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Area of Member given Strain Energy Stored by Member Formula

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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. Check FAQs

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

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

Area of Member given Strain Energy Stored by Member Example

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

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

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

5599.9995 = \frac{2 \cdot 20000 \cdot 301.2107}{3000 \cdot {26.78}^{2}}

5599.9995mm² = \frac{2 \cdot 20000MPa \cdot 301.2107N*m}{3000mm \cdot {26.78MPa}^{2}}

5599.9995 = \frac{2 \cdot 20000 \cdot 301.2107}{3000 \cdot {26.78}^{2}}

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Strength of Materials » fx Area of Member given Strain Energy Stored by Member

Area of Member given Strain Energy Stored by Member Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

A = \frac{2 \cdot 20000MPa \cdot 301.2107N*m}{3000mm \cdot {26.78MPa}^{2}}

Next Step Convert Units

∴

A = \frac{2 \cdot 2E+10Pa \cdot 301.2107J}{3m \cdot {2.7E+7Pa}^{2}}

Next Step Prepare to Evaluate

∴

A = \frac{2 \cdot 2E+10 \cdot 301.2107}{3 \cdot {2.7E+7}^{2}}

Next Step Evaluate

∴

A = 0.00559999947943421m²

Next Step Convert to Output's Unit

∴

A = 5599.99947943421mm²

LAST Step Rounding Answer

∴

A = 5599.9995mm²

Area of Member given Strain Energy Stored by Member Formula Elements

Variables

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

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

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

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 Length of Member given Strain Energy Stored by Member

L = \frac{2 \cdot E \cdot U member}{A \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 Area of Member given Strain Energy Stored by Member?

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

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

FAQs on Area of Member given Strain Energy Stored by Member

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

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

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

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

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

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

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

Area of Member given Strain Energy Stored by Member 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 Area of Member given Strain Energy Stored by Member can be measured.

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Area of Member given Strain Energy Stored by Member Formula

Area of Member given Strain Energy Stored by Member Example

Area of Member given Strain Energy Stored by Member Solution

Area of Member given Strain Energy Stored by Member Formula Elements

Other formulas in Strain Energy stored by the Member category

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

FAQs on Area of Member given Strain Energy Stored by Member

Variable Name