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, say, 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 for Inelastic Buckling is the distance between two end points for inelastic lateral buckling.ⓘ Limiting Laterally Unbraced Length for Inelastic Lateral Buckling [L_r]

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Formula

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Limiting Laterally Unbraced Length for Inelastic Lateral Buckling

Formula

`"L"_{"r"} = (("r"_{"y"}*"X"_{"1"})/("F"_{"yw"}-"F"_{"r"}))*sqrt(1+sqrt(1+("X"_{"2"}*"F"_{"l"}^2)))`

Example

`"30235.04mm"=(("20mm"*"3005")/("139MPa"-"80MPa"))*sqrt(1+sqrt(1+("64"*("110MPa")^2)))`

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Limiting Laterally Unbraced Length for Inelastic Lateral Buckling Solution

STEP 0: Pre-Calculation Summary

Formula Used

Limiting Length for Inelastic Buckling = ((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_r = ((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 for Inelastic Buckling - (Measured in Meter) - Limiting Length for Inelastic Buckling is the distance between two end points for inelastic lateral buckling.
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, say, 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_r = ((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_r = 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 for Inelastic Buckling

(Calculation completed in 00.011 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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NSS College of Engineering (NSSCE), Palakkad

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Meerut Institute of Engineering and Technology (MIET), Meerut

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< 13 Beams Calculators

Critical Elastic Moment

Go Critical Elastic Moment = ((Moment Gradient Factor*pi)/Unbraced Length of Member)*sqrt(((Elastic Modulus of Steel*Y Axis Moment of Inertia*Shear Modulus in Steel Structures*Torsional constant)+(Y Axis Moment of Inertia*Warping Constant*((pi*Elastic Modulus of Steel)/(Unbraced Length of Member)^2))))

Limiting Laterally Unbraced Length for Inelastic Lateral Buckling

Go Limiting Length for Inelastic Buckling = ((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)))

Specified Minimum Yield Stress for Web given Limiting Laterally Unbraced Length

Go Specified Minimum Yield Stress = ((Radius of gyration about minor axis*Beam Buckling Factor 1*sqrt(1+sqrt(1+(Beam Buckling Factor 2*Smaller Yield Stress^2))))/Limiting Length for Inelastic Buckling)+Compressive Residual Stress in Flange

Beam Buckling Factor 1

Go Beam Buckling Factor 1 = (pi/Section Modulus about Major Axis)*sqrt((Elastic Modulus of Steel*Shear Modulus in Steel Structures*Torsional constant*Cross Sectional Area in Steel Structures)/2)

Limiting Laterally Unbraced Length for Inelastic Lateral Buckling for Box Beams

Go Limiting Length for Inelastic Buckling = (2*Radius of gyration about minor axis*Elastic Modulus of Steel*sqrt(Torsional constant*Cross Sectional Area in Steel Structures))/Limiting buckling moment

Critical Elastic Moment for Box Sections and Solid Bars

Go Critical Elastic Moment = (57000*Moment Gradient Factor*sqrt(Torsional constant*Cross Sectional Area in Steel Structures))/(Unbraced Length of Member/Radius of gyration about minor axis)

Beam Buckling Factor 2

Go Beam Buckling Factor 2 = ((4*Warping Constant)/Y Axis Moment of Inertia)*((Section Modulus about Major Axis)/(Shear Modulus in Steel Structures*Torsional constant))^2

Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for Solid Bar and Box Beams

Go Limiting Laterally Unbraced Length = (3750*(Radius of gyration about minor axis/Plastic Moment))/(sqrt(Torsional constant*Cross Sectional Area in Steel Structures))

Maximum Laterally Unbraced Length for Plastic Analysis

Go Laterally Unbraced Length for Plastic Analysis = Radius of gyration about minor axis*(3600+2200*(Smaller Moments of Unbraced Beam/Plastic Moment))/(Minimum Yield Stress of Compression Flange)

Maximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams

Go Laterally Unbraced Length for Plastic Analysis = (Radius of gyration about minor axis*(5000+3000*(Smaller Moments of Unbraced Beam/Plastic Moment)))/Yield Stress of Steel

Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for I and Channel Sections

Go Limiting Laterally Unbraced Length = (300*Radius of gyration about minor axis)/sqrt(Flange Yield Stress)

Limiting Buckling Moment

Go Limiting buckling moment = Smaller Yield Stress*Section Modulus about Major Axis

Plastic Moment

Go Plastic Moment = Specified Minimum Yield Stress*Plastic modulus

Limiting Laterally Unbraced Length for Inelastic Lateral Buckling Formula

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 for Inelastic Buckling = ((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 for Inelastic 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. Limiting Length for Inelastic Buckling is denoted by L_r 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_r = ((r_y*X₁)/(F_yw-F_r))*sqrt(1+sqrt(1+(X₂*F_l^2))) or Limiting Length for Inelastic Buckling = ((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, say, 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 for Inelastic Buckling = ((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.

How many ways are there to calculate Limiting Length for Inelastic Buckling?

In this formula, Limiting Length for Inelastic Buckling uses 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. We can use 1 other way(s) to calculate the same, which is/are as follows -

Limiting Length for Inelastic Buckling = (2*Radius of gyration about minor axis*Elastic Modulus of Steel*sqrt(Torsional constant*Cross Sectional Area in Steel Structures))/Limiting buckling moment

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