Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment Calculator

✖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 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 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.ⓘ Area Moment of Inertia [I]			+10% -10%
✖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 Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment [L]

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Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Strain Energy: 37.13919 Joule --> 37.13919 Joule No Conversion Required
Modulus of Elasticity: 105548.9 Newton per Square Millimeter --> 105548900000 Pascal (Check conversion here)
Area Moment of Inertia: 552.5 Millimeter⁴ --> 5.525E-10 Meter⁴ (Check conversion here)
Bending Moment: 55001 Newton Millimeter --> 55.001 Newton Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L = 2*U*E*I/(M_b^2) --> 2*37.13919*105548900000*5.525E-10/(55.001^2)

Evaluating ... ...

L = 1.431882053332

STEP 3: Convert Result to Output's Unit

1.431882053332 Meter -->1431.882053332 Millimeter (Check conversion here)

FINAL ANSWER

1431.882053332 ≈ 1431.882 Millimeter <-- Length of Rod or Shaft

(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

Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment Formula

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

Define Strain Energy?

Strain energy is a type of potential energy that is stored in a structural member as a result of elastic deformation. The external work done on such a member when it is deformed from its unstressed state is transformed into, and considered equal to the strain energy stored in it.

How to Calculate Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment?

Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment calculator uses Length of Rod or Shaft = 2*Strain Energy*Modulus of Elasticity*Area Moment of Inertia/(Bending Moment^2) to calculate the Length of Rod or Shaft, Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment formula is defined as a method to determine the length of a shaft based on the strain energy it stores when subjected to bending moments, reflecting the relationship between material properties and structural design. Length of Rod or Shaft is denoted by L symbol.

How to calculate Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment using this online calculator? To use this online calculator for Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment, enter Strain Energy (U), Modulus of Elasticity (E), Area Moment of Inertia (I) & Bending Moment (M_b) and hit the calculate button. Here is how the Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment calculation can be explained with given input values -> 2.7E+8 = 2*37.13919*105548900000*5.525E-10/(55.001^2).

FAQ

What is Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment?

Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment formula is defined as a method to determine the length of a shaft based on the strain energy it stores when subjected to bending moments, reflecting the relationship between material properties and structural design and is represented as L = 2*U*E*I/(M_b^2) or Length of Rod or Shaft = 2*Strain Energy*Modulus of Elasticity*Area Moment of Inertia/(Bending Moment^2). 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, 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 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 & The Bending Moment is the internal moment that causes a beam to bend, reflecting the distribution of forces along its length in structural engineering.

How to calculate Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment?

Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment formula is defined as a method to determine the length of a shaft based on the strain energy it stores when subjected to bending moments, reflecting the relationship between material properties and structural design is calculated using Length of Rod or Shaft = 2*Strain Energy*Modulus of Elasticity*Area Moment of Inertia/(Bending Moment^2). To calculate Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment, you need Strain Energy (U), Modulus of Elasticity (E), Area Moment of Inertia (I) & Bending Moment (M_b). With our tool, you need to enter the respective value for Strain Energy, Modulus of Elasticity, Area Moment of Inertia & Bending Moment and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Length of Rod or Shaft?

In this formula, Length of Rod or Shaft uses Strain Energy, Modulus of Elasticity, Area Moment of Inertia & Bending Moment. We can use 2 other way(s) to calculate the same, which is/are as follows -

Length of Rod or Shaft = Strain Energy*2*Cross Sectional Area of Rod*Modulus of Elasticity/Axial Force on Beam^2
Length of Rod or Shaft = (2*Strain Energy*Polar Moment of Inertia*Modulus of Rigidity)/(Torque^2)

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