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Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam Formula

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Moment of Inertia about Minor Axis is a geometrical property of an area which reflects how its points are distributed with regard to a minor axis. Check FAQs

I y = \frac{{(M Cr(Rect) \cdot Len)}^{2}}{(π^{2}) \cdot e \cdot G \cdot J}

I_y - Moment of Inertia about Minor Axis?M_Cr(Rect) - Critical Bending Moment for Rectangular?Len - Length of Rectangular Beam?e - Elastic Modulus?G - Shear Modulus of Elasticity?J - Torsional Constant?π - Archimedes' constant?

Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam Example

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Here is how the Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam equation looks like with Values.

Here is how the Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam equation looks like with Units.

Here is how the Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam equation looks like.

10.0137 = \frac{{(741 \cdot 3)}^{2}}{({3.1416}^{2}) \cdot 50 \cdot 100.002 \cdot 10.0001}

10.0137kg·m² = \frac{{(741N*m \cdot 3m)}^{2}}{({3.1416}^{2}) \cdot 50Pa \cdot 100.002N/m² \cdot 10.0001}

10.0137 = \frac{{(741 \cdot 3)}^{2}}{({3.1416}^{2}) \cdot 50 \cdot 100.002 \cdot 10.0001}

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Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam Solution

Follow our step by step solution on how to calculate Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam?

FIRST Step Consider the formula

I y = \frac{{(M Cr(Rect) \cdot Len)}^{2}}{(π^{2}) \cdot e \cdot G \cdot J}

Next Step Substitute values of Variables

∴

I y = \frac{{(741N*m \cdot 3m)}^{2}}{(π^{2}) \cdot 50Pa \cdot 100.002N/m² \cdot 10.0001}

Next Step Substitute values of Constants

∴

I y = \frac{{(741N*m \cdot 3m)}^{2}}{({3.1416}^{2}) \cdot 50Pa \cdot 100.002N/m² \cdot 10.0001}

Next Step Convert Units

∴

I y = \frac{{(741N*m \cdot 3m)}^{2}}{({3.1416}^{2}) \cdot 50Pa \cdot 100.002Pa \cdot 10.0001}

Next Step Prepare to Evaluate

∴

I y = \frac{{(741 \cdot 3)}^{2}}{({3.1416}^{2}) \cdot 50 \cdot 100.002 \cdot 10.0001}

Next Step Evaluate

∴

I y = 10.0137362163041kg·m²

LAST Step Rounding Answer

∴

I y = 10.0137kg·m²

Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam Formula Elements

Variables

Constants

Moment of Inertia about Minor Axis

Moment of Inertia about Minor Axis is a geometrical property of an area which reflects how its points are distributed with regard to a minor axis.

Symbol: I_y

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Moment of Inertia about Minor Axis

Critical Bending Moment for Rectangular

Critical Bending Moment for Rectangular is crucial in the proper design of bent beams susceptible to LTB, as it allows for slenderness calculation.

Symbol: M_Cr(Rect)

Measurement: Moment of ForceUnit: N*m

Note: Value should be greater than 0.

Formulas to find Critical Bending Moment for Rectangular

Length of Rectangular Beam

Length of Rectangular Beam is the measurement or extent of something from end to end.

Symbol: Len

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Rectangular Beam

Elastic Modulus

The Elastic Modulus is the ratio of Stress to Strain.

Symbol: e

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Elastic Modulus

Shear Modulus of Elasticity

Shear Modulus of Elasticity is one of the measures of mechanical properties of solids. Other elastic moduli are Young's modulus and bulk modulus.

Symbol: G

Measurement: PressureUnit: N/m²

Note: Value should be greater than 0.

Formulas to find Shear Modulus of Elasticity

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.

Symbol: J

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Torsional Constant

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

Other formulas in Elastic Lateral Buckling of Beams category

Go Critical Bending Moment for Simply Supported Rectangular Beam

M Cr(Rect) = (\frac{π}{Len}) \cdot (\sqrt{e \cdot I y \cdot G \cdot J})

Go Unbraced Member Length given Critical Bending Moment of Rectangular Beam

Len = (\frac{π}{M Cr(Rect)}) \cdot (\sqrt{e \cdot I y \cdot G \cdot J})

Go Elasticity Modulus given Critical Bending Moment of Rectangular Beam

e = \frac{{(M Cr(Rect) \cdot Len)}^{2}}{(π^{2}) \cdot I y \cdot G \cdot J}

Go Shear Elasticity Modulus for Critical Bending Moment of Rectangular Beam

G = \frac{{(M Cr(Rect) \cdot Len)}^{2}}{(π^{2}) \cdot I y \cdot e \cdot J}

How to Evaluate Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam?

Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam evaluator uses Moment of Inertia about Minor Axis = ((Critical Bending Moment for Rectangular*Length of Rectangular Beam)^2)/((pi^2)*Elastic Modulus*Shear Modulus of Elasticity*Torsional Constant) to evaluate the Moment of Inertia about Minor Axis, The Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam is defined as a simply supported beam of rectangular cross section subjected to uniform bending, buckling occurs at the critical bending moment, and knowing the critical bending moment, the moment of inertia about the minor axis can be found. Moment of Inertia about Minor Axis is denoted by I_y symbol.

How to evaluate Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam using this online evaluator? To use this online evaluator for Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam, enter Critical Bending Moment for Rectangular (M_Cr(Rect)), Length of Rectangular Beam (Len), Elastic Modulus (e), Shear Modulus of Elasticity (G) & Torsional Constant (J) and hit the calculate button.

FAQs on Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam

What is the formula to find Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam?

The formula of Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam is expressed as Moment of Inertia about Minor Axis = ((Critical Bending Moment for Rectangular*Length of Rectangular Beam)^2)/((pi^2)*Elastic Modulus*Shear Modulus of Elasticity*Torsional Constant). Here is an example- 10.01374 = ((741*3)^2)/((pi^2)*50*100.002*10.0001).

How to calculate Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam?

With Critical Bending Moment for Rectangular (M_Cr(Rect)), Length of Rectangular Beam (Len), Elastic Modulus (e), Shear Modulus of Elasticity (G) & Torsional Constant (J) we can find Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam using the formula - Moment of Inertia about Minor Axis = ((Critical Bending Moment for Rectangular*Length of Rectangular Beam)^2)/((pi^2)*Elastic Modulus*Shear Modulus of Elasticity*Torsional Constant). This formula also uses Archimedes' constant .

Can the Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam be negative?

No, the Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam, measured in Moment of Inertia cannot be negative.

Which unit is used to measure Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam?

Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam is usually measured using the Kilogram Square Meter[kg·m²] for Moment of Inertia. Kilogram Square Centimeter[kg·m²], Kilogram Square Millimeter[kg·m²], Gram Square Centimeter[kg·m²] are the few other units in which Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam can be measured.

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Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam Formula

Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam Example

Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam Solution

Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam Formula Elements

Other formulas in Elastic Lateral Buckling of Beams category

How to Evaluate Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam?

FAQs on Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam

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