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Length of Cantilever given Deflection of Spring at load point Formula

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

GoLength of Cantilever given Deflection at end of Spring 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 E \cdot n g \cdot b \cdot \frac{t^{3}}{4 \cdot P g})}^{\frac{1}{3}}

L - Length of Cantilever of Leaf Spring?δ - Deflection at End of Leaf Spring?E - Modulus of Elasticity of Spring?n_g - Number of Graduated Length Leaves?b - Width of Leaf?t - Thickness of Leaf?P_g - Force Taken by Graduated Length Leaves?

Length of Cantilever given Deflection of Spring at load point Example

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

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

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

500 = {(37.3353 \cdot 207000 \cdot 15 \cdot 108 \cdot \frac{12^{3}}{4 \cdot 43269.23})}^{\frac{1}{3}}

500mm = {(37.3353mm \cdot 207000N/mm² \cdot 15 \cdot 108mm \cdot \frac{{12mm}^{3}}{4 \cdot 43269.23N})}^{\frac{1}{3}}

500 = {(37.3353 \cdot 207000 \cdot 15 \cdot 108 \cdot \frac{12^{3}}{4 \cdot 43269.23})}^{\frac{1}{3}}

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Length of Cantilever given Deflection of Spring at load point Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

L = {(37.3353mm \cdot 207000N/mm² \cdot 15 \cdot 108mm \cdot \frac{{12mm}^{3}}{4 \cdot 43269.23N})}^{\frac{1}{3}}

Next Step Convert Units

∴

L = {(0.0373m \cdot 2.1E+11Pa \cdot 15 \cdot 0.108m \cdot \frac{{0.012m}^{3}}{4 \cdot 43269.23N})}^{\frac{1}{3}}

Next Step Prepare to Evaluate

∴

L = {(0.0373 \cdot 2.1E+11 \cdot 15 \cdot 0.108 \cdot \frac{{0.012}^{3}}{4 \cdot 43269.23})}^{\frac{1}{3}}

Next Step Evaluate

∴

L = 0.500000014468763m

Next Step Convert to Output's Unit

∴

L = 500.000014468763mm

LAST Step Rounding Answer

∴

L = 500mm

Length of Cantilever given Deflection of Spring at load point 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

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

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

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 Taken by Graduated Length Leaves

Force Taken by Graduated Length Leaves is the force exerted by graduated length leaves on an object, measured in a specific unit of measurement.

Symbol: P_g

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Force Taken by Graduated Length Leaves

Other Formulas to find Length of Cantilever of Leaf Spring

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}

Go Length of Cantilever given Deflection at end of Spring

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}}

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 of Spring at load point?

Length of Cantilever given Deflection of Spring at load point evaluator uses 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) to evaluate the Length of Cantilever of Leaf Spring, Length of Cantilever given Deflection of Spring at load point formula is defined as a measure of the distance from the fixed end to the point of application of the load, which is essential in determining the stability and structural integrity of cantilever beams and springs in various engineering applications. Length of Cantilever of Leaf Spring is denoted by L symbol.

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

FAQs on Length of Cantilever given Deflection of Spring at load point

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

The formula of Length of Cantilever given Deflection of Spring at load point is expressed as 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). Here is an example- 500000 = (0.03733534*207000000000*15*0.108*0.012^3/(4*43269.23))^(1/3).

How to calculate Length of Cantilever given Deflection of Spring at load point?

With Deflection at End of Leaf Spring (δ), Modulus of Elasticity of Spring (E), Number of Graduated Length Leaves (n_g), Width of Leaf (b), Thickness of Leaf (t) & Force Taken by Graduated Length Leaves (P_g) we can find Length of Cantilever given Deflection of Spring at load point using the formula - 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).

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=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)
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)

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

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

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

Length of Cantilever given Deflection of Spring at load point 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 of Spring at load point can be measured.

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Length of Cantilever given Deflection of Spring at load point Formula

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

​GoLength of Cantilever given Deflection at end of Spring Formula

Length of Cantilever given Deflection of Spring at load point Example

Length of Cantilever given Deflection of Spring at load point Solution

Length of Cantilever given Deflection of Spring at load point 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 of Spring at load point?

FAQs on Length of Cantilever given Deflection of Spring at load point

Variable Name

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

GoLength of Cantilever given Deflection at end of Spring Formula