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%
✖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 area of a particular section of a structural element, such as a beam or column, when cut perpendicular to its longitudinal axis.ⓘ Cross Sectional Area in Steel Structures [A]			+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%
✖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 for Box Section is the maximum moment a box-section beam can withstand before it reaches the elastic buckling stage.ⓘ Critical Elastic Moment for Box Sections and Solid Bars [M_bs]

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Formula

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Critical Elastic Moment for Box Sections and Solid Bars

Formula

M bs = \frac{57000 \cdot C b \cdot \sqrt{J \cdot A}}{\frac{L}{r y}}

Example

69.70946 N*m = \frac{57000 \cdot 1.960 \cdot \sqrt{21.9 \cdot 6400 mm²}}{\frac{12 m}{20 mm}}

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Critical Elastic Moment for Box Sections and Solid Bars Solution

STEP 0: Pre-Calculation Summary

Formula Used

Critical Elastic Moment for Box Section = (57000*Moment Gradient Factor*sqrt(Torsional Constant*Cross Sectional Area in Steel Structures))/(Unbraced Length of Member/Radius of Gyration about Minor Axis)
M_bs = (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 for Box Section - (Measured in Newton Meter) - Critical Elastic Moment for Box Section is the maximum moment a box-section beam can withstand before it reaches the elastic buckling stage.
Moment Gradient Factor - Moment Gradient Factor is rate at which moment is changing with length of beam.
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.
Cross Sectional Area in Steel Structures - (Measured in Square Meter) - Cross Sectional Area in Steel Structures is the area of a particular section of a structural element, such as a beam or column, when cut perpendicular to its longitudinal axis.
Unbraced Length of Member - (Measured in Meter) - Unbraced Length of Member is the distance between two points along a structural member where lateral support is provided.
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_bs = (57000*C_b*sqrt(J*A))/(L/r_y) --> (57000*1.96*sqrt(21.9*0.0064))/(12/0.02)

Evaluating ... ...

M_bs = 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 for Box Section

(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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< Beams Calculators

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)

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 for Box Section = (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 for Box Section, 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. It is the maximum moment a box-section beam can withstand before it reaches the elastic buckling stage. Elastic buckling is a condition where a structural member deforms significantly due to instability under compressive stresses, but the material has not yet yielded. Critical Elastic Moment for Box Section is denoted by M_bs 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 -> 69.70946 = (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. It is the maximum moment a box-section beam can withstand before it reaches the elastic buckling stage. Elastic buckling is a condition where a structural member deforms significantly due to instability under compressive stresses, but the material has not yet yielded and is represented as M_bs = (57000*C_b*sqrt(J*A))/(L/r_y) or Critical Elastic Moment for Box Section = (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, 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 area of a particular section of a structural element, such as a beam or column, when cut perpendicular to its longitudinal axis, Unbraced Length of Member is the distance between two points along a structural member where lateral support is provided & 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. It is the maximum moment a box-section beam can withstand before it reaches the elastic buckling stage. Elastic buckling is a condition where a structural member deforms significantly due to instability under compressive stresses, but the material has not yet yielded is calculated using Critical Elastic Moment for Box Section = (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.

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