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

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GoBending Moment due to Force given Bending Stress induced in Spring Formula

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GoBending Moment due to Force Formula

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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. Check FAQs

M = θ \cdot E \cdot b \cdot \frac{t^{3}}{12 \cdot l}

M - Bending moment in spiral spring?θ - Angle of Rotation of Arbor?E - Modulus of elasticity of spiral spring?b - Width of Strip of Spiral Spring?t - Thickness of Strip of Spring?l - Length of Strip of Spiral Spring?

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

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Here is how the Bending Moment due to Force given Angle of Rotation of Arbor with Respect to Drum equation looks like with Values.

Here is how the Bending Moment due to Force given Angle of Rotation of Arbor with Respect to Drum equation looks like with Units.

Here is how the Bending Moment due to Force given Angle of Rotation of Arbor with Respect to Drum equation looks like.

1222.7885 = 18.84 \cdot 207000 \cdot 11.52 \cdot \frac{{1.25}^{3}}{12 \cdot 5980}

1222.7885N*mm = 18.84rad \cdot 207000N/mm² \cdot 11.52mm \cdot \frac{{1.25mm}^{3}}{12 \cdot 5980mm}

1222.7885 = 18.84 \cdot 207000 \cdot 11.52 \cdot \frac{{1.25}^{3}}{12 \cdot 5980}

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Home » Physics » Mechanical » Design of Automobile Elements » 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 Solution

Follow our step by step solution on how to calculate Bending Moment due to Force given Angle of Rotation of Arbor with Respect to Drum?

FIRST Step Consider the formula

M = θ \cdot E \cdot b \cdot \frac{t^{3}}{12 \cdot l}

Next Step Substitute values of Variables

∴

M = 18.84rad \cdot 207000N/mm² \cdot 11.52mm \cdot \frac{{1.25mm}^{3}}{12 \cdot 5980mm}

Next Step Convert Units

∴

M = 18.84rad \cdot 2.1E+11Pa \cdot 0.0115m \cdot \frac{{0.0012m}^{3}}{12 \cdot 5.98m}

Next Step Prepare to Evaluate

∴

M = 18.84 \cdot 2.1E+11 \cdot 0.0115 \cdot \frac{{0.0012}^{3}}{12 \cdot 5.98}

Next Step Evaluate

∴

M = 1.22278846153846N*m

Next Step Convert to Output's Unit

∴

M = 1222.78846153846N*mm

LAST Step Rounding Answer

∴

M = 1222.7885N*mm

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

Variables

Bending moment in spiral spring

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.

Symbol: M

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Angle of Rotation of Arbor

Angle of Rotation of Arbor is defined as how many degrees the arbor is rotated with respect to the drum line.

Symbol: θ

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Modulus of elasticity of spiral spring

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.

Symbol: E

Measurement: PressureUnit: N/mm²

Note: Value should be greater than 0.

Width of Strip of Spiral Spring

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.

Symbol: b

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Thickness of Strip of Spring

The Thickness of Strip of Spring is defined as the thickness of the wired strip by which the spiral spring is manufactured.

Symbol: t

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Length of Strip of Spiral Spring

Length of Strip of Spiral Spring is defined as the length of the thin strip of which spiral spring coils are manufactured.

Symbol: l

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Credits

Creator Image

Created by Kethavath Srinath

Osmania University (OU), Hyderabad

Kethavath Srinath has created this Formula and 1000+ more formulas!

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Verified by Urvi Rathod

Vishwakarma Government Engineering College (VGEC), Ahmedabad

Urvi Rathod has verified this Formula and 1900+ more formulas!

Other Formulas to find Bending moment in spiral spring

Go Bending Moment due to Force given Bending Stress induced in Spring

M = σ b \cdot b \cdot \frac{t^{2}}{12}

Go Bending Moment due to Force

M = P \cdot r

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

M = \frac{δ \cdot E \cdot b \cdot t^{3}}{12 \cdot l \cdot r}

Go Bending Moment given Strain Energy Stored in Spring

M = \sqrt{U \cdot E \cdot b \cdot \frac{t^{3}}{6 \cdot l}}

Other formulas in Bending Moment in Spiral Spring category

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

r = \frac{M}{P}

Go Deflection of one End of Spring with Respect to Other End

δ = 12 \cdot M \cdot l \cdot \frac{r}{E \cdot b \cdot t^{3}}

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

r = δ \cdot E \cdot b \cdot \frac{t^{3}}{12 \cdot M \cdot l}

How to Evaluate 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 evaluator 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 Strip of Spiral Spring) to evaluate the Bending moment in spiral spring, Bending Moment due to Force given Angle of Rotation of Arbor with Respect to Drum formula is defined as a measure of the twisting force that causes a spiral spring to deform, resulting in a change in its shape and size, which is critical in determining the spring's mechanical behavior and performance. Bending moment in spiral spring is denoted by M symbol.

How to evaluate Bending Moment due to Force given Angle of Rotation of Arbor with Respect to Drum using this online evaluator? To use this online evaluator 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 Strip of Spiral Spring (l) and hit the calculate button.

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

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

The formula of Bending Moment due to Force given Angle of Rotation of Arbor with Respect to Drum is expressed as 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 Strip of Spiral Spring). Here is an example- 1.2E+6 = 18.84*207000000000*0.01152*0.00125^3/(12*5.98).

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

With 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 Strip of Spiral Spring (l) we can find Bending Moment due to Force given Angle of Rotation of Arbor with Respect to Drum using the formula - 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 Strip of Spiral Spring).

What are the other ways to Calculate Bending moment in spiral spring?

Here are the different ways to Calculate Bending moment in spiral spring-

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 Strip of Spiral Spring*Distance of CG of Spiral Spring)

Can the Bending Moment due to Force given Angle of Rotation of Arbor with Respect to Drum be negative?

No, the Bending Moment due to Force given Angle of Rotation of Arbor with Respect to Drum, measured in Torque cannot be negative.

Which unit is used to measure 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 is usually measured using the Newton Millimeter[N*mm] for Torque. Newton Meter[N*mm], Newton Centimeter[N*mm], Kilonewton Meter[N*mm] are the few other units in which Bending Moment due to Force given Angle of Rotation of Arbor with Respect to Drum can be measured.

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