Maximum Laterally Unbraced Length for Plastic Analysis 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%
✖Smaller Moments of Unbraced Beam is the smallest moment in the ends of beams which is unbraced.ⓘ Smaller Moments of Unbraced Beam [M₁]			+10% -10%
✖Plastic Moment is the moment at which the entire cross section has reached its yield stress.ⓘ Plastic Moment [M_p]			+10% -10%
✖Minimum Yield Stress of Compression Flange is the yield stress that can be experienced by the compression flange which can at least cause plastic deformation.ⓘ Minimum Yield Stress of Compression Flange [F_yc]			+10% -10%

✖Laterally Unbraced Length for Plastic Analysis is the distance between two ends of a member which is prevented from movement and contain plastic hinges.ⓘ Maximum Laterally Unbraced Length for Plastic Analysis [L_pd]

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Maximum Laterally Unbraced Length for Plastic Analysis Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
L_pd = r_y*(3600+2200*(M₁/M_p))/(F_yc)
This formula uses 5 Variables

Variables Used

Laterally Unbraced Length for Plastic Analysis - (Measured in Meter) - Laterally Unbraced Length for Plastic Analysis is the distance between two ends of a member which is prevented from movement and contain plastic hinges.
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.
Smaller Moments of Unbraced Beam - (Measured in Newton Meter) - Smaller Moments of Unbraced Beam is the smallest moment in the ends of beams which is unbraced.
Plastic Moment - (Measured in Newton Meter) - Plastic Moment is the moment at which the entire cross section has reached its yield stress.
Minimum Yield Stress of Compression Flange - (Measured in Megapascal) - Minimum Yield Stress of Compression Flange is the yield stress that can be experienced by the compression flange which can at least cause plastic deformation.

STEP 1: Convert Input(s) to Base Unit

Radius of Gyration about Minor Axis: 20 Millimeter --> 0.02 Meter (Check conversion here)
Smaller Moments of Unbraced Beam: 100 Newton Millimeter --> 0.1 Newton Meter (Check conversion here)
Plastic Moment: 1000 Newton Millimeter --> 1 Newton Meter (Check conversion here)
Minimum Yield Stress of Compression Flange: 180 Megapascal --> 180 Megapascal No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_pd = r_y*(3600+2200*(M₁/M_p))/(F_yc) --> 0.02*(3600+2200*(0.1/1))/(180)

Evaluating ... ...

L_pd = 0.424444444444444

STEP 3: Convert Result to Output's Unit

0.424444444444444 Meter -->424.444444444444 Millimeter (Check conversion here)

FINAL ANSWER

424.444444444444 ≈ 424.4444 Millimeter <-- Laterally Unbraced Length for Plastic Analysis

(Calculation completed in 00.020 seconds)

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Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

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Meerut Institute of Engineering and Technology (MIET), Meerut

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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

Maximum Laterally Unbraced Length for Plastic Analysis Formula

LaTeX Go

What is Plastic Analysis?

The Plastic Analysis can be defined as the analysis of inelastic materials which are studied beyond their elastic limit. Plastic analysis is defined as the analysis in which the criterion for the design of structures is the ultimate load. Plastic analysis has its application in the analysis and design of indeterminate structures.

How to Calculate Maximum Laterally Unbraced Length for Plastic Analysis?

Maximum Laterally Unbraced Length for Plastic Analysis calculator uses 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) to calculate the Laterally Unbraced Length for Plastic Analysis, The Maximum Laterally Unbraced Length for Plastic Analysis formula is defined as the maximum distance between lateral supports in a steel member (such as a beam) where the member can still be analyzed and designed using plastic analysis methods. Laterally Unbraced Length for Plastic Analysis is denoted by L_pd symbol.

How to calculate Maximum Laterally Unbraced Length for Plastic Analysis using this online calculator? To use this online calculator for Maximum Laterally Unbraced Length for Plastic Analysis, enter Radius of Gyration about Minor Axis (r_y), Smaller Moments of Unbraced Beam (M₁), Plastic Moment (M_p) & Minimum Yield Stress of Compression Flange (F_yc) and hit the calculate button. Here is how the Maximum Laterally Unbraced Length for Plastic Analysis calculation can be explained with given input values -> 424444.4 = 0.02*(3600+2200*(0.1/1))/(180000000).

FAQ

What is Maximum Laterally Unbraced Length for Plastic Analysis?

The Maximum Laterally Unbraced Length for Plastic Analysis formula is defined as the maximum distance between lateral supports in a steel member (such as a beam) where the member can still be analyzed and designed using plastic analysis methods and is represented as L_pd = r_y*(3600+2200*(M₁/M_p))/(F_yc) or 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). 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, Smaller Moments of Unbraced Beam is the smallest moment in the ends of beams which is unbraced, Plastic Moment is the moment at which the entire cross section has reached its yield stress & Minimum Yield Stress of Compression Flange is the yield stress that can be experienced by the compression flange which can at least cause plastic deformation.

How to calculate Maximum Laterally Unbraced Length for Plastic Analysis?

The Maximum Laterally Unbraced Length for Plastic Analysis formula is defined as the maximum distance between lateral supports in a steel member (such as a beam) where the member can still be analyzed and designed using plastic analysis methods is calculated using 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). To calculate Maximum Laterally Unbraced Length for Plastic Analysis, you need Radius of Gyration about Minor Axis (r_y), Smaller Moments of Unbraced Beam (M₁), Plastic Moment (M_p) & Minimum Yield Stress of Compression Flange (F_yc). With our tool, you need to enter the respective value for Radius of Gyration about Minor Axis, Smaller Moments of Unbraced Beam, Plastic Moment & Minimum Yield Stress of Compression Flange 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 Laterally Unbraced Length for Plastic Analysis?

In this formula, Laterally Unbraced Length for Plastic Analysis uses Radius of Gyration about Minor Axis, Smaller Moments of Unbraced Beam, Plastic Moment & Minimum Yield Stress of Compression Flange. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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