Torsional Shear Stress of Screw 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%
✖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%

✖Torsional shear stress in screw is the shear stress produced in the screw due to the twisting.ⓘ Torsional Shear Stress of Screw [τ]

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Formula

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Torsional Shear Stress of Screw

Formula

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

Example

`"45.28036N/mm²"=16*"658700N*mm"/(pi*(("42mm")^3))`

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Torsional Shear Stress of Screw Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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.
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.
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

Torsional Moment on Screw: 658700 Newton Millimeter --> 658.7 Newton 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

τ = 16*Mt_t/(pi*(d_c^3)) --> 16*658.7/(pi*(0.042^3))

Evaluating ... ...

τ = 45280363.2500298

STEP 3: Convert Result to Output's Unit

45280363.2500298 Pascal -->45.2803632500298 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

45.2803632500298 ≈ 45.28036 Newton per Square Millimeter <-- Torsional shear stress in screw

(Calculation completed in 00.004 seconds)

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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

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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

Torsional Shear Stress of Screw Formula

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

Why Torsional Shear Stress is calculated at the Root of The Screw?

The Root or Core body of the Screw has the minimum cross-section in the structure, hence the Polar Moment of Inertia is minimum resulting in maximum Torsional Shear Stress in the structure. This value of Stress is then used as a reference because everywhere else, Torsional Stress will be smaller and the structure won't fail.

How to Calculate Torsional Shear Stress of Screw?

Torsional Shear Stress of Screw calculator uses Torsional shear stress in screw = 16*Torsional Moment on Screw/(pi*(Core diameter of screw^3)) to calculate the Torsional shear stress in screw, The Torsional Shear Stress of Screw is defined as the stress that arises in the Screw body due to torsion or twisting during tightening. Torsional Shear Stress is often calculated at the minimum cross-section of the screw (Root of the screw). Torsional shear stress in screw is denoted by τ symbol.

How to calculate Torsional Shear Stress of Screw using this online calculator? To use this online calculator for Torsional Shear Stress of Screw, enter Torsional Moment on Screw (Mt_t) & Core diameter of screw (d_c) and hit the calculate button. Here is how the Torsional Shear Stress of Screw calculation can be explained with given input values -> 4.5E-5 = 16*658.7/(pi*(0.042^3)).

FAQ

What is Torsional Shear Stress of Screw?

The Torsional Shear Stress of Screw is defined as the stress that arises in the Screw body due to torsion or twisting during tightening. Torsional Shear Stress is often calculated at the minimum cross-section of the screw (Root of the screw) and is represented as τ = 16*Mt_t/(pi*(d_c^3)) or Torsional shear stress in screw = 16*Torsional Moment on Screw/(pi*(Core diameter of screw^3)). Torsional moment on screw is the torque applied which generates a torsion (twist) within the screw body & 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 Torsional Shear Stress of Screw?

The Torsional Shear Stress of Screw is defined as the stress that arises in the Screw body due to torsion or twisting during tightening. Torsional Shear Stress is often calculated at the minimum cross-section of the screw (Root of the screw) is calculated using Torsional shear stress in screw = 16*Torsional Moment on Screw/(pi*(Core diameter of screw^3)). To calculate Torsional Shear Stress of Screw, you need Torsional Moment on Screw (Mt_t) & Core diameter of screw (d_c). With our tool, you need to enter the respective value for Torsional Moment on 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.

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