Elasticity Modulus given Critical Bending Moment of Rectangular Beam Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
e = ((MCr(Rect)*Len)^2)/((pi^2)*Iy*G*J)
This formula uses 1 Constants, 6 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Elastic Modulus - (Measured in Pascal) - The Elastic Modulus is the ratio of Stress to Strain.
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.
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
Critical Bending Moment for Rectangular: 741 Newton Meter --> 741 Newton Meter No Conversion Required
Length of Rectangular Beam: 3 Meter --> 3 Meter 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
e = ((MCr(Rect)*Len)^2)/((pi^2)*Iy*G*J) --> ((741*3)^2)/((pi^2)*10.001*100.002*10.0001)
Evaluating ... ...
e = 50.063674714049
STEP 3: Convert Result to Output's Unit
50.063674714049 Pascal --> No Conversion Required
FINAL ANSWER
50.063674714049 50.06367 Pascal <-- Elastic Modulus
(Calculation completed in 00.020 seconds)

Credits

Created by Alithea Fernandes
Don Bosco College of Engineering (DBCE), Goa
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Cummins College of Engineering for Women (CCEW), Pune
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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)

Elasticity Modulus given Critical Bending Moment of Rectangular Beam Formula

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)
e = ((MCr(Rect)*Len)^2)/((pi^2)*Iy*G*J)

What is Modulus of Elasticity?

Elastic Modulus (also known as 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.

How to Calculate Elasticity Modulus given Critical Bending Moment of Rectangular Beam?

Elasticity Modulus given Critical Bending Moment of Rectangular Beam calculator uses 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) to calculate the Elastic Modulus, The Elasticity Modulus given Critical Bending Moment of Rectangular Beam is defined as the measure of material stiffness under stress. Elastic Modulus is denoted by e symbol.

How to calculate Elasticity Modulus given Critical Bending Moment of Rectangular Beam using this online calculator? To use this online calculator for Elasticity Modulus given Critical Bending Moment of Rectangular Beam, enter Critical Bending Moment for Rectangular (MCr(Rect)), Length of Rectangular Beam (Len), Moment of Inertia about Minor Axis (Iy), Shear Modulus of Elasticity (G) & Torsional Constant (J) and hit the calculate button. Here is how the Elasticity Modulus given Critical Bending Moment of Rectangular Beam calculation can be explained with given input values -> 50.06868 = ((741*3)^2)/((pi^2)*10.001*100.002*10.0001).

FAQ

What is Elasticity Modulus given Critical Bending Moment of Rectangular Beam?
The Elasticity Modulus given Critical Bending Moment of Rectangular Beam is defined as the measure of material stiffness under stress and is represented as e = ((MCr(Rect)*Len)^2)/((pi^2)*Iy*G*J) or 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 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 is the measurement or extent of something from end to end, 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 Elasticity Modulus given Critical Bending Moment of Rectangular Beam?
The Elasticity Modulus given Critical Bending Moment of Rectangular Beam is defined as the measure of material stiffness under stress is calculated using 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). To calculate Elasticity Modulus given Critical Bending Moment of Rectangular Beam, you need Critical Bending Moment for Rectangular (MCr(Rect)), Length of Rectangular Beam (Len), Moment of Inertia about Minor Axis (Iy), Shear Modulus of Elasticity (G) & Torsional Constant (J). With our tool, you need to enter the respective value for Critical Bending Moment for Rectangular, Length of Rectangular Beam, 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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