Strain Energy Stored in Tension Rod Calculator

✖Axial Force on Beam is defined as the compression or tension force acting on a beam, rod, or shaft.ⓘ Axial Force on Beam [P]			+10% -10%
✖Length of Rod or Shaft is defined as the total length of the rod or the shaft according to Castiglano's theorom.ⓘ Length of Rod or Shaft [L]			+10% -10%
✖Cross Sectional Area of Rod is the area of a two-dimensional shape that is obtained when a three-dimensional rod is sliced perpendicular to some specified axis at a point.ⓘ Cross Sectional Area of Rod [A]			+10% -10%
✖Modulus of elasticity of rod or shaft is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.ⓘ Modulus of elasticity of rod or shaft [E]			+10% -10%

✖Strain Energy in Rod or Shaft is defined as the energy stored in a rod or a shaft due to deformation.ⓘ Strain Energy Stored in Tension Rod [U]

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Formula

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Strain Energy Stored in Tension Rod

Formula

`"U" = (("P"^2)*"L")/(2*"A"*"E")`

Example

`"39.98673J"=((("55000N")^2)*"1330mm")/(2*"513.34mm²"*"98000N/mm²")`

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Strain Energy Stored in Tension Rod Solution

STEP 0: Pre-Calculation Summary

Formula Used

Strain Energy in Rod or Shaft = ((Axial Force on Beam^2)*Length of Rod or Shaft)/(2*Cross Sectional Area of Rod*Modulus of elasticity of rod or shaft)
U = ((P^2)*L)/(2*A*E)
This formula uses 5 Variables

Variables Used

Strain Energy in Rod or Shaft - (Measured in Joule) - Strain Energy in Rod or Shaft is defined as the energy stored in a rod or a shaft due to deformation.
Axial Force on Beam - (Measured in Newton) - Axial Force on Beam is defined as the compression or tension force acting on a beam, rod, or shaft.
Length of Rod or Shaft - (Measured in Meter) - Length of Rod or Shaft is defined as the total length of the rod or the shaft according to Castiglano's theorom.
Cross Sectional Area of Rod - (Measured in Square Meter) - Cross Sectional Area of Rod is the area of a two-dimensional shape that is obtained when a three-dimensional rod is sliced perpendicular to some specified axis at a point.
Modulus of elasticity of rod or shaft - (Measured in Pascal) - Modulus of elasticity of rod or shaft is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.

STEP 1: Convert Input(s) to Base Unit

Axial Force on Beam: 55000 Newton --> 55000 Newton No Conversion Required
Length of Rod or Shaft: 1330 Millimeter --> 1.33 Meter (Check conversion here)
Cross Sectional Area of Rod: 513.34 Square Millimeter --> 0.00051334 Square Meter (Check conversion here)
Modulus of elasticity of rod or shaft: 98000 Newton per Square Millimeter --> 98000000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

U = ((P^2)*L)/(2*A*E) --> ((55000^2)*1.33)/(2*0.00051334*98000000000)

Evaluating ... ...

U = 39.9867255898346

STEP 3: Convert Result to Output's Unit

39.9867255898346 Joule --> No Conversion Required

FINAL ANSWER

39.9867255898346 ≈ 39.98673 Joule <-- Strain Energy in Rod or Shaft

(Calculation completed in 00.004 seconds)

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

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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Vishwakarma Government Engineering College (VGEC), Ahmedabad

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< 14 Castigliano's Theorem for Deflection in Complex Structures Calculators

Torque given Strain Energy in Rod Subjected to External Torque

Go Torque on Rod or Shaft = sqrt(2*Strain Energy in Rod or Shaft*Polar Moment of Inertia of rod or shaft*Modulus of rigidity of rod or shaft/Length of Rod or Shaft)

Force Applied on Rod given Strain Energy Stored in Tension Rod

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

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

Go Area Moment of Inertia of rod or shaft = (Bending Moment in Shaft or Beam^2)*Length of Rod or Shaft/(2*Modulus of elasticity of rod or shaft*Strain Energy in Rod or Shaft)

Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment

Go Modulus of elasticity of rod or shaft = (Bending Moment in Shaft or Beam^2)*Length of Rod or Shaft/(2*Strain Energy in Rod or Shaft*Area Moment of Inertia of rod or shaft)

Strain Energy Stored in Rod Subjected to Bending Moment

Go Strain Energy in Rod or Shaft = (Bending Moment in Shaft or Beam^2)*Length of Rod or Shaft/(2*Modulus of elasticity of rod or shaft*Area Moment of Inertia of rod or shaft)

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

Go Length of Rod or Shaft = 2*Strain Energy in Rod or Shaft*Modulus of elasticity of rod or shaft*Area Moment of Inertia of rod or shaft/(Bending Moment in Shaft or Beam^2)

Length of Shaft when Strain Energy in Shaft Subjected to External Torque

Go Length of Rod or Shaft = (2*Strain Energy in Rod or Shaft*Polar Moment of Inertia of rod or shaft*Modulus of rigidity of rod or shaft)/(Torque on Rod or Shaft^2)

Strain Energy in Rod when it is Subjected to External Torque

Go Strain Energy in Rod or Shaft = (Torque on Rod or Shaft^2)*Length of Rod or Shaft/(2*Polar Moment of Inertia of rod or shaft*Modulus of rigidity of rod or shaft)

Polar Moment of Inertia of Rod given Strain Energy in Rod

Go Polar Moment of Inertia of rod or shaft = (Torque on Rod or Shaft^2)*Length of Rod or Shaft/(2*Strain Energy in Rod or Shaft*Modulus of rigidity of rod or shaft)

Modulus of Rigidity of Rod given Strain Energy in Rod

Go Modulus of rigidity of rod or shaft = (Torque on Rod or Shaft^2)*Length of Rod or Shaft/(2*Polar Moment of Inertia of rod or shaft*Strain Energy in Rod or Shaft)

Strain Energy Stored in Tension Rod

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

Cross-sectional Area of Rod given Strain Energy stored in Rod

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

Modulus of Elasticity of Rod given Strain Energy Stored

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

Length of Rod given Strain Energy Stored

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

Strain Energy Stored in Tension Rod Formula

Strain Energy in Rod or Shaft = ((Axial Force on Beam^2)*Length of Rod or Shaft)/(2*Cross Sectional Area of Rod*Modulus of elasticity of rod or shaft)
U = ((P^2)*L)/(2*A*E)

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 Strain Energy Stored in Tension Rod?

Strain Energy Stored in Tension Rod calculator uses Strain Energy in Rod or Shaft = ((Axial Force on Beam^2)*Length of Rod or Shaft)/(2*Cross Sectional Area of Rod*Modulus of elasticity of rod or shaft) to calculate the Strain Energy in Rod or Shaft, The Strain Energy Stored in Tension Rod formula is defined as a type of potential energy that is stored in a structural member as a result of elastic deformation. Strain Energy in Rod or Shaft is denoted by U symbol.

How to calculate Strain Energy Stored in Tension Rod using this online calculator? To use this online calculator for Strain Energy Stored in Tension Rod, enter Axial Force on Beam (P), Length of Rod or Shaft (L), Cross Sectional Area of Rod (A) & Modulus of elasticity of rod or shaft (E) and hit the calculate button. Here is how the Strain Energy Stored in Tension Rod calculation can be explained with given input values -> 39.98673 = ((55000^2)*1.33)/(2*0.00051334*98000000000).

FAQ

What is Strain Energy Stored in Tension Rod?

The Strain Energy Stored in Tension Rod formula is defined as a type of potential energy that is stored in a structural member as a result of elastic deformation and is represented as U = ((P^2)*L)/(2*A*E) or Strain Energy in Rod or Shaft = ((Axial Force on Beam^2)*Length of Rod or Shaft)/(2*Cross Sectional Area of Rod*Modulus of elasticity of rod or shaft). Axial Force on Beam is defined as the compression or tension force acting on a beam, rod, or shaft, Length of Rod or Shaft is defined as the total length of the rod or the shaft according to Castiglano's theorom, Cross Sectional Area of Rod is the area of a two-dimensional shape that is obtained when a three-dimensional rod is sliced perpendicular to some specified axis at a point & Modulus of elasticity of rod or shaft is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.

How to calculate Strain Energy Stored in Tension Rod?

The Strain Energy Stored in Tension Rod formula is defined as a type of potential energy that is stored in a structural member as a result of elastic deformation is calculated using Strain Energy in Rod or Shaft = ((Axial Force on Beam^2)*Length of Rod or Shaft)/(2*Cross Sectional Area of Rod*Modulus of elasticity of rod or shaft). To calculate Strain Energy Stored in Tension Rod, you need Axial Force on Beam (P), Length of Rod or Shaft (L), Cross Sectional Area of Rod (A) & Modulus of elasticity of rod or shaft (E). With our tool, you need to enter the respective value for Axial Force on Beam, Length of Rod or Shaft, Cross Sectional Area of Rod & Modulus of elasticity of rod or shaft 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 Strain Energy in Rod or Shaft?

In this formula, Strain Energy in Rod or Shaft uses Axial Force on Beam, Length of Rod or Shaft, Cross Sectional Area of Rod & Modulus of elasticity of rod or shaft. We can use 2 other way(s) to calculate the same, which is/are as follows -

Strain Energy in Rod or Shaft = (Torque on Rod or Shaft^2)*Length of Rod or Shaft/(2*Polar Moment of Inertia of rod or shaft*Modulus of rigidity of rod or shaft)
Strain Energy in Rod or Shaft = (Bending Moment in Shaft or Beam^2)*Length of Rod or Shaft/(2*Modulus of elasticity of rod or shaft*Area Moment of Inertia of rod or shaft)

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