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Length of Cantilever given Deflection at end of Spring Formula

GoLength of Cantilever given Deflection of Spring at load point Formula

GoLength of Cantilever given Bending Stress in extra full length leaves Formula

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Length of Cantilever of Leaf Spring is the distance from the fixed point to the end of the cantilever in an extra full-length leaf spring system. Check FAQs

L = {(δ \cdot \frac{(3 \cdot n f + 2 \cdot n g) \cdot E \cdot b \cdot t^{3}}{12 \cdot P})}^{\frac{1}{3}}

L - Length of Cantilever of Leaf Spring?δ - Deflection at End of Leaf Spring?n_f - Number of Full length Leaves?n_g - Number of Graduated Length Leaves?E - Modulus of Elasticity of Spring?b - Width of Leaf?t - Thickness of Leaf?P - Force Applied at End of Leaf Spring?

Length of Cantilever given Deflection at end of Spring Example

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Here is how the Length of Cantilever given Deflection at end of Spring equation looks like with Values.

Here is how the Length of Cantilever given Deflection at end of Spring equation looks like with Units.

Here is how the Length of Cantilever given Deflection at end of Spring equation looks like.

500 = {(37.3353 \cdot \frac{(3 \cdot 3 + 2 \cdot 15) \cdot 207000 \cdot 108 \cdot 12^{3}}{12 \cdot 37500})}^{\frac{1}{3}}

500mm = {(37.3353mm \cdot \frac{(3 \cdot 3 + 2 \cdot 15) \cdot 207000N/mm² \cdot 108mm \cdot {12mm}^{3}}{12 \cdot 37500N})}^{\frac{1}{3}}

500 = {(37.3353 \cdot \frac{(3 \cdot 3 + 2 \cdot 15) \cdot 207000 \cdot 108 \cdot 12^{3}}{12 \cdot 37500})}^{\frac{1}{3}}

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Length of Cantilever given Deflection at end of Spring Solution

Follow our step by step solution on how to calculate Length of Cantilever given Deflection at end of Spring?

FIRST Step Consider the formula

L = {(δ \cdot \frac{(3 \cdot n f + 2 \cdot n g) \cdot E \cdot b \cdot t^{3}}{12 \cdot P})}^{\frac{1}{3}}

Next Step Substitute values of Variables

∴

L = {(37.3353mm \cdot \frac{(3 \cdot 3 + 2 \cdot 15) \cdot 207000N/mm² \cdot 108mm \cdot {12mm}^{3}}{12 \cdot 37500N})}^{\frac{1}{3}}

Next Step Convert Units

∴

L = {(0.0373m \cdot \frac{(3 \cdot 3 + 2 \cdot 15) \cdot 2.1E+11Pa \cdot 0.108m \cdot {0.012m}^{3}}{12 \cdot 37500N})}^{\frac{1}{3}}

Next Step Prepare to Evaluate

∴

L = {(0.0373 \cdot \frac{(3 \cdot 3 + 2 \cdot 15) \cdot 2.1E+11 \cdot 0.108 \cdot {0.012}^{3}}{12 \cdot 37500})}^{\frac{1}{3}}

Next Step Evaluate

∴

L = 0.5000000115058m

Next Step Convert to Output's Unit

∴

L = 500.0000115058mm

LAST Step Rounding Answer

∴

L = 500mm

Length of Cantilever given Deflection at end of Spring Formula Elements

Variables

Length of Cantilever of Leaf Spring

Length of Cantilever of Leaf Spring is the distance from the fixed point to the end of the cantilever in an extra full-length leaf spring system.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Cantilever of Leaf Spring

Deflection at End of Leaf Spring

Deflection at end of leaf spring is the maximum displacement of the leaf spring's end from its original position when a force is applied.

Symbol: δ

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Deflection at End of Leaf Spring

Number of Full length Leaves

Number of Full Length Leaves is the count of leaves that have reached their maximum possible length.

Symbol: n_f

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Full length Leaves

Number of Graduated Length Leaves

Number of Graduated Length Leaves is defined as the number of graduated-length leaves including master leaf.

Symbol: n_g

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Graduated Length Leaves

Modulus of Elasticity of Spring

Modulus of Elasticity of Spring is the measure of the spring's stiffness, representing the amount of stress it can withstand without deforming.

Symbol: E

Measurement: PressureUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity of Spring

Width of Leaf

Width of Leaf is defined as the width of each leaf present in a multi-leaf spring.

Symbol: b

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Width of Leaf

Thickness of Leaf

Thickness of Leaf is the measure of the distance from the top surface to the bottom surface of a leaf in extra full length leaves.

Symbol: t

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Thickness of Leaf

Force Applied at End of Leaf Spring

Force Applied at End of Leaf Spring is the force exerted at the end of a leaf spring with extra full length leaves, affecting its overall performance.

Symbol: P

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Force Applied at End of Leaf Spring

Other Formulas to find Length of Cantilever of Leaf Spring

Go Length of Cantilever given Deflection of Spring at load point

L = {(δ \cdot E \cdot n g \cdot b \cdot \frac{t^{3}}{4 \cdot P g})}^{\frac{1}{3}}

Go Length of Cantilever given Bending Stress in extra full length leaves

L = σ b f \cdot (3 \cdot n f + 2 \cdot n g) \cdot b \cdot \frac{t^{2}}{18 \cdot P}

Other formulas in Extra Full Length Leaves category

Go Bending Stress in Plate Graduated Length Leaves

σ b f = 6 \cdot P g \cdot \frac{L}{n g \cdot b \cdot t^{2}}

Go Deflection at Load Point Graduated Length Leaves

δ g = 6 \cdot P g \cdot \frac{L^{3}}{E \cdot n g \cdot b \cdot t^{3}}

How to Evaluate Length of Cantilever given Deflection at end of Spring?

Length of Cantilever given Deflection at end of Spring evaluator uses Length of Cantilever of Leaf Spring = (Deflection at End of Leaf Spring*((3*Number of Full length Leaves+2*Number of Graduated Length Leaves)*Modulus of Elasticity of Spring*Width of Leaf*Thickness of Leaf^3)/(12*Force Applied at End of Leaf Spring))^(1/3) to evaluate the Length of Cantilever of Leaf Spring, Length of Cantilever given Deflection at end of Spring formula is defined as a measure of the length of a cantilever beam in terms of its deflection at the end of the spring, considering factors such as the modulus of elasticity, breadth, and thickness of the beam, as well as the point load applied. Length of Cantilever of Leaf Spring is denoted by L symbol.

How to evaluate Length of Cantilever given Deflection at end of Spring using this online evaluator? To use this online evaluator for Length of Cantilever given Deflection at end of Spring, enter Deflection at End of Leaf Spring (δ), Number of Full length Leaves (n_f), Number of Graduated Length Leaves (n_g), Modulus of Elasticity of Spring (E), Width of Leaf (b), Thickness of Leaf (t) & Force Applied at End of Leaf Spring (P) and hit the calculate button.

FAQs on Length of Cantilever given Deflection at end of Spring

What is the formula to find Length of Cantilever given Deflection at end of Spring?

The formula of Length of Cantilever given Deflection at end of Spring is expressed as Length of Cantilever of Leaf Spring = (Deflection at End of Leaf Spring*((3*Number of Full length Leaves+2*Number of Graduated Length Leaves)*Modulus of Elasticity of Spring*Width of Leaf*Thickness of Leaf^3)/(12*Force Applied at End of Leaf Spring))^(1/3). Here is an example- 408248.3 = (0.03733534*((3*3+2*15)*207000000000*0.108*0.012^3)/(12*37500))^(1/3).

How to calculate Length of Cantilever given Deflection at end of Spring?

With Deflection at End of Leaf Spring (δ), Number of Full length Leaves (n_f), Number of Graduated Length Leaves (n_g), Modulus of Elasticity of Spring (E), Width of Leaf (b), Thickness of Leaf (t) & Force Applied at End of Leaf Spring (P) we can find Length of Cantilever given Deflection at end of Spring using the formula - Length of Cantilever of Leaf Spring = (Deflection at End of Leaf Spring*((3*Number of Full length Leaves+2*Number of Graduated Length Leaves)*Modulus of Elasticity of Spring*Width of Leaf*Thickness of Leaf^3)/(12*Force Applied at End of Leaf Spring))^(1/3).

What are the other ways to Calculate Length of Cantilever of Leaf Spring?

Here are the different ways to Calculate Length of Cantilever of Leaf Spring-

Length of Cantilever of Leaf Spring=(Deflection at End of Leaf Spring*Modulus of Elasticity of Spring*Number of Graduated Length Leaves*Width of Leaf*Thickness of Leaf^3/(4*Force Taken by Graduated Length Leaves))^(1/3)
Length of Cantilever of Leaf Spring=Bending Stress in Full Leaf*(3*Number of Full length Leaves+2*Number of Graduated Length Leaves)*Width of Leaf*Thickness of Leaf^2/(18*Force Applied at End of Leaf Spring)

Can the Length of Cantilever given Deflection at end of Spring be negative?

No, the Length of Cantilever given Deflection at end of Spring, measured in Length cannot be negative.

Which unit is used to measure Length of Cantilever given Deflection at end of Spring?

Length of Cantilever given Deflection at end of Spring is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Length of Cantilever given Deflection at end of Spring can be measured.

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Length of Cantilever given Deflection at end of Spring Formula

​GoLength of Cantilever given Deflection of Spring at load point Formula

​GoLength of Cantilever given Bending Stress in extra full length leaves Formula

Length of Cantilever given Deflection at end of Spring Example

Length of Cantilever given Deflection at end of Spring Solution

Length of Cantilever given Deflection at end of Spring Formula Elements

Other Formulas to find Length of Cantilever of Leaf Spring

Other formulas in Extra Full Length Leaves category

How to Evaluate Length of Cantilever given Deflection at end of Spring?

FAQs on Length of Cantilever given Deflection at end of Spring

Variable Name

GoLength of Cantilever given Deflection of Spring at load point Formula

GoLength of Cantilever given Bending Stress in extra full length leaves Formula