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Stress of Member given Strain Energy Stored by Member Formula

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

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

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

Stress of Member given Strain Energy Stored by Member Example

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

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

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

26.78 = \sqrt{\frac{2 \cdot 301.2107 \cdot 20000}{5600 \cdot 3000}}

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

26.78 = \sqrt{\frac{2 \cdot 301.2107 \cdot 20000}{5600 \cdot 3000}}

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Stress of Member given Strain Energy Stored by Member Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

σ = \sqrt{\frac{2 \cdot 301.2107N*m \cdot 20000MPa}{5600mm² \cdot 3000mm}}

Next Step Convert Units

∴

σ = \sqrt{\frac{2 \cdot 301.2107J \cdot 2E+10Pa}{0.0056m² \cdot 3m}}

Next Step Prepare to Evaluate

∴

σ = \sqrt{\frac{2 \cdot 301.2107 \cdot 2E+10}{0.0056 \cdot 3}}

Next Step Evaluate

∴

σ = 26779998.75529Pa

Next Step Convert to Output's Unit

∴

σ = 26.77999875529MPa

LAST Step Rounding Answer

∴

σ = 26.78MPa

Stress of Member given Strain Energy Stored by Member Formula Elements

Variables

Functions

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

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

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

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 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 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}

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

Stress of Member given Strain Energy Stored by Member evaluator uses Direct Stress = sqrt((2*Strain Energy stored by Member*Young's Modulus)/(Area of Cross-Section*Length of Member)) to evaluate the Direct Stress, The Stress of Member given Strain Energy Stored by Member formula is defined as the stress applied on a member to get required strain energy. Direct Stress is denoted by σ symbol.

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

FAQs on Stress of Member given Strain Energy Stored by Member

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

The formula of Stress of Member given Strain Energy Stored by Member is expressed as Direct Stress = sqrt((2*Strain Energy stored by Member*Young's Modulus)/(Area of Cross-Section*Length of Member)). Here is an example- 2.7E-5 = sqrt((2*301.2107*20000000000)/(0.0056*3)).

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

With Strain Energy stored by Member (U_member), Young's Modulus (E), Area of Cross-Section (A) & Length of Member (L) we can find Stress of Member given Strain Energy Stored by Member using the formula - Direct Stress = sqrt((2*Strain Energy stored by Member*Young's Modulus)/(Area of Cross-Section*Length of Member)). This formula also uses Square Root (sqrt) function(s).

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

Yes, the Stress of Member given Strain Energy Stored by Member, measured in Stress can be negative.

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

Stress of Member given Strain Energy Stored by Member is usually measured using the Megapascal[MPa] for Stress. Pascal[MPa], Newton per Square Meter[MPa], Newton per Square Millimeter[MPa] are the few other units in which Stress of Member given Strain Energy Stored by Member can be measured.

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Stress of Member given Strain Energy Stored by Member Formula

Stress of Member given Strain Energy Stored by Member Example

Stress of Member given Strain Energy Stored by Member Solution

Stress of Member given Strain Energy Stored by Member Formula Elements

Other formulas in Strain Energy stored by the Member category

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

FAQs on Stress of Member given Strain Energy Stored by Member

Variable Name