Critical Elastic Moment Calculator

✖Moment Gradient Factor is rate at which moment is changing with length of beam.ⓘ Moment Gradient Factor [C_b]			+10% -10%
✖Unbraced Length of Member is the distance between two points along a structural member where lateral support is provided.ⓘ Unbraced Length of Member [L]			+10% -10%
✖Elastic Modulus of Steel is a measure of the stiffness of steel. It quantifies the ability of steel to resist deformation under stress.ⓘ Elastic Modulus of Steel [E]			+10% -10%
✖Y Axis Moment of Inertia is a geometric property of a cross-section that measures its resistance to bending about the y-axis, also known as the second moment of area about the y-axis.ⓘ Y Axis Moment of Inertia [I_y]			+10% -10%
✖Shear Modulus is the slope of the linear elastic region of the shear stress–strain curve.ⓘ Shear Modulus [G]			+10% -10%
✖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%
✖Warping Constant is a measure of the resistance of a thin-walled open cross-section to warping. Warping refers to the out-of-plane deformation of the cross-section that occurs during torsion.ⓘ Warping Constant [C_w]			+10% -10%

✖Critical Elastic Moment represents the maximum moment a beam can carry in its elastic range before it becomes unstable due to lateral-torsional buckling.ⓘ Critical Elastic Moment [M_cr]

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Critical Elastic Moment Solution

STEP 0: Pre-Calculation Summary

Formula Used

Critical Elastic Moment = ((Moment Gradient Factor*pi)/Unbraced Length of Member)*sqrt(((Elastic Modulus of Steel*Y Axis Moment of Inertia*Shear Modulus*Torsional Constant)+(Y Axis Moment of Inertia*Warping Constant*((pi*Elastic Modulus of Steel)/(Unbraced Length of Member)^2))))
M_cr = ((C_b*pi)/L)*sqrt(((E*I_y*G*J)+(I_y*C_w*((pi*E)/(L)^2))))
This formula uses 1 Constants, 1 Functions, 8 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

Critical Elastic Moment - (Measured in Kilonewton Meter) - Critical Elastic Moment represents the maximum moment a beam can carry in its elastic range before it becomes unstable due to lateral-torsional buckling.
Moment Gradient Factor - Moment Gradient Factor is rate at which moment is changing with length of beam.
Unbraced Length of Member - (Measured in Centimeter) - Unbraced Length of Member is the distance between two points along a structural member where lateral support is provided.
Elastic Modulus of Steel - (Measured in Gigapascal) - Elastic Modulus of Steel is a measure of the stiffness of steel. It quantifies the ability of steel to resist deformation under stress.
Y Axis Moment of Inertia - (Measured in Meter⁴ per Meter) - Y Axis Moment of Inertia is a geometric property of a cross-section that measures its resistance to bending about the y-axis, also known as the second moment of area about the y-axis.
Shear Modulus - (Measured in Gigapascal) - Shear Modulus is the slope of the linear elastic region of the shear stress–strain curve.
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.
Warping Constant - Warping Constant is a measure of the resistance of a thin-walled open cross-section to warping. Warping refers to the out-of-plane deformation of the cross-section that occurs during torsion.

STEP 1: Convert Input(s) to Base Unit

Moment Gradient Factor: 1.96 --> No Conversion Required
Unbraced Length of Member: 12 Meter --> 1200 Centimeter (Check conversion here)
Elastic Modulus of Steel: 200 Gigapascal --> 200 Gigapascal No Conversion Required
Y Axis Moment of Inertia: 5000 Millimeter⁴ per Millimeter --> 5E-06 Meter⁴ per Meter (Check conversion here)
Shear Modulus: 80 Gigapascal --> 80 Gigapascal No Conversion Required
Torsional Constant: 21.9 --> No Conversion Required
Warping Constant: 0.2 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M_cr = ((C_b*pi)/L)*sqrt(((E*I_y*G*J)+(I_y*C_w*((pi*E)/(L)^2)))) --> ((1.96*pi)/1200)*sqrt(((200*5E-06*80*21.9)+(5E-06*0.2*((pi*200)/(1200)^2))))

Evaluating ... ...

M_cr = 0.00679190728759447

STEP 3: Convert Result to Output's Unit

6.79190728759447 Newton Meter --> No Conversion Required

FINAL ANSWER

6.79190728759447 ≈ 6.791907 Newton Meter <-- Critical Elastic Moment

(Calculation completed in 00.006 seconds)

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Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

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Coorg Institute of Technology (CIT), Coorg

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< Beams Calculators

Maximum Laterally Unbraced Length for Plastic Analysis

LaTeX Go Laterally Unbraced Length for Plastic Analysis = Radius of Gyration about Minor Axis*(3600+2200*(Smaller Moments of Unbraced Beam/Plastic Moment))/(Minimum Yield Stress of Compression Flange)

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

LaTeX Go Laterally Unbraced Length for Plastic Analysis = (Radius of Gyration about Minor Axis*(5000+3000*(Smaller Moments of Unbraced Beam/Plastic Moment)))/Yield Stress of Steel

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

LaTeX Go Limiting Laterally Unbraced Length = (300*Radius of Gyration about Minor Axis)/sqrt(Flange Yield Stress)

Plastic Moment

LaTeX Go Plastic Moment = Specified Minimum Yield Stress*Plastic Modulus

Critical Elastic Moment Formula

LaTeX Go

What is Buckling of a Section?

Buckling is the event where a beam spontaneously bends from straight to curved under a compressive load. Also, it describes the relation between the force and the distance between the two ends of the beam, the force-strain curve.

What are the causes of Lateral Buckling & measures to prevent it?

The applied vertical load results in compression and tension in the flanges of the section. The compression flange tries to deflect laterally away from its original position, whereas the tension flange tries to keep the member straight.
The best way to prevent this type of buckling from occurring is to restrain the flange under compression, which prevents it from rotating along its axis. Some beams have restraints such as walls or braced elements periodically along their lengths, as well as on the ends.

How to Calculate Critical Elastic Moment?

Critical Elastic Moment calculator uses Critical Elastic Moment = ((Moment Gradient Factor*pi)/Unbraced Length of Member)*sqrt(((Elastic Modulus of Steel*Y Axis Moment of Inertia*Shear Modulus*Torsional Constant)+(Y Axis Moment of Inertia*Warping Constant*((pi*Elastic Modulus of Steel)/(Unbraced Length of Member)^2)))) to calculate the Critical Elastic Moment, The Critical Elastic Moment formula is defined as the methods given in design codes for determining the slenderness of a section. The elastic critical moment (Mcr) is similar to the Euler (flexural) buckling of a strut in that it defines a buckling load. Critical Elastic Moment is denoted by M_cr symbol.

How to calculate Critical Elastic Moment using this online calculator? To use this online calculator for Critical Elastic Moment, enter Moment Gradient Factor (C_b), Unbraced Length of Member (L), Elastic Modulus of Steel (E), Y Axis Moment of Inertia (I_y), Shear Modulus (G), Torsional Constant (J) & Warping Constant (C_w) and hit the calculate button. Here is how the Critical Elastic Moment calculation can be explained with given input values -> 6.791907 = ((1.96*pi)/12)*sqrt(((200000000000*5E-06*80000000000*21.9)+(5E-06*0.2*((pi*200000000000)/(12)^2)))).

FAQ

What is Critical Elastic Moment?

The Critical Elastic Moment formula is defined as the methods given in design codes for determining the slenderness of a section. The elastic critical moment (Mcr) is similar to the Euler (flexural) buckling of a strut in that it defines a buckling load and is represented as M_cr = ((C_b*pi)/L)*sqrt(((E*I_y*G*J)+(I_y*C_w*((pi*E)/(L)^2)))) or Critical Elastic Moment = ((Moment Gradient Factor*pi)/Unbraced Length of Member)*sqrt(((Elastic Modulus of Steel*Y Axis Moment of Inertia*Shear Modulus*Torsional Constant)+(Y Axis Moment of Inertia*Warping Constant*((pi*Elastic Modulus of Steel)/(Unbraced Length of Member)^2)))). Moment Gradient Factor is rate at which moment is changing with length of beam, Unbraced Length of Member is the distance between two points along a structural member where lateral support is provided, Elastic Modulus of Steel is a measure of the stiffness of steel. It quantifies the ability of steel to resist deformation under stress, Y Axis Moment of Inertia is a geometric property of a cross-section that measures its resistance to bending about the y-axis, also known as the second moment of area about the y-axis, Shear Modulus is the slope of the linear elastic region of the shear stress–strain curve, 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 & Warping Constant is a measure of the resistance of a thin-walled open cross-section to warping. Warping refers to the out-of-plane deformation of the cross-section that occurs during torsion.

How to calculate Critical Elastic Moment?

The Critical Elastic Moment formula is defined as the methods given in design codes for determining the slenderness of a section. The elastic critical moment (Mcr) is similar to the Euler (flexural) buckling of a strut in that it defines a buckling load is calculated using Critical Elastic Moment = ((Moment Gradient Factor*pi)/Unbraced Length of Member)*sqrt(((Elastic Modulus of Steel*Y Axis Moment of Inertia*Shear Modulus*Torsional Constant)+(Y Axis Moment of Inertia*Warping Constant*((pi*Elastic Modulus of Steel)/(Unbraced Length of Member)^2)))). To calculate Critical Elastic Moment, you need Moment Gradient Factor (C_b), Unbraced Length of Member (L), Elastic Modulus of Steel (E), Y Axis Moment of Inertia (I_y), Shear Modulus (G), Torsional Constant (J) & Warping Constant (C_w). With our tool, you need to enter the respective value for Moment Gradient Factor, Unbraced Length of Member, Elastic Modulus of Steel, Y Axis Moment of Inertia, Shear Modulus, Torsional Constant & Warping 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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