Stress of Member given Strain Energy Stored by Member Calculator

✖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.ⓘ Young's Modulus [E]			+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%

✖Direct Stress is the stress developed due to force applied which is parallel or collinear to the axis of the component.ⓘ Stress of Member given Strain Energy Stored by Member [σ]

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Stress of Member given Strain Energy Stored by Member Solution

STEP 0: Pre-Calculation Summary

Formula Used

Direct Stress = sqrt((2*Strain Energy stored by Member*Young's Modulus)/(Area of Cross-Section*Length of Member))
σ = sqrt((2*U_member*E)/(A*L))
This formula uses 1 Functions, 5 Variables

Functions Used

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., sqrt(Number)

Variables Used

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.
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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Strain Energy stored by Member: 301.2107 Newton Meter --> 301.2107 Joule (Check conversion here)
Young's Modulus: 20000 Megapascal --> 20000000000 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)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ = sqrt((2*U_member*E)/(A*L)) --> sqrt((2*301.2107*20000000000)/(0.0056*3))

Evaluating ... ...

σ = 26779998.75529

STEP 3: Convert Result to Output's Unit

26779998.75529 Pascal -->26.77999875529 Megapascal (Check conversion here)

FINAL ANSWER

26.77999875529 ≈ 26.78 Megapascal <-- Direct Stress

(Calculation completed in 00.020 seconds)

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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Coorg Institute of Technology (CIT), Coorg

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< Strain Energy stored by the Member Calculators

Modulus of Elasticity of Member given Strain Energy Stored by Member

LaTeX 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

LaTeX 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

LaTeX 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

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

Stress of Member given Strain Energy Stored by Member Formula

LaTeX Go

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

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 Stress of Member given Strain Energy Stored by Member?

Stress of Member given Strain Energy Stored by Member calculator uses Direct Stress = sqrt((2*Strain Energy stored by Member*Young's Modulus)/(Area of Cross-Section*Length of Member)) to calculate 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 calculate Stress of Member given Strain Energy Stored by Member using this online calculator? To use this online calculator 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. Here is how the Stress of Member given Strain Energy Stored by Member calculation can be explained with given input values -> 2.7E-5 = sqrt((2*301.2107*20000000000)/(0.0056*3)).

FAQ

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

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 and is represented as σ = sqrt((2*U_member*E)/(A*L)) or Direct Stress = sqrt((2*Strain Energy stored by Member*Young's Modulus)/(Area of Cross-Section*Length of Member)). Strain Energy stored by Member is the energy stored in a body due to its elastic deformation, Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain, 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.

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

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 is calculated using Direct Stress = sqrt((2*Strain Energy stored by Member*Young's Modulus)/(Area of Cross-Section*Length of Member)). To calculate Stress of Member given Strain Energy Stored by Member, you need Strain Energy stored by Member (U_member), Young's Modulus (E), Area of Cross-Section (A) & Length of Member (L). With our tool, you need to enter the respective value for Strain Energy stored by Member, Young's Modulus, Area of Cross-Section & Length of 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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