Critical Bending Moment for Simply Supported Rectangular Beam Calculator

✖Length of Rectangular Beam is the measurement or extent of something from end to end.ⓘ Length of Rectangular Beam [Len]			+10% -10%
✖The Elastic Modulus is the ratio of Stress to Strain.ⓘ Elastic Modulus [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%

✖Critical Bending Moment for Rectangular is crucial in the proper design of bent beams susceptible to LTB, as it allows for slenderness calculation.ⓘ Critical Bending Moment for Simply Supported Rectangular Beam [M_Cr(Rect)]

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Formula

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Critical Bending Moment for Simply Supported Rectangular Beam

Formula

`"M"_{"Cr(Rect)"} = (pi/"Len")*(sqrt("e"*"I"_{"y"}*"G"*"J"))`

Example

`"740.5286N*m"=(pi/"3m")*(sqrt("50Pa"*"10.001kg·m²"*"100.002N/m²"*"10.0001"))`

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Critical Bending Moment for Simply Supported Rectangular Beam Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
M_Cr(Rect) = (pi/Len)*(sqrt(e*I_y*G*J))
This formula uses 1 Constants, 1 Functions, 6 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 for Rectangular - (Measured in Newton Meter) - Critical Bending Moment for Rectangular is crucial in the proper design of bent beams susceptible to LTB, as it allows for slenderness calculation.
Length of Rectangular Beam - (Measured in Meter) - Length of Rectangular Beam is the measurement or extent of something from end to end.
Elastic Modulus - (Measured in Pascal) - The Elastic Modulus is the ratio of Stress to Strain.
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 Pascal) - 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.

STEP 1: Convert Input(s) to Base Unit

Length of Rectangular Beam: 3 Meter --> 3 Meter No Conversion Required
Elastic Modulus: 50 Pascal --> 50 Pascal 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 --> 100.002 Pascal (Check conversion here)
Torsional Constant: 10.0001 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M_Cr(Rect) = (pi/Len)*(sqrt(e*I_y*G*J)) --> (pi/3)*(sqrt(50*10.001*100.002*10.0001))

Evaluating ... ...

M_Cr(Rect) = 740.528620545427

STEP 3: Convert Result to Output's Unit

740.528620545427 Newton Meter --> No Conversion Required

FINAL ANSWER

740.528620545427 ≈ 740.5286 Newton Meter <-- Critical Bending Moment for Rectangular

(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 Rectangular Beam

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Created by Alithea Fernandes

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 Moment for Simply Supported Rectangular Beam Formula

What is Critical Bending Moment for Simply Supported Rectangular Beam?

Critical Bending Moment for Simply Supported Rectangular Beam is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend.

How to Calculate Critical Bending Moment for Simply Supported Rectangular Beam?

Critical Bending Moment for Simply Supported Rectangular Beam calculator uses 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)) to calculate the Critical Bending Moment for Rectangular, The Critical Bending Moment for Simply Supported Rectangular Beam formula is defined as the maximum load-induced moment causing beam failure. Critical Bending Moment for Rectangular is denoted by M_Cr(Rect) symbol.

How to calculate Critical Bending Moment for Simply Supported Rectangular Beam using this online calculator? To use this online calculator for Critical Bending Moment for Simply Supported Rectangular Beam, enter Length of Rectangular Beam (Len), Elastic Modulus (e), Moment of Inertia about Minor Axis (I_y), Shear Modulus of Elasticity (G) & Torsional Constant (J) and hit the calculate button. Here is how the Critical Bending Moment for Simply Supported Rectangular Beam calculation can be explained with given input values -> 740.4916 = (pi/3)*(sqrt(50*10.001*100.002*10.0001)).

FAQ

What is Critical Bending Moment for Simply Supported Rectangular Beam?

The Critical Bending Moment for Simply Supported Rectangular Beam formula is defined as the maximum load-induced moment causing beam failure and is represented as M_Cr(Rect) = (pi/Len)*(sqrt(e*I_y*G*J)) or 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)). Length of Rectangular Beam is the measurement or extent of something from end to end, The Elastic Modulus is the ratio of Stress to Strain, 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.

How to calculate Critical Bending Moment for Simply Supported Rectangular Beam?

The Critical Bending Moment for Simply Supported Rectangular Beam formula is defined as the maximum load-induced moment causing beam failure is calculated using 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)). To calculate Critical Bending Moment for Simply Supported Rectangular Beam, you need Length of Rectangular Beam (Len), Elastic Modulus (e), Moment of Inertia about Minor Axis (I_y), Shear Modulus of Elasticity (G) & Torsional Constant (J). With our tool, you need to enter the respective value for Length of Rectangular Beam, Elastic Modulus, Moment of Inertia about Minor Axis, Shear Modulus of Elasticity & Torsional 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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