Shear Area given Strain Energy in Shear Calculator

✖Shear Force is the force which causes shear deformation to occur in the shear plane.ⓘ Shear Force [V]			+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 is the energy adsorption of material due to strain under an applied load. It is also equal to the work done on a specimen by an external force.ⓘ Strain Energy [U]			+10% -10%
✖Modulus of Rigidity is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. It is often denoted by G.ⓘ Modulus of Rigidity [G_Torsion]			+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.ⓘ Shear Area given Strain Energy in Shear [A]

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Formula

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Shear Area given Strain Energy in Shear

Formula

`"A" = ("V"^2)*"L"/(2*"U"*"G"_{"Torsion"})`

Example

`"5635.196mm²"=(("143kN")^2)*"3000mm"/(2*"136.08N*m"*"40GPa")`

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Shear Area given Strain Energy in Shear Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Cross-Section = (Shear Force^2)*Length of Member/(2*Strain Energy*Modulus of Rigidity)
A = (V^2)*L/(2*U*G_Torsion)
This formula uses 5 Variables

Variables Used

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.
Shear Force - (Measured in Newton) - Shear Force is the force which causes shear deformation to occur in the shear plane.
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 - (Measured in Joule) - Strain Energy is the energy adsorption of material due to strain under an applied load. It is also equal to the work done on a specimen by an external force.
Modulus of Rigidity - (Measured in Pascal) - Modulus of Rigidity is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. It is often denoted by G.

STEP 1: Convert Input(s) to Base Unit

Shear Force: 143 Kilonewton --> 143000 Newton (Check conversion here)
Length of Member: 3000 Millimeter --> 3 Meter (Check conversion here)
Strain Energy: 136.08 Newton Meter --> 136.08 Joule (Check conversion here)
Modulus of Rigidity: 40 Gigapascal --> 40000000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = (V^2)*L/(2*U*G_Torsion) --> (143000^2)*3/(2*136.08*40000000000)

Evaluating ... ...

A = 0.00563519620811287

STEP 3: Convert Result to Output's Unit

0.00563519620811287 Square Meter -->5635.19620811287 Square Millimeter (Check conversion here)

FINAL ANSWER

5635.19620811287 ≈ 5635.196 Square Millimeter <-- Area of Cross-Section

(Calculation completed in 00.006 seconds)

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< 19 Strain Energy in Structural Members Calculators

Strain Energy in Torsion given Angle of Twist

Go Strain Energy = (Polar Moment of Inertia*Modulus of Rigidity*(Angle of Twist*(pi/180))^2)/(2*Length of Member)

Strain Energy for Pure Bending when Beam rotates in One End

Go Strain Energy = (Young's Modulus*Area Moment of Inertia*((Angle of Twist*(pi/180))^2)/(2*Length of Member))

Bending Moment using Strain Energy

Go Bending Moment = sqrt(Strain Energy*(2*Young's Modulus*Area Moment of Inertia)/Length of Member)

Torque given Strain Energy in Torsion

Go Torque SOM = sqrt(2*Strain Energy*Polar Moment of Inertia*Modulus of Rigidity/Length of Member)

Shear Force using Strain Energy

Go Shear Force = sqrt(2*Strain Energy*Area of Cross-Section*Modulus of Rigidity/Length of Member)

Strain Energy in Shear given Shear Deformation

Go Strain Energy = (Area of Cross-Section*Modulus of Rigidity*(Shear Deformation^2))/(2*Length of Member)

Length over which Deformation takes place using Strain Energy

Go Length of Member = (Strain Energy*(2*Young's Modulus*Area Moment of Inertia)/(Bending Moment^2))

Modulus of Elasticity with given Strain Energy

Go Young's Modulus = (Length of Member*(Bending Moment^2)/(2*Strain Energy*Area Moment of Inertia))

Moment of Inertia using Strain Energy

Go Area Moment of Inertia = Length of Member*((Bending Moment^2)/(2*Strain Energy*Young's Modulus))

Strain Energy in Bending

Go Strain Energy = ((Bending Moment^2)*Length of Member/(2*Young's Modulus*Area Moment of Inertia))

Strain Energy in Torsion given Polar MI and Shear Modulus of Elasticity

Go Strain Energy = (Torque SOM^2)*Length of Member/(2*Polar Moment of Inertia*Modulus of Rigidity)

Shear Modulus of Elasticity given Strain Energy in Torsion

Go Modulus of Rigidity = (Torque SOM^2)*Length of Member/(2*Polar Moment of Inertia*Strain Energy)

Polar Moment of Inertia given Strain Energy in Torsion

Go Polar Moment of Inertia = (Torque SOM^2)*Length of Member/(2*Strain Energy*Modulus of Rigidity)

Shear Modulus of Elasticity given Strain Energy in Shear

Go Modulus of Rigidity = (Shear Force^2)*Length of Member/(2*Area of Cross-Section*Strain Energy)

Shear Area given Strain Energy in Shear

Go Area of Cross-Section = (Shear Force^2)*Length of Member/(2*Strain Energy*Modulus of Rigidity)

Strain Energy in Shear

Go Strain Energy = (Shear Force^2)*Length of Member/(2*Area of Cross-Section*Modulus of Rigidity)

Length over which Deformation takes place given Strain Energy in Torsion

Go Length of Member = (2*Strain Energy*Polar Moment of Inertia*Modulus of Rigidity)/Torque SOM^2

Length over which Deformation takes place given Strain Energy in Shear

Go Length of Member = 2*Strain Energy*Area of Cross-Section*Modulus of Rigidity/(Shear Force^2)

Stress using Hook's Law

Go Direct Stress = Young's Modulus*Lateral Strain

Shear Area given Strain Energy in Shear Formula

Area of Cross-Section = (Shear Force^2)*Length of Member/(2*Strain Energy*Modulus of Rigidity)
A = (V^2)*L/(2*U*G_Torsion)

What is Shear Area?

The shear area of the member is a cross-sectional property and is defined as the area of the section which is effective in resisting shear deformation. ‘Shear Area’ is generally understood to be the effective area of the section participating in the shear deformation and as such is a nebulous value ranging from the gross cross-sectional area to the area of the web for a wide flange section.

How does Shear Deformation take place?

Shearing forces cause shearing deformation. An element subject to shear does not change in length alone but undergoes a change in shape, this is how a shear deformation takes place.

How to Calculate Shear Area given Strain Energy in Shear?

Shear Area given Strain Energy in Shear calculator uses Area of Cross-Section = (Shear Force^2)*Length of Member/(2*Strain Energy*Modulus of Rigidity) to calculate the Area of Cross-Section, The Shear Area given Strain Energy in Shear formula is defined as the calculated reduction of a cross-sectional area. By using this value, one can consider the shear deformation when determining the internal forces. Area of Cross-Section is denoted by A symbol.

How to calculate Shear Area given Strain Energy in Shear using this online calculator? To use this online calculator for Shear Area given Strain Energy in Shear, enter Shear Force (V), Length of Member (L), Strain Energy (U) & Modulus of Rigidity (G_Torsion) and hit the calculate button. Here is how the Shear Area given Strain Energy in Shear calculation can be explained with given input values -> 0.005635 = (143000^2)*3/(2*136.08*40000000000).

FAQ

What is Shear Area given Strain Energy in Shear?

The Shear Area given Strain Energy in Shear formula is defined as the calculated reduction of a cross-sectional area. By using this value, one can consider the shear deformation when determining the internal forces and is represented as A = (V^2)*L/(2*U*G_Torsion) or Area of Cross-Section = (Shear Force^2)*Length of Member/(2*Strain Energy*Modulus of Rigidity). Shear Force is the force which causes shear deformation to occur in the shear plane, Length of Member is the measurement or extent of member (beam or column) from end to end, Strain Energy is the energy adsorption of material due to strain under an applied load. It is also equal to the work done on a specimen by an external force & Modulus of Rigidity is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. It is often denoted by G.

How to calculate Shear Area given Strain Energy in Shear?

The Shear Area given Strain Energy in Shear formula is defined as the calculated reduction of a cross-sectional area. By using this value, one can consider the shear deformation when determining the internal forces is calculated using Area of Cross-Section = (Shear Force^2)*Length of Member/(2*Strain Energy*Modulus of Rigidity). To calculate Shear Area given Strain Energy in Shear, you need Shear Force (V), Length of Member (L), Strain Energy (U) & Modulus of Rigidity (G_Torsion). With our tool, you need to enter the respective value for Shear Force, Length of Member, Strain Energy & Modulus of Rigidity 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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