Beam Buckling Factor 1 Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
X1 = (pi/Sx)*sqrt((E*G*J*A)/2)
This formula uses 1 Constants, 1 Functions, 6 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
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
Beam Buckling Factor 1 - Beam Buckling Factor 1 is the value which is considered as the factor of safety against buckling to currently applied loads.
Section Modulus about Major Axis - (Measured in Cubic Millimeter) - Section Modulus about Major Axis is the ratio between second moment of area to distance from neutral axis to extreme fiber about the major axis.
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.
Shear Modulus in Steel Structures - (Measured in Gigapascal) - Shear Modulus in Steel Structures is the slope of the linear elastic region of the shear stress–strain curve.
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.
STEP 1: Convert Input(s) to Base Unit
Section Modulus about Major Axis: 35 Cubic Millimeter --> 35 Cubic Millimeter No Conversion Required
Elastic Modulus of Steel: 200 Gigapascal --> 200 Gigapascal No Conversion Required
Shear Modulus in Steel Structures: 80 Gigapascal --> 80 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
STEP 2: Evaluate Formula
Substituting Input Values in Formula
X1 = (pi/Sx)*sqrt((E*G*J*A)/2) --> (pi/35)*sqrt((200*80*21.9*6400)/2)
Evaluating ... ...
X1 = 3005.65318010313
STEP 3: Convert Result to Output's Unit
3005.65318010313 --> No Conversion Required
FINAL ANSWER
3005.65318010313 3005.653 <-- Beam Buckling Factor 1
(Calculation completed in 00.004 seconds)

Credits

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

Beam Buckling Factor 1 Formula

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)
X1 = (pi/Sx)*sqrt((E*G*J*A)/2)

Why is Beam Buckling Factor used?

The Buckling Failure can cause serious catastrophic results, a high factor of safety will be used for design purpose. Here, for calculating the limiting unbraced length two different safety factors are considered, among which one of them is evaluated using the above formula.

How to Calculate Beam Buckling Factor 1?

Beam Buckling Factor 1 calculator uses 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) to calculate the Beam Buckling Factor 1, The Beam Buckling Factor 1 formula is defined as the factor which is considered as the factor of safety against buckling load. Beam Buckling Factor 1 is denoted by X1 symbol.

How to calculate Beam Buckling Factor 1 using this online calculator? To use this online calculator for Beam Buckling Factor 1, enter Section Modulus about Major Axis (Sx), Elastic Modulus of Steel (E), Shear Modulus in Steel Structures (G), Torsional constant (J) & Cross Sectional Area in Steel Structures (A) and hit the calculate button. Here is how the Beam Buckling Factor 1 calculation can be explained with given input values -> 3E+6 = (pi/3.5E-08)*sqrt((200000000000*80000000000*21.9*0.0064)/2).

FAQ

What is Beam Buckling Factor 1?
The Beam Buckling Factor 1 formula is defined as the factor which is considered as the factor of safety against buckling load and is represented as X1 = (pi/Sx)*sqrt((E*G*J*A)/2) or 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). Section Modulus about Major Axis is the ratio between second moment of area to distance from neutral axis to extreme fiber about the major axis, Elastic Modulus of Steel is a measure of the stiffness of steel. It quantifies the ability of steel to resist deformation under stress, Shear Modulus in Steel Structures is the slope of the linear elastic region of the shear stress–strain curve, 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 Beam Buckling Factor 1?
The Beam Buckling Factor 1 formula is defined as the factor which is considered as the factor of safety against buckling load is calculated using 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). To calculate Beam Buckling Factor 1, you need Section Modulus about Major Axis (Sx), Elastic Modulus of Steel (E), Shear Modulus in Steel Structures (G), Torsional constant (J) & Cross Sectional Area in Steel Structures (A). With our tool, you need to enter the respective value for Section Modulus about Major Axis, Elastic Modulus of Steel, Shear Modulus in Steel Structures, 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.
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