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

✖Turning moment where the turning force is called a torque and the effect it produces is called a moment.ⓘ Turning moment [T]			+10% -10%
✖Outer Radius Of Hollow circular Cylinder of any figure is the radius of a larger circle of the two concentric circles that form its boundary.ⓘ Outer Radius Of Hollow circular Cylinder [r_hollow]			+10% -10%
✖Inner Radius Of Hollow Circular Cylinder of any figure is the radius of its cavity and the smaller radius among two concentric circles.ⓘ Inner Radius Of Hollow Circular Cylinder [r_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 Total Turning Moment on Hollow Circular Shaft [𝜏_max]

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

Formula

`"𝜏"_{"max"} = ("T"*2*"r"_{"hollow"})/(pi*(("r"_{"hollow"}^4)-("r"_{"inner"}^4)))`

Example

`"4.8E^-8MPa"=("4N*m"*2*"5500mm")/(pi*((("5500mm")^4)-(("5000mm")^4)))`

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

STEP 0: Pre-Calculation Summary

Formula Used

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)))
𝜏_max = (T*2*r_hollow)/(pi*((r_hollow^4)-(r_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.
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.
Outer Radius Of Hollow circular Cylinder - (Measured in Meter) - Outer Radius Of Hollow circular Cylinder of any figure is the radius of a larger circle of the two concentric circles that form its boundary.
Inner Radius Of Hollow Circular Cylinder - (Measured in Meter) - Inner Radius Of Hollow Circular Cylinder of any figure is the radius of its cavity and the smaller radius among two concentric circles.

STEP 1: Convert Input(s) to Base Unit

Turning moment: 4 Newton Meter --> 4 Newton Meter No Conversion Required
Outer Radius Of Hollow circular Cylinder: 5500 Millimeter --> 5.5 Meter (Check conversion here)
Inner Radius Of Hollow Circular Cylinder: 5000 Millimeter --> 5 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝜏_max = (T*2*r_hollow)/(pi*((r_hollow^4)-(r_inner^4))) --> (4*2*5.5)/(pi*((5.5^4)-(5^4)))

Evaluating ... ...

𝜏_max = 0.048284886850547

STEP 3: Convert Result to Output's Unit

0.048284886850547 Pascal -->4.8284886850547E-08 Megapascal (Check conversion here)

FINAL ANSWER

4.8284886850547E-08 ≈ 4.8E-8 Megapascal <-- Maximum Shear Stress on Shaft

(Calculation completed in 00.020 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 Total Turning Moment on Hollow Circular Shaft

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National Institute Of Technology (NIT), Hamirpur

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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 Total Turning Moment on Hollow Circular Shaft Formula

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 Total Turning Moment on Hollow Circular Shaft?

Maximum Shear Stress at Outer Surface given Total Turning Moment on Hollow Circular Shaft calculator uses 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))) to calculate the Maximum Shear Stress on Shaft, The Maximum Shear Stress at Outer Surface given Total Turning Moment 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 Total Turning Moment on Hollow Circular Shaft using this online calculator? To use this online calculator for Maximum Shear Stress at Outer Surface given Total Turning Moment on Hollow Circular Shaft, enter Turning moment (T), Outer Radius Of Hollow circular Cylinder (r_hollow) & Inner Radius Of Hollow Circular Cylinder (r_inner) and hit the calculate button. Here is how the Maximum Shear Stress at Outer Surface given Total Turning Moment on Hollow Circular Shaft calculation can be explained with given input values -> 4.8E-14 = (4*2*5.5)/(pi*((5.5^4)-(5^4))).

FAQ

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

The Maximum Shear Stress at Outer Surface given Total Turning Moment 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 = (T*2*r_hollow)/(pi*((r_hollow^4)-(r_inner^4))) or 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))). Turning moment where the turning force is called a torque and the effect it produces is called a moment, Outer Radius Of Hollow circular Cylinder of any figure is the radius of a larger circle of the two concentric circles that form its boundary & Inner Radius Of Hollow Circular Cylinder of any figure is the radius of its cavity and the smaller radius among two concentric circles.

How to calculate Maximum Shear Stress at Outer Surface given Total Turning Moment on Hollow Circular Shaft?

The Maximum Shear Stress at Outer Surface given Total Turning Moment 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 = (Turning moment*2*Outer Radius Of Hollow circular Cylinder)/(pi*((Outer Radius Of Hollow circular Cylinder^4)-(Inner Radius Of Hollow Circular Cylinder^4))). To calculate Maximum Shear Stress at Outer Surface given Total Turning Moment on Hollow Circular Shaft, you need Turning moment (T), Outer Radius Of Hollow circular Cylinder (r_hollow) & Inner Radius Of Hollow Circular Cylinder (r_inner). With our tool, you need to enter the respective value for Turning moment, Outer Radius Of Hollow circular Cylinder & Inner Radius Of Hollow Circular Cylinder 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 Turning moment, Outer Radius Of Hollow circular Cylinder & Inner Radius Of Hollow Circular Cylinder. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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