Slenderness Parameter Calculator

✖Effective Length Factor used for the members in the frame is the ratio of compression member stiffness to the end restraint stiffness.ⓘ Effective Length Factor [k]			+10% -10%
✖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.ⓘ Effective Column Length [l]			+10% -10%
✖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.ⓘ Radius of Gyration [r]			+10% -10%
✖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.ⓘ Yield Stress of Steel [F_y]			+10% -10%

✖Slenderness Parameter is the value which demarcates between the elastic and inelastic behavior of the member.ⓘ Slenderness Parameter [λ_c]

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Slenderness Parameter Solution

STEP 0: Pre-Calculation Summary

Formula Used

Slenderness Parameter = ((Effective Length Factor*Effective Column Length)/(Radius of Gyration))^2*(Yield Stress of Steel/286220)
λ_c = ((k*l)/(r))^2*(F_y/286220)
This formula uses 5 Variables

Variables Used

Slenderness Parameter - Slenderness Parameter is the value which demarcates between the elastic and inelastic behavior of the member.
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.
Effective Column Length - (Measured in Meter) - 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.
Radius of Gyration - (Measured in Meter) - 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.
Yield Stress of Steel - (Measured in Megapascal) - 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.

STEP 1: Convert Input(s) to Base Unit

Effective Length Factor: 5 --> No Conversion Required
Effective Column Length: 932 Millimeter --> 0.932 Meter (Check conversion here)
Radius of Gyration: 87 Millimeter --> 0.087 Meter (Check conversion here)
Yield Stress of Steel: 250 Megapascal --> 250 Megapascal No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

λ_c = ((k*l)/(r))^2*(F_y/286220) --> ((5*0.932)/(0.087))^2*(250/286220)

Evaluating ... ...

λ_c = 2.50595552754964

STEP 3: Convert Result to Output's Unit

2.50595552754964 --> No Conversion Required

FINAL ANSWER

2.50595552754964 ≈ 2.505956 <-- Slenderness Parameter

(Calculation completed in 00.020 seconds)

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Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

Chandana P Dev has created this Calculator and 500+ more calculators!

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Meerut Institute of Engineering and Technology (MIET), Meerut

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< Columns Calculators

Slenderness Parameter

LaTeX Go Slenderness Parameter = ((Effective Length Factor*Effective Column Length)/(Radius of Gyration))^2*(Yield Stress of Steel/286220)

Critical Buckling Stress when Slenderness Parameter is greater than 2.25

LaTeX Go Critical Buckling Stress = (0.877*Yield Stress of Steel)/Slenderness Parameter

Critical Buckling Stress when Slenderness Parameter is Less than 2.25

LaTeX Go Critical Buckling Stress = 0.658^(Slenderness Parameter)*Yield Stress of Steel

Maximum Load on Axially Loaded Members

LaTeX Go Maximum Axial Load = 0.85*Gross Cross-Sectional Area*Critical Buckling Stress

Slenderness Parameter Formula

LaTeX Go

Slenderness Parameter = ((Effective Length Factor*Effective Column Length)/(Radius of Gyration))^2*(Yield Stress of Steel/286220)
λ_c = ((k*l)/(r))^2*(F_y/286220)

What is the use of Slenderness Ratio?

The Columns are classified on the basis of slenderness ratio. Strength of column is also dependent over the slenderness ratio. With increase in slenderness ratio, column will have more tendencies to buckle. Hence, compressive strength of column decreases with increase in Slenderness ratio.

How to Calculate Slenderness Parameter?

Slenderness Parameter calculator uses Slenderness Parameter = ((Effective Length Factor*Effective Column Length)/(Radius of Gyration))^2*(Yield Stress of Steel/286220) to calculate 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 calculate Slenderness Parameter using this online calculator? To use this online calculator 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. Here is how the Slenderness Parameter calculation can be explained with given input values -> 25.96474 = ((5*0.932)/(0.087))^2*(250000000/286220).

FAQ

What is 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 and is represented as λ_c = ((k*l)/(r))^2*(F_y/286220) or Slenderness Parameter = ((Effective Length Factor*Effective Column Length)/(Radius of Gyration))^2*(Yield Stress of Steel/286220). Effective Length Factor used for the members in the frame is the ratio of compression member stiffness to the end restraint stiffness, 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, 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 & 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.

How to calculate 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 is calculated using Slenderness Parameter = ((Effective Length Factor*Effective Column Length)/(Radius of Gyration))^2*(Yield Stress of Steel/286220). To calculate Slenderness Parameter, you need Effective Length Factor (k), Effective Column Length (l), Radius of Gyration (r) & Yield Stress of Steel (F_y). With our tool, you need to enter the respective value for Effective Length Factor, Effective Column Length, Radius of Gyration & Yield Stress of Steel 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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