Length of Rod given Strain Energy Stored 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 Cross Sectional Area of Rod is the area of the cut surface of a rod, which influences its strength and stiffness in structural applications.ⓘ Cross Sectional Area of Rod [A]			+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 Axial Force on Beam is the internal force acting along the length of a beam, influencing its stability and structural integrity under various loads.ⓘ Axial Force on Beam [P]			+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 given Strain Energy Stored [L]

⎘ Copy

👎

Formula

Reset

👍

Download Castigliano's Theorem for Deflection in Complex Structures Formulas PDF PDF Image

Length of Rod given Strain Energy Stored Solution

STEP 0: Pre-Calculation Summary

Formula Used

Length of Rod or Shaft = Strain Energy*2*Cross Sectional Area of Rod*Modulus of Elasticity/Axial Force on Beam^2
L = U*2*A*E/P^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.
Cross Sectional Area of Rod - (Measured in Square Meter) - The Cross Sectional Area of Rod is the area of the cut surface of a rod, which influences its strength and stiffness in structural applications.
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.
Axial Force on Beam - (Measured in Newton) - The Axial Force on Beam is the internal force acting along the length of a beam, influencing its stability and structural integrity under various loads.

STEP 1: Convert Input(s) to Base Unit

Strain Energy: 37.13919 Joule --> 37.13919 Joule No Conversion Required
Cross Sectional Area of Rod: 552.6987 Square Millimeter --> 0.0005526987 Square Meter (Check conversion here)
Modulus of Elasticity: 105548.9 Newton per Square Millimeter --> 105548900000 Pascal (Check conversion here)
Axial Force on Beam: 55000 Newton --> 55000 Newton No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L = U*2*A*E/P^2 --> 37.13919*2*0.0005526987*105548900000/55000^2

Evaluating ... ...

L = 1.43244910018047

STEP 3: Convert Result to Output's Unit

1.43244910018047 Meter -->1432.44910018047 Millimeter (Check conversion here)

FINAL ANSWER

1432.44910018047 ≈ 1432.449 Millimeter <-- Length of Rod or Shaft

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Mechanical » Machine Design » Castigliano's Theorem for Deflection in Complex Structures » Length of Rod given Strain Energy Stored

Credits

Created by Kethavath Srinath

Osmania University (OU), Hyderabad

Kethavath Srinath has created this Calculator and 1000+ more calculators!

Verified by Urvi Rathod

Vishwakarma Government Engineering College (VGEC), Ahmedabad

Urvi Rathod has verified this Calculator and 1900+ more calculators!

< 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 Rod given Strain Energy Stored Formula

Length of Rod or Shaft = Strain Energy*2*Cross Sectional Area of Rod*Modulus of Elasticity/Axial Force on Beam^2
L = U*2*A*E/P^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 Rod given Strain Energy Stored?

Length of Rod given Strain Energy Stored calculator uses Length of Rod or Shaft = Strain Energy*2*Cross Sectional Area of Rod*Modulus of Elasticity/Axial Force on Beam^2 to calculate the Length of Rod or Shaft, Length of Rod given Strain Energy Stored formula is defined as a relationship that quantifies the length of a rod based on the strain energy it stores, the cross-sectional area, the modulus of elasticity, and the applied load. This concept is essential in mechanical design and structural analysis. Length of Rod or Shaft is denoted by L symbol.

How to calculate Length of Rod given Strain Energy Stored using this online calculator? To use this online calculator for Length of Rod given Strain Energy Stored, enter Strain Energy (U), Cross Sectional Area of Rod (A), Modulus of Elasticity (E) & Axial Force on Beam (P) and hit the calculate button. Here is how the Length of Rod given Strain Energy Stored calculation can be explained with given input values -> 1.2E+6 = 37.13919*2*0.0005526987*105548900000/55000^2.

FAQ

What is Length of Rod given Strain Energy Stored?

Length of Rod given Strain Energy Stored formula is defined as a relationship that quantifies the length of a rod based on the strain energy it stores, the cross-sectional area, the modulus of elasticity, and the applied load. This concept is essential in mechanical design and structural analysis and is represented as L = U*2*A*E/P^2 or Length of Rod or Shaft = Strain Energy*2*Cross Sectional Area of Rod*Modulus of Elasticity/Axial Force on Beam^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 Cross Sectional Area of Rod is the area of the cut surface of a rod, which influences its strength and stiffness in structural applications, 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 Axial Force on Beam is the internal force acting along the length of a beam, influencing its stability and structural integrity under various loads.

How to calculate Length of Rod given Strain Energy Stored?

Length of Rod given Strain Energy Stored formula is defined as a relationship that quantifies the length of a rod based on the strain energy it stores, the cross-sectional area, the modulus of elasticity, and the applied load. This concept is essential in mechanical design and structural analysis is calculated using Length of Rod or Shaft = Strain Energy*2*Cross Sectional Area of Rod*Modulus of Elasticity/Axial Force on Beam^2. To calculate Length of Rod given Strain Energy Stored, you need Strain Energy (U), Cross Sectional Area of Rod (A), Modulus of Elasticity (E) & Axial Force on Beam (P). With our tool, you need to enter the respective value for Strain Energy, Cross Sectional Area of Rod, Modulus of Elasticity & Axial Force on Beam 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, Cross Sectional Area of Rod, Modulus of Elasticity & Axial Force on Beam. We can use 2 other way(s) to calculate the same, which is/are as follows -

Length of Rod or Shaft = (2*Strain Energy*Polar Moment of Inertia*Modulus of Rigidity)/(Torque^2)
Length of Rod or Shaft = 2*Strain Energy*Modulus of Elasticity*Area Moment of Inertia/(Bending Moment^2)

Home

FREE PDFs

🔍 Search