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Length of Member given Strain Energy Stored by Member Formula

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

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

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

Length of Member given Strain Energy Stored by Member Example

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

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

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

2999.9997 = \frac{2 \cdot 20000 \cdot 301.2107}{5600 \cdot {26.78}^{2}}

2999.9997mm = \frac{2 \cdot 20000MPa \cdot 301.2107N*m}{5600mm² \cdot {26.78MPa}^{2}}

2999.9997 = \frac{2 \cdot 20000 \cdot 301.2107}{5600 \cdot {26.78}^{2}}

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Length of Member given Strain Energy Stored by Member Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

L = \frac{2 \cdot 20000MPa \cdot 301.2107N*m}{5600mm² \cdot {26.78MPa}^{2}}

Next Step Convert Units

∴

L = \frac{2 \cdot 2E+10Pa \cdot 301.2107J}{0.0056m² \cdot {2.7E+7Pa}^{2}}

Next Step Prepare to Evaluate

∴

L = \frac{2 \cdot 2E+10 \cdot 301.2107}{0.0056 \cdot {2.7E+7}^{2}}

Next Step Evaluate

∴

L = 2.99999972112547m

Next Step Convert to Output's Unit

∴

L = 2999.99972112547mm

LAST Step Rounding Answer

∴

L = 2999.9997mm

Length of Member given Strain Energy Stored by Member Formula Elements

Variables

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

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

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

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

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

Other formulas in Strain Energy stored by the Member category

Go Strain Energy Stored by Member

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

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 Length of Member given Strain Energy Stored by Member?

Length of Member given Strain Energy Stored by Member evaluator uses Length of Member = (2*Young's Modulus*Strain Energy stored by Member)/(Area of Cross-Section*Direct Stress^2) to evaluate the Length of Member, The Length of Member given Strain Energy Stored by Member formula is defined as the length of a member before application of pull. Length of Member is denoted by L symbol.

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

FAQs on Length of Member given Strain Energy Stored by Member

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

The formula of Length of Member given Strain Energy Stored by Member is expressed as Length of Member = (2*Young's Modulus*Strain Energy stored by Member)/(Area of Cross-Section*Direct Stress^2). Here is an example- 3E+6 = (2*20000000000*301.2107)/(0.0056*26780000^2).

How to calculate Length of Member given Strain Energy Stored by Member?

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

Can the Length of Member given Strain Energy Stored by Member be negative?

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

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

Length of Member given Strain Energy Stored by Member is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Length of Member given Strain Energy Stored by Member can be measured.

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Length of Member given Strain Energy Stored by Member Formula

Length of Member given Strain Energy Stored by Member Example

Length of Member given Strain Energy Stored by Member Solution

Length of Member given Strain Energy Stored by Member Formula Elements

Other formulas in Strain Energy stored by the Member category

How to Evaluate Length of Member given Strain Energy Stored by Member?

FAQs on Length of Member given Strain Energy Stored by Member

Variable Name