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

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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. Check FAQs

A = P^{2} \cdot \frac{L}{2 \cdot U \cdot E}

A - Cross Sectional Area of Rod?P - Axial Force on Beam?L - Length of Rod or Shaft?U - Strain Energy?E - Modulus of Elasticity?

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

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Here is how the Cross-sectional Area of Rod given Strain Energy stored in Rod equation looks like with Values.

Here is how the Cross-sectional Area of Rod given Strain Energy stored in Rod equation looks like with Units.

Here is how the Cross-sectional Area of Rod given Strain Energy stored in Rod equation looks like.

552.6987 = 55000^{2} \cdot \frac{1432.449}{2 \cdot 37.1392 \cdot 105548.9}

552.6987mm² = {55000N}^{2} \cdot \frac{1432.449mm}{2 \cdot 37.1392J \cdot 105548.9N/mm²}

552.6987 = 55000^{2} \cdot \frac{1432.449}{2 \cdot 37.1392 \cdot 105548.9}

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

Follow our step by step solution on how to calculate Cross-sectional Area of Rod given Strain Energy stored in Rod?

FIRST Step Consider the formula

A = P^{2} \cdot \frac{L}{2 \cdot U \cdot E}

Next Step Substitute values of Variables

∴

A = {55000N}^{2} \cdot \frac{1432.449mm}{2 \cdot 37.1392J \cdot 105548.9N/mm²}

Next Step Convert Units

∴

A = {55000N}^{2} \cdot \frac{1.4324m}{2 \cdot 37.1392J \cdot 1.1E+11Pa}

Next Step Prepare to Evaluate

∴

A = 55000^{2} \cdot \frac{1.4324}{2 \cdot 37.1392 \cdot 1.1E+11}

Next Step Evaluate

∴

A = 0.00055269866134619m²

Next Step Convert to Output's Unit

∴

A = 552.69866134619mm²

LAST Step Rounding Answer

∴

A = 552.6987mm²

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

Variables

Cross Sectional Area of Rod

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.

Symbol: A

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Formulas to find Cross Sectional Area of Rod

Axial Force on Beam

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.

Symbol: P

Measurement: ForceUnit: N

Note: Value can be positive or negative.

Formulas to find Axial Force on Beam

Length of Rod or Shaft

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.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Rod or Shaft

Strain Energy

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.

Symbol: U

Measurement: EnergyUnit: J

Note: Value should be greater than 0.

Formulas to find Strain Energy

Modulus of Elasticity

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.

Symbol: E

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity

Other formulas in Castigliano's Theorem for Deflection in Complex Structures category

Go Strain Energy Stored in Tension Rod

U = \frac{P^{2} \cdot L}{2 \cdot A \cdot E}

Go Force Applied on Rod given Strain Energy Stored in Tension Rod

P = \sqrt{U \cdot 2 \cdot A \cdot \frac{E}{L}}

Go Length of Rod given Strain Energy Stored

L = U \cdot 2 \cdot A \cdot \frac{E}{P^{2}}

Go Modulus of Elasticity of Rod given Strain Energy Stored

E = P^{2} \cdot \frac{L}{2 \cdot A \cdot U}

How to Evaluate Cross-sectional Area of Rod given Strain Energy stored in Rod?

Cross-sectional Area of Rod given Strain Energy stored in Rod evaluator uses Cross Sectional Area of Rod = Axial Force on Beam^2*Length of Rod or Shaft/(2*Strain Energy*Modulus of Elasticity) to evaluate 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 evaluate Cross-sectional Area of Rod given Strain Energy stored in Rod using this online evaluator? To use this online evaluator 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.

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

What is the formula to find Cross-sectional Area of Rod given Strain Energy stored in Rod?

The formula of Cross-sectional Area of Rod given Strain Energy stored in Rod is expressed as Cross Sectional Area of Rod = Axial Force on Beam^2*Length of Rod or Shaft/(2*Strain Energy*Modulus of Elasticity). Here is an example- 5.5E+8 = 55000^2*1.432449/(2*37.13919*105548900000).

How to calculate Cross-sectional Area of Rod given Strain Energy stored in Rod?

With Axial Force on Beam (P), Length of Rod or Shaft (L), Strain Energy (U) & Modulus of Elasticity (E) we can find Cross-sectional Area of Rod given Strain Energy stored in Rod using the formula - Cross Sectional Area of Rod = Axial Force on Beam^2*Length of Rod or Shaft/(2*Strain Energy*Modulus of Elasticity).

Can the Cross-sectional Area of Rod given Strain Energy stored in Rod be negative?

No, the Cross-sectional Area of Rod given Strain Energy stored in Rod, measured in Area cannot be negative.

Which unit is used to measure Cross-sectional Area of Rod given Strain Energy stored in Rod?

Cross-sectional Area of Rod given Strain Energy stored in Rod is usually measured using the Square Millimeter[mm²] for Area. Square Meter[mm²], Square Kilometer[mm²], Square Centimeter[mm²] are the few other units in which Cross-sectional Area of Rod given Strain Energy stored in Rod can be measured.

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

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

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

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

Other formulas in Castigliano's Theorem for Deflection in Complex Structures category

How to Evaluate Cross-sectional Area of Rod given Strain Energy stored in Rod?

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

Variable Name