Cross-sectional Area of Rod given Strain Energy stored in 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%
✖Strain Energy in Rod or Shaft is defined as the energy stored in a rod or a shaft due to deformation.ⓘ Strain Energy in Rod or Shaft [U]			+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%

✖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 given Strain Energy stored in Rod [A]

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Formula

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

Formula

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

Example

`"513.1696mm²"=("55000N")^2*"1330mm"/(2*"40J"*"98000N/mm²")`

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

STEP 0: Pre-Calculation Summary

Formula Used

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)
A = P^2*L/(2*U*E)
This formula uses 5 Variables

Variables Used

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.
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.
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.
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)
Strain Energy in Rod or Shaft: 40 Joule --> 40 Joule No Conversion Required
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

A = P^2*L/(2*U*E) --> 55000^2*1.33/(2*40*98000000000)

Evaluating ... ...

A = 0.000513169642857143

STEP 3: Convert Result to Output's Unit

0.000513169642857143 Square Meter -->513.169642857143 Square Millimeter (Check conversion here)

FINAL ANSWER

513.169642857143 ≈ 513.1696 Square Millimeter <-- Cross Sectional Area of Rod

(Calculation completed in 00.020 seconds)

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Home » Engineering » Mechanical » Machine Design » Castigliano's Theorem for Deflection in Complex Structures » Cross-sectional Area of Rod given Strain Energy stored in Rod

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Osmania University (OU), Hyderabad

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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

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

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)
A = P^2*L/(2*U*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 Cross-sectional Area of Rod given Strain Energy stored in Rod?

Cross-sectional Area of Rod given Strain Energy stored in Rod calculator uses 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) to calculate the Cross Sectional Area of Rod, The Cross-sectional Area of Rod given Strain Energy stored in Rod formula is defined as the representation of the intersection of an object by a plane along its axis. A cross-section is a shape that is yielded from a solid, when intersected by a plane. Cross Sectional Area of Rod is denoted by A symbol.

How to calculate Cross-sectional Area of Rod given Strain Energy stored in Rod using this online calculator? To use this online calculator for Cross-sectional Area of Rod given Strain Energy stored in Rod, enter Axial Force on Beam (P), Length of Rod or Shaft (L), Strain Energy in Rod or Shaft (U) & Modulus of elasticity of rod or shaft (E) and hit the calculate button. Here is how the Cross-sectional Area of Rod given Strain Energy stored in Rod calculation can be explained with given input values -> 5.1E+8 = 55000^2*1.33/(2*40*98000000000).

FAQ

What is Cross-sectional Area of Rod given Strain Energy stored in Rod?

The Cross-sectional Area of Rod given Strain Energy stored in Rod formula is defined as the representation of the intersection of an object by a plane along its axis. A cross-section is a shape that is yielded from a solid, when intersected by a plane and is represented as A = P^2*L/(2*U*E) or 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). 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, Strain Energy in Rod or Shaft is defined as the energy stored in a rod or a shaft due to deformation & 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 Cross-sectional Area of Rod given Strain Energy stored in Rod?

The Cross-sectional Area of Rod given Strain Energy stored in Rod formula is defined as the representation of the intersection of an object by a plane along its axis. A cross-section is a shape that is yielded from a solid, when intersected by a plane is calculated using 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). To calculate Cross-sectional Area of Rod given Strain Energy stored in Rod, you need Axial Force on Beam (P), Length of Rod or Shaft (L), Strain Energy in Rod or Shaft (U) & 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, Strain Energy in Rod or Shaft & 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.

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