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)))
Llim = ((ry*X1)/(Fyw-Fr))*sqrt(1+sqrt(1+(X2*Fl^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
Llim = ((ry*X1)/(Fyw-Fr))*sqrt(1+sqrt(1+(X2*Fl^2))) --> ((0.02*3005)/(139-80))*sqrt(1+sqrt(1+(64*110^2)))
Evaluating ... ...
Llim = 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 00.004 seconds)

Credits

Creator Image
Created by Chandana P Dev
NSS College of Engineering (NSSCE), Palakkad
Chandana P Dev has created this Calculator and 500+ more calculators!
Verifier Image
Verified by Ishita Goyal
Meerut Institute of Engineering and Technology (MIET), Meerut
Ishita Goyal has verified this Calculator and 2600+ more calculators!

Beams Calculators

Maximum Laterally Unbraced Length for Plastic Analysis
​ LaTeX ​ 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
​ LaTeX ​ 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
​ 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
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)))
Llim = ((ry*X1)/(Fyw-Fr))*sqrt(1+sqrt(1+(X2*Fl^2)))

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 Llim 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 (ry), Beam Buckling Factor 1 (X1), Specified Minimum Yield Stress (Fyw), Compressive Residual Stress in Flange (Fr), Beam Buckling Factor 2 (X2) & Smaller Yield Stress (Fl) 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 Llim = ((ry*X1)/(Fyw-Fr))*sqrt(1+sqrt(1+(X2*Fl^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 (ry), Beam Buckling Factor 1 (X1), Specified Minimum Yield Stress (Fyw), Compressive Residual Stress in Flange (Fr), Beam Buckling Factor 2 (X2) & Smaller Yield Stress (Fl). 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.
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!