bearing Pressure calculation can be explained with given input values -> 41901.25 = sqrt((0.05)^2-(4*131000/(24900000*pi*9))).

FAQ

What is Core Diameter of Screw given Unit Bearing Pressure?
Core Diameter of Screw given Unit Bearing Pressure 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 and is represented as dc = sqrt((d)^2-(4*Wa/(Sb*pi*z))) or 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))). Nominal diameter of screw is defined as the diameter of the cylinder touching the external threads of the screw, 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 & 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.
How to calculate Core Diameter of Screw given Unit Bearing Pressure?
Core Diameter of Screw given Unit Bearing Pressure 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 is calculated using 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))). To calculate Core Diameter of Screw given Unit Bearing Pressure, you need Nominal diameter of screw (d), Axial load on screw (Wa), Unit bearing pressure for nut (Sb) & Number of Engaged Threads (z). With our tool, you need to enter the respective value for Nominal diameter of screw, Axial load on screw, Unit bearing pressure for nut & Number of Engaged Threads 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 Core diameter of screw?
In this formula, Core diameter of screw uses Nominal diameter of screw, Axial load on screw, Unit bearing pressure for nut & Number of Engaged Threads. We can use 4 other way(s) to calculate the same, which is/are as follows -
  • Core diameter of screw = sqrt((4*Axial load on screw)/(pi*Compressive stress in screw))
  • Core diameter of screw = (16*Torsional Moment on Screw/(pi*Torsional shear stress in screw))^(1/3)
  • Core diameter of screw = Axial load on screw/(Transverse Shear Stress in Screw*pi*Thread Thickness*Number of Engaged Threads)
  • Core diameter of screw = Nominal diameter of screw-Pitch of power screw thread
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