Critical Bending Moment for Simply Supported Open Section Beam Calculator

✖Unbraced length of member is defined as the distance between adjacent Points.ⓘ Unbraced Length of Member [L]			+10% -10%
✖Modulus of Elasticity is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it.ⓘ Modulus of Elasticity [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%
✖The Warping Constant is often referred to as the warping moment of inertia. It is a quantity derived from a cross-section.ⓘ Warping Constant [C_w]			+10% -10%

✖The Critical Bending Moment is crucial in the proper design of bent beams susceptible to LTB, as it allows for slenderness calculation.ⓘ Critical Bending Moment for Simply Supported Open Section Beam [M_cr]

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Formula

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Critical Bending Moment for Simply Supported Open Section Beam

Formula

`"M"_{"cr"} = (pi/"L")*sqrt("E"*"I"_{"y"}*(("G"*"J")+"E"*"C"_{"w"}*((pi^2)/("L")^2)))`

Example

`"9.802145N*m"=(pi/"10.04cm")*sqrt("10.01MPa"*"10.001kg·m²"*(("100.002N/m²"*"10.0001")+"10.01MPa"*"10.0005kg·m²"*((pi^2)/("10.04cm")^2)))`

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Critical Bending Moment for Simply Supported Open Section Beam Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
M_cr = (pi/L)*sqrt(E*I_y*((G*J)+E*C_w*((pi^2)/(L)^2)))
This formula uses 1 Constants, 1 Functions, 7 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 Bending Moment - (Measured in Newton Meter) - The Critical Bending Moment is crucial in the proper design of bent beams susceptible to LTB, as it allows for slenderness calculation.
Unbraced Length of Member - (Measured in Centimeter) - Unbraced length of member is defined as the distance between adjacent Points.
Modulus of Elasticity - (Measured in Megapascal) - Modulus of Elasticity is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it.
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 Megapascal) - 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.
Warping Constant - (Measured in Kilogram Square Meter) - The Warping Constant is often referred to as the warping moment of inertia. It is a quantity derived from a cross-section.

STEP 1: Convert Input(s) to Base Unit

Unbraced Length of Member: 10.04 Centimeter --> 10.04 Centimeter No Conversion Required
Modulus of Elasticity: 10.01 Megapascal --> 10.01 Megapascal 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 --> 0.000100002 Megapascal (Check conversion here)
Torsional Constant: 10.0001 --> No Conversion Required
Warping Constant: 10.0005 Kilogram Square Meter --> 10.0005 Kilogram Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M_cr = (pi/L)*sqrt(E*I_y*((G*J)+E*C_w*((pi^2)/(L)^2))) --> (pi/10.04)*sqrt(10.01*10.001*((0.000100002*10.0001)+10.01*10.0005*((pi^2)/(10.04)^2)))

Evaluating ... ...

M_cr = 9.80214499156555

STEP 3: Convert Result to Output's Unit

9.80214499156555 Newton Meter --> No Conversion Required

FINAL ANSWER

9.80214499156555 ≈ 9.802145 Newton Meter <-- Critical Bending Moment

(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 » Critical Bending Moment for Simply Supported Open Section Beam

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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 Moment for Simply Supported Open Section Beam Formula

Define Critical Bending Moment

The Bending moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend. The most common or simplest structural element subjected to bending moments is the beam.

How to Calculate Critical Bending Moment for Simply Supported Open Section Beam?

Critical Bending Moment for Simply Supported Open Section Beam calculator uses 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))) to calculate the Critical Bending Moment, The Critical Bending Moment for Simply Supported Open Section Beam formula is defined as the reaction induced in a structural element when an external force or moment is applied to the element. Critical Bending Moment is denoted by M_cr symbol.

How to calculate Critical Bending Moment for Simply Supported Open Section Beam using this online calculator? To use this online calculator for Critical Bending Moment for Simply Supported Open Section Beam, enter Unbraced Length of Member (L), Modulus of Elasticity (E), Moment of Inertia about Minor Axis (I_y), Shear Modulus of Elasticity (G), Torsional Constant (J) & Warping Constant (C_w) and hit the calculate button. Here is how the Critical Bending Moment for Simply Supported Open Section Beam calculation can be explained with given input values -> 9.801655 = (pi/0.1004)*sqrt(10010000*10.001*((100.002*10.0001)+10010000*10.0005*((pi^2)/(0.1004)^2))).

FAQ

What is Critical Bending Moment for Simply Supported Open Section Beam?

The Critical Bending Moment for Simply Supported Open Section Beam formula is defined as the reaction induced in a structural element when an external force or moment is applied to the element and is represented as M_cr = (pi/L)*sqrt(E*I_y*((G*J)+E*C_w*((pi^2)/(L)^2))) or 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 length of member is defined as the distance between adjacent Points, Modulus of Elasticity is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it, 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 & The Warping Constant is often referred to as the warping moment of inertia. It is a quantity derived from a cross-section.

How to calculate Critical Bending Moment for Simply Supported Open Section Beam?

The Critical Bending Moment for Simply Supported Open Section Beam formula is defined as the reaction induced in a structural element when an external force or moment is applied to the element is calculated using 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))). To calculate Critical Bending Moment for Simply Supported Open Section Beam, you need Unbraced Length of Member (L), Modulus of Elasticity (E), Moment of Inertia about Minor Axis (I_y), Shear Modulus of Elasticity (G), Torsional Constant (J) & Warping Constant (C_w). With our tool, you need to enter the respective value for Unbraced Length of Member, Modulus of Elasticity, Moment of Inertia about Minor Axis, Shear Modulus of Elasticity, 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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