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Shear Elasticity Modulus for Critical Bending Moment of Rectangular Beam Formula

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Shear Modulus of Elasticity is one of the measures of mechanical properties of solids. Other elastic moduli are Young's modulus and bulk modulus. Check FAQs

G = \frac{{(M Cr(Rect) \cdot Len)}^{2}}{(π^{2}) \cdot I y \cdot e \cdot J}

G - Shear Modulus of Elasticity?M_Cr(Rect) - Critical Bending Moment for Rectangular?Len - Length of Rectangular Beam?I_y - Moment of Inertia about Minor Axis?e - Elastic Modulus?J - Torsional Constant?π - Archimedes' constant?

Shear Elasticity Modulus for Critical Bending Moment of Rectangular Beam Example

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Here is how the Shear Elasticity Modulus for Critical Bending Moment of Rectangular Beam equation looks like with Values.

Here is how the Shear Elasticity Modulus for Critical Bending Moment of Rectangular Beam equation looks like with Units.

Here is how the Shear Elasticity Modulus for Critical Bending Moment of Rectangular Beam equation looks like.

100.1294 = \frac{{(741 \cdot 3)}^{2}}{({3.1416}^{2}) \cdot 10.001 \cdot 50 \cdot 10.0001}

100.1294N/m² = \frac{{(741N*m \cdot 3m)}^{2}}{({3.1416}^{2}) \cdot 10.001kg·m² \cdot 50Pa \cdot 10.0001}

100.1294 = \frac{{(741 \cdot 3)}^{2}}{({3.1416}^{2}) \cdot 10.001 \cdot 50 \cdot 10.0001}

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Shear Elasticity Modulus for Critical Bending Moment of Rectangular Beam Solution

Follow our step by step solution on how to calculate Shear Elasticity Modulus for Critical Bending Moment of Rectangular Beam?

FIRST Step Consider the formula

G = \frac{{(M Cr(Rect) \cdot Len)}^{2}}{(π^{2}) \cdot I y \cdot e \cdot J}

Next Step Substitute values of Variables

∴

G = \frac{{(741N*m \cdot 3m)}^{2}}{(π^{2}) \cdot 10.001kg·m² \cdot 50Pa \cdot 10.0001}

Next Step Substitute values of Constants

∴

G = \frac{{(741N*m \cdot 3m)}^{2}}{({3.1416}^{2}) \cdot 10.001kg·m² \cdot 50Pa \cdot 10.0001}

Next Step Prepare to Evaluate

∴

G = \frac{{(741 \cdot 3)}^{2}}{({3.1416}^{2}) \cdot 10.001 \cdot 50 \cdot 10.0001}

Next Step Evaluate

∴

G = 100.129351975087Pa

Next Step Convert to Output's Unit

∴

G = 100.129351975087N/m²

LAST Step Rounding Answer

∴

G = 100.1294N/m²

Shear Elasticity Modulus for Critical Bending Moment of Rectangular Beam Formula Elements

Variables

Constants

Shear Modulus of Elasticity

Shear Modulus of Elasticity is one of the measures of mechanical properties of solids. Other elastic moduli are Young's modulus and bulk modulus.

Symbol: G

Measurement: PressureUnit: N/m²

Note: Value should be greater than 0.

Formulas to find Shear Modulus of Elasticity

Critical Bending Moment for Rectangular

Critical Bending Moment for Rectangular is crucial in the proper design of bent beams susceptible to LTB, as it allows for slenderness calculation.

Symbol: M_Cr(Rect)

Measurement: Moment of ForceUnit: N*m

Note: Value should be greater than 0.

Formulas to find Critical Bending Moment for Rectangular

Length of Rectangular Beam

Length of Rectangular Beam is the measurement or extent of something from end to end.

Symbol: Len

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Rectangular Beam

Moment of Inertia about Minor Axis

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.

Symbol: I_y

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Moment of Inertia about Minor Axis

Elastic Modulus

The Elastic Modulus is the ratio of Stress to Strain.

Symbol: e

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Elastic 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.

Symbol: J

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Torsional Constant

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other formulas in Elastic Lateral Buckling of Beams category

Go Critical Bending Moment for Simply Supported Rectangular Beam

M Cr(Rect) = (\frac{π}{Len}) \cdot (\sqrt{e \cdot I y \cdot G \cdot J})

Go Unbraced Member Length given Critical Bending Moment of Rectangular Beam

Len = (\frac{π}{M Cr(Rect)}) \cdot (\sqrt{e \cdot I y \cdot G \cdot J})

Go Elasticity Modulus given Critical Bending Moment of Rectangular Beam

e = \frac{{(M Cr(Rect) \cdot Len)}^{2}}{(π^{2}) \cdot I y \cdot G \cdot J}

Go Minor Axis Moment of Inertia for Critical Bending Moment of Rectangular Beam

I y = \frac{{(M Cr(Rect) \cdot Len)}^{2}}{(π^{2}) \cdot e \cdot G \cdot J}

How to Evaluate Shear Elasticity Modulus for Critical Bending Moment of Rectangular Beam?

Shear Elasticity Modulus for Critical Bending Moment of Rectangular Beam evaluator uses 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) to evaluate the Shear Modulus of Elasticity, The Shear Elasticity Modulus for Critical Bending Moment of Rectangular Beam is defined as the material's resistance to shear deformation affecting bending stability. Shear Modulus of Elasticity is denoted by G symbol.

How to evaluate Shear Elasticity Modulus for Critical Bending Moment of Rectangular Beam using this online evaluator? To use this online evaluator for Shear Elasticity Modulus for 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), Elastic Modulus (e) & Torsional Constant (J) and hit the calculate button.

FAQs on Shear Elasticity Modulus for Critical Bending Moment of Rectangular Beam

What is the formula to find Shear Elasticity Modulus for Critical Bending Moment of Rectangular Beam?

The formula of Shear Elasticity Modulus for Critical Bending Moment of Rectangular Beam is expressed as 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). Here is an example- 100.1394 = ((741*3)^2)/((pi^2)*10.001*50*10.0001).

How to calculate Shear Elasticity Modulus for Critical Bending Moment of Rectangular Beam?

With Critical Bending Moment for Rectangular (M_Cr(Rect)), Length of Rectangular Beam (Len), Moment of Inertia about Minor Axis (I_y), Elastic Modulus (e) & Torsional Constant (J) we can find Shear Elasticity Modulus for Critical Bending Moment of Rectangular Beam using the formula - 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). This formula also uses Archimedes' constant .

Can the Shear Elasticity Modulus for Critical Bending Moment of Rectangular Beam be negative?

No, the Shear Elasticity Modulus for Critical Bending Moment of Rectangular Beam, measured in Pressure cannot be negative.

Which unit is used to measure Shear Elasticity Modulus for Critical Bending Moment of Rectangular Beam?

Shear Elasticity Modulus for Critical Bending Moment of Rectangular Beam is usually measured using the Newton per Square Meter[N/m²] for Pressure. Pascal[N/m²], Kilopascal[N/m²], Bar[N/m²] are the few other units in which Shear Elasticity Modulus for Critical Bending Moment of Rectangular Beam can be measured.

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Shear Elasticity Modulus for Critical Bending Moment of Rectangular Beam Formula

Shear Elasticity Modulus for Critical Bending Moment of Rectangular Beam Example

Shear Elasticity Modulus for Critical Bending Moment of Rectangular Beam Solution

Shear Elasticity Modulus for Critical Bending Moment of Rectangular Beam Formula Elements

Other formulas in Elastic Lateral Buckling of Beams category

How to Evaluate Shear Elasticity Modulus for Critical Bending Moment of Rectangular Beam?

FAQs on Shear Elasticity Modulus for Critical Bending Moment of Rectangular Beam

Variable Name