Critical Bending Coefficient Calculator

✖The maximum Moment is the absolute value of the maximum moment in the unbraced beam segment.ⓘ Maximum Moment [M'max]			+10% -10%
✖The moment at Quarter Point is the absolute value of the moment at the quarter point of the unbraced beam segment.ⓘ Moment at Quarter Point [M_A]			+10% -10%
✖The moment at Centerline is the absolute value of moment at the centerline of the unbraced beam segment.ⓘ Moment at Centerline [M_B]			+10% -10%
✖Moment at Three-quarter Point is the absolute value of moment at three-quarter point of the unbraced beam segment.ⓘ Moment at Three-quarter Point [M_C]			+10% -10%

✖The Bending Moment coefficient of moments can be calculated by dividing the support moments by the span length.ⓘ Critical Bending Coefficient [M_coeff]

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Formula

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Critical Bending Coefficient

Formula

`"M"_{"coeff"} = (12.5*"M'max")/((2.5*"M'max")+(3*"M"_{"A"})+(4*"M"_{"B"})+(3*"M"_{"C"}))`

Example

`"1.315679N*m"=(12.5*"50.01N*m")/((2.5*"50.01N*m")+(3*"30N*m")+(4*"50.02N*m")+(3*"20.01N*m"))`

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Critical Bending Coefficient Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
M_coeff = (12.5*M'max)/((2.5*M'max)+(3*M_A)+(4*M_B)+(3*M_C))
This formula uses 5 Variables

Variables Used

Bending Moment Coefficient - (Measured in Newton Meter) - The Bending Moment coefficient of moments can be calculated by dividing the support moments by the span length.
Maximum Moment - (Measured in Newton Meter) - The maximum Moment is the absolute value of the maximum moment in the unbraced beam segment.
Moment at Quarter Point - (Measured in Newton Meter) - The moment at Quarter Point is the absolute value of the moment at the quarter point of the unbraced beam segment.
Moment at Centerline - (Measured in Newton Meter) - The moment at Centerline is the absolute value of moment at the centerline of the unbraced beam segment.
Moment at Three-quarter Point - (Measured in Newton Meter) - Moment at Three-quarter Point is the absolute value of moment at three-quarter point of the unbraced beam segment.

STEP 1: Convert Input(s) to Base Unit

Maximum Moment: 50.01 Newton Meter --> 50.01 Newton Meter No Conversion Required
Moment at Quarter Point: 30 Newton Meter --> 30 Newton Meter No Conversion Required
Moment at Centerline: 50.02 Newton Meter --> 50.02 Newton Meter No Conversion Required
Moment at Three-quarter Point: 20.01 Newton Meter --> 20.01 Newton Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M_coeff = (12.5*M'max)/((2.5*M'max)+(3*M_A)+(4*M_B)+(3*M_C)) --> (12.5*50.01)/((2.5*50.01)+(3*30)+(4*50.02)+(3*20.01))

Evaluating ... ...

M_coeff = 1.31567870184263

STEP 3: Convert Result to Output's Unit

1.31567870184263 Newton Meter --> No Conversion Required

FINAL ANSWER

1.31567870184263 ≈ 1.315679 Newton Meter <-- Bending Moment Coefficient

(Calculation completed in 00.020 seconds)

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Home » Engineering » Civil » Structural Engineering » Structural Analysis » Miscellaneous Topics » Structural Analysis of Beams » Elastic Lateral Buckling of Beams » Critical Bending Coefficient

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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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)

Critical Bending Coefficient Formula

Define 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. In “typical” cases everything is ok since code equations allow engineers to obtain the value of the critical moment.

How to Calculate Critical Bending Coefficient?

Critical Bending Coefficient calculator uses 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)) to calculate the Bending Moment Coefficient, Critical Bending Coefficient is defined as the ratio of each load case critical moment to the pure bending critical moment of the beam. Bending Moment Coefficient is denoted by M_coeff symbol.

How to calculate Critical Bending Coefficient using this online calculator? To use this online calculator for Critical Bending Coefficient, enter Maximum Moment (M'max), Moment at Quarter Point (M_A), Moment at Centerline (M_B) & Moment at Three-quarter Point (M_C) and hit the calculate button. Here is how the Critical Bending Coefficient calculation can be explained with given input values -> 1.315762 = (12.5*50.01)/((2.5*50.01)+(3*30)+(4*50.02)+(3*20.01)).

FAQ

What is Critical Bending Coefficient?

Critical Bending Coefficient is defined as the ratio of each load case critical moment to the pure bending critical moment of the beam and is represented as M_coeff = (12.5*M'max)/((2.5*M'max)+(3*M_A)+(4*M_B)+(3*M_C)) or 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)). The maximum Moment is the absolute value of the maximum moment in the unbraced beam segment, The moment at Quarter Point is the absolute value of the moment at the quarter point of the unbraced beam segment, The moment at Centerline is the absolute value of moment at the centerline of the unbraced beam segment & Moment at Three-quarter Point is the absolute value of moment at three-quarter point of the unbraced beam segment.

How to calculate Critical Bending Coefficient?

Critical Bending Coefficient is defined as the ratio of each load case critical moment to the pure bending critical moment of the beam is calculated using 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)). To calculate Critical Bending Coefficient, you need Maximum Moment (M'max), Moment at Quarter Point (M_A), Moment at Centerline (M_B) & Moment at Three-quarter Point (M_C). With our tool, you need to enter the respective value for Maximum Moment, Moment at Quarter Point, Moment at Centerline & Moment at Three-quarter Point 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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