Unbraced Member Length given 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%
✖The Elastic Modulus is the ratio of Stress to Strain.ⓘ Elastic Modulus [e]			+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.ⓘ Moment of Inertia about Minor Axis [I_y]			+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%

✖Length of Rectangular Beam is the measurement or extent of something from end to end.ⓘ Unbraced Member Length given Critical Bending Moment of Rectangular Beam [Len]

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Formula

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Unbraced Member Length given Critical Bending Moment of Rectangular Beam

Formula

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

Example

`"2.998092m"=(pi/"741N*m")*(sqrt("50Pa"*"10.001kg·m²"*"100.002N/m²"*"10.0001"))`

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Unbraced Member Length given Critical Bending Moment of Rectangular Beam Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
Len = (pi/M_Cr(Rect))*(sqrt(e*I_y*G*J))
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

Length of Rectangular Beam - (Measured in Meter) - Length of Rectangular Beam is the measurement or extent of something from end to end.
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.
Elastic Modulus - (Measured in Pascal) - The Elastic Modulus is the ratio of Stress to Strain.
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.
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
Elastic Modulus: 50 Pascal --> 50 Pascal No Conversion Required
Moment of Inertia about Minor Axis: 10.001 Kilogram Square Meter --> 10.001 Kilogram Square Meter 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

Len = (pi/M_Cr(Rect))*(sqrt(e*I_y*G*J)) --> (pi/741)*(sqrt(50*10.001*100.002*10.0001))

Evaluating ... ...

Len = 2.99809158115557

STEP 3: Convert Result to Output's Unit

2.99809158115557 Meter --> No Conversion Required

FINAL ANSWER

2.99809158115557 ≈ 2.998092 Meter <-- Length of Rectangular Beam

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Structural Engineering » Structural Analysis » Miscellaneous Topics » Structural Analysis of Beams » Elastic Lateral Buckling of Beams » Unbraced Member Length given Critical Bending Moment of Rectangular Beam

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Created by Alithea Fernandes

Don Bosco College of Engineering (DBCE), Goa

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< 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)

Unbraced Member Length given Critical Bending Moment of Rectangular Beam Formula

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 given Critical Bending Moment of Rectangular Beam?

Unbraced Member Length given Critical Bending Moment of Rectangular Beam calculator uses 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)) to calculate the Length of Rectangular Beam, Unbraced Member Length given Critical Bending Moment of Rectangular Beam formula is defined as the span where buckling occurs under load. Length of Rectangular Beam is denoted by Len symbol.

How to calculate Unbraced Member Length given Critical Bending Moment of Rectangular Beam using this online calculator? To use this online calculator for Unbraced Member Length given Critical Bending Moment of Rectangular Beam, enter Critical Bending Moment for Rectangular (M_Cr(Rect)), Elastic Modulus (e), Moment of Inertia about Minor Axis (I_y), Shear Modulus of Elasticity (G) & Torsional Constant (J) and hit the calculate button. Here is how the Unbraced Member Length given Critical Bending Moment of Rectangular Beam calculation can be explained with given input values -> 2.997942 = (pi/741)*(sqrt(50*10.001*100.002*10.0001)).

FAQ

What is Unbraced Member Length given Critical Bending Moment of Rectangular Beam?

Unbraced Member Length given Critical Bending Moment of Rectangular Beam formula is defined as the span where buckling occurs under load and is represented as Len = (pi/M_Cr(Rect))*(sqrt(e*I_y*G*J)) or 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 Rectangular is crucial in the proper design of bent beams susceptible to LTB, as it allows for slenderness calculation, The Elastic Modulus is the ratio of Stress to Strain, 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 & 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 given Critical Bending Moment of Rectangular Beam?

Unbraced Member Length given Critical Bending Moment of Rectangular Beam formula is defined as the span where buckling occurs under load is calculated using 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)). To calculate Unbraced Member Length given Critical Bending Moment of Rectangular Beam, you need Critical Bending Moment for Rectangular (M_Cr(Rect)), Elastic Modulus (e), Moment of Inertia about Minor Axis (I_y), Shear Modulus of Elasticity (G) & Torsional Constant (J). With our tool, you need to enter the respective value for Critical Bending Moment for Rectangular, Elastic Modulus, Moment of Inertia about Minor Axis, 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.

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