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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Formula

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Maximum Laterally Unbraced Length for Plastic Analysis

Formula

`"L"_{"pd"} = "r"_{"y"}*(3600+2200*("M"_{"1"}/"M"_{"p"}))/("F"_{"yc"})`

Example

`"424.4444mm"="20mm"*(3600+2200*("100N*mm"/"1000N*mm"))/("180MPa")`

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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 00.004 seconds)

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Home » Engineering » Civil » Design of Steel Structures » Load-and-Resistance Factor Design for Buildings » Beams » Maximum Laterally Unbraced Length for Plastic Analysis

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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!

Verified by Ishita Goyal

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

Maximum Laterally Unbraced Length for Plastic Analysis Formula

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 distance between two end points of the member which is restrained to move and have plastic hinges. 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 distance between two end points of the member which is restrained to move and have plastic hinges 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 distance between two end points of the member which is restrained to move and have plastic hinges 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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