Bending Moment due to Force given Angle of Rotation of Arbor with Respect to Drum Calculator

✖Angle of rotation of arbor is defined as how many degrees the arbor is rotated with respect to the drum line.ⓘ Angle of rotation of arbor [θ]			+10% -10%
✖Modulus of elasticity of spiral spring is a quantity that measures the spring's resistance to being deformed elastically when stress is applied to it.ⓘ Modulus of elasticity of spiral spring [E]			+10% -10%
✖The Width of Strip of Spiral Spring is defined as the thickness of the wired strip measured in the lateral direction and by which the spiral spring is manufactured.ⓘ Width of Strip of Spiral Spring [b]			+10% -10%
✖The Thickness of Strip of Spring is defined as the thickness of the wired strip by which the spiral spring is manufactured.ⓘ Thickness of Strip of Spring [t]			+10% -10%
✖The Length of Spiral Spring Strip is defined as the length of the thin strip of which spiral spring coils are manufactured.ⓘ Length of Spiral Spring Strip [l]			+10% -10%

✖Bending moment in spiral spring is the reaction induced in a spiral spring when an external force or moment is applied to the element, causing the element to bend.ⓘ Bending Moment due to Force given Angle of Rotation of Arbor with Respect to Drum [M]

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Formula

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Bending Moment due to Force given Angle of Rotation of Arbor with Respect to Drum

Formula

`"M" = "θ"*"E"*"b"*"t"^3/(12*"l")`

Example

`"1222.788N*mm"="18.84rad"*"207000N/mm²"*"11.52mm"*("1.25mm")^3/(12*"5980mm")`

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Bending Moment due to Force given Angle of Rotation of Arbor with Respect to Drum Solution

STEP 0: Pre-Calculation Summary

Formula Used

Bending moment in spiral spring = Angle of rotation of arbor*Modulus of elasticity of spiral spring*Width of Strip of Spiral Spring*Thickness of Strip of Spring^3/(12*Length of Spiral Spring Strip)
M = θ*E*b*t^3/(12*l)
This formula uses 6 Variables

Variables Used

Bending moment in spiral spring - (Measured in Newton Meter) - Bending moment in spiral spring is the reaction induced in a spiral spring when an external force or moment is applied to the element, causing the element to bend.
Angle of rotation of arbor - (Measured in Radian) - Angle of rotation of arbor is defined as how many degrees the arbor is rotated with respect to the drum line.
Modulus of elasticity of spiral spring - (Measured in Pascal) - Modulus of elasticity of spiral spring is a quantity that measures the spring's resistance to being deformed elastically when stress is applied to it.
Width of Strip of Spiral Spring - (Measured in Meter) - The Width of Strip of Spiral Spring is defined as the thickness of the wired strip measured in the lateral direction and by which the spiral spring is manufactured.
Thickness of Strip of Spring - (Measured in Meter) - The Thickness of Strip of Spring is defined as the thickness of the wired strip by which the spiral spring is manufactured.
Length of Spiral Spring Strip - (Measured in Meter) - The Length of Spiral Spring Strip is defined as the length of the thin strip of which spiral spring coils are manufactured.

STEP 1: Convert Input(s) to Base Unit

Angle of rotation of arbor: 18.84 Radian --> 18.84 Radian No Conversion Required
Modulus of elasticity of spiral spring: 207000 Newton per Square Millimeter --> 207000000000 Pascal (Check conversion here)
Width of Strip of Spiral Spring: 11.52 Millimeter --> 0.01152 Meter (Check conversion here)
Thickness of Strip of Spring: 1.25 Millimeter --> 0.00125 Meter (Check conversion here)
Length of Spiral Spring Strip: 5980 Millimeter --> 5.98 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M = θ*E*b*t^3/(12*l) --> 18.84*207000000000*0.01152*0.00125^3/(12*5.98)

Evaluating ... ...

M = 1.22278846153846

STEP 3: Convert Result to Output's Unit

1.22278846153846 Newton Meter -->1222.78846153846 Newton Millimeter (Check conversion here)

FINAL ANSWER

1222.78846153846 ≈ 1222.788 Newton Millimeter <-- Bending moment in spiral spring

(Calculation completed in 00.004 seconds)

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Home » Physics » Design of Automobile Elements » Design of Springs » Spiral Springs » Bending Moment in Spiral Spring » Bending Moment due to Force given Angle of Rotation of Arbor with Respect to Drum

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Osmania University (OU), Hyderabad

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< 8 Bending Moment in Spiral Spring Calculators

Bending Moment due to Force given Deflection of one End of Spring

Go Bending moment in spiral spring = (Deflection of Spiral Spring*Modulus of elasticity of spiral spring*Width of Strip of Spiral Spring*Thickness of Strip of Spring^3)/(12*Length of Spiral Spring Strip*Distance of CG of Spiral Spring)

Distance of centre of Gravity of Spiral from outer end given Deflection of one End of Spring

Go Distance of CG of Spiral Spring = Deflection of Spiral Spring*Modulus of elasticity of spiral spring*Width of Strip of Spiral Spring*Thickness of Strip of Spring^3/(12*Bending moment in spiral spring*Length of Spiral Spring Strip)

Deflection of one End of Spring with Respect to Other End

Go Deflection of Spiral Spring = 12*Bending moment in spiral spring*Length of Spiral Spring Strip*Distance of CG of Spiral Spring/(Modulus of elasticity of spiral spring*Width of Strip of Spiral Spring*Thickness of Strip of Spring^3)

Bending Moment given Strain Energy Stored in Spring

Go Bending moment in spiral spring = sqrt(Strain energy in spiral spring*Modulus of elasticity of spiral spring*Width of Strip of Spiral Spring*Thickness of Strip of Spring^3/(6*Length of Spiral Spring Strip))

Bending Moment due to Force given Angle of Rotation of Arbor with Respect to Drum

Go Bending moment in spiral spring = Angle of rotation of arbor*Modulus of elasticity of spiral spring*Width of Strip of Spiral Spring*Thickness of Strip of Spring^3/(12*Length of Spiral Spring Strip)

Bending Moment due to Force given Bending Stress induced in Spring

Go Bending moment in spiral spring = Bending Stress in Spiral Spring*Width of Strip of Spiral Spring*Thickness of Strip of Spring^2/12

Distance of centre of Gravity of Spiral from outer end given Bending Moment due to Force

Go Distance of CG of Spiral Spring = Bending moment in spiral spring/Force on spiral spring

Bending Moment due to Force

Go Bending moment in spiral spring = Force on spiral spring*Distance of CG of Spiral Spring

Bending Moment due to Force given Angle of Rotation of Arbor with Respect to Drum Formula

Define Bending Moment?

In solid mechanics, a bending moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend. The most common or simplest structural element subjected to bending moments is the beam.

How to Calculate Bending Moment due to Force given Angle of Rotation of Arbor with Respect to Drum?

Bending Moment due to Force given Angle of Rotation of Arbor with Respect to Drum calculator uses Bending moment in spiral spring = Angle of rotation of arbor*Modulus of elasticity of spiral spring*Width of Strip of Spiral Spring*Thickness of Strip of Spring^3/(12*Length of Spiral Spring Strip) to calculate the Bending moment in spiral spring, The Bending Moment due to Force given Angle of Rotation of Arbor with Respect to Drum formula is defined as the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend. Bending moment in spiral spring is denoted by M symbol.

How to calculate Bending Moment due to Force given Angle of Rotation of Arbor with Respect to Drum using this online calculator? To use this online calculator for Bending Moment due to Force given Angle of Rotation of Arbor with Respect to Drum, enter Angle of rotation of arbor (θ), Modulus of elasticity of spiral spring (E), Width of Strip of Spiral Spring (b), Thickness of Strip of Spring (t) & Length of Spiral Spring Strip (l) and hit the calculate button. Here is how the Bending Moment due to Force given Angle of Rotation of Arbor with Respect to Drum calculation can be explained with given input values -> 1.2E+6 = 18.84*207000000000*0.01152*0.00125^3/(12*5.98).

FAQ

What is Bending Moment due to Force given Angle of Rotation of Arbor with Respect to Drum?

The Bending Moment due to Force given Angle of Rotation of Arbor with Respect to Drum formula is defined as the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend and is represented as M = θ*E*b*t^3/(12*l) or Bending moment in spiral spring = Angle of rotation of arbor*Modulus of elasticity of spiral spring*Width of Strip of Spiral Spring*Thickness of Strip of Spring^3/(12*Length of Spiral Spring Strip). Angle of rotation of arbor is defined as how many degrees the arbor is rotated with respect to the drum line, Modulus of elasticity of spiral spring is a quantity that measures the spring's resistance to being deformed elastically when stress is applied to it, The Width of Strip of Spiral Spring is defined as the thickness of the wired strip measured in the lateral direction and by which the spiral spring is manufactured, The Thickness of Strip of Spring is defined as the thickness of the wired strip by which the spiral spring is manufactured & The Length of Spiral Spring Strip is defined as the length of the thin strip of which spiral spring coils are manufactured.

How to calculate Bending Moment due to Force given Angle of Rotation of Arbor with Respect to Drum?

The Bending Moment due to Force given Angle of Rotation of Arbor with Respect to Drum formula is defined as the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend is calculated using Bending moment in spiral spring = Angle of rotation of arbor*Modulus of elasticity of spiral spring*Width of Strip of Spiral Spring*Thickness of Strip of Spring^3/(12*Length of Spiral Spring Strip). To calculate Bending Moment due to Force given Angle of Rotation of Arbor with Respect to Drum, you need Angle of rotation of arbor (θ), Modulus of elasticity of spiral spring (E), Width of Strip of Spiral Spring (b), Thickness of Strip of Spring (t) & Length of Spiral Spring Strip (l). With our tool, you need to enter the respective value for Angle of rotation of arbor, Modulus of elasticity of spiral spring, Width of Strip of Spiral Spring, Thickness of Strip of Spring & Length of Spiral Spring Strip 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 Bending moment in spiral spring?

In this formula, Bending moment in spiral spring uses Angle of rotation of arbor, Modulus of elasticity of spiral spring, Width of Strip of Spiral Spring, Thickness of Strip of Spring & Length of Spiral Spring Strip. We can use 4 other way(s) to calculate the same, which is/are as follows -

Bending moment in spiral spring = Bending Stress in Spiral Spring*Width of Strip of Spiral Spring*Thickness of Strip of Spring^2/12
Bending moment in spiral spring = Force on spiral spring*Distance of CG of Spiral Spring
Bending moment in spiral spring = (Deflection of Spiral Spring*Modulus of elasticity of spiral spring*Width of Strip of Spiral Spring*Thickness of Strip of Spring^3)/(12*Length of Spiral Spring Strip*Distance of CG of Spiral Spring)
Bending moment in spiral spring = sqrt(Strain energy in spiral spring*Modulus of elasticity of spiral spring*Width of Strip of Spiral Spring*Thickness of Strip of Spring^3/(6*Length of Spiral Spring Strip))

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