Critical Elastic Moment for Box Sections and Solid Bars Calculator

✖Moment Gradient Factor is rate at which moment is changing with length of beam.ⓘ Moment Gradient Factor [C_b]			+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%
✖Cross Sectional Area in Steel Structures is the enclosed surface area, product of length and breadth.ⓘ Cross Sectional Area in Steel Structures [A]			+10% -10%
✖Unbraced Length of Member is defined as the distance between adjacent Points.ⓘ Unbraced Length of Member [L]			+10% -10%
✖Radius of gyration about minor axis is the root mean square distance of the object's parts from either its center of mass or a given minor axis, depending on the relevant application.ⓘ Radius of gyration about minor axis [r_y]			+10% -10%

✖Critical Elastic Moment is similar to the Euler (flexural) buckling of a strut in that it defines a buckling load.ⓘ Critical Elastic Moment for Box Sections and Solid Bars [M_cr]

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Formula

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Critical Elastic Moment for Box Sections and Solid Bars

Formula

`"M"_{"cr"} = (57000*"C"_{"b"}*sqrt("J"*"A"))/("L"/"r"_{"y"})`

Example

`"69.70946N*m"=(57000*"1.960"*sqrt("21.9"*"6400mm²"))/("12m"/"20mm")`

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Critical Elastic Moment for Box Sections and Solid Bars Solution

STEP 0: Pre-Calculation Summary

Formula Used

Critical Elastic Moment = (57000*Moment Gradient Factor*sqrt(Torsional constant*Cross Sectional Area in Steel Structures))/(Unbraced Length of Member/Radius of gyration about minor axis)
M_cr = (57000*C_b*sqrt(J*A))/(L/r_y)
This formula uses 1 Functions, 6 Variables

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 Newton Meter) - Critical Elastic Moment is similar to the Euler (flexural) buckling of a strut in that it defines a buckling load.
Moment Gradient Factor - Moment Gradient Factor is rate at which moment is changing with length of beam.
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.
Cross Sectional Area in Steel Structures - (Measured in Square Meter) - Cross Sectional Area in Steel Structures is the enclosed surface area, product of length and breadth.
Unbraced Length of Member - (Measured in Meter) - Unbraced Length of Member is defined as the distance between adjacent Points.
Radius of gyration about minor axis - (Measured in Meter) - Radius of gyration about minor axis is the root mean square distance of the object's parts from either its center of mass or a given minor axis, depending on the relevant application.

STEP 1: Convert Input(s) to Base Unit

Moment Gradient Factor: 1.96 --> No Conversion Required
Torsional constant: 21.9 --> No Conversion Required
Cross Sectional Area in Steel Structures: 6400 Square Millimeter --> 0.0064 Square Meter (Check conversion here)
Unbraced Length of Member: 12 Meter --> 12 Meter No Conversion Required
Radius of gyration about minor axis: 20 Millimeter --> 0.02 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M_cr = (57000*C_b*sqrt(J*A))/(L/r_y) --> (57000*1.96*sqrt(21.9*0.0064))/(12/0.02)

Evaluating ... ...

M_cr = 69.7094604081828

STEP 3: Convert Result to Output's Unit

69.7094604081828 Newton Meter --> No Conversion Required

FINAL ANSWER

69.7094604081828 ≈ 69.70946 Newton Meter <-- Critical Elastic Moment

(Calculation completed in 00.004 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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< 13 Beams Calculators

Critical Elastic Moment

Go Critical Elastic Moment = ((Moment Gradient Factor*pi)/Unbraced Length of Member)*sqrt(((Elastic Modulus of Steel*Y Axis Moment of Inertia*Shear Modulus in Steel Structures*Torsional constant)+(Y Axis Moment of Inertia*Warping Constant*((pi*Elastic Modulus of Steel)/(Unbraced Length of Member)^2))))

Limiting Laterally Unbraced Length for Inelastic Lateral Buckling

Go Limiting Length for Inelastic Buckling = ((Radius of gyration about minor axis*Beam Buckling Factor 1)/(Specified Minimum Yield Stress-Compressive Residual Stress in Flange))*sqrt(1+sqrt(1+(Beam Buckling Factor 2*Smaller Yield Stress^2)))

Specified Minimum Yield Stress for Web given Limiting Laterally Unbraced Length

Go Specified Minimum Yield Stress = ((Radius of gyration about minor axis*Beam Buckling Factor 1*sqrt(1+sqrt(1+(Beam Buckling Factor 2*Smaller Yield Stress^2))))/Limiting Length for Inelastic Buckling)+Compressive Residual Stress in Flange

Beam Buckling Factor 1

Go Beam Buckling Factor 1 = (pi/Section Modulus about Major Axis)*sqrt((Elastic Modulus of Steel*Shear Modulus in Steel Structures*Torsional constant*Cross Sectional Area in Steel Structures)/2)

Limiting Laterally Unbraced Length for Inelastic Lateral Buckling for Box Beams

Go Limiting Length for Inelastic Buckling = (2*Radius of gyration about minor axis*Elastic Modulus of Steel*sqrt(Torsional constant*Cross Sectional Area in Steel Structures))/Limiting buckling moment

Critical Elastic Moment for Box Sections and Solid Bars

Go Critical Elastic Moment = (57000*Moment Gradient Factor*sqrt(Torsional constant*Cross Sectional Area in Steel Structures))/(Unbraced Length of Member/Radius of gyration about minor axis)

Beam Buckling Factor 2

Go Beam Buckling Factor 2 = ((4*Warping Constant)/Y Axis Moment of Inertia)*((Section Modulus about Major Axis)/(Shear Modulus in Steel Structures*Torsional constant))^2

Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for Solid Bar and Box Beams

Go Limiting Laterally Unbraced Length = (3750*(Radius of gyration about minor axis/Plastic Moment))/(sqrt(Torsional constant*Cross Sectional Area in Steel Structures))

Maximum Laterally Unbraced Length for Plastic Analysis

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

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

Go Limiting Laterally Unbraced Length = (300*Radius of gyration about minor axis)/sqrt(Flange Yield Stress)

Limiting Buckling Moment

Go Limiting buckling moment = Smaller Yield Stress*Section Modulus about Major Axis

Plastic Moment

Go Plastic Moment = Specified Minimum Yield Stress*Plastic modulus

Critical Elastic Moment for Box Sections and Solid Bars Formula

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 for Box Sections and Solid Bars?

Critical Elastic Moment for Box Sections and Solid Bars calculator uses Critical Elastic Moment = (57000*Moment Gradient Factor*sqrt(Torsional constant*Cross Sectional Area in Steel Structures))/(Unbraced Length of Member/Radius of gyration about minor axis) to calculate the Critical Elastic Moment, The Critical Elastic Moment for Box Sections and Solid Bars formula is defined as the maximum limit of the moment a box beam or solid bar can withstand, any further moment can make the beam or member in failure. Critical Elastic Moment is denoted by M_cr symbol.

How to calculate Critical Elastic Moment for Box Sections and Solid Bars using this online calculator? To use this online calculator for Critical Elastic Moment for Box Sections and Solid Bars, enter Moment Gradient Factor (C_b), Torsional constant (J), Cross Sectional Area in Steel Structures (A), Unbraced Length of Member (L) & Radius of gyration about minor axis (r_y) and hit the calculate button. Here is how the Critical Elastic Moment for Box Sections and Solid Bars calculation can be explained with given input values -> 7E-5 = (57000*1.96*sqrt(21.9*0.0064))/(12/0.02).

FAQ

What is Critical Elastic Moment for Box Sections and Solid Bars?

The Critical Elastic Moment for Box Sections and Solid Bars formula is defined as the maximum limit of the moment a box beam or solid bar can withstand, any further moment can make the beam or member in failure and is represented as M_cr = (57000*C_b*sqrt(J*A))/(L/r_y) or Critical Elastic Moment = (57000*Moment Gradient Factor*sqrt(Torsional constant*Cross Sectional Area in Steel Structures))/(Unbraced Length of Member/Radius of gyration about minor axis). Moment Gradient Factor is rate at which moment is changing with length of beam, 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, Cross Sectional Area in Steel Structures is the enclosed surface area, product of length and breadth, Unbraced Length of Member is defined as the distance between adjacent Points & Radius of gyration about minor axis is the root mean square distance of the object's parts from either its center of mass or a given minor axis, depending on the relevant application.

How to calculate Critical Elastic Moment for Box Sections and Solid Bars?

The Critical Elastic Moment for Box Sections and Solid Bars formula is defined as the maximum limit of the moment a box beam or solid bar can withstand, any further moment can make the beam or member in failure is calculated using Critical Elastic Moment = (57000*Moment Gradient Factor*sqrt(Torsional constant*Cross Sectional Area in Steel Structures))/(Unbraced Length of Member/Radius of gyration about minor axis). To calculate Critical Elastic Moment for Box Sections and Solid Bars, you need Moment Gradient Factor (C_b), Torsional constant (J), Cross Sectional Area in Steel Structures (A), Unbraced Length of Member (L) & Radius of gyration about minor axis (r_y). With our tool, you need to enter the respective value for Moment Gradient Factor, Torsional constant, Cross Sectional Area in Steel Structures, Unbraced Length of Member & Radius of gyration about minor axis 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 Critical Elastic Moment?

In this formula, Critical Elastic Moment uses Moment Gradient Factor, Torsional constant, Cross Sectional Area in Steel Structures, Unbraced Length of Member & Radius of gyration about minor axis. We can use 1 other way(s) to calculate the same, which is/are as follows -

Critical Elastic Moment = ((Moment Gradient Factor*pi)/Unbraced Length of Member)*sqrt(((Elastic Modulus of Steel*Y Axis Moment of Inertia*Shear Modulus in Steel Structures*Torsional constant)+(Y Axis Moment of Inertia*Warping Constant*((pi*Elastic Modulus of Steel)/(Unbraced Length of Member)^2))))

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