Length of Cantilever given Bending Stress on Graduated Length Leaves Calculator

✖Bending Stress in graduated leaf is the normal bending stress that is induced at a point in an extra graduated length leaves of a leaf spring.ⓘ Bending Stress in graduated leaf [σ_bg]			+10% -10%
✖Number of Full length Leaves is defined as the total number of extra full length leaves present in a multi-leaf spring.ⓘ Number of Full length Leaves [n_f]			+10% -10%
✖Number of Graduated Length Leaves is defined as the number of graduated-length leaves including master leaf.ⓘ Number of Graduated Length Leaves [n_g]			+10% -10%
✖Width of Leaf is defined as the width of each leaf present in a multi-leaf spring.ⓘ Width of Leaf [b]			+10% -10%
✖Thickness of Leaf is defined as the thickness of each leaf present in a multi-leaf spring.ⓘ Thickness of Leaf [t]			+10% -10%
✖Force Applied at End of Leaf Spring is defined as the net amount of force that is acting onto the spring.ⓘ Force Applied at End of Leaf Spring [P]			+10% -10%

✖The Length of Cantilever of Leaf Spring is defined as half the length of a semi-elliptic spring.ⓘ Length of Cantilever given Bending Stress on Graduated Length Leaves [L]

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Formula

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Length of Cantilever given Bending Stress on Graduated Length Leaves

Formula

`"L" = ("σ"_{"b"}"g")*(3*"n"_{"f"}+2*"n"_{"g"})*"b"*"t"^2/(12*"P")`

Example

`"603.8323mm"="448N/mm²"*(3*"3"+2*"15")*"108mm"*("12mm")^2/(12*"37500N")`

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Length of Cantilever given Bending Stress on Graduated Length Leaves Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
L = σ_bg*(3*n_f+2*n_g)*b*t^2/(12*P)
This formula uses 7 Variables

Variables Used

Length of Cantilever of Leaf Spring - (Measured in Meter) - The Length of Cantilever of Leaf Spring is defined as half the length of a semi-elliptic spring.
Bending Stress in graduated leaf - (Measured in Pascal) - Bending Stress in graduated leaf is the normal bending stress that is induced at a point in an extra graduated length leaves of a leaf spring.
Number of Full length Leaves - Number of Full length Leaves is defined as the total number of extra full length leaves present in a multi-leaf spring.
Number of Graduated Length Leaves - Number of Graduated Length Leaves is defined as the number of graduated-length leaves including master leaf.
Width of Leaf - (Measured in Meter) - Width of Leaf is defined as the width of each leaf present in a multi-leaf spring.
Thickness of Leaf - (Measured in Meter) - Thickness of Leaf is defined as the thickness of each leaf present in a multi-leaf spring.
Force Applied at End of Leaf Spring - (Measured in Newton) - Force Applied at End of Leaf Spring is defined as the net amount of force that is acting onto the spring.

STEP 1: Convert Input(s) to Base Unit

Bending Stress in graduated leaf: 448 Newton per Square Millimeter --> 448000000 Pascal (Check conversion here)
Number of Full length Leaves: 3 --> No Conversion Required
Number of Graduated Length Leaves: 15 --> No Conversion Required
Width of Leaf: 108 Millimeter --> 0.108 Meter (Check conversion here)
Thickness of Leaf: 12 Millimeter --> 0.012 Meter (Check conversion here)
Force Applied at End of Leaf Spring: 37500 Newton --> 37500 Newton No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L = σ_bg*(3*n_f+2*n_g)*b*t^2/(12*P) --> 448000000*(3*3+2*15)*0.108*0.012^2/(12*37500)

Evaluating ... ...

L = 0.60383232

STEP 3: Convert Result to Output's Unit

0.60383232 Meter -->603.83232 Millimeter (Check conversion here)

FINAL ANSWER

603.83232 ≈ 603.8323 Millimeter <-- Length of Cantilever of Leaf Spring

(Calculation completed in 00.004 seconds)

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Home » Physics » Design of Automobile Elements » Design of Springs » Multi-Leaf Spring » Length of Cantilever » Length of Cantilever given Bending Stress on Graduated Length Leaves

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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< 4 Length of Cantilever Calculators

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

Go 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)

Length of Cantilever given Bending Stress on Graduated Length Leaves

Go 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)

Length of Cantilever given Bending Stress in Plate

Go 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 given Bending Stress in Plate of Extra Full Length

Go 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 given Bending Stress on Graduated Length Leaves Formula

Define Bending Stress?

Bending stress is the normal stress that an object encounters when it is subjected to a large load at a particular point that causes the object to bend and become fatigued. Bending stress occurs when operating industrial equipment and in concrete and metallic structures when they are subjected to a tensile load.

How to Calculate Length of Cantilever given Bending Stress on Graduated Length Leaves?

Length of Cantilever given Bending Stress on Graduated Length Leaves calculator uses 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) to calculate the Length of Cantilever of Leaf Spring, The Length of Cantilever given Bending Stress on Graduated Length Leaves formula is defined as rigid structural element that extends horizontally and is supported at only one end. Length of Cantilever of Leaf Spring is denoted by L symbol.

How to calculate Length of Cantilever given Bending Stress on Graduated Length Leaves using this online calculator? To use this online calculator for Length of Cantilever given Bending Stress on Graduated Length Leaves, enter Bending Stress in graduated leaf (σ_bg), Number of Full length Leaves (n_f), Number of Graduated Length Leaves (n_g), Width of Leaf (b), Thickness of Leaf (t) & Force Applied at End of Leaf Spring (P) and hit the calculate button. Here is how the Length of Cantilever given Bending Stress on Graduated Length Leaves calculation can be explained with given input values -> 603832.3 = 448000000*(3*3+2*15)*0.108*0.012^2/(12*37500).

FAQ

What is Length of Cantilever given Bending Stress on Graduated Length Leaves?

The Length of Cantilever given Bending Stress on Graduated Length Leaves formula is defined as rigid structural element that extends horizontally and is supported at only one end and is represented as L = σ_bg*(3*n_f+2*n_g)*b*t^2/(12*P) or 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). Bending Stress in graduated leaf is the normal bending stress that is induced at a point in an extra graduated length leaves of a leaf spring, Number of Full length Leaves is defined as the total number of extra full length leaves present in a multi-leaf spring, Number of Graduated Length Leaves is defined as the number of graduated-length leaves including master leaf, Width of Leaf is defined as the width of each leaf present in a multi-leaf spring, Thickness of Leaf is defined as the thickness of each leaf present in a multi-leaf spring & Force Applied at End of Leaf Spring is defined as the net amount of force that is acting onto the spring.

How to calculate Length of Cantilever given Bending Stress on Graduated Length Leaves?

The Length of Cantilever given Bending Stress on Graduated Length Leaves formula is defined as rigid structural element that extends horizontally and is supported at only one end is calculated using 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). To calculate Length of Cantilever given Bending Stress on Graduated Length Leaves, you need Bending Stress in graduated leaf (σ_bg), Number of Full length Leaves (n_f), Number of Graduated Length Leaves (n_g), Width of Leaf (b), Thickness of Leaf (t) & Force Applied at End of Leaf Spring (P). With our tool, you need to enter the respective value for Bending Stress in graduated leaf, Number of Full length Leaves, Number of Graduated Length Leaves, Width of Leaf, Thickness of Leaf & Force Applied at End of Leaf Spring and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Length of Cantilever of Leaf Spring?

In this formula, Length of Cantilever of Leaf Spring uses Bending Stress in graduated leaf, Number of Full length Leaves, Number of Graduated Length Leaves, Width of Leaf, Thickness of Leaf & Force Applied at End of Leaf Spring. We can use 3 other way(s) to calculate the same, which is/are as follows -

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 = (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)
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)

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