Transverse Shear Stress at Root of Nut Calculator

✖Axial load on screw is the instantaneous load applied to the screw along its axis.ⓘ Axial load on screw [W_a]			+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%
✖Thread Thickness is defined as the thickness of a single thread.ⓘ Thread Thickness [t]			+10% -10%
✖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%

✖Transverse shear stress in nut is the resistance force developed per unit cross-sectional area by the nut to avoid transverse deformation.ⓘ Transverse Shear Stress at Root of Nut [t_n]

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Formula

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Transverse Shear Stress at Root of Nut

Formula

`"t"_{"n"} = "W"_{"a"}/(pi*"d"*"t"*"z")`

Example

`"23.16589N/mm²"="131000N"/(pi*"50mm"*"4mm"*"9")`

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Transverse Shear Stress at Root of Nut Solution

STEP 0: Pre-Calculation Summary

Formula Used

Transverse shear stress in nut = Axial load on screw/(pi*Nominal diameter of screw*Thread Thickness*Number of Engaged Threads)
t_n = W_a/(pi*d*t*z)
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Transverse shear stress in nut - (Measured in Pascal) - Transverse shear stress in nut is the resistance force developed per unit cross-sectional area by the nut to avoid transverse deformation.
Axial load on screw - (Measured in Newton) - Axial load on screw is the instantaneous load applied to the screw along its axis.
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.
Thread Thickness - (Measured in Meter) - Thread Thickness is defined as the thickness of a single thread.
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

Axial load on screw: 131000 Newton --> 131000 Newton No Conversion Required
Nominal diameter of screw: 50 Millimeter --> 0.05 Meter (Check conversion here)
Thread Thickness: 4 Millimeter --> 0.004 Meter (Check conversion here)
Number of Engaged Threads: 9 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t_n = W_a/(pi*d*t*z) --> 131000/(pi*0.05*0.004*9)

Evaluating ... ...

t_n = 23165886.1611537

STEP 3: Convert Result to Output's Unit

23165886.1611537 Pascal -->23.1658861611537 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

23.1658861611537 ≈ 23.16589 Newton per Square Millimeter <-- Transverse shear stress in nut

(Calculation completed in 00.004 seconds)

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Home » Engineering » Mechanical » Machine Design » Power Screws » Design of Screw and Nut » Transverse Shear Stress at Root of Nut

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

Transverse Shear Stress at Root of Nut Formula

Transverse shear stress in nut = Axial load on screw/(pi*Nominal diameter of screw*Thread Thickness*Number of Engaged Threads)
t_n = W_a/(pi*d*t*z)

How does Transverse Shear Stress arise?

In an engaged pair of Screw and Nut, the thread of the Nut experiences a force parallel to the area of contact. This happens due to the bending of the threads and their tendency to slide over one another, thus tending to shear off at the nominal diameter.

How to Calculate Transverse Shear Stress at Root of Nut?

Transverse Shear Stress at Root of Nut calculator uses Transverse shear stress in nut = Axial load on screw/(pi*Nominal diameter of screw*Thread Thickness*Number of Engaged Threads) to calculate the Transverse shear stress in nut, Transverse Shear Stress at Root of Nut is the measure of Shear Stress that arises due to bending under the action of the load W, per thread. Transverse shear stress in nut is denoted by t_n symbol.

How to calculate Transverse Shear Stress at Root of Nut using this online calculator? To use this online calculator for Transverse Shear Stress at Root of Nut, enter Axial load on screw (W_a), Nominal diameter of screw (d), Thread Thickness (t) & Number of Engaged Threads (z) and hit the calculate button. Here is how the Transverse Shear Stress at Root of Nut calculation can be explained with given input values -> 2.3E-5 = 131000/(pi*0.05*0.004*9).

FAQ

What is Transverse Shear Stress at Root of Nut?

Transverse Shear Stress at Root of Nut is the measure of Shear Stress that arises due to bending under the action of the load W, per thread and is represented as t_n = W_a/(pi*d*t*z) or Transverse shear stress in nut = Axial load on screw/(pi*Nominal diameter of screw*Thread Thickness*Number of Engaged Threads). Axial load on screw is the instantaneous load applied to the screw along its axis, Nominal diameter of screw is defined as the diameter of the cylinder touching the external threads of the screw, Thread Thickness is defined as the thickness of a single thread & 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 Transverse Shear Stress at Root of Nut?

Transverse Shear Stress at Root of Nut is the measure of Shear Stress that arises due to bending under the action of the load W, per thread is calculated using Transverse shear stress in nut = Axial load on screw/(pi*Nominal diameter of screw*Thread Thickness*Number of Engaged Threads). To calculate Transverse Shear Stress at Root of Nut, you need Axial load on screw (W_a), Nominal diameter of screw (d), Thread Thickness (t) & Number of Engaged Threads (z). With our tool, you need to enter the respective value for Axial load on screw, Nominal diameter of screw, Thread Thickness & 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.

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