Maximum Shear Stress at Outer Surface given Diameter of Shaft on Hollow Circular Shaft Calculator

✖Outer Diameter of Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft.ⓘ Outer Diameter of Shaft [d_outer]			+10% -10%
✖Turning moment where the turning force is called a torque and the effect it produces is called a moment.ⓘ Turning moment [T]			+10% -10%
✖The Inner Diameter of Shaft is defined as the length of the longest chord inside the hollow shaft.ⓘ Inner Diameter of Shaft [d_inner]			+10% -10%

✖Maximum Shear Stress on Shaft that acts coplanar with a cross-section of material arises due to shear forces.ⓘ Maximum Shear Stress at Outer Surface given Diameter of Shaft on Hollow Circular Shaft [𝜏_max]

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Formula

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Maximum Shear Stress at Outer Surface given Diameter of Shaft on Hollow Circular Shaft

Formula

`"𝜏"_{"max"} = (16*"d"_{"outer"}*"T")/(pi*(("d"_{"outer"}^4)-("d"_{"inner"}^4)))`

Example

`"3.2E^-7MPa"=(16*"4000mm"*"4N*m")/(pi*((("4000mm")^4)-(("1000mm")^4)))`

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Maximum Shear Stress at Outer Surface given Diameter of Shaft on Hollow Circular Shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Shear Stress on Shaft = (16*Outer Diameter of Shaft*Turning moment)/(pi*((Outer Diameter of Shaft^4)-(Inner Diameter of Shaft^4)))
𝜏_max = (16*d_outer*T)/(pi*((d_outer^4)-(d_inner^4)))
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Maximum Shear Stress on Shaft - (Measured in Pascal) - Maximum Shear Stress on Shaft that acts coplanar with a cross-section of material arises due to shear forces.
Outer Diameter of Shaft - (Measured in Meter) - Outer Diameter of Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft.
Turning moment - (Measured in Newton Meter) - Turning moment where the turning force is called a torque and the effect it produces is called a moment.
Inner Diameter of Shaft - (Measured in Meter) - The Inner Diameter of Shaft is defined as the length of the longest chord inside the hollow shaft.

STEP 1: Convert Input(s) to Base Unit

Outer Diameter of Shaft: 4000 Millimeter --> 4 Meter (Check conversion here)
Turning moment: 4 Newton Meter --> 4 Newton Meter No Conversion Required
Inner Diameter of Shaft: 1000 Millimeter --> 1 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝜏_max = (16*d_outer*T)/(pi*((d_outer^4)-(d_inner^4))) --> (16*4*4)/(pi*((4^4)-(1^4)))

Evaluating ... ...

𝜏_max = 0.319558160247257

STEP 3: Convert Result to Output's Unit

0.319558160247257 Pascal -->3.19558160247257E-07 Megapascal (Check conversion here)

FINAL ANSWER

3.19558160247257E-07 ≈ 3.2E-7 Megapascal <-- Maximum Shear Stress on Shaft

(Calculation completed in 00.009 seconds)

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Home » Physics » Strength of Materials » Torsion of Shafts And Springs » Torque Transmitted by a Hollow Circular Shaft » Maximum Shear Stress at Outer Surface given Diameter of Shaft on Hollow Circular Shaft

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< 16 Torque Transmitted by a Hollow Circular Shaft Calculators

Maximum Shear Stress at Outer Surface given Total Turning Moment on Hollow Circular Shaft

Go Maximum Shear Stress on Shaft = (Turning moment*2*Outer Radius Of Hollow circular Cylinder)/(pi*((Outer Radius Of Hollow circular Cylinder^4)-(Inner Radius Of Hollow Circular Cylinder^4)))

Total Turning Moment on Hollow Circular Shaft given Radius of Shaft

Go Turning moment = (pi*Maximum Shear Stress on Shaft*((Outer Radius Of Hollow circular Cylinder^4)-(Inner Radius Of Hollow Circular Cylinder^4)))/(2*Outer Radius Of Hollow circular Cylinder)

Radius of Elementary Ring given Turning Force of Elementary Ring

Go Radius of elementary circular ring = sqrt((Turning force*Outer Diameter of Shaft)/(4*pi*Maximum Shear Stress*Thickness of ring))

Maximum Shear Stress at Outer Surface given Diameter of Shaft on Hollow Circular Shaft

Go Maximum Shear Stress on Shaft = (16*Outer Diameter of Shaft*Turning moment)/(pi*((Outer Diameter of Shaft^4)-(Inner Diameter of Shaft^4)))

Total Turning Moment on Hollow Circular Shaft given Diameter of Shaft

Go Turning moment = (pi*Maximum Shear Stress on Shaft*((Outer Diameter of Shaft^4)-(Inner Diameter of Shaft^4)))/(16*Outer Diameter of Shaft)

Radius of Elementary Ring given Turning Moment of Elementary Ring

Go Radius of elementary circular ring = ((Turning moment*Outer Diameter of Shaft)/(4*pi*Maximum Shear Stress*Thickness of ring))^(1/3)

Maximum Shear Stress Induced at Outer Surface given Turning Moment on Elementary Ring

Go Maximum Shear Stress = (Turning moment*Outer Diameter of Shaft)/(4*pi*(Radius of elementary circular ring^3)*Thickness of ring)

Maximum Shear Stress at Outer Surface given Turning Force on Elementary Ring

Go Maximum Shear Stress = (Turning force*Outer Diameter of Shaft)/(4*pi*(Radius of elementary circular ring^2)*Thickness of ring)

Turning Moment on Elementary Ring

Go Turning moment = (4*pi*Maximum Shear Stress*(Radius of elementary circular ring^3)*Thickness of ring)/Outer Diameter of Shaft

Turning Force on Elementary Ring

Go Turning force = (4*pi*Maximum Shear Stress*(Radius of elementary circular ring^2)*Thickness of ring)/Outer Diameter of Shaft

Outer Radius of Shaft using Turning Force on Elementary Ring given Turning Moment

Go Outer Radius Of shaft = (2*pi*Maximum Shear Stress*(Radius of elementary circular ring^2)*Thickness of ring)/Turning moment

Outer Radius of Shaft using Turning Force on Elementary Ring

Go Outer Radius Of shaft = (2*pi*Maximum Shear Stress*(Radius of elementary circular ring^2)*Thickness of ring)/Turning force

Maximum shear stress induced at outer surface given shear stress of elementary ring

Go Maximum Shear Stress = (Outer Diameter of Shaft*Shear stress at elementary ring)/(2*Radius of elementary circular ring)

Radius of Elementary Ring given Shear Stress of Elementary Ring

Go Radius of elementary circular ring = (Outer Diameter of Shaft*Shear stress at elementary ring)/(2*Maximum Shear Stress)

Shear Stress at Elementary Ring of Hollow Circular Shaft

Go Shear stress at elementary ring = (2*Maximum Shear Stress*Radius of elementary circular ring)/Outer Diameter of Shaft

Outer Radius of Shaft given Shear Stress of Elementary Ring

Go Outer Radius Of shaft = (Maximum Shear Stress*Radius of elementary circular ring)/Shear stress at elementary ring

Maximum Shear Stress at Outer Surface given Diameter of Shaft on Hollow Circular Shaft Formula

Maximum Shear Stress on Shaft = (16*Outer Diameter of Shaft*Turning moment)/(pi*((Outer Diameter of Shaft^4)-(Inner Diameter of Shaft^4)))
𝜏_max = (16*d_outer*T)/(pi*((d_outer^4)-(d_inner^4)))

What does the turning effect of a force depend on?

The effect that a force has in turning an object round depends on the size of the force, the perpendicular (shortest) distance between the force line, and the pivot (the axis of rotation).

How to Calculate Maximum Shear Stress at Outer Surface given Diameter of Shaft on Hollow Circular Shaft?

Maximum Shear Stress at Outer Surface given Diameter of Shaft on Hollow Circular Shaft calculator uses Maximum Shear Stress on Shaft = (16*Outer Diameter of Shaft*Turning moment)/(pi*((Outer Diameter of Shaft^4)-(Inner Diameter of Shaft^4))) to calculate the Maximum Shear Stress on Shaft, The Maximum Shear Stress at Outer Surface given Diameter of Shaft on Hollow Circular Shaft formula is defined as a force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress. Maximum Shear Stress on Shaft is denoted by 𝜏_max symbol.

How to calculate Maximum Shear Stress at Outer Surface given Diameter of Shaft on Hollow Circular Shaft using this online calculator? To use this online calculator for Maximum Shear Stress at Outer Surface given Diameter of Shaft on Hollow Circular Shaft, enter Outer Diameter of Shaft (d_outer), Turning moment (T) & Inner Diameter of Shaft (d_inner) and hit the calculate button. Here is how the Maximum Shear Stress at Outer Surface given Diameter of Shaft on Hollow Circular Shaft calculation can be explained with given input values -> 3.2E-13 = (16*4*4)/(pi*((4^4)-(1^4))).

FAQ

What is Maximum Shear Stress at Outer Surface given Diameter of Shaft on Hollow Circular Shaft?

The Maximum Shear Stress at Outer Surface given Diameter of Shaft on Hollow Circular Shaft formula is defined as a force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress and is represented as 𝜏_max = (16*d_outer*T)/(pi*((d_outer^4)-(d_inner^4))) or Maximum Shear Stress on Shaft = (16*Outer Diameter of Shaft*Turning moment)/(pi*((Outer Diameter of Shaft^4)-(Inner Diameter of Shaft^4))). Outer Diameter of Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft, Turning moment where the turning force is called a torque and the effect it produces is called a moment & The Inner Diameter of Shaft is defined as the length of the longest chord inside the hollow shaft.

How to calculate Maximum Shear Stress at Outer Surface given Diameter of Shaft on Hollow Circular Shaft?

The Maximum Shear Stress at Outer Surface given Diameter of Shaft on Hollow Circular Shaft formula is defined as a force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress is calculated using Maximum Shear Stress on Shaft = (16*Outer Diameter of Shaft*Turning moment)/(pi*((Outer Diameter of Shaft^4)-(Inner Diameter of Shaft^4))). To calculate Maximum Shear Stress at Outer Surface given Diameter of Shaft on Hollow Circular Shaft, you need Outer Diameter of Shaft (d_outer), Turning moment (T) & Inner Diameter of Shaft (d_inner). With our tool, you need to enter the respective value for Outer Diameter of Shaft, Turning moment & Inner Diameter of Shaft 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 Maximum Shear Stress on Shaft?

In this formula, Maximum Shear Stress on Shaft uses Outer Diameter of Shaft, Turning moment & Inner Diameter of Shaft. We can use 1 other way(s) to calculate the same, which is/are as follows -

Maximum Shear Stress on Shaft = (Turning moment*2*Outer Radius Of Hollow circular Cylinder)/(pi*((Outer Radius Of Hollow circular Cylinder^4)-(Inner Radius Of Hollow Circular Cylinder^4)))

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