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Beam Buckling Factor 1 Formula

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Beam Buckling Factor 1 is the value which is considered as the factor of safety against buckling to currently applied loads. Check FAQs

X 1 = (\frac{π}{S x}) \cdot \sqrt{\frac{E \cdot G \cdot J \cdot A}{2}}

X₁ - Beam Buckling Factor 1?S_x - Section Modulus about Major Axis?E - Elastic Modulus of Steel?G - Shear Modulus?J - Torsional Constant?A - Cross Sectional Area in Steel Structures?π - Archimedes' constant?

Beam Buckling Factor 1 Example

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Here is how the Beam Buckling Factor 1 equation looks like with Units.

Here is how the Beam Buckling Factor 1 equation looks like.

3005.6532 = (\frac{3.1416}{35}) \cdot \sqrt{\frac{200 \cdot 80 \cdot 21.9 \cdot 6400}{2}}

3005.6532 = (\frac{3.1416}{35mm³}) \cdot \sqrt{\frac{200GPa \cdot 80GPa \cdot 21.9 \cdot 6400mm²}{2}}

3005.6532 = (\frac{3.1416}{35}) \cdot \sqrt{\frac{200 \cdot 80 \cdot 21.9 \cdot 6400}{2}}

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Beam Buckling Factor 1 Solution

Follow our step by step solution on how to calculate Beam Buckling Factor 1?

FIRST Step Consider the formula

X 1 = (\frac{π}{S x}) \cdot \sqrt{\frac{E \cdot G \cdot J \cdot A}{2}}

Next Step Substitute values of Variables

∴

X 1 = (\frac{π}{35mm³}) \cdot \sqrt{\frac{200GPa \cdot 80GPa \cdot 21.9 \cdot 6400mm²}{2}}

Next Step Substitute values of Constants

∴

X 1 = (\frac{3.1416}{35mm³}) \cdot \sqrt{\frac{200GPa \cdot 80GPa \cdot 21.9 \cdot 6400mm²}{2}}

Next Step Prepare to Evaluate

∴

X 1 = (\frac{3.1416}{35}) \cdot \sqrt{\frac{200 \cdot 80 \cdot 21.9 \cdot 6400}{2}}

Next Step Evaluate

∴

X 1 = 3005.65318010313

LAST Step Rounding Answer

∴

X 1 = 3005.6532

Beam Buckling Factor 1 Formula Elements

Variables

Constants

Functions

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.

Symbol: X₁

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Beam Buckling Factor 1

Section Modulus about Major Axis

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.

Symbol: S_x

Measurement: VolumeUnit: mm³

Note: Value should be greater than 0.

Formulas to find Section Modulus about Major Axis

Elastic Modulus of Steel

Elastic Modulus of Steel is a measure of the stiffness of steel. It quantifies the ability of steel to resist deformation under stress.

Symbol: E

Measurement: PressureUnit: GPa

Note: Value should be greater than 0.

Formulas to find Elastic Modulus of Steel

Shear Modulus

Shear Modulus is the slope of the linear elastic region of the shear stress–strain curve.

Symbol: G

Measurement: PressureUnit: GPa

Note: Value should be greater than 0.

Formulas to find Shear Modulus

Torsional Constant

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.

Symbol: J

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Torsional Constant

Cross Sectional Area in Steel Structures

Cross Sectional Area in Steel Structures is the area of a particular section of a structural element, such as a beam or column, when cut perpendicular to its longitudinal axis.

Symbol: A

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Formulas to find Cross Sectional Area in Steel Structures

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: sqrt(Number)

Other formulas in Beams category

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

L pd = \frac{r y \cdot (5000 + 3000 \cdot (\frac{M 1}{M p}))}{F y}

Go Plastic Moment

M p = F yw \cdot Z p

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

L p = \frac{300 \cdot r y}{\sqrt{F yf}}

How to Evaluate Beam Buckling Factor 1?

Beam Buckling Factor 1 evaluator uses Beam Buckling Factor 1 = (pi/Section Modulus about Major Axis)*sqrt((Elastic Modulus of Steel*Shear Modulus*Torsional Constant*Cross Sectional Area in Steel Structures)/2) to evaluate the Beam Buckling Factor 1, The Beam Buckling Factor 1 formula is defined as the factor which is considered as the FOS against buckling load. It is a coefficient used in the design and analysis of steel structures to account for the effects of moment gradient on the lateral-torsional buckling strength of beams. Beam Buckling Factor 1 is denoted by X₁ symbol.

How to evaluate Beam Buckling Factor 1 using this online evaluator? To use this online evaluator for Beam Buckling Factor 1, enter Section Modulus about Major Axis (S_x), Elastic Modulus of Steel (E), Shear Modulus (G), Torsional Constant (J) & Cross Sectional Area in Steel Structures (A) and hit the calculate button.

FAQs on Beam Buckling Factor 1

What is the formula to find Beam Buckling Factor 1?

The formula of Beam Buckling Factor 1 is expressed as Beam Buckling Factor 1 = (pi/Section Modulus about Major Axis)*sqrt((Elastic Modulus of Steel*Shear Modulus*Torsional Constant*Cross Sectional Area in Steel Structures)/2). Here is an example- 3005.653 = (pi/3.5E-08)*sqrt((200000000000*80000000000*21.9*0.0064)/2).

How to calculate Beam Buckling Factor 1?

With Section Modulus about Major Axis (S_x), Elastic Modulus of Steel (E), Shear Modulus (G), Torsional Constant (J) & Cross Sectional Area in Steel Structures (A) we can find Beam Buckling Factor 1 using the formula - Beam Buckling Factor 1 = (pi/Section Modulus about Major Axis)*sqrt((Elastic Modulus of Steel*Shear Modulus*Torsional Constant*Cross Sectional Area in Steel Structures)/2). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

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Beam Buckling Factor 1 Formula

Beam Buckling Factor 1 Example

Beam Buckling Factor 1 Solution

Beam Buckling Factor 1 Formula Elements

Other formulas in Beams category

How to Evaluate Beam Buckling Factor 1?

FAQs on Beam Buckling Factor 1

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