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

✖Critical Bending Moment for Rectangular is crucial in the proper design of bent beams susceptible to LTB, as it allows for slenderness calculation.ⓘ Critical Bending Moment for Rectangular [M_Cr(Rect)]			+10% -10%
✖Length of Rectangular Beam is the measurement or extent of something from end to end.ⓘ Length of Rectangular Beam [Len]			+10% -10%
✖The Elastic Modulus is the ratio of Stress to Strain.ⓘ Elastic Modulus [e]			+10% -10%
✖Shear Modulus of Elasticity is one of the measures of mechanical properties of solids. Other elastic moduli are Young's modulus and bulk modulus.ⓘ Shear Modulus of Elasticity [G]			+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%

✖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.ⓘ Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam [I_y]

⎘ Copy

👎

Formula

✖

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

Formula

`"I"_{"y"} = (("M"_{"Cr(Rect)"}*"Len")^2)/((pi^2)*"e"*"G"*"J")`

Example

`"10.01374kg·m²"=(("741N*m"*"3m")^2)/((pi^2)*"50Pa"*"100.002N/m²"*"10.0001")`

Calculator

LaTeX

Reset

👍

Download Structural Analysis of Beams Formulas PDF PDF Image

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

STEP 0: Pre-Calculation Summary

Formula Used

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)
I_y = ((M_Cr(Rect)*Len)^2)/((pi^2)*e*G*J)
This formula uses 1 Constants, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Moment of Inertia about Minor Axis - (Measured in Kilogram Square Meter) - 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.
Critical Bending Moment for Rectangular - (Measured in Newton Meter) - Critical Bending Moment for Rectangular is crucial in the proper design of bent beams susceptible to LTB, as it allows for slenderness calculation.
Length of Rectangular Beam - (Measured in Meter) - Length of Rectangular Beam is the measurement or extent of something from end to end.
Elastic Modulus - (Measured in Pascal) - The Elastic Modulus is the ratio of Stress to Strain.
Shear Modulus of Elasticity - (Measured in Pascal) - Shear Modulus of Elasticity is one of the measures of mechanical properties of solids. Other elastic moduli are Young's modulus and bulk modulus.
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.

STEP 1: Convert Input(s) to Base Unit

Critical Bending Moment for Rectangular: 741 Newton Meter --> 741 Newton Meter No Conversion Required
Length of Rectangular Beam: 3 Meter --> 3 Meter No Conversion Required
Elastic Modulus: 50 Pascal --> 50 Pascal No Conversion Required
Shear Modulus of Elasticity: 100.002 Newton per Square Meter --> 100.002 Pascal (Check conversion here)
Torsional Constant: 10.0001 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I_y = ((M_Cr(Rect)*Len)^2)/((pi^2)*e*G*J) --> ((741*3)^2)/((pi^2)*50*100.002*10.0001)

Evaluating ... ...

I_y = 10.0137362163041

STEP 3: Convert Result to Output's Unit

10.0137362163041 Kilogram Square Meter --> No Conversion Required

FINAL ANSWER

10.0137362163041 ≈ 10.01374 Kilogram Square Meter <-- Moment of Inertia about Minor Axis

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Civil » Structural Engineering » Structural Analysis » Miscellaneous Topics » Structural Analysis of Beams » Elastic Lateral Buckling of Beams » Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam

Credits

Created by Alithea Fernandes

Don Bosco College of Engineering (DBCE), Goa

Alithea Fernandes has created this Calculator and 100+ more calculators!

Verified by Rudrani Tidke

Cummins College of Engineering for Women (CCEW), Pune

Rudrani Tidke has verified this Calculator and 50+ more calculators!

< 11 Elastic Lateral Buckling of Beams Calculators

Critical Bending Moment for Simply Supported Open Section Beam

Go Critical Bending Moment = (pi/Unbraced Length of Member)*sqrt(Modulus of Elasticity*Moment of Inertia about Minor Axis*((Shear Modulus of Elasticity*Torsional Constant)+Modulus of Elasticity*Warping Constant*((pi^2)/(Unbraced Length of Member)^2)))

Unbraced Member Length given Critical Bending Moment of Rectangular Beam

Go Length of Rectangular Beam = (pi/Critical Bending Moment for Rectangular)*(sqrt(Elastic Modulus*Moment of Inertia about Minor Axis*Shear Modulus of Elasticity*Torsional Constant))

Critical Bending Moment for Simply Supported Rectangular Beam

Go Critical Bending Moment for Rectangular = (pi/Length of Rectangular Beam)*(sqrt(Elastic Modulus*Moment of Inertia about Minor Axis*Shear Modulus of Elasticity*Torsional Constant))

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

Go 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)

Shear Elasticity Modulus for Critical Bending Moment of Rectangular Beam

Go Shear Modulus of Elasticity = ((Critical Bending Moment for Rectangular*Length of Rectangular Beam)^2)/((pi^2)*Moment of Inertia about Minor Axis*Elastic Modulus*Torsional Constant)

Elasticity Modulus given Critical Bending Moment of Rectangular Beam

Go Elastic Modulus = ((Critical Bending Moment for Rectangular*Length of Rectangular Beam)^2)/((pi^2)*Moment of Inertia about Minor Axis*Shear Modulus of Elasticity*Torsional Constant)

Critical Bending Coefficient

Go Bending Moment Coefficient = (12.5*Maximum Moment)/((2.5*Maximum Moment)+(3*Moment at Quarter Point)+(4*Moment at Centerline)+(3*Moment at Three-quarter Point))

Absolute Value of Moment at Three-Quarter Point of Unbraced Beam Segment

Go Moment at Three-quarter Point = ((12.5*Maximum Moment)-(2.5*Maximum Moment+4*Moment at Centerline+3*Moment at Quarter Point))/3

Absolute Value of Moment at Quarter Point of Unbraced Beam Segment

Go Moment at Quarter Point = ((12.5*Maximum Moment)-(2.5*Maximum Moment+4*Moment at Centerline+3*Moment at Three-quarter Point))/3

Absolute Value of Moment at Centerline of Unbraced Beam Segment

Go Moment at Centerline = ((12.5*Maximum Moment)-(2.5*Maximum Moment+3*Moment at Quarter Point+3*Moment at Three-quarter Point))/4

Critical Bending Moment in Non-Uniform Bending

Go Non-Uniform Critical Bending Moment = (Bending Moment Coefficient*Critical Bending Moment)

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

What is Minor Axis Moment of Inertia when Critical Bending Moment of Rectangular Beam?

Minor Axis Moment of Inertia when Critical Bending Moment of Rectangular Beam is a geometrical property of an area which reflects how its points are distributed with regard to the minor axis.

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

Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam calculator 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 calculate 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 calculate Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam using this online calculator? To use this online calculator 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. Here is how the Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam calculation can be explained with given input values -> 10.01374 = ((741*3)^2)/((pi^2)*50*100.002*10.0001).

FAQ

What is Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam?

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 and is represented as I_y = ((M_Cr(Rect)*Len)^2)/((pi^2)*e*G*J) or 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). Critical Bending Moment for Rectangular is crucial in the proper design of bent beams susceptible to LTB, as it allows for slenderness calculation, Length of Rectangular Beam is the measurement or extent of something from end to end, The Elastic Modulus is the ratio of Stress to Strain, Shear Modulus of Elasticity is one of the measures of mechanical properties of solids. Other elastic moduli are Young's modulus and bulk modulus & 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.

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

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 is calculated using 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 calculate Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam, you need Critical Bending Moment for Rectangular (M_Cr(Rect)), Length of Rectangular Beam (Len), Elastic Modulus (e), Shear Modulus of Elasticity (G) & Torsional Constant (J). With our tool, you need to enter the respective value for Critical Bending Moment for Rectangular, Length of Rectangular Beam, Elastic Modulus, Shear Modulus of Elasticity & Torsional Constant and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search