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## Credits

Don Bosco College of Engineering (DBCE), Goa
Alithea Fernandes has created this Calculator and 100+ more calculators!
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## Unbraced Member Length when Critical Bending Moment of Rectangular Beam is Given Solution

STEP 0: Pre-Calculation Summary
Formula Used
length = (pi/Critical Bending Moment)*(sqrt(Modulus Of Elasticity*Moment of Inertia about Minor Axis*Shear Modulus of Elasticity*Torsional constant))
l = (pi/Mcr)*(sqrt(E*Iy*G*J))
This formula uses 1 Constants, 1 Functions, 5 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Critical Bending Moment - The Critical Bending Moment is crucial in the proper design of bent beams susceptible to LTB, as it allows for slenderness calculation. (Measured in Newton Meter)
Modulus Of Elasticity - Modulus Of Elasticity is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it. (Measured in Kilonewton per Square Meter)
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. (Measured in Kilogram Meter²)
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. (Measured in Newton per Square Meter)
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: 10 Newton Meter --> 10 Newton Meter No Conversion Required
Modulus Of Elasticity: 10 Kilonewton per Square Meter --> 10000 Pascal (Check conversion here)
Moment of Inertia about Minor Axis: 10 Kilogram Meter² --> 10 Kilogram Meter² No Conversion Required
Shear Modulus of Elasticity: 100 Newton per Square Meter --> 100 Pascal (Check conversion here)
Torsional constant: 10 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
l = (pi/Mcr)*(sqrt(E*Iy*G*J)) --> (pi/10)*(sqrt(10000*10*100*10))
Evaluating ... ...
l = 3141.59265358979
STEP 3: Convert Result to Output's Unit
3141.59265358979 Meter --> No Conversion Required
3141.59265358979 Meter <-- Length
(Calculation completed in 00.015 seconds)

## < 10+ Elastic Lateral Buckling of Beams Calculators

Shear Elasticity Modulus when Critical Bending Moment of Simply Supported Open Beam is Given
shear_modulus_of_elasticity = ((Critical Bending Moment^2)*(Unbraced Length of the member^4)-((Modulus Of Elasticity^2)*Moment of Inertia about minor axis*Warping Constant*pi^4))/((pi^2)*(Unbraced Length of the member^2)*Modulus Of Elasticity*Moment of Inertia about minor axis*Torsional constant) Go
Critical Bending Moment for Simply Supported Open Section Beam
critical_bending_moment = (pi/Unbraced Length of the 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 the member)^2))) Go
Minor Axis Moment of Inertia when Critical Bending Moment of Simply Supported Open Beam is Given
moment_inertia_about_minor_axis = ((Critical Bending Moment^2)*(Unbraced Length of the member^2))/(((Shear Modulus of Elasticity*Torsional constant)+Modulus Of Elasticity*Warping Constant*((pi^2)/(Unbraced Length of the member^2)))*Modulus Of Elasticity) Go
Unbraced Member Length when Critical Bending Moment of Rectangular Beam is Given
length = (pi/Critical Bending Moment)*(sqrt(Modulus Of Elasticity*Moment of Inertia about Minor Axis*Shear Modulus of Elasticity*Torsional constant)) Go
Critical Bending Moment for Simply Supported Rectangular Beam
critical_bending_moment = (pi/Length)*(sqrt(Modulus Of Elasticity*Moment of Inertia about Minor Axis*Shear Modulus of Elasticity*Torsional constant)) Go
Critical Bending Coefficient
bending_coefficient = (12.5*Maximum Moment)/((2.5*Maximum Moment)+(3*Moment at Quater point)+(4*Moment at Centerline)+(3*Moment at Three-quarter Point)) Go
Minor Axis Moment of Inertia when Critical Bending Moment of Rectangular Beam is Given
moment_of_inertia_about_minor_axis = ((Critical Bending Moment*Length)^2)/((pi^2)*Modulus Of Elasticity*Shear Modulus of Elasticity*Torsional constant) Go
Shear Elasticity Modulus when Critical Bending Moment of Rectangular Beam is Given
shear_modulus_of_elasticity = ((Critical Bending Moment*Length)^2)/((pi^2)*Moment of Inertia about Minor Axis*Modulus Of Elasticity*Torsional constant) Go
Elasticity Modulus when Critical Bending Moment of Rectangular Beam is Given
modulus_of_elasticity = ((Critical Bending Moment*Length)^2)/((pi^2)*Moment of Inertia about Minor Axis*Shear Modulus of Elasticity*Torsional constant) Go
Critical Bending Moment in Non-Uniform Bending
non_uniform_critical_bending_moment = (Bending Moment coefficient*Critical Bending Moment) Go

### Unbraced Member Length when Critical Bending Moment of Rectangular Beam is Given Formula

length = (pi/Critical Bending Moment)*(sqrt(Modulus Of Elasticity*Moment of Inertia about Minor Axis*Shear Modulus of Elasticity*Torsional constant))
l = (pi/Mcr)*(sqrt(E*Iy*G*J))

## What is Unbraced Member Length when Critical Bending Moment of Rectangular Beam is Given?

Unbraced Member Length when Critical Bending Moment of Rectangular Beam is Given is the distance between ends of a structural member which are prevented from moving normal to the axis of the member.

## How to Calculate Unbraced Member Length when Critical Bending Moment of Rectangular Beam is Given?

Unbraced Member Length when Critical Bending Moment of Rectangular Beam is Given calculator uses length = (pi/Critical Bending Moment)*(sqrt(Modulus Of Elasticity*Moment of Inertia about Minor Axis*Shear Modulus of Elasticity*Torsional constant)) to calculate the Length, The Unbraced Member Length when Critical Bending Moment of Rectangular Beam is Given formula is defined as (Pi/Critical Bending Moment)*(SQRT(Modulus of Elasticity*Moment of Inertia about Minor Axis*Shear Modulus of Elasticity*Torsional Constant)) For a simply supported beam of rectangular cross section subjected to uniform bending, buckling occurs at the critical bending moment, and knowing this value the unbraced member length can be found. Length and is denoted by l symbol.

How to calculate Unbraced Member Length when Critical Bending Moment of Rectangular Beam is Given using this online calculator? To use this online calculator for Unbraced Member Length when Critical Bending Moment of Rectangular Beam is Given, enter Critical Bending Moment (Mcr), Modulus Of Elasticity (E), Moment of Inertia about Minor Axis (Iy), Shear Modulus of Elasticity (G) and Torsional constant (J) and hit the calculate button. Here is how the Unbraced Member Length when Critical Bending Moment of Rectangular Beam is Given calculation can be explained with given input values -> 3141.593 = (pi/10)*(sqrt(10000*10*100*10)).

### FAQ

What is Unbraced Member Length when Critical Bending Moment of Rectangular Beam is Given?
The Unbraced Member Length when Critical Bending Moment of Rectangular Beam is Given formula is defined as (Pi/Critical Bending Moment)*(SQRT(Modulus of Elasticity*Moment of Inertia about Minor Axis*Shear Modulus of Elasticity*Torsional Constant)) For a simply supported beam of rectangular cross section subjected to uniform bending, buckling occurs at the critical bending moment, and knowing this value the unbraced member length can be found and is represented as l = (pi/Mcr)*(sqrt(E*Iy*G*J)) or length = (pi/Critical Bending Moment)*(sqrt(Modulus Of Elasticity*Moment of Inertia about Minor Axis*Shear Modulus of Elasticity*Torsional constant)). The Critical Bending Moment is crucial in the proper design of bent beams susceptible to LTB, as it allows for slenderness calculation, Modulus Of Elasticity is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it, 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, Shear Modulus of Elasticity is one of the measures of mechanical properties of solids. Other elastic moduli are Young's modulus and bulk modulus and 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 Unbraced Member Length when Critical Bending Moment of Rectangular Beam is Given?
The Unbraced Member Length when Critical Bending Moment of Rectangular Beam is Given formula is defined as (Pi/Critical Bending Moment)*(SQRT(Modulus of Elasticity*Moment of Inertia about Minor Axis*Shear Modulus of Elasticity*Torsional Constant)) For a simply supported beam of rectangular cross section subjected to uniform bending, buckling occurs at the critical bending moment, and knowing this value the unbraced member length can be found is calculated using length = (pi/Critical Bending Moment)*(sqrt(Modulus Of Elasticity*Moment of Inertia about Minor Axis*Shear Modulus of Elasticity*Torsional constant)). To calculate Unbraced Member Length when Critical Bending Moment of Rectangular Beam is Given, you need Critical Bending Moment (Mcr), Modulus Of Elasticity (E), Moment of Inertia about Minor Axis (Iy), Shear Modulus of Elasticity (G) and Torsional constant (J). With our tool, you need to enter the respective value for Critical Bending Moment, Modulus Of Elasticity, Moment of Inertia about Minor Axis, Shear Modulus of Elasticity and Torsional constant 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 Length?
In this formula, Length uses Critical Bending Moment, Modulus Of Elasticity, Moment of Inertia about Minor Axis, Shear Modulus of Elasticity and Torsional constant. We can use 10 other way(s) to calculate the same, which is/are as follows -
• critical_bending_moment = (pi/Length)*(sqrt(Modulus Of Elasticity*Moment of Inertia about Minor Axis*Shear Modulus of Elasticity*Torsional constant))
• length = (pi/Critical Bending Moment)*(sqrt(Modulus Of Elasticity*Moment of Inertia about Minor Axis*Shear Modulus of Elasticity*Torsional constant))
• modulus_of_elasticity = ((Critical Bending Moment*Length)^2)/((pi^2)*Moment of Inertia about Minor Axis*Shear Modulus of Elasticity*Torsional constant)
• moment_of_inertia_about_minor_axis = ((Critical Bending Moment*Length)^2)/((pi^2)*Modulus Of Elasticity*Shear Modulus of Elasticity*Torsional constant)
• shear_modulus_of_elasticity = ((Critical Bending Moment*Length)^2)/((pi^2)*Moment of Inertia about Minor Axis*Modulus Of Elasticity*Torsional constant)
• critical_bending_moment = (pi/Unbraced Length of the 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 the member)^2)))
• moment_inertia_about_minor_axis = ((Critical Bending Moment^2)*(Unbraced Length of the member^2))/(((Shear Modulus of Elasticity*Torsional constant)+Modulus Of Elasticity*Warping Constant*((pi^2)/(Unbraced Length of the member^2)))*Modulus Of Elasticity)
• shear_modulus_of_elasticity = ((Critical Bending Moment^2)*(Unbraced Length of the member^4)-((Modulus Of Elasticity^2)*Moment of Inertia about minor axis*Warping Constant*pi^4))/((pi^2)*(Unbraced Length of the member^2)*Modulus Of Elasticity*Moment of Inertia about minor axis*Torsional constant)
• non_uniform_critical_bending_moment = (Bending Moment coefficient*Critical Bending Moment)
• bending_coefficient = (12.5*Maximum Moment)/((2.5*Maximum Moment)+(3*Moment at Quater point)+(4*Moment at Centerline)+(3*Moment at Three-quarter Point))
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