Limiting Laterally Unbraced Length for Inelastic Lateral Buckling for Box Beams Solution

STEP 0: Pre-Calculation Summary
Formula Used
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
Lr = (2*ry*E*sqrt(J*A))/Mr
This formula uses 1 Functions, 6 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 Length for Inelastic Buckling - (Measured in Millimeter) - Limiting Length for Inelastic Buckling is the distance between two end points for inelastic lateral buckling.
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.
Elastic Modulus of Steel - (Measured in Gigapascal) - Elastic Modulus of Steel is a measure of the stiffness of steel. It quantifies the ability of steel to resist deformation under 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 Millimeter) - Cross Sectional Area in Steel Structures is the enclosed surface area, product of length and breadth.
Limiting buckling moment - (Measured in Newton Meter) - Limiting buckling moment is the maximum value for the moment causing buckling in the member.
STEP 1: Convert Input(s) to Base Unit
Radius of gyration about minor axis: 20 Millimeter --> 20 Millimeter No Conversion Required
Elastic Modulus of Steel: 200 Gigapascal --> 200 Gigapascal No Conversion Required
Torsional constant: 21.9 --> No Conversion Required
Cross Sectional Area in Steel Structures: 6400 Square Millimeter --> 6400 Square Millimeter No Conversion Required
Limiting buckling moment: 3.85 Kilonewton Meter --> 3850 Newton Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Lr = (2*ry*E*sqrt(J*A))/Mr --> (2*20*200*sqrt(21.9*6400))/3850
Evaluating ... ...
Lr = 777.931400763684
STEP 3: Convert Result to Output's Unit
0.777931400763684 Meter -->777.931400763684 Millimeter (Check conversion here)
FINAL ANSWER
777.931400763684 777.9314 Millimeter <-- Limiting Length for Inelastic Buckling
(Calculation completed in 00.004 seconds)

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NSS College of Engineering (NSSCE), Palakkad
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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 Inelastic Lateral Buckling for Box Beams Formula

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
Lr = (2*ry*E*sqrt(J*A))/Mr

What is Inelastic Buckling?

In between, for a column with intermediate length, buckling occurs after the stress in the column exceeds the proportional limit of the column material and before the stress reaches the ultimate strength. This kind of situation is called inelastic buckling. Elastic buckling occurs before yielding of material of which the member is made. And in case if the material of the member yields first followed by buckling in the inelastic zone , it is called plastic buckling.

How to Calculate Limiting Laterally Unbraced Length for Inelastic Lateral Buckling for Box Beams?

Limiting Laterally Unbraced Length for Inelastic Lateral Buckling for Box Beams calculator uses 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 to calculate the Limiting Length for Inelastic Buckling, The Limiting Laterally Unbraced Length for Inelastic Lateral Buckling for Box Beams formula is defined as the maximum unbraced length, particularly for box and solid sections. It involves the relationship between the radius of gyration, modulus of elasticity, torsional coefficient, buckling moment and area of the cross-section. Limiting Length for Inelastic Buckling is denoted by Lr symbol.

How to calculate Limiting Laterally Unbraced Length for Inelastic Lateral Buckling for Box Beams using this online calculator? To use this online calculator for Limiting Laterally Unbraced Length for Inelastic Lateral Buckling for Box Beams, enter Radius of gyration about minor axis (ry), Elastic Modulus of Steel (E), Torsional constant (J), Cross Sectional Area in Steel Structures (A) & Limiting buckling moment (Mr) and hit the calculate button. Here is how the Limiting Laterally Unbraced Length for Inelastic Lateral Buckling for Box Beams calculation can be explained with given input values -> 777931.4 = (2*0.02*200000000000*sqrt(21.9*0.0064))/3850.

FAQ

What is Limiting Laterally Unbraced Length for Inelastic Lateral Buckling for Box Beams?
The Limiting Laterally Unbraced Length for Inelastic Lateral Buckling for Box Beams formula is defined as the maximum unbraced length, particularly for box and solid sections. It involves the relationship between the radius of gyration, modulus of elasticity, torsional coefficient, buckling moment and area of the cross-section and is represented as Lr = (2*ry*E*sqrt(J*A))/Mr or 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. 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, Elastic Modulus of Steel is a measure of the stiffness of steel. It quantifies the ability of steel to resist deformation under 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 & Limiting buckling moment is the maximum value for the moment causing buckling in the member.
How to calculate Limiting Laterally Unbraced Length for Inelastic Lateral Buckling for Box Beams?
The Limiting Laterally Unbraced Length for Inelastic Lateral Buckling for Box Beams formula is defined as the maximum unbraced length, particularly for box and solid sections. It involves the relationship between the radius of gyration, modulus of elasticity, torsional coefficient, buckling moment and area of the cross-section is calculated using 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. To calculate Limiting Laterally Unbraced Length for Inelastic Lateral Buckling for Box Beams, you need Radius of gyration about minor axis (ry), Elastic Modulus of Steel (E), Torsional constant (J), Cross Sectional Area in Steel Structures (A) & Limiting buckling moment (Mr). With our tool, you need to enter the respective value for Radius of gyration about minor axis, Elastic Modulus of Steel, Torsional constant, Cross Sectional Area in Steel Structures & Limiting buckling moment 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 Length for Inelastic Buckling?
In this formula, Limiting Length for Inelastic Buckling uses Radius of gyration about minor axis, Elastic Modulus of Steel, Torsional constant, Cross Sectional Area in Steel Structures & Limiting buckling moment. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • 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)))
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