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Length of Cantilever given Deflection at Load Point of Graduated length leaves Formula

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GoLength of Cantilever given Bending Stress in Plate Formula

3

GoLength of Cantilever given Bending Stress in Plate of Extra Full Length Formula

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The Length of Cantilever of Leaf Spring is defined as half the length of a semi-elliptic spring. Check FAQs

L = {(δ g \cdot E \cdot n g \cdot b \cdot \frac{t^{3}}{6 \cdot P g})}^{\frac{1}{3}}

L - Length of Cantilever of Leaf Spring?δ_g - Deflection of Graduated Leaf at Load Point?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 at Load Point of Graduated length leaves Example

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Here is how the Length of Cantilever given Deflection at Load Point of Graduated length leaves equation looks like with Values.

Here is how the Length of Cantilever given Deflection at Load Point of Graduated length leaves equation looks like with Units.

Here is how the Length of Cantilever given Deflection at Load Point of Graduated length leaves equation looks like.

500.0221 = {(37.41 \cdot 207000 \cdot 15 \cdot 108 \cdot \frac{12^{3}}{6 \cdot 28900})}^{\frac{1}{3}}

500.0221mm = {(37.41mm \cdot 207000N/mm² \cdot 15 \cdot 108mm \cdot \frac{{12mm}^{3}}{6 \cdot 28900N})}^{\frac{1}{3}}

500.0221 = {(37.41 \cdot 207000 \cdot 15 \cdot 108 \cdot \frac{12^{3}}{6 \cdot 28900})}^{\frac{1}{3}}

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Home » Physics » Mechanical » Design of Automobile Elements » Length of Cantilever given Deflection at Load Point of Graduated length leaves

Length of Cantilever given Deflection at Load Point of Graduated length leaves Solution

Follow our step by step solution on how to calculate Length of Cantilever given Deflection at Load Point of Graduated length leaves?

FIRST Step Consider the formula

L = {(δ g \cdot E \cdot n g \cdot b \cdot \frac{t^{3}}{6 \cdot P g})}^{\frac{1}{3}}

Next Step Substitute values of Variables

∴

L = {(37.41mm \cdot 207000N/mm² \cdot 15 \cdot 108mm \cdot \frac{{12mm}^{3}}{6 \cdot 28900N})}^{\frac{1}{3}}

Next Step Convert Units

∴

L = {(0.0374m \cdot 2.1E+11Pa \cdot 15 \cdot 0.108m \cdot \frac{{0.012m}^{3}}{6 \cdot 28900N})}^{\frac{1}{3}}

Next Step Prepare to Evaluate

∴

L = {(0.0374 \cdot 2.1E+11 \cdot 15 \cdot 0.108 \cdot \frac{{0.012}^{3}}{6 \cdot 28900})}^{\frac{1}{3}}

Next Step Evaluate

∴

L = 0.500022143757471m

Next Step Convert to Output's Unit

∴

L = 500.022143757471mm

LAST Step Rounding Answer

∴

L = 500.0221mm

Length of Cantilever given Deflection at Load Point of Graduated length leaves Formula Elements

Variables

Length of Cantilever of Leaf Spring

The Length of Cantilever of Leaf Spring is defined as half the length of a semi-elliptic spring.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Deflection of Graduated Leaf at Load Point

Deflection of graduated leaf at load point is how much the leaf of the spring deviates from its position at the load application point.

Symbol: δ_g

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Modulus of Elasticity of Spring

Modulus of Elasticity of Spring is a quantity that measures the spring's wire resistance to being deformed elastically when a stress is applied to it.

Symbol: E

Measurement: PressureUnit: N/mm²

Note: Value should be greater than 0.

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.

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.

Thickness of Leaf

Thickness of Leaf is defined as the thickness of each leaf present in a multi-leaf spring.

Symbol: t

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Force Taken by Graduated Length Leaves

Force Taken by Graduated Length Leaves is defined as the portion of force that is taken by graduated length leaves.

Symbol: P_g

Measurement: ForceUnit: N

Note: Value should be greater than 0.

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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 Length of Cantilever of Leaf Spring

Go Length of Cantilever given Bending Stress in Plate

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

Go Length of Cantilever given Bending Stress in Plate of Extra Full Length

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

How to Evaluate Length of Cantilever given Deflection at Load Point of Graduated length leaves?

Length of Cantilever given Deflection at Load Point of Graduated length leaves evaluator uses Length of Cantilever of Leaf Spring = (Deflection of Graduated Leaf at Load Point*Modulus of Elasticity of Spring*Number of Graduated Length Leaves*Width of Leaf*Thickness of Leaf^3/(6*Force Taken by Graduated Length Leaves))^(1/3) to evaluate the Length of Cantilever of Leaf Spring, Length of Cantilever given Deflection at Load Point of Graduated length leaves formula is defined as a measure of the length of a cantilever beam, which is a crucial parameter in structural analysis, determined by the deflection at the load point and other physical properties of the beam, providing valuable insights into the beam's behavior under various loads. Length of Cantilever of Leaf Spring is denoted by L symbol.

How to evaluate Length of Cantilever given Deflection at Load Point of Graduated length leaves using this online evaluator? To use this online evaluator for Length of Cantilever given Deflection at Load Point of Graduated length leaves, enter Deflection of Graduated Leaf at Load Point (δ_g), 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 at Load Point of Graduated length leaves

What is the formula to find Length of Cantilever given Deflection at Load Point of Graduated length leaves?

The formula of Length of Cantilever given Deflection at Load Point of Graduated length leaves is expressed as Length of Cantilever of Leaf Spring = (Deflection of Graduated Leaf at Load Point*Modulus of Elasticity of Spring*Number of Graduated Length Leaves*Width of Leaf*Thickness of Leaf^3/(6*Force Taken by Graduated Length Leaves))^(1/3). Here is an example- 500111.2 = (0.03741*207000000000*15*0.108*0.012^3/(6*28900))^(1/3).

How to calculate Length of Cantilever given Deflection at Load Point of Graduated length leaves?

With Deflection of Graduated Leaf at Load Point (δ_g), 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 at Load Point of Graduated length leaves using the formula - Length of Cantilever of Leaf Spring = (Deflection of Graduated Leaf at Load Point*Modulus of Elasticity of Spring*Number of Graduated Length Leaves*Width of Leaf*Thickness of Leaf^3/(6*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 Graduated Leaf*Number of Graduated Length Leaves*Width of Leaf*Thickness of Leaf^2/(6*Force Taken by Graduated Length Leaves)
Length of Cantilever of Leaf Spring=Bending Stress in Full Leaf*Number of Full length Leaves*Width of Leaf*Thickness of Leaf^2/(6*Force Taken by Full Length Leaves)
Length of Cantilever of Leaf Spring=Bending Stress in Graduated Leaf*(3*Number of Full length Leaves+2*Number of Graduated Length Leaves)*Width of Leaf*Thickness of Leaf^2/(12*Force Applied at End of Leaf Spring)

Can the Length of Cantilever given Deflection at Load Point of Graduated length leaves be negative?

No, the Length of Cantilever given Deflection at Load Point of Graduated length leaves, measured in Length cannot be negative.

Which unit is used to measure Length of Cantilever given Deflection at Load Point of Graduated length leaves?

Length of Cantilever given Deflection at Load Point of Graduated length leaves 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 Load Point of Graduated length leaves can be measured.

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