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

✖Direct Stress is the stress developed due to force applied which is parallel or collinear to the axis of the component.ⓘ Direct Stress [σ]			+10% -10%
✖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.ⓘ Area of Cross-Section [A]			+10% -10%
✖Length of Member is the measurement or extent of member (beam or column) from end to end.ⓘ Length of Member [L]			+10% -10%
✖Strain Energy stored by Member is the energy stored in a body due to its elastic deformation.ⓘ Strain Energy stored by Member [U_member]			+10% -10%

✖Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.ⓘ Modulus of Elasticity of Member given Strain Energy Stored by Member [E]

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Formula

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Modulus of Elasticity of Member given Strain Energy Stored by Member

Formula

`"E" = (("σ"^2)*"A"*"L")/(2*"U"_{"member"})`

Example

`"20000MPa"=((("26.78MPa")^2)*"5600mm²"*"3000mm")/(2*"301.2107N*m")`

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

STEP 0: Pre-Calculation Summary

Formula Used

Young's Modulus = ((Direct Stress^2)*Area of Cross-Section*Length of Member)/(2*Strain Energy stored by Member)
E = ((σ^2)*A*L)/(2*U_member)
This formula uses 5 Variables

Variables Used

Young's Modulus - (Measured in Pascal) - Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.
Direct Stress - (Measured in Pascal) - Direct Stress is the stress developed due to force applied which is parallel or collinear to the axis of the component.
Area of Cross-Section - (Measured in Square Meter) - 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.
Length of Member - (Measured in Meter) - Length of Member is the measurement or extent of member (beam or column) from end to end.
Strain Energy stored by Member - (Measured in Joule) - Strain Energy stored by Member is the energy stored in a body due to its elastic deformation.

STEP 1: Convert Input(s) to Base Unit

Direct Stress: 26.78 Megapascal --> 26780000 Pascal (Check conversion here)
Area of Cross-Section: 5600 Square Millimeter --> 0.0056 Square Meter (Check conversion here)
Length of Member: 3000 Millimeter --> 3 Meter (Check conversion here)
Strain Energy stored by Member: 301.2107 Newton Meter --> 301.2107 Joule (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E = ((σ^2)*A*L)/(2*U_member) --> ((26780000^2)*0.0056*3)/(2*301.2107)

Evaluating ... ...

E = 20000001859.1637

STEP 3: Convert Result to Output's Unit

20000001859.1637 Pascal -->20000.0018591637 Megapascal (Check conversion here)

FINAL ANSWER

20000.0018591637 ≈ 20000 Megapascal <-- Young's Modulus

(Calculation completed in 00.004 seconds)

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< 5 Strain Energy stored by the Member Calculators

Stress of Member given Strain Energy Stored by Member

Go Direct Stress = sqrt((2*Strain Energy stored by Member*Young's Modulus)/(Area of Cross-Section*Length of Member))

Modulus of Elasticity of Member given Strain Energy Stored by Member

Go Young's Modulus = ((Direct Stress^2)*Area of Cross-Section*Length of Member)/(2*Strain Energy stored by Member)

Strain Energy Stored by Member

Go Strain Energy stored by Member = ((Direct Stress^2)/(2*Young's Modulus))*Area of Cross-Section*Length of Member

Length of Member given Strain Energy Stored by Member

Go Length of Member = (2*Young's Modulus*Strain Energy stored by Member)/(Area of Cross-Section*Direct Stress^2)

Area of Member given Strain Energy Stored by Member

Go Area of Cross-Section = (2*Young's Modulus*Strain Energy stored by Member)/(Length of Member*Direct Stress^2)

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

Young's Modulus = ((Direct Stress^2)*Area of Cross-Section*Length of Member)/(2*Strain Energy stored by Member)
E = ((σ^2)*A*L)/(2*U_member)

Define Stress & Strain Energy

The stress definition in engineering says that stress is the force applied to an object divided by its cross-section area.
The strain energy is the energy stored in any body due to its deformation, also known as Resilience.

What is Eccentric Loading & Beam of Uniform Strength?

A load, whose line of action does not coincide with the axis of a column or a strut, is known as an eccentric load.
These beams have uniform cross section throughout their length. When they are loaded, there is a variation in bending moment from section to section along the length.

How to Calculate Modulus of Elasticity of Member given Strain Energy Stored by Member?

Modulus of Elasticity of Member given Strain Energy Stored by Member calculator uses Young's Modulus = ((Direct Stress^2)*Area of Cross-Section*Length of Member)/(2*Strain Energy stored by Member) to calculate the Young's Modulus, The Modulus of Elasticity of Member given Strain Energy Stored by Member formula is defined as the modulus of elasticity of material used to make member. Young's Modulus is denoted by E symbol.

How to calculate Modulus of Elasticity of Member given Strain Energy Stored by Member using this online calculator? To use this online calculator for Modulus of Elasticity of Member given Strain Energy Stored by Member, enter Direct Stress (σ), Area of Cross-Section (A), Length of Member (L) & Strain Energy stored by Member (U_member) and hit the calculate button. Here is how the Modulus of Elasticity of Member given Strain Energy Stored by Member calculation can be explained with given input values -> 0.02 = ((26780000^2)*0.0056*3)/(2*301.2107).

FAQ

What is Modulus of Elasticity of Member given Strain Energy Stored by Member?

The Modulus of Elasticity of Member given Strain Energy Stored by Member formula is defined as the modulus of elasticity of material used to make member and is represented as E = ((σ^2)*A*L)/(2*U_member) or Young's Modulus = ((Direct Stress^2)*Area of Cross-Section*Length of Member)/(2*Strain Energy stored by Member). Direct Stress is the stress developed due to force applied which is parallel or collinear to the axis of the component, 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, Length of Member is the measurement or extent of member (beam or column) from end to end & Strain Energy stored by Member is the energy stored in a body due to its elastic deformation.

How to calculate Modulus of Elasticity of Member given Strain Energy Stored by Member?

The Modulus of Elasticity of Member given Strain Energy Stored by Member formula is defined as the modulus of elasticity of material used to make member is calculated using Young's Modulus = ((Direct Stress^2)*Area of Cross-Section*Length of Member)/(2*Strain Energy stored by Member). To calculate Modulus of Elasticity of Member given Strain Energy Stored by Member, you need Direct Stress (σ), Area of Cross-Section (A), Length of Member (L) & Strain Energy stored by Member (U_member). With our tool, you need to enter the respective value for Direct Stress, Area of Cross-Section, Length of Member & Strain Energy stored by Member and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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