Length of Member given Strain Energy Stored by Member Calculator

✖Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.ⓘ Young's Modulus [E]			+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%
✖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%
✖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%

✖Length of Member is the measurement or extent of member (beam or column) from end to end.ⓘ Length of Member given Strain Energy Stored by Member [L]

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Formula

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Length of Member given Strain Energy Stored by Member

Formula

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

Example

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

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Length of Member given Strain Energy Stored by Member Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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

STEP 1: Convert Input(s) to Base Unit

Young's Modulus: 20000 Megapascal --> 20000000000 Pascal (Check conversion here)
Strain Energy stored by Member: 301.2107 Newton Meter --> 301.2107 Joule (Check conversion here)
Area of Cross-Section: 5600 Square Millimeter --> 0.0056 Square Meter (Check conversion here)
Direct Stress: 26.78 Megapascal --> 26780000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L = (2*E*U_member)/(A*σ^2) --> (2*20000000000*301.2107)/(0.0056*26780000^2)

Evaluating ... ...

L = 2.99999972112547

STEP 3: Convert Result to Output's Unit

2.99999972112547 Meter -->2999.99972112547 Millimeter (Check conversion here)

FINAL ANSWER

2999.99972112547 ≈ 3000 Millimeter <-- Length of Member

(Calculation completed in 00.004 seconds)

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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Meerut Institute of Engineering and Technology (MIET), Meerut

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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)

Length of Member given Strain Energy Stored by Member Formula

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

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 Length of Member given Strain Energy Stored by Member?

Length of Member given Strain Energy Stored by Member calculator uses Length of Member = (2*Young's Modulus*Strain Energy stored by Member)/(Area of Cross-Section*Direct Stress^2) to calculate 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 calculate Length of Member given Strain Energy Stored by Member using this online calculator? To use this online calculator 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. Here is how the Length of Member given Strain Energy Stored by Member calculation can be explained with given input values -> 3E+6 = (2*20000000000*301.2107)/(0.0056*26780000^2).

FAQ

What is Length of Member given Strain Energy Stored by Member?

The Length of Member given Strain Energy Stored by Member formula is defined as the length of a member before application of pull and is represented as L = (2*E*U_member)/(A*σ^2) or Length of Member = (2*Young's Modulus*Strain Energy stored by Member)/(Area of Cross-Section*Direct Stress^2). Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain, Strain Energy stored by Member is the energy stored in a body due to its elastic deformation, 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 & Direct Stress is the stress developed due to force applied which is parallel or collinear to the axis of the component.

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

The Length of Member given Strain Energy Stored by Member formula is defined as the length of a member before application of pull is calculated using Length of Member = (2*Young's Modulus*Strain Energy stored by Member)/(Area of Cross-Section*Direct Stress^2). To calculate Length of Member given Strain Energy Stored by Member, you need Young's Modulus (E), Strain Energy stored by Member (U_member), Area of Cross-Section (A) & Direct Stress (σ). With our tool, you need to enter the respective value for Young's Modulus, Strain Energy stored by Member, Area of Cross-Section & Direct Stress 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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