Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for I and Channel Sections 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%
✖Flange Yield Stress is the stress at which a flange (the flat or projecting rim on a beam or column, typically in I-beams or H-beams) in a steel structure begins to deform plastically.ⓘ Flange Yield Stress [F_yf]			+10% -10%

✖Limiting Laterally Unbraced Length is the maximum unbraced length of a section which have full plastic flexural strength or full plastic bending capacity.ⓘ Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for I and Channel Sections [L_p]

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

STEP 0: Pre-Calculation Summary

Formula Used

Limiting Laterally Unbraced Length = (300*Radius of Gyration about Minor Axis)/sqrt(Flange Yield Stress)
L_p = (300*r_y)/sqrt(F_yf)
This formula uses 1 Functions, 3 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 Laterally Unbraced Length - (Measured in Millimeter) - Limiting Laterally Unbraced Length is the maximum unbraced length of a section which have full plastic flexural strength or full plastic bending capacity.
Radius of Gyration about Minor Axis - (Measured in Millimeter) - 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.
Flange Yield Stress - (Measured in Megapascal) - Flange Yield Stress is the stress at which a flange (the flat or projecting rim on a beam or column, typically in I-beams or H-beams) in a steel structure begins to deform plastically.

STEP 1: Convert Input(s) to Base Unit

Radius of Gyration about Minor Axis: 20 Millimeter --> 20 Millimeter No Conversion Required
Flange Yield Stress: 900 Megapascal --> 900 Megapascal No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_p = (300*r_y)/sqrt(F_yf) --> (300*20)/sqrt(900)

Evaluating ... ...

L_p = 200

STEP 3: Convert Result to Output's Unit

0.2 Meter -->200 Millimeter (Check conversion here)

FINAL ANSWER

200 Millimeter <-- Limiting Laterally Unbraced Length

(Calculation completed in 00.008 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

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

LaTeX Go

Limiting Laterally Unbraced Length = (300*Radius of Gyration about Minor Axis)/sqrt(Flange Yield Stress)
L_p = (300*r_y)/sqrt(F_yf)

What is Plastic Moment?

The Plastic Moment is defined as the moment at which the entire cross section has reached its yield stress. This is theoretically the maximum bending moment that the section can resist - when this point is reached a plastic hinge is formed and any load beyond this point will result in theoretically infinite plastic deformation.

How to Calculate Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for I and Channel Sections?

Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for I and Channel Sections calculator uses Limiting Laterally Unbraced Length = (300*Radius of Gyration about Minor Axis)/sqrt(Flange Yield Stress) to calculate the Limiting Laterally Unbraced Length, The Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for I and Channel Sections formula is defined as the function of the radius of gyration about a minor axis and yield stress of the flange section. It is the maximum span length between lateral supports over which a steel beam or girder can be unbraced while still being able to reach its full plastic moment capacity without experiencing lateral-torsional buckling. Limiting Laterally Unbraced Length is denoted by L_p symbol.

How to calculate Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for I and Channel Sections using this online calculator? To use this online calculator for Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for I and Channel Sections, enter Radius of Gyration about Minor Axis (r_y) & Flange Yield Stress (F_yf) and hit the calculate button. Here is how the Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for I and Channel Sections calculation can be explained with given input values -> 866025.4 = (300*0.02)/sqrt(900000000).

FAQ

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

The Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for I and Channel Sections formula is defined as the function of the radius of gyration about a minor axis and yield stress of the flange section. It is the maximum span length between lateral supports over which a steel beam or girder can be unbraced while still being able to reach its full plastic moment capacity without experiencing lateral-torsional buckling and is represented as L_p = (300*r_y)/sqrt(F_yf) or Limiting Laterally Unbraced Length = (300*Radius of Gyration about Minor Axis)/sqrt(Flange Yield Stress). 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 & Flange Yield Stress is the stress at which a flange (the flat or projecting rim on a beam or column, typically in I-beams or H-beams) in a steel structure begins to deform plastically.

How to calculate Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for I and Channel Sections?

The Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for I and Channel Sections formula is defined as the function of the radius of gyration about a minor axis and yield stress of the flange section. It is the maximum span length between lateral supports over which a steel beam or girder can be unbraced while still being able to reach its full plastic moment capacity without experiencing lateral-torsional buckling is calculated using Limiting Laterally Unbraced Length = (300*Radius of Gyration about Minor Axis)/sqrt(Flange Yield Stress). To calculate Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for I and Channel Sections, you need Radius of Gyration about Minor Axis (r_y) & Flange Yield Stress (F_yf). With our tool, you need to enter the respective value for Radius of Gyration about Minor Axis & Flange 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 Laterally Unbraced Length?

In this formula, Limiting Laterally Unbraced Length uses Radius of Gyration about Minor Axis & Flange Yield Stress. We can use 1 other way(s) to calculate the same, which is/are as follows -

Limiting Laterally Unbraced Length = (3750*(Radius of Gyration about Minor Axis/Plastic Moment))/(sqrt(Torsional Constant*Cross Sectional Area in Steel Structures))

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