Outer Radius of Shaft given Shear Stress of Elementary Ring Calculator

✖Maximum Shear Stress that acts coplanar with cross-section of material, arises due to shear forces.ⓘ Maximum Shear Stress [𝜏_max]			+10% -10%
✖Radius of elementary circular ring is defined as any of the line segments from its center to its perimeter.ⓘ Radius of elementary circular ring [r]			+10% -10%
✖Shear stress at elementary ring is defined as force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.ⓘ Shear stress at elementary ring [q]			+10% -10%

✖Outer Radius Of shaft of any figure is the radius of a larger circle of the two concentric circles that form its boundary.ⓘ Outer Radius of Shaft given Shear Stress of Elementary Ring [r_outer]

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Outer Radius of Shaft given Shear Stress of Elementary Ring

Formula

`"r"_{"outer"} = ("𝜏"_{"max"}*"r")/"q"`

Example

`"5.333333mm"=("16MPa"*"2mm")/"6MPa"`

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Outer Radius of Shaft given Shear Stress of Elementary Ring Solution

STEP 0: Pre-Calculation Summary

Formula Used

Outer Radius Of shaft = (Maximum Shear Stress*Radius of elementary circular ring)/Shear stress at elementary ring
r_outer = (𝜏_max*r)/q
This formula uses 4 Variables

Variables Used

Outer Radius Of shaft - (Measured in Meter) - Outer Radius Of shaft of any figure is the radius of a larger circle of the two concentric circles that form its boundary.
Maximum Shear Stress - (Measured in Pascal) - Maximum Shear Stress that acts coplanar with cross-section of material, arises due to shear forces.
Radius of elementary circular ring - (Measured in Meter) - Radius of elementary circular ring is defined as any of the line segments from its center to its perimeter.
Shear stress at elementary ring - (Measured in Pascal) - Shear stress at elementary ring is defined as force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.

STEP 1: Convert Input(s) to Base Unit

Maximum Shear Stress: 16 Megapascal --> 16000000 Pascal (Check conversion here)
Radius of elementary circular ring: 2 Millimeter --> 0.002 Meter (Check conversion here)
Shear stress at elementary ring: 6 Megapascal --> 6000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_outer = (𝜏_max*r)/q --> (16000000*0.002)/6000000

Evaluating ... ...

r_outer = 0.00533333333333333

STEP 3: Convert Result to Output's Unit

0.00533333333333333 Meter -->5.33333333333333 Millimeter (Check conversion here)

FINAL ANSWER

5.33333333333333 ≈ 5.333333 Millimeter <-- Outer Radius Of 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 » Outer Radius of Shaft given Shear Stress of Elementary Ring

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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

Outer Radius of Shaft given Shear Stress of Elementary Ring Formula

Outer Radius Of shaft = (Maximum Shear Stress*Radius of elementary circular ring)/Shear stress at elementary ring
r_outer = (𝜏_max*r)/q

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 Outer Radius of Shaft given Shear Stress of Elementary Ring?

Outer Radius of Shaft given Shear Stress of Elementary Ring calculator uses Outer Radius Of shaft = (Maximum Shear Stress*Radius of elementary circular ring)/Shear stress at elementary ring to calculate the Outer Radius Of shaft, The Outer radius of shaft given shear stress of elementary ring formula is defined as any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. Outer Radius Of shaft is denoted by r_outer symbol.

How to calculate Outer Radius of Shaft given Shear Stress of Elementary Ring using this online calculator? To use this online calculator for Outer Radius of Shaft given Shear Stress of Elementary Ring, enter Maximum Shear Stress (𝜏_max), Radius of elementary circular ring (r) & Shear stress at elementary ring (q) and hit the calculate button. Here is how the Outer Radius of Shaft given Shear Stress of Elementary Ring calculation can be explained with given input values -> 5333.333 = (16000000*0.002)/6000000.

FAQ

What is Outer Radius of Shaft given Shear Stress of Elementary Ring?

The Outer radius of shaft given shear stress of elementary ring formula is defined as any of the line segments from its center to its perimeter, and in more modern usage, it is also their length and is represented as r_outer = (𝜏_max*r)/q or Outer Radius Of shaft = (Maximum Shear Stress*Radius of elementary circular ring)/Shear stress at elementary ring. Maximum Shear Stress that acts coplanar with cross-section of material, arises due to shear forces, Radius of elementary circular ring is defined as any of the line segments from its center to its perimeter & Shear stress at elementary ring is defined as force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.

How to calculate Outer Radius of Shaft given Shear Stress of Elementary Ring?

The Outer radius of shaft given shear stress of elementary ring formula is defined as any of the line segments from its center to its perimeter, and in more modern usage, it is also their length is calculated using Outer Radius Of shaft = (Maximum Shear Stress*Radius of elementary circular ring)/Shear stress at elementary ring. To calculate Outer Radius of Shaft given Shear Stress of Elementary Ring, you need Maximum Shear Stress (𝜏_max), Radius of elementary circular ring (r) & Shear stress at elementary ring (q). With our tool, you need to enter the respective value for Maximum Shear Stress, Radius of elementary circular ring & Shear stress at elementary ring 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 Outer Radius Of shaft?

In this formula, Outer Radius Of shaft uses Maximum Shear Stress, Radius of elementary circular ring & Shear stress at elementary ring. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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