Core Diameter of Screw given Torsional Shear Stress Calculator

✖Torsional moment on screw is the torque applied which generates a torsion (twist) within the screw body.ⓘ Torsional Moment on Screw [Mt_t]			+10% -10%
✖Torsional shear stress in screw is the shear stress produced in the screw due to the twisting.ⓘ Torsional shear stress in screw [τ]			+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 given Torsional Shear Stress [d_c]

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Formula

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Core Diameter of Screw given Torsional Shear Stress

Formula

`"d"_{"c"} = (16*"Mt"_{"t"}/(pi*"τ"))^(1/3)`

Example

`"42.00011mm"=(16*"658700N*mm"/(pi*"45.28N/mm²"))^(1/3)`

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Core Diameter of Screw given Torsional Shear Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Core diameter of screw = (16*Torsional Moment on Screw/(pi*Torsional shear stress in screw))^(1/3)
d_c = (16*Mt_t/(pi*τ))^(1/3)
This formula uses 1 Constants, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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.
Torsional Moment on Screw - (Measured in Newton Meter) - Torsional moment on screw is the torque applied which generates a torsion (twist) within the screw body.
Torsional shear stress in screw - (Measured in Pascal) - Torsional shear stress in screw is the shear stress produced in the screw due to the twisting.

STEP 1: Convert Input(s) to Base Unit

Torsional Moment on Screw: 658700 Newton Millimeter --> 658.7 Newton Meter (Check conversion here)
Torsional shear stress in screw: 45.28 Newton per Square Millimeter --> 45280000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_c = (16*Mt_t/(pi*τ))^(1/3) --> (16*658.7/(pi*45280000))^(1/3)

Evaluating ... ...

d_c = 0.042000112311988

STEP 3: Convert Result to Output's Unit

0.042000112311988 Meter -->42.000112311988 Millimeter (Check conversion here)

FINAL ANSWER

42.000112311988 ≈ 42.00011 Millimeter <-- Core diameter of screw

(Calculation completed in 00.004 seconds)

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Home » Engineering » Mechanical » Machine Design » Power Screws » Design of Screw and Nut » Core Diameter of Screw given Torsional Shear Stress

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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

Core Diameter of Screw given Torsional Shear Stress Formula

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

Variation in Core Diameter

Core diameter directly influences the strength of the structure. A larger core diameter implies the structure can withstand more Torsion in comparison to a smaller Core Diametral structure. Hence it is preferred that the actual structure has a Core Diameter slightly larger than the calculated one.

How to Calculate Core Diameter of Screw given Torsional Shear Stress?

Core Diameter of Screw given Torsional Shear Stress calculator uses Core diameter of screw = (16*Torsional Moment on Screw/(pi*Torsional shear stress in screw))^(1/3) to calculate the Core diameter of screw, Core Diameter of Screw given Torsional Shear Stress is a way of calculating the Core (or Root) Diameter of a screw of selected material, that can function against the working load without failure. It 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 d_c symbol.

How to calculate Core Diameter of Screw given Torsional Shear Stress using this online calculator? To use this online calculator for Core Diameter of Screw given Torsional Shear Stress, enter Torsional Moment on Screw (Mt_t) & Torsional shear stress in screw (τ) and hit the calculate button. Here is how the Core Diameter of Screw given Torsional Shear Stress calculation can be explained with given input values -> 42000.11 = (16*658.7/(pi*45280000))^(1/3).

FAQ

What is Core Diameter of Screw given Torsional Shear Stress?

Core Diameter of Screw given Torsional Shear Stress is a way of calculating the Core (or Root) Diameter of a screw of selected material, that can function against the working load without failure. It 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 d_c = (16*Mt_t/(pi*τ))^(1/3) or Core diameter of screw = (16*Torsional Moment on Screw/(pi*Torsional shear stress in screw))^(1/3). Torsional moment on screw is the torque applied which generates a torsion (twist) within the screw body & Torsional shear stress in screw is the shear stress produced in the screw due to the twisting.

How to calculate Core Diameter of Screw given Torsional Shear Stress?

Core Diameter of Screw given Torsional Shear Stress is a way of calculating the Core (or Root) Diameter of a screw of selected material, that can function against the working load without failure. It 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 = (16*Torsional Moment on Screw/(pi*Torsional shear stress in screw))^(1/3). To calculate Core Diameter of Screw given Torsional Shear Stress, you need Torsional Moment on Screw (Mt_t) & Torsional shear stress in screw (τ). With our tool, you need to enter the respective value for Torsional Moment on Screw & Torsional shear stress in 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 Core diameter of screw?

In this formula, Core diameter of screw uses Torsional Moment on Screw & Torsional shear stress in screw. We can use 4 other way(s) to calculate the same, which is/are as follows -

Core diameter of screw = Nominal diameter of screw-Pitch of power screw thread
Core diameter of screw = sqrt((4*Axial load on screw)/(pi*Compressive stress in screw))
Core diameter of screw = Axial load on screw/(Transverse Shear Stress in Screw*pi*Thread Thickness*Number of Engaged Threads)
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)))

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