Maximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams 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%
✖Yield Stress of Steel is the stress at which the material begins to deform plastically, meaning it will not return to its original shape when the applied force is removed.ⓘ Yield Stress of Steel [F_y]			+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 in Solid Bars and Box Beams [L_pd]

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

Formula

`"L"_{"pd"} = ("r"_{"y"}*(5000+3000*("M"_{"1"}/"M"_{"p"})))/"F"_{"y"}`

Example

`"424mm"=("20mm"*(5000+3000*("100N*mm"/"1000N*mm")))/"250MPa"`

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

STEP 0: Pre-Calculation Summary

Formula Used

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
L_pd = (r_y*(5000+3000*(M₁/M_p)))/F_y
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.
Yield Stress of Steel - (Measured in Megapascal) - Yield Stress of Steel is the stress at which the material begins to deform plastically, meaning it will not return to its original shape when the applied force is removed.

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)
Yield Stress of Steel: 250 Megapascal --> 250 Megapascal No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_pd = (r_y*(5000+3000*(M₁/M_p)))/F_y --> (0.02*(5000+3000*(0.1/1)))/250

Evaluating ... ...

L_pd = 0.424

STEP 3: Convert Result to Output's Unit

0.424 Meter -->424 Millimeter (Check conversion here)

FINAL ANSWER

424 Millimeter <-- Laterally Unbraced Length for Plastic Analysis

(Calculation completed in 00.004 seconds)

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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 in Solid Bars and Box Beams Formula

What is a Plastic Hinge?

In the structural engineering beam theory, the term "Plastic Hinge" is used to describe the deformation of a section of a beam where plastic bending occurs. By inserting a plastic hinge at a plastic limit load into a statically determinate beam, a kinematic mechanism permitting an unbounded displacement of the system can be formed. It is known as the collapse mechanism.

How to Calculate Maximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams?

Maximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams calculator uses 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 to calculate the Laterally Unbraced Length for Plastic Analysis, The Maximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams formula is defined as the limiting lateral unbraced length of beams which are boxed in shape and of solid bars when plastic hinges are present. Laterally Unbraced Length for Plastic Analysis is denoted by L_pd symbol.

How to calculate Maximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams using this online calculator? To use this online calculator for Maximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams, enter Radius of gyration about minor axis (r_y), Smaller Moments of Unbraced Beam (M₁), Plastic Moment (M_p) & Yield Stress of Steel (F_y) and hit the calculate button. Here is how the Maximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams calculation can be explained with given input values -> 424000 = (0.02*(5000+3000*(0.1/1)))/250000000.

FAQ

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

The Maximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams formula is defined as the limiting lateral unbraced length of beams which are boxed in shape and of solid bars when plastic hinges are present and is represented as L_pd = (r_y*(5000+3000*(M₁/M_p)))/F_y or 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. 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 & Yield Stress of Steel is the stress at which the material begins to deform plastically, meaning it will not return to its original shape when the applied force is removed.

How to calculate Maximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams?

The Maximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams formula is defined as the limiting lateral unbraced length of beams which are boxed in shape and of solid bars when plastic hinges are present is calculated using 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. To calculate Maximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams, you need Radius of gyration about minor axis (r_y), Smaller Moments of Unbraced Beam (M₁), Plastic Moment (M_p) & Yield Stress of Steel (F_y). With our tool, you need to enter the respective value for Radius of gyration about minor axis, Smaller Moments of Unbraced Beam, Plastic Moment & Yield Stress of Steel 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 & Yield Stress of Steel. 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*(3600+2200*(Smaller Moments of Unbraced Beam/Plastic Moment))/(Minimum Yield Stress of Compression Flange)

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