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Bending Moment given Strain Energy Stored in Spring Formula

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

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

M - Bending moment in spiral spring?U - Strain energy in spiral spring?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 given Strain Energy Stored in Spring Example

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Here is how the Bending Moment given Strain Energy Stored in Spring equation looks like with Values.

Here is how the Bending Moment given Strain Energy Stored in Spring equation looks like with Units.

Here is how the Bending Moment given Strain Energy Stored in Spring equation looks like.

1199.8197 = \sqrt{11.09 \cdot 207000 \cdot 11.52 \cdot \frac{{1.25}^{3}}{6 \cdot 5980}}

1199.8197N*mm = \sqrt{11.09J \cdot 207000N/mm² \cdot 11.52mm \cdot \frac{{1.25mm}^{3}}{6 \cdot 5980mm}}

1199.8197 = \sqrt{11.09 \cdot 207000 \cdot 11.52 \cdot \frac{{1.25}^{3}}{6 \cdot 5980}}

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Bending Moment given Strain Energy Stored in Spring Solution

Follow our step by step solution on how to calculate Bending Moment given Strain Energy Stored in Spring?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

M = \sqrt{11.09J \cdot 207000N/mm² \cdot 11.52mm \cdot \frac{{1.25mm}^{3}}{6 \cdot 5980mm}}

Next Step Convert Units

∴

M = \sqrt{11.09J \cdot 2.1E+11Pa \cdot 0.0115m \cdot \frac{{0.0012m}^{3}}{6 \cdot 5.98m}}

Next Step Prepare to Evaluate

∴

M = \sqrt{11.09 \cdot 2.1E+11 \cdot 0.0115 \cdot \frac{{0.0012}^{3}}{6 \cdot 5.98}}

Next Step Evaluate

∴

M = 1.19981969799312N*m

Next Step Convert to Output's Unit

∴

M = 1199.81969799312N*mm

LAST Step Rounding Answer

∴

M = 1199.8197N*mm

Bending Moment given Strain Energy Stored in Spring Formula Elements

Variables

Functions

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.

Formulas to find Bending moment in spiral spring

Strain energy in spiral spring

Strain energy in spiral spring is the energy stored in a spiral spring by virtue of its deformation.

Symbol: U

Measurement: EnergyUnit: J

Note: Value should be greater than 0.

Formulas to find Strain energy in spiral spring

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.

Formulas to find Modulus of elasticity of spiral spring

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.

Formulas to find Width of Strip of Spiral Spring

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.

Formulas to find Thickness of Strip of Spring

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.

Formulas to find Length of Strip of Spiral Spring

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

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 Angle of Rotation of Arbor with Respect to Drum

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

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}

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 given Strain Energy Stored in Spring?

Bending Moment given Strain Energy Stored in Spring evaluator uses 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 Strip of Spiral Spring)) to evaluate the Bending moment in spiral spring, Bending Moment given Strain Energy Stored in Spring formula is defined as a measure of the twisting force that causes an object to deform when a spring is subjected to an external force, providing insight into the spring's mechanical behavior and stability in spiral spring systems. Bending moment in spiral spring is denoted by M symbol.

How to evaluate Bending Moment given Strain Energy Stored in Spring using this online evaluator? To use this online evaluator for Bending Moment given Strain Energy Stored in Spring, enter Strain energy in spiral spring (U), 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 given Strain Energy Stored in Spring

What is the formula to find Bending Moment given Strain Energy Stored in Spring?

The formula of Bending Moment given Strain Energy Stored in Spring is expressed as 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 Strip of Spiral Spring)). Here is an example- 1.2E+6 = sqrt(11.09*207000000000*0.01152*0.00125^3/(6*5.98)).

How to calculate Bending Moment given Strain Energy Stored in Spring?

With Strain energy in spiral spring (U), 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 given Strain Energy Stored in Spring using the formula - 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 Strip of Spiral Spring)). This formula also uses Square Root (sqrt) function(s).

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=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)

Can the Bending Moment given Strain Energy Stored in Spring be negative?

No, the Bending Moment given Strain Energy Stored in Spring, measured in Torque cannot be negative.

Which unit is used to measure Bending Moment given Strain Energy Stored in Spring?

Bending Moment given Strain Energy Stored in Spring 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 given Strain Energy Stored in Spring can be measured.

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Bending Moment given Strain Energy Stored in Spring Formula

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

​GoBending Moment due to Force Formula

Bending Moment given Strain Energy Stored in Spring Example

Bending Moment given Strain Energy Stored in Spring Solution

Bending Moment given Strain Energy Stored in Spring Formula Elements

Other Formulas to find Bending moment in spiral spring

Other formulas in Bending Moment in Spiral Spring category

How to Evaluate Bending Moment given Strain Energy Stored in Spring?

FAQs on Bending Moment given Strain Energy Stored in Spring

Variable Name

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

GoBending Moment due to Force Formula