Elasticity Modulus given Critical Bending Moment of Rectangular Beam Calculator

✖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 Rectangular [M_Cr(Rect)]			+10% -10%
✖Length of Rectangular Beam is the measurement or extent of something from end to end.ⓘ Length of Rectangular Beam [Len]			+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 Elastic Modulus is the ratio of Stress to Strain.ⓘ Elasticity Modulus given Critical Bending Moment of Rectangular Beam [e]

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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 = ((M_Cr(Rect)*Len)^2)/((pi^2)*I_y*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 = ((M_Cr(Rect)*Len)^2)/((pi^2)*I_y*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)

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Home » Engineering » Civil » Structural Engineering » Structural Analysis » Miscellaneous Topics » Structural Analysis of Beams » Elastic Lateral Buckling of Beams » Elasticity Modulus given Critical Bending Moment of Rectangular Beam

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< Elastic Lateral Buckling of Beams Calculators

Unbraced Member Length given Critical Bending Moment of Rectangular Beam

LaTeX 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

LaTeX 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

LaTeX 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)

Elasticity Modulus given Critical Bending Moment of Rectangular Beam

LaTeX 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)

Elasticity Modulus given Critical Bending Moment of Rectangular Beam Formula

LaTeX Go

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 (M_Cr(Rect)), Length of Rectangular Beam (Len), 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 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 = ((M_Cr(Rect)*Len)^2)/((pi^2)*I_y*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 (M_Cr(Rect)), Length of Rectangular Beam (Len), 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 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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