Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment Calculator

✖The Bending Moment is the internal moment that causes a beam to bend, reflecting the distribution of forces along its length in structural engineering.ⓘ Bending Moment [M_b]			+10% -10%
✖The Length of Rod or Shaft is the measurement of the distance from one end of the rod or shaft to the other, crucial for structural analysis.ⓘ Length of Rod or Shaft [L]			+10% -10%
✖The Modulus of Elasticity is a measure of a material's stiffness, indicating how much it deforms under stress in relation to its original dimensions.ⓘ Modulus of Elasticity [E]			+10% -10%
✖The Strain Energy is the energy stored in a material due to deformation, which can be released when the material returns to its original shape.ⓘ Strain Energy [U]			+10% -10%

✖The Area Moment of Inertia is a property that measures an object's resistance to bending and deflection under load, crucial for structural analysis and design.ⓘ Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment [I]

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Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area Moment of Inertia = Bending Moment^2*Length of Rod or Shaft/(2*Modulus of Elasticity*Strain Energy)
I = M_b^2*L/(2*E*U)
This formula uses 5 Variables

Variables Used

Area Moment of Inertia - (Measured in Meter⁴) - The Area Moment of Inertia is a property that measures an object's resistance to bending and deflection under load, crucial for structural analysis and design.
Bending Moment - (Measured in Newton Meter) - The Bending Moment is the internal moment that causes a beam to bend, reflecting the distribution of forces along its length in structural engineering.
Length of Rod or Shaft - (Measured in Meter) - The Length of Rod or Shaft is the measurement of the distance from one end of the rod or shaft to the other, crucial for structural analysis.
Modulus of Elasticity - (Measured in Pascal) - The Modulus of Elasticity is a measure of a material's stiffness, indicating how much it deforms under stress in relation to its original dimensions.
Strain Energy - (Measured in Joule) - The Strain Energy is the energy stored in a material due to deformation, which can be released when the material returns to its original shape.

STEP 1: Convert Input(s) to Base Unit

Bending Moment: 55001 Newton Millimeter --> 55.001 Newton Meter (Check conversion here)
Length of Rod or Shaft: 1432.449 Millimeter --> 1.432449 Meter (Check conversion here)
Modulus of Elasticity: 105548.9 Newton per Square Millimeter --> 105548900000 Pascal (Check conversion here)
Strain Energy: 37.13919 Joule --> 37.13919 Joule No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I = M_b^2*L/(2*E*U) --> 55.001^2*1.432449/(2*105548900000*37.13919)

Evaluating ... ...

I = 5.5271875966204E-10

STEP 3: Convert Result to Output's Unit

5.5271875966204E-10 Meter⁴ -->552.71875966204 Millimeter⁴ (Check conversion here)

FINAL ANSWER

552.71875966204 ≈ 552.7188 Millimeter⁴ <-- Area Moment of Inertia

(Calculation completed in 00.004 seconds)

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< Castigliano's Theorem for Deflection in Complex Structures Calculators

Force Applied on Rod given Strain Energy Stored in Tension Rod

Go Axial Force on Beam = sqrt(Strain Energy*2*Cross Sectional Area of Rod*Modulus of Elasticity/Length of Rod or Shaft)

Strain Energy Stored in Tension Rod

Go Strain Energy = (Axial Force on Beam^2*Length of Rod or Shaft)/(2*Cross Sectional Area of Rod*Modulus of Elasticity)

Modulus of Elasticity of Rod given Strain Energy Stored

Go Modulus of Elasticity = Axial Force on Beam^2*Length of Rod or Shaft/(2*Cross Sectional Area of Rod*Strain Energy)

Length of Rod given Strain Energy Stored

Go Length of Rod or Shaft = Strain Energy*2*Cross Sectional Area of Rod*Modulus of Elasticity/Axial Force on Beam^2

Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment Formula

Area Moment of Inertia = Bending Moment^2*Length of Rod or Shaft/(2*Modulus of Elasticity*Strain Energy)
I = M_b^2*L/(2*E*U)

Define Moment of Inertia?

The moment of inertia, otherwise known as the mass moment of inertia, angular mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for a desired acceleration.

How to Calculate Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment?

Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment calculator uses Area Moment of Inertia = Bending Moment^2*Length of Rod or Shaft/(2*Modulus of Elasticity*Strain Energy) to calculate the Area Moment of Inertia, Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment formula is defined as a measure of an object's resistance to angular acceleration when subjected to bending moments. It reflects how the distribution of mass affects the shaft's ability to store strain energy. Area Moment of Inertia is denoted by I symbol.

How to calculate Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment using this online calculator? To use this online calculator for Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment, enter Bending Moment (M_b), Length of Rod or Shaft (L), Modulus of Elasticity (E) & Strain Energy (U) and hit the calculate button. Here is how the Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment calculation can be explained with given input values -> 5.5E+14 = 55.001^2*1.432449/(2*105548900000*37.13919).

FAQ

What is Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment?

Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment formula is defined as a measure of an object's resistance to angular acceleration when subjected to bending moments. It reflects how the distribution of mass affects the shaft's ability to store strain energy and is represented as I = M_b^2*L/(2*E*U) or Area Moment of Inertia = Bending Moment^2*Length of Rod or Shaft/(2*Modulus of Elasticity*Strain Energy). The Bending Moment is the internal moment that causes a beam to bend, reflecting the distribution of forces along its length in structural engineering, The Length of Rod or Shaft is the measurement of the distance from one end of the rod or shaft to the other, crucial for structural analysis, The Modulus of Elasticity is a measure of a material's stiffness, indicating how much it deforms under stress in relation to its original dimensions & The Strain Energy is the energy stored in a material due to deformation, which can be released when the material returns to its original shape.

How to calculate Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment?

Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment formula is defined as a measure of an object's resistance to angular acceleration when subjected to bending moments. It reflects how the distribution of mass affects the shaft's ability to store strain energy is calculated using Area Moment of Inertia = Bending Moment^2*Length of Rod or Shaft/(2*Modulus of Elasticity*Strain Energy). To calculate Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment, you need Bending Moment (M_b), Length of Rod or Shaft (L), Modulus of Elasticity (E) & Strain Energy (U). With our tool, you need to enter the respective value for Bending Moment, Length of Rod or Shaft, Modulus of Elasticity & Strain Energy 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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