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Slenderness Parameter Formula

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Slenderness Parameter is the value which demarcates between the elastic and inelastic behavior of the member. Check FAQs

λ c = {(\frac{k \cdot l}{r})}^{2} \cdot (\frac{F y}{286220})

λ_c - Slenderness Parameter?k - Effective Length Factor?l - Effective Column Length?r - Radius of Gyration?F_y - Yield Stress of Steel?

Slenderness Parameter Example

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

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

Here is how the Slenderness Parameter equation looks like.

2.506 = {(\frac{5 \cdot 932}{87})}^{2} \cdot (\frac{250}{286220})

2.506 = {(\frac{5 \cdot 932mm}{87mm})}^{2} \cdot (\frac{250MPa}{286220})

2.506 = {(\frac{5 \cdot 932}{87})}^{2} \cdot (\frac{250}{286220})

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Slenderness Parameter Solution

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

FIRST Step Consider the formula

λ c = {(\frac{k \cdot l}{r})}^{2} \cdot (\frac{F y}{286220})

Next Step Substitute values of Variables

∴

λ c = {(\frac{5 \cdot 932mm}{87mm})}^{2} \cdot (\frac{250MPa}{286220})

Next Step Convert Units

∴

λ c = {(\frac{5 \cdot 0.932m}{0.087m})}^{2} \cdot (\frac{250MPa}{286220})

Next Step Prepare to Evaluate

∴

λ c = {(\frac{5 \cdot 0.932}{0.087})}^{2} \cdot (\frac{250}{286220})

Next Step Evaluate

∴

λ c = 2.50595552754964

LAST Step Rounding Answer

∴

λ c = 2.506

Slenderness Parameter Formula Elements

Variables

Slenderness Parameter

Slenderness Parameter is the value which demarcates between the elastic and inelastic behavior of the member.

Symbol: λ_c

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Slenderness Parameter

Effective Length Factor

Effective Length Factor used for the members in the frame is the ratio of compression member stiffness to the end restraint stiffness.

Symbol: k

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Effective Length Factor

Effective Column Length

Effective Column Length of a column is the length of an equivalent pin-ended column that has the same load-carrying capacity and buckling behavior as the actual column with different end conditions.

Symbol: l

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Effective Column Length

Radius of Gyration

Radius of Gyration is the distance from the axis of rotation to a point where the total mass of any body is supposed to be concentrated.

Symbol: r

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Gyration

Yield Stress of Steel

Yield Stress of Steel is the stress at which the material begins to deform plastically, meaning it will not return to its original shape when the applied force is removed.

Symbol: F_y

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Yield Stress of Steel

Other formulas in Columns category

Go Maximum Load on Axially Loaded Members

P u = 0.85 \cdot A g \cdot F cr

Go Critical Buckling Stress when Slenderness Parameter is Less than 2.25

F cr = {0.658}^{λ c} \cdot F y

Go Critical Buckling Stress when Slenderness Parameter is greater than 2.25

F cr = \frac{0.877 \cdot F y}{λ c}

How to Evaluate Slenderness Parameter?

Slenderness Parameter evaluator uses Slenderness Parameter = ((Effective Length Factor*Effective Column Length)/(Radius of Gyration))^2*(Yield Stress of Steel/286220) to evaluate the Slenderness Parameter, The Slenderness Parameter formula is defined as a geometrical parameter defined for a compression member, such as a column and is the ratio of the effective length of the member to its lateral dimensions. Slenderness Parameter is denoted by λ_c symbol.

How to evaluate Slenderness Parameter using this online evaluator? To use this online evaluator for Slenderness Parameter, enter Effective Length Factor (k), Effective Column Length (l), Radius of Gyration (r) & Yield Stress of Steel (F_y) and hit the calculate button.

FAQs on Slenderness Parameter

What is the formula to find Slenderness Parameter?

The formula of Slenderness Parameter is expressed as Slenderness Parameter = ((Effective Length Factor*Effective Column Length)/(Radius of Gyration))^2*(Yield Stress of Steel/286220). Here is an example- 25.96474 = ((5*0.932)/(0.087))^2*(250000000/286220).

How to calculate Slenderness Parameter?

With Effective Length Factor (k), Effective Column Length (l), Radius of Gyration (r) & Yield Stress of Steel (F_y) we can find Slenderness Parameter using the formula - Slenderness Parameter = ((Effective Length Factor*Effective Column Length)/(Radius of Gyration))^2*(Yield Stress of Steel/286220).

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Slenderness Parameter Formula

Slenderness Parameter Example

Slenderness Parameter Solution

Slenderness Parameter Formula Elements

Other formulas in Columns category

How to Evaluate Slenderness Parameter?

FAQs on Slenderness Parameter

Variable Name