Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for Solid Bar 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%
✖Plastic Moment is the moment at which the entire cross section has reached its yield stress.ⓘ Plastic Moment [M_p]			+10% -10%
✖The Torsional constant is a geometrical property of a bar's cross-section which is involved in the relationship between the angle of twist and applied torque along the axis of the bar.ⓘ Torsional constant [J]			+10% -10%
✖Cross Sectional Area in Steel Structures is the enclosed surface area, product of length and breadth.ⓘ Cross Sectional Area in Steel Structures [A]			+10% -10%

✖Limiting Laterally Unbraced Length here given 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 Solid Bar and Box Beams [L_p]

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Formula

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Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for Solid Bar and Box Beams

Formula

`"L"_{"p"} = (3750*("r"_{"y"}/"M"_{"p"}))/(sqrt("J"*"A"))`

Example

`"200.3315mm"=(3750*("20mm"/"1000N*mm"))/(sqrt("21.9"*"6400mm²"))`

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Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for Solid Bar and Box Beams Solution

STEP 0: Pre-Calculation Summary

Formula Used

Limiting Laterally Unbraced Length = (3750*(Radius of gyration about minor axis/Plastic Moment))/(sqrt(Torsional constant*Cross Sectional Area in Steel Structures))
L_p = (3750*(r_y/M_p))/(sqrt(J*A))
This formula uses 1 Functions, 5 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 here given 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.
Plastic Moment - (Measured in Newton Millimeter) - Plastic Moment is the moment at which the entire cross section has reached its yield stress.
Torsional constant - The Torsional constant is a geometrical property of a bar's cross-section which is involved in the relationship between the angle of twist and applied torque along the axis of the bar.
Cross Sectional Area in Steel Structures - (Measured in Square Meter) - Cross Sectional Area in Steel Structures is the enclosed surface area, product of length and breadth.

STEP 1: Convert Input(s) to Base Unit

Radius of gyration about minor axis: 20 Millimeter --> 20 Millimeter No Conversion Required
Plastic Moment: 1000 Newton Millimeter --> 1000 Newton Millimeter No Conversion Required
Torsional constant: 21.9 --> No Conversion Required
Cross Sectional Area in Steel Structures: 6400 Square Millimeter --> 0.0064 Square Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_p = (3750*(r_y/M_p))/(sqrt(J*A)) --> (3750*(20/1000))/(sqrt(21.9*0.0064))

Evaluating ... ...

L_p = 200.33148898626

STEP 3: Convert Result to Output's Unit

0.20033148898626 Meter -->200.33148898626 Millimeter (Check conversion here)

FINAL ANSWER

200.33148898626 ≈ 200.3315 Millimeter <-- Limiting Laterally Unbraced Length

(Calculation completed in 00.004 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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< 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

Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for Solid Bar and Box Beams Formula

Limiting Laterally Unbraced Length = (3750*(Radius of gyration about minor axis/Plastic Moment))/(sqrt(Torsional constant*Cross Sectional Area in Steel Structures))
L_p = (3750*(r_y/M_p))/(sqrt(J*A))

What is Torsion Constant?

The Torsion Constant, together with material properties and length, describes a bar's torsional stiffness. The SI unit for torsion constant is m^4. It is a geometrical property defined using the parameters, torque, angle of twist and shear modulus.

How to Calculate Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for Solid Bar and Box Beams?

Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for Solid Bar and Box Beams calculator uses Limiting Laterally Unbraced Length = (3750*(Radius of gyration about minor axis/Plastic Moment))/(sqrt(Torsional constant*Cross Sectional Area in Steel Structures)) to calculate the Limiting Laterally Unbraced Length, The Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for Solid Bar and Box Beams formula is defined as the maximum unbraced length of a plastic section which involves the relationship between radius of gyration about minor axis, plastic moment, torsional constant and area of cross section. Limiting Laterally Unbraced Length is denoted by L_p symbol.

How to calculate Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for Solid Bar and Box Beams using this online calculator? To use this online calculator for Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for Solid Bar and Box Beams, enter Radius of gyration about minor axis (r_y), Plastic Moment (M_p), Torsional constant (J) & Cross Sectional Area in Steel Structures (A) and hit the calculate button. Here is how the Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for Solid Bar and Box Beams calculation can be explained with given input values -> 2E+11 = (3750*(0.02/1))/(sqrt(21.9*0.0064)).

FAQ

What is Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for Solid Bar and Box Beams?

The Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for Solid Bar and Box Beams formula is defined as the maximum unbraced length of a plastic section which involves the relationship between radius of gyration about minor axis, plastic moment, torsional constant and area of cross section and is represented as L_p = (3750*(r_y/M_p))/(sqrt(J*A)) or Limiting Laterally Unbraced Length = (3750*(Radius of gyration about minor axis/Plastic Moment))/(sqrt(Torsional constant*Cross Sectional Area in Steel Structures)). 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, Plastic Moment is the moment at which the entire cross section has reached its yield stress, The Torsional constant is a geometrical property of a bar's cross-section which is involved in the relationship between the angle of twist and applied torque along the axis of the bar & Cross Sectional Area in Steel Structures is the enclosed surface area, product of length and breadth.

How to calculate Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for Solid Bar and Box Beams?

The Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for Solid Bar and Box Beams formula is defined as the maximum unbraced length of a plastic section which involves the relationship between radius of gyration about minor axis, plastic moment, torsional constant and area of cross section is calculated using Limiting Laterally Unbraced Length = (3750*(Radius of gyration about minor axis/Plastic Moment))/(sqrt(Torsional constant*Cross Sectional Area in Steel Structures)). To calculate Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for Solid Bar and Box Beams, you need Radius of gyration about minor axis (r_y), Plastic Moment (M_p), Torsional constant (J) & Cross Sectional Area in Steel Structures (A). With our tool, you need to enter the respective value for Radius of gyration about minor axis, Plastic Moment, Torsional constant & Cross Sectional Area in Steel Structures 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, Plastic Moment, Torsional constant & Cross Sectional Area in Steel Structures. We can use 1 other way(s) to calculate the same, which is/are as follows -

Limiting Laterally Unbraced Length = (300*Radius of gyration about minor axis)/sqrt(Flange Yield Stress)

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