Slenderness Ratio Calculator

✖The Effective Length is the length which resists against buckling.ⓘ Effective Length [L_eff]			+10% -10%
✖The Least Radius of Gyration is the smallest value of the radius of gyration is used for structural calculations.ⓘ Least Radius of Gyration [r]			+10% -10%

✖The Slenderness ratio is the ratio of the length of a column and the least radius of gyration of its cross section.ⓘ Slenderness Ratio [λ]

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Formula

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Slenderness Ratio

Formula

`"λ" = "L"_{"eff"}/"r"`

Example

`"335"="50.25m"/"0.15m"`

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Slenderness Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Slenderness Ratio = Effective Length/Least Radius of Gyration
λ = L_eff/r
This formula uses 3 Variables

Variables Used

Slenderness Ratio - The Slenderness ratio is the ratio of the length of a column and the least radius of gyration of its cross section.
Effective Length - (Measured in Meter) - The Effective Length is the length which resists against buckling.
Least Radius of Gyration - (Measured in Meter) - The Least Radius of Gyration is the smallest value of the radius of gyration is used for structural calculations.

STEP 1: Convert Input(s) to Base Unit

Effective Length: 50.25 Meter --> 50.25 Meter No Conversion Required
Least Radius of Gyration: 0.15 Meter --> 0.15 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

λ = L_eff/r --> 50.25/0.15

Evaluating ... ...

λ = 335

STEP 3: Convert Result to Output's Unit

335 --> No Conversion Required

FINAL ANSWER

335 <-- Slenderness Ratio

(Calculation completed in 00.006 seconds)

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Credits

Created by Pragati Jaju

College Of Engineering (COEP), Pune

Pragati Jaju has created this Calculator and 50+ more calculators!

Verified by Kethavath Srinath

Osmania University (OU), Hyderabad

Kethavath Srinath has verified this Calculator and 1200+ more calculators!

< 18 Stress and Strain Calculators

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Go Elongation = (4*Load*Length of Bar)/(pi*Diameter of Bigger End*Diameter of Smaller End*Elastic Modulus)

Total Angle of Twist

Go Total Angle of Twist = (Torque Exerted on Wheel*Shaft Length)/(Shear Modulus*Polar Moment of Inertia)

Moment of Inertia for Hollow Circular Shaft

Go Polar Moment of Inertia = pi/32*(Outer Diameter of Hollow Circular Section^(4)-Inner Diameter of Hollow Circular Section^(4))

Equivalent Bending Moment

Go Equivalent Bending Moment = Bending Moment+sqrt(Bending Moment^(2)+Torque Exerted on Wheel^(2))

Deflection of Fixed Beam with Uniformly Distributed Load

Go Deflection of Beam = (Width of Beam*Beam Length^4)/(384*Elastic Modulus*Moment of Inertia)

Deflection of Fixed Beam with Load at Center

Go Deflection of Beam = (Width of Beam*Beam Length^3)/(192*Elastic Modulus*Moment of Inertia)

Elongation of Prismatic Bar due to its Own Weight

Go Elongation = (2*Load*Length of Bar)/(Area of Prismatic Bar*Elastic Modulus)

Axial Elongation of Prismatic Bar due to External Load

Go Elongation = (Load*Length of Bar)/(Area of Prismatic Bar*Elastic Modulus)

Hooke's Law

Go Young's Modulus = (Load*Elongation)/(Area of Base*Initial Length)

Equivalent Torsional Moment

Go Equivalent Torsion Moment = sqrt(Bending Moment^(2)+Torque Exerted on Wheel^(2))

Rankine's Formula for Columns

Go Rankine’s Critical Load = 1/(1/Euler’s Buckling Load+1/Ultimate Crushing Load for Columns)

Slenderness Ratio

Go Slenderness Ratio = Effective Length/Least Radius of Gyration

Moment of Inertia about Polar Axis

Go Polar Moment of Inertia = (pi*Diameter of Shaft^(4))/32

Bulk Modulus given Volume Stress and Strain

Go Bulk Modulus = Volume Stress/Volumetric Strain

Shear Modulus

Go Shear Modulus = Shear Stress/Shear Strain

Bulk Modulus given Bulk Stress and Strain

Go Bulk Modulus = Bulk Stress/Bulk Strain

Young's Modulus

Go Young's Modulus = Stress/Strain

Elastic Modulus

Go Young's Modulus = Stress/Strain

Slenderness Ratio Formula

Slenderness Ratio = Effective Length/Least Radius of Gyration
λ = L_eff/r

What is Slenderness Ratio?

Slenderness ratio is the ratio of the length of a column and the least radius of gyration of its cross section. Often denoted by lambda.It is used extensively for finding out the design load as well as in classifying various columns in short/intermediate/long.

How to Calculate Slenderness Ratio?

Slenderness Ratio calculator uses Slenderness Ratio = Effective Length/Least Radius of Gyration to calculate the Slenderness Ratio, The Slenderness Ratio is the ratio of the length of a column and the least radius of gyration of its cross section.The larger the slenderness ratio, the less strength there is in a column. Slenderness Ratio is denoted by λ symbol.

How to calculate Slenderness Ratio using this online calculator? To use this online calculator for Slenderness Ratio, enter Effective Length (L_eff) & Least Radius of Gyration (r) and hit the calculate button. Here is how the Slenderness Ratio calculation can be explained with given input values -> 335 = 50.25/0.15.

FAQ

What is Slenderness Ratio?

The Slenderness Ratio is the ratio of the length of a column and the least radius of gyration of its cross section.The larger the slenderness ratio, the less strength there is in a column and is represented as λ = L_eff/r or Slenderness Ratio = Effective Length/Least Radius of Gyration. The Effective Length is the length which resists against buckling & The Least Radius of Gyration is the smallest value of the radius of gyration is used for structural calculations.

How to calculate Slenderness Ratio?

The Slenderness Ratio is the ratio of the length of a column and the least radius of gyration of its cross section.The larger the slenderness ratio, the less strength there is in a column is calculated using Slenderness Ratio = Effective Length/Least Radius of Gyration. To calculate Slenderness Ratio, you need Effective Length (L_eff) & Least Radius of Gyration (r). With our tool, you need to enter the respective value for Effective Length & Least Radius of Gyration and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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