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Slenderness Ratio Formula

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Slenderness Ratio is the ratio of the length of a column and the least radius of gyration of its cross section. Check FAQs

λ = \frac{L eff}{r}

λ - Slenderness Ratio?L_eff - Effective Length?r - Least Radius of Gyration?

Slenderness Ratio Example

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Here is how the Slenderness Ratio equation looks like with Values.

Here is how the Slenderness Ratio equation looks like with Units.

Here is how the Slenderness Ratio equation looks like.

0.5657 = \frac{1.98}{3.5}

0.5657 = \frac{1.98m}{3.5m}

0.5657 = \frac{1.98}{3.5}

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Slenderness Ratio Solution

Follow our step by step solution on how to calculate Slenderness Ratio?

FIRST Step Consider the formula

λ = \frac{L eff}{r}

Next Step Substitute values of Variables

∴

λ = \frac{1.98m}{3.5m}

Next Step Prepare to Evaluate

∴

λ = \frac{1.98}{3.5}

Next Step Evaluate

∴

λ = 0.565714285714286

LAST Step Rounding Answer

∴

λ = 0.5657

Slenderness Ratio Formula Elements

Variables

Slenderness Ratio

Slenderness Ratio is the ratio of the length of a column and the least radius of gyration of its cross section.

Symbol: λ

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Slenderness Ratio

Effective Length

The Effective Length is the length which resists against buckling.

Symbol: L_eff

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Effective Length

Least Radius of Gyration

The Least Radius of Gyration is the smallest value of the radius of gyration is used for structural calculations.

Symbol: r

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Least Radius of Gyration

Other formulas in Stress and Strain category

Go Elongation Circular Tapered Bar

Δ c = \frac{4 \cdot W load \cdot L bar}{π \cdot D 1 \cdot D 2 \cdot e}

Go Moment of Inertia for Hollow Circular Shaft

J h = \frac{π}{32} \cdot ({d ho}^{4} - {d hi}^{4})

Go Moment of Inertia about Polar Axis

J = \frac{π \cdot {d s}^{4}}{32}

Go Elongation of Prismatic Bar due to its Own Weight

Δ p = \frac{W load \cdot L bar}{2 \cdot A \cdot e}

How to Evaluate Slenderness Ratio?

Slenderness Ratio evaluator uses Slenderness Ratio = Effective Length/Least Radius of Gyration to evaluate the Slenderness Ratio, The Slenderness Ratio formula is defined as a measure of the ratio of the effective length of a column to its least radius of gyration, providing a way to quantify the tendency of a column to buckle under compressive loads, which is critical in understanding the behavior of columns under various stress and strain conditions. Slenderness Ratio is denoted by λ symbol.

How to evaluate Slenderness Ratio using this online evaluator? To use this online evaluator for Slenderness Ratio, enter Effective Length (L_eff) & Least Radius of Gyration (r) and hit the calculate button.

FAQs on Slenderness Ratio

What is the formula to find Slenderness Ratio?

The formula of Slenderness Ratio is expressed as Slenderness Ratio = Effective Length/Least Radius of Gyration. Here is an example- 13.2 = 1.98/3.5.

How to calculate Slenderness Ratio?

With Effective Length (L_eff) & Least Radius of Gyration (r) we can find Slenderness Ratio using the formula - Slenderness Ratio = Effective Length/Least Radius of Gyration.

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