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

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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. Check FAQs

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

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

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

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Here is how the Force Applied on Rod given Strain Energy Stored in Tension Rod equation looks like with Values.

Here is how the Force Applied on Rod given Strain Energy Stored in Tension Rod equation looks like with Units.

Here is how the Force Applied on Rod given Strain Energy Stored in Tension Rod equation looks like.

55000.0019 = \sqrt{37.1392 \cdot 2 \cdot 552.6987 \cdot \frac{105548.9}{1432.449}}

55000.0019N = \sqrt{37.1392J \cdot 2 \cdot 552.6987mm² \cdot \frac{105548.9N/mm²}{1432.449mm}}

55000.0019 = \sqrt{37.1392 \cdot 2 \cdot 552.6987 \cdot \frac{105548.9}{1432.449}}

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

Follow our step by step solution on how to calculate Force Applied on Rod given Strain Energy Stored in Tension Rod?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

P = \sqrt{37.1392J \cdot 2 \cdot 0.0006m² \cdot \frac{1.1E+11Pa}{1.4324m}}

Next Step Prepare to Evaluate

∴

P = \sqrt{37.1392 \cdot 2 \cdot 0.0006 \cdot \frac{1.1E+11}{1.4324}}

Next Step Evaluate

∴

P = 55000.0019232537N

LAST Step Rounding Answer

∴

P = 55000.0019N

Force Applied on Rod given Strain Energy Stored in Tension Rod Formula Elements

Variables

Functions

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

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

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

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

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

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

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 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}

Go Strain Energy in Rod when it is Subjected to External Torque

U = τ^{2} \cdot \frac{L}{2 \cdot J \cdot G}

How to Evaluate Force Applied on Rod given Strain Energy Stored in Tension Rod?

Force Applied on Rod given Strain Energy Stored in Tension Rod evaluator uses Axial Force on Beam = sqrt(Strain Energy*2*Cross Sectional Area of Rod*Modulus of Elasticity/Length of Rod or Shaft) to evaluate the Axial Force on Beam, Force Applied on Rod given Strain Energy Stored in Tension Rod formula is defined as a method to determine the force exerted on a rod based on the strain energy it has stored. This concept is crucial in understanding material behavior under tension in mechanical design. Axial Force on Beam is denoted by P symbol.

How to evaluate Force Applied on Rod given Strain Energy Stored in Tension Rod using this online evaluator? To use this online evaluator for Force Applied on Rod given Strain Energy Stored in Tension Rod, enter Strain Energy (U), Cross Sectional Area of Rod (A), Modulus of Elasticity (E) & Length of Rod or Shaft (L) and hit the calculate button.

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

What is the formula to find Force Applied on Rod given Strain Energy Stored in Tension Rod?

The formula of Force Applied on Rod given Strain Energy Stored in Tension Rod is expressed as Axial Force on Beam = sqrt(Strain Energy*2*Cross Sectional Area of Rod*Modulus of Elasticity/Length of Rod or Shaft). Here is an example- 51066.39 = sqrt(37.13919*2*0.0005526987*105548900000/1.432449).

How to calculate Force Applied on Rod given Strain Energy Stored in Tension Rod?

With Strain Energy (U), Cross Sectional Area of Rod (A), Modulus of Elasticity (E) & Length of Rod or Shaft (L) we can find Force Applied on Rod given Strain Energy Stored in Tension Rod using the formula - Axial Force on Beam = sqrt(Strain Energy*2*Cross Sectional Area of Rod*Modulus of Elasticity/Length of Rod or Shaft). This formula also uses Square Root (sqrt) function(s).

Can the Force Applied on Rod given Strain Energy Stored in Tension Rod be negative?

Yes, the Force Applied on Rod given Strain Energy Stored in Tension Rod, measured in Force can be negative.

Which unit is used to measure Force Applied on Rod given Strain Energy Stored in Tension Rod?

Force Applied on Rod given Strain Energy Stored in Tension Rod is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which Force Applied on Rod given Strain Energy Stored in Tension Rod can be measured.

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

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

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

Force Applied on Rod given Strain Energy Stored in Tension Rod Formula Elements

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

How to Evaluate Force Applied on Rod given Strain Energy Stored in Tension Rod?

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

Variable Name