Limiting Laterally Unbraced Length for Inelastic Lateral Buckling Calculator

✖Radius of Gyration about Minor Axis is the root mean square distance of the object's parts from either its center of mass or a given minor axis, depending on the relevant application.ⓘ Radius of Gyration about Minor Axis [r_y]			+10% -10%
✖Beam Buckling Factor 1 is the value which is considered as the factor of safety against buckling to currently applied loads.ⓘ Beam Buckling Factor 1 [X₁]			+10% -10%
✖Specified Minimum Yield Stress represents the minimum tensile stress or yield stress required by the flexural member, ex- web.ⓘ Specified Minimum Yield Stress [F_yw]			+10% -10%
✖Compressive Residual Stress in Flange is the stress formed after plastic deformation, if the residue at a location has a value of -100 MPa, it is said to be compressive residual stress.ⓘ Compressive Residual Stress in Flange [F_r]			+10% -10%
✖Beam Buckling Factor 2 is the value used as factor of safety against buckling by applied loads.ⓘ Beam Buckling Factor 2 [X₂]			+10% -10%
✖Smaller Yield Stress is the yield stress value, which is smallest among, yield stress in web, flange or residual stress.ⓘ Smaller Yield Stress [F_l]			+10% -10%

✖Limiting Length is the maximum length of a structural member before certain design considerations, such as buckling, vibration, and deflection, become critical.ⓘ Limiting Laterally Unbraced Length for Inelastic Lateral Buckling [L_lim]

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Limiting Laterally Unbraced Length for Inelastic Lateral Buckling Solution

STEP 0: Pre-Calculation Summary

Formula Used

Limiting Length = ((Radius of Gyration about Minor Axis*Beam Buckling Factor 1)/(Specified Minimum Yield Stress-Compressive Residual Stress in Flange))*sqrt(1+sqrt(1+(Beam Buckling Factor 2*Smaller Yield Stress^2)))
L_lim = ((r_y*X₁)/(F_yw-F_r))*sqrt(1+sqrt(1+(X₂*F_l^2)))
This formula uses 1 Functions, 7 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Limiting Length - (Measured in Meter) - Limiting Length is the maximum length of a structural member before certain design considerations, such as buckling, vibration, and deflection, become critical.
Radius of Gyration about Minor Axis - (Measured in Meter) - Radius of Gyration about Minor Axis is the root mean square distance of the object's parts from either its center of mass or a given minor axis, depending on the relevant application.
Beam Buckling Factor 1 - Beam Buckling Factor 1 is the value which is considered as the factor of safety against buckling to currently applied loads.
Specified Minimum Yield Stress - (Measured in Megapascal) - Specified Minimum Yield Stress represents the minimum tensile stress or yield stress required by the flexural member, ex- web.
Compressive Residual Stress in Flange - (Measured in Megapascal) - Compressive Residual Stress in Flange is the stress formed after plastic deformation, if the residue at a location has a value of -100 MPa, it is said to be compressive residual stress.
Beam Buckling Factor 2 - Beam Buckling Factor 2 is the value used as factor of safety against buckling by applied loads.
Smaller Yield Stress - (Measured in Megapascal) - Smaller Yield Stress is the yield stress value, which is smallest among, yield stress in web, flange or residual stress.

STEP 1: Convert Input(s) to Base Unit

Radius of Gyration about Minor Axis: 20 Millimeter --> 0.02 Meter (Check conversion here)
Beam Buckling Factor 1: 3005 --> No Conversion Required
Specified Minimum Yield Stress: 139 Megapascal --> 139 Megapascal No Conversion Required
Compressive Residual Stress in Flange: 80 Megapascal --> 80 Megapascal No Conversion Required
Beam Buckling Factor 2: 64 --> No Conversion Required
Smaller Yield Stress: 110 Megapascal --> 110 Megapascal No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_lim = ((r_y*X₁)/(F_yw-F_r))*sqrt(1+sqrt(1+(X₂*F_l^2))) --> ((0.02*3005)/(139-80))*sqrt(1+sqrt(1+(64*110^2)))

Evaluating ... ...

L_lim = 30.2350404950413

STEP 3: Convert Result to Output's Unit

30.2350404950413 Meter -->30235.0404950413 Millimeter (Check conversion here)

FINAL ANSWER

30235.0404950413 ≈ 30235.04 Millimeter <-- Limiting Length

(Calculation completed in 00.257 seconds)

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Home » Engineering » Civil » Design of Steel Structures » Load and Resistance Factor Design for Buildings » Beams » Limiting Laterally Unbraced Length for Inelastic Lateral Buckling

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LaTeX Go Limiting Laterally Unbraced Length = (300*Radius of Gyration about Minor Axis)/sqrt(Flange Yield Stress)

Plastic Moment

LaTeX Go Plastic Moment = Specified Minimum Yield Stress*Plastic Modulus

Limiting Laterally Unbraced Length for Inelastic Lateral Buckling Formula

LaTeX Go

What is a Residual Stress?

The Residual Stresses are generated, upon equilibrium of material, after plastic deformation that is caused by applied mechanical loads, thermal loads, or phase changes. Mechanical and thermal processes applied to a component during service may also alter its residual stress state.

How to Calculate Limiting Laterally Unbraced Length for Inelastic Lateral Buckling?

Limiting Laterally Unbraced Length for Inelastic Lateral Buckling calculator uses Limiting Length = ((Radius of Gyration about Minor Axis*Beam Buckling Factor 1)/(Specified Minimum Yield Stress-Compressive Residual Stress in Flange))*sqrt(1+sqrt(1+(Beam Buckling Factor 2*Smaller Yield Stress^2))) to calculate the Limiting Length, The Limiting Laterally Unbraced Length for Inelastic Lateral Buckling formula is defined as the unbraced maximum length of an inelastic buckling member involving a relation between various parameters like buckling factors, yield stress of web and flange, residual compressive stress and radius of gyration. Limiting Length is denoted by L_lim symbol.

How to calculate Limiting Laterally Unbraced Length for Inelastic Lateral Buckling using this online calculator? To use this online calculator for Limiting Laterally Unbraced Length for Inelastic Lateral Buckling, enter Radius of Gyration about Minor Axis (r_y), Beam Buckling Factor 1 (X₁), Specified Minimum Yield Stress (F_yw), Compressive Residual Stress in Flange (F_r), Beam Buckling Factor 2 (X₂) & Smaller Yield Stress (F_l) and hit the calculate button. Here is how the Limiting Laterally Unbraced Length for Inelastic Lateral Buckling calculation can be explained with given input values -> 3E+7 = ((0.02*3005)/(139000000-80000000))*sqrt(1+sqrt(1+(64*110000000^2))).

FAQ

What is Limiting Laterally Unbraced Length for Inelastic Lateral Buckling?

The Limiting Laterally Unbraced Length for Inelastic Lateral Buckling formula is defined as the unbraced maximum length of an inelastic buckling member involving a relation between various parameters like buckling factors, yield stress of web and flange, residual compressive stress and radius of gyration and is represented as L_lim = ((r_y*X₁)/(F_yw-F_r))*sqrt(1+sqrt(1+(X₂*F_l^2))) or Limiting Length = ((Radius of Gyration about Minor Axis*Beam Buckling Factor 1)/(Specified Minimum Yield Stress-Compressive Residual Stress in Flange))*sqrt(1+sqrt(1+(Beam Buckling Factor 2*Smaller Yield Stress^2))). Radius of Gyration about Minor Axis is the root mean square distance of the object's parts from either its center of mass or a given minor axis, depending on the relevant application, Beam Buckling Factor 1 is the value which is considered as the factor of safety against buckling to currently applied loads, Specified Minimum Yield Stress represents the minimum tensile stress or yield stress required by the flexural member, ex- web, Compressive Residual Stress in Flange is the stress formed after plastic deformation, if the residue at a location has a value of -100 MPa, it is said to be compressive residual stress, Beam Buckling Factor 2 is the value used as factor of safety against buckling by applied loads & Smaller Yield Stress is the yield stress value, which is smallest among, yield stress in web, flange or residual stress.

How to calculate Limiting Laterally Unbraced Length for Inelastic Lateral Buckling?

The Limiting Laterally Unbraced Length for Inelastic Lateral Buckling formula is defined as the unbraced maximum length of an inelastic buckling member involving a relation between various parameters like buckling factors, yield stress of web and flange, residual compressive stress and radius of gyration is calculated using Limiting Length = ((Radius of Gyration about Minor Axis*Beam Buckling Factor 1)/(Specified Minimum Yield Stress-Compressive Residual Stress in Flange))*sqrt(1+sqrt(1+(Beam Buckling Factor 2*Smaller Yield Stress^2))). To calculate Limiting Laterally Unbraced Length for Inelastic Lateral Buckling, you need Radius of Gyration about Minor Axis (r_y), Beam Buckling Factor 1 (X₁), Specified Minimum Yield Stress (F_yw), Compressive Residual Stress in Flange (F_r), Beam Buckling Factor 2 (X₂) & Smaller Yield Stress (F_l). With our tool, you need to enter the respective value for Radius of Gyration about Minor Axis, Beam Buckling Factor 1, Specified Minimum Yield Stress, Compressive Residual Stress in Flange, Beam Buckling Factor 2 & Smaller Yield Stress 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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