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

✖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 or Shaft [L]			+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 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 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 given Strain Energy stored in Rod [A]

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

Variables Used

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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Axial Force on Beam: 55000 Newton --> 55000 Newton No Conversion Required
Length of Rod or Shaft: 1432.449 Millimeter --> 1.432449 Meter (Check conversion here)
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)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = P^2*L/(2*U*E) --> 55000^2*1.432449/(2*37.13919*105548900000)

Evaluating ... ...

A = 0.00055269866134619

STEP 3: Convert Result to Output's Unit

0.00055269866134619 Square Meter -->552.69866134619 Square Millimeter (Check conversion here)

FINAL ANSWER

552.69866134619 ≈ 552.6987 Square Millimeter <-- Cross Sectional Area of Rod

(Calculation completed in 00.020 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

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*Modulus of Elasticity)
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*Modulus of Elasticity) to calculate the Cross Sectional Area of Rod, Cross-sectional Area of Rod given Strain Energy stored in Rod formula is defined as a method to determine the cross-sectional area of a rod based on the strain energy it stores under applied loads. This concept is essential in mechanical design for ensuring structural integrity and performance. 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 (U) & Modulus of Elasticity (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 -> 5.5E+8 = 55000^2*1.432449/(2*37.13919*105548900000).

FAQ

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

Cross-sectional Area of Rod given Strain Energy stored in Rod formula is defined as a method to determine the cross-sectional area of a rod based on the strain energy it stores under applied loads. This concept is essential in mechanical design for ensuring structural integrity and performance 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*Modulus of Elasticity). 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, 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 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.

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 formula is defined as a method to determine the cross-sectional area of a rod based on the strain energy it stores under applied loads. This concept is essential in mechanical design for ensuring structural integrity and performance is calculated using Cross Sectional Area of Rod = Axial Force on Beam^2*Length of Rod or Shaft/(2*Strain Energy*Modulus of Elasticity). 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 (U) & Modulus of Elasticity (E). With our tool, you need to enter the respective value for Axial Force on Beam, Length of Rod or Shaft, Strain Energy & Modulus of Elasticity 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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