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Strain Energy Stored by Member Formula

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Strain Energy stored by Member is the energy stored in a body due to its elastic deformation. Check FAQs

U member = (\frac{σ^{2}}{2 \cdot E}) \cdot A \cdot L

U_member - Strain Energy stored by Member?σ - Direct Stress?E - Young's Modulus?A - Area of Cross-Section?L - Length of Member?

Strain Energy Stored by Member Example

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Here is how the Strain Energy Stored by Member equation looks like with Values.

Here is how the Strain Energy Stored by Member equation looks like with Units.

Here is how the Strain Energy Stored by Member equation looks like.

301.2107 = (\frac{{26.78}^{2}}{2 \cdot 20000}) \cdot 5600 \cdot 3000

301.2107N*m = (\frac{{26.78MPa}^{2}}{2 \cdot 20000MPa}) \cdot 5600mm² \cdot 3000mm

301.2107 = (\frac{{26.78}^{2}}{2 \cdot 20000}) \cdot 5600 \cdot 3000

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Strain Energy Stored by Member Solution

Follow our step by step solution on how to calculate Strain Energy Stored by Member?

FIRST Step Consider the formula

U member = (\frac{σ^{2}}{2 \cdot E}) \cdot A \cdot L

Next Step Substitute values of Variables

∴

U member = (\frac{{26.78MPa}^{2}}{2 \cdot 20000MPa}) \cdot 5600mm² \cdot 3000mm

Next Step Convert Units

∴

U member = (\frac{{2.7E+7Pa}^{2}}{2 \cdot 2E+10Pa}) \cdot 0.0056m² \cdot 3m

Next Step Prepare to Evaluate

∴

U member = (\frac{{2.7E+7}^{2}}{2 \cdot 2E+10}) \cdot 0.0056 \cdot 3

Next Step Evaluate

∴

U member = 301.210728J

Next Step Convert to Output's Unit

∴

U member = 301.210728N*m

LAST Step Rounding Answer

∴

U member = 301.2107N*m

Strain Energy Stored by Member Formula Elements

Variables

Strain Energy stored by Member

Strain Energy stored by Member is the energy stored in a body due to its elastic deformation.

Symbol: U_member

Measurement: EnergyUnit: N*m

Note: Value should be greater than 0.

Formulas to find Strain Energy stored by Member

Direct Stress

Direct Stress is the stress developed due to force applied which is parallel or collinear to the axis of the component.

Symbol: σ

Measurement: StressUnit: MPa

Note: Value can be positive or negative.

Formulas to find Direct Stress

Young's Modulus

Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.

Symbol: E

Measurement: StressUnit: MPa

Note: Value can be positive or negative.

Formulas to find Young's Modulus

Area of Cross-Section

Area of Cross-section is a cross-sectional area which we obtain when the same object is cut into two pieces. The area of that particular cross-section is known as the cross-sectional area.

Symbol: A

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Formulas to find Area of Cross-Section

Length of Member

Length of Member is the measurement or extent of member (beam or column) from end to end.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Member

Other formulas in Strain Energy stored by the Member category

Go Length of Member given Strain Energy Stored by Member

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

Go Area of Member given Strain Energy Stored by Member

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

Go Modulus of Elasticity of Member given Strain Energy Stored by Member

E = \frac{(σ^{2}) \cdot A \cdot L}{2 \cdot U member}

Go Stress of Member given Strain Energy Stored by Member

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

How to Evaluate Strain Energy Stored by Member?

Strain Energy Stored by Member evaluator uses Strain Energy stored by Member = ((Direct Stress^2)/(2*Young's Modulus))*Area of Cross-Section*Length of Member to evaluate the Strain Energy stored by Member, The Strain Energy Stored by Member formula is defined as the amount of energy stored in member due to extension under pull. Strain Energy stored by Member is denoted by U_member symbol.

How to evaluate Strain Energy Stored by Member using this online evaluator? To use this online evaluator for Strain Energy Stored by Member, enter Direct Stress (σ), Young's Modulus (E), Area of Cross-Section (A) & Length of Member (L) and hit the calculate button.

FAQs on Strain Energy Stored by Member

What is the formula to find Strain Energy Stored by Member?

The formula of Strain Energy Stored by Member is expressed as Strain Energy stored by Member = ((Direct Stress^2)/(2*Young's Modulus))*Area of Cross-Section*Length of Member. Here is an example- 301.2107 = ((26780000^2)/(2*20000000000))*0.0056*3.

How to calculate Strain Energy Stored by Member?

With Direct Stress (σ), Young's Modulus (E), Area of Cross-Section (A) & Length of Member (L) we can find Strain Energy Stored by Member using the formula - Strain Energy stored by Member = ((Direct Stress^2)/(2*Young's Modulus))*Area of Cross-Section*Length of Member.

Can the Strain Energy Stored by Member be negative?

No, the Strain Energy Stored by Member, measured in Energy cannot be negative.

Which unit is used to measure Strain Energy Stored by Member?

Strain Energy Stored by Member is usually measured using the Newton Meter[N*m] for Energy. Joule[N*m], Kilojoule[N*m], Gigajoule[N*m] are the few other units in which Strain Energy Stored by Member can be measured.

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Strain Energy Stored by Member Formula

Strain Energy Stored by Member Example

Strain Energy Stored by Member Solution

Strain Energy Stored by Member Formula Elements

Other formulas in Strain Energy stored by the Member category

How to Evaluate Strain Energy Stored by Member?

FAQs on Strain Energy Stored by Member

Variable Name