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

✖Turning force is called a torque and the effect it produces is called a moment.ⓘ Turning force [T_force]			+10% -10%
✖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%
✖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%
✖Thickness of ring is defined as the distance through an object, as distinct from width or height.ⓘ Thickness of ring [b_ring]			+10% -10%

✖Maximum Shear Stress that acts coplanar with cross-section of material, arises due to shear forces.ⓘ Maximum Shear Stress at Outer Surface given Turning Force on Elementary Ring [𝜏_max]

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Formula

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

Formula

`"𝜏"_{"max"} = ("T"_{"force"}*"d"_{"outer"})/(4*pi*("r"^2)*"b"_{"ring"})`

Example

`"111.4085MPa"=("7N"*"4000mm")/(4*pi*(("2mm")^2)*"5mm")`

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

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Shear Stress = (Turning force*Outer Diameter of Shaft)/(4*pi*(Radius of elementary circular ring^2)*Thickness of ring)
𝜏_max = (T_force*d_outer)/(4*pi*(r^2)*b_ring)
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Maximum Shear Stress - (Measured in Pascal) - Maximum Shear Stress that acts coplanar with cross-section of material, arises due to shear forces.
Turning force - (Measured in Newton) - Turning force is called a torque and the effect it produces is called a moment.
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.
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.
Thickness of ring - (Measured in Meter) - Thickness of ring is defined as the distance through an object, as distinct from width or height.

STEP 1: Convert Input(s) to Base Unit

Turning force: 7 Newton --> 7 Newton No Conversion Required
Outer Diameter of Shaft: 4000 Millimeter --> 4 Meter (Check conversion here)
Radius of elementary circular ring: 2 Millimeter --> 0.002 Meter (Check conversion here)
Thickness of ring: 5 Millimeter --> 0.005 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝜏_max = (T_force*d_outer)/(4*pi*(r^2)*b_ring) --> (7*4)/(4*pi*(0.002^2)*0.005)

Evaluating ... ...

𝜏_max = 111408460.164327

STEP 3: Convert Result to Output's Unit

111408460.164327 Pascal -->111.408460164327 Megapascal (Check conversion here)

FINAL ANSWER

111.408460164327 ≈ 111.4085 Megapascal <-- Maximum Shear Stress

(Calculation completed in 00.004 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 Turning Force on Elementary Ring

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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 Turning Force on Elementary Ring Formula

Maximum Shear Stress = (Turning force*Outer Diameter of Shaft)/(4*pi*(Radius of elementary circular ring^2)*Thickness of ring)
𝜏_max = (T_force*d_outer)/(4*pi*(r^2)*b_ring)

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 Turning Force on Elementary Ring?

Maximum Shear Stress at Outer Surface given Turning Force on Elementary Ring calculator uses Maximum Shear Stress = (Turning force*Outer Diameter of Shaft)/(4*pi*(Radius of elementary circular ring^2)*Thickness of ring) to calculate the Maximum Shear Stress, The Maximum shear stress at outer surface given turning force on elementary ring formula is defined as force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress. Maximum Shear Stress is denoted by 𝜏_max symbol.

How to calculate Maximum Shear Stress at Outer Surface given Turning Force on Elementary Ring using this online calculator? To use this online calculator for Maximum Shear Stress at Outer Surface given Turning Force on Elementary Ring, enter Turning force (T_force), Outer Diameter of Shaft (d_outer), Radius of elementary circular ring (r) & Thickness of ring (b_ring) and hit the calculate button. Here is how the Maximum Shear Stress at Outer Surface given Turning Force on Elementary Ring calculation can be explained with given input values -> 0.000111 = (7*4)/(4*pi*(0.002^2)*0.005).

FAQ

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

The Maximum shear stress at outer surface given turning force on elementary ring formula is defined as 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_force*d_outer)/(4*pi*(r^2)*b_ring) or Maximum Shear Stress = (Turning force*Outer Diameter of Shaft)/(4*pi*(Radius of elementary circular ring^2)*Thickness of ring). Turning force is called a torque and the effect it produces is called a moment, Outer Diameter of Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft, Radius of elementary circular ring is defined as any of the line segments from its center to its perimeter & Thickness of ring is defined as the distance through an object, as distinct from width or height.

How to calculate Maximum Shear Stress at Outer Surface given Turning Force on Elementary Ring?

The Maximum shear stress at outer surface given turning force on elementary ring formula is defined as 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 = (Turning force*Outer Diameter of Shaft)/(4*pi*(Radius of elementary circular ring^2)*Thickness of ring). To calculate Maximum Shear Stress at Outer Surface given Turning Force on Elementary Ring, you need Turning force (T_force), Outer Diameter of Shaft (d_outer), Radius of elementary circular ring (r) & Thickness of ring (b_ring). With our tool, you need to enter the respective value for Turning force, Outer Diameter of Shaft, Radius of elementary circular ring & Thickness of 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 Maximum Shear Stress?

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

Maximum Shear Stress = (Turning moment*Outer Diameter of Shaft)/(4*pi*(Radius of elementary circular ring^3)*Thickness of ring)
Maximum Shear Stress = (Outer Diameter of Shaft*Shear stress at elementary ring)/(2*Radius of elementary circular ring)

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