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Length of the Rod When Strain Energy Stored is Given Solution

STEP 0: Pre-Calculation Summary
Formula Used
length_of_rod = Strain Energy*2*Cross sectional area*Modulus Of Elasticity/Axial Force^2
l = U*2*A*E/P^2
This formula uses 4 Variables
Variables Used
Strain Energy - The Strain energy is defined as the energy stored in a body due to deformation. (Measured in Joule)
Cross sectional area - Cross sectional area is the area of a two-dimensional shape that is obtained when a three dimensional shape is sliced perpendicular to some specifies axis at a point. (Measured in Square Meter)
Modulus Of Elasticity - Modulus Of Elasticity is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it. (Measured in Kilonewton per Square Meter)
Axial Force - The Axial Force value/ axial force (Measured in Newton)
STEP 1: Convert Input(s) to Base Unit
Strain Energy: 50 Joule --> 50 Joule No Conversion Required
Cross sectional area: 10 Square Meter --> 10 Square Meter No Conversion Required
Modulus Of Elasticity: 10 Kilonewton per Square Meter --> 10000 Pascal (Check conversion here)
Axial Force: 10 Newton --> 10 Newton No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
l = U*2*A*E/P^2 --> 50*2*10*10000/10^2
Evaluating ... ...
l = 100000
STEP 3: Convert Result to Output's Unit
100000 Meter --> No Conversion Required
FINAL ANSWER
100000 Meter <-- Length of Rod
(Calculation completed in 00.016 seconds)

10+ Castigliano's Theorem Calculators

Force Applied on the Rod When Strain Energy Stored in Tension Rod is Given
axial_force = sqrt(Strain Energy*2*Cross sectional area*Modulus Of Elasticity/Length of Rod) Go
Torque When Strain Energy in the Rod When Subjected to External Torque is Given
torque = sqrt(Strain Energy*Polar moment of Inertia*Modulus of rigidity/Length of Shaft) Go
Strain Energy Stored in the Rod Subjected to Bending Moment
strain_energy = (Bending moment^2)*Length of Shaft/Modulus Of Elasticity*Moment of Inertia Go
Modulus of Elasticity of the Rod When Strain Energy Stored is Given
modulus_of_elasticity = Axial Force^2*Length of Rod/2*Cross sectional area*Strain Energy Go
Length of the Rod When Strain Energy Stored is Given
length_of_rod = Strain Energy*2*Cross sectional area*Modulus Of Elasticity/Axial Force^2 Go
Strain Energy Stored in Tension Rod
strain_energy = Axial Force^2*Length of Rod/2*Cross sectional area*Modulus Of Elasticity Go
Length of Shaft When Strain Energy in the Shaft Subjected to External Torque
length_of_shaft = Strain Energy*Polar moment of Inertia*Modulus of rigidity/(Torque^2) Go
Polar Moment of Inertia of the Rod When Strain Energy in the Rod is Given
polar_moment_of_inertia = (Torque^2)*Length of Shaft/Strain Energy*Modulus of rigidity Go
Modulus of Rigidity of the Rod When Strain Energy in the Rod is Given
modulus_of_rigidity = (Torque^2)*Length of Shaft/Polar moment of Inertia*Strain Energy Go
Strain Energy in the Rod When it is Subjected to External Torque
strain_energy = (Torque^2)*Length of Shaft/Polar moment of Inertia*Modulus of rigidity Go

Length of the Rod When Strain Energy Stored is Given Formula

length_of_rod = Strain Energy*2*Cross sectional area*Modulus Of Elasticity/Axial Force^2
l = U*2*A*E/P^2

Define Strain Energy?

Strain energy is a type of potential energy that is stored in a structural member as a result of elastic deformation. The external work done on such a member when it is deformed from its unstressed state is transformed into, and considered equal to the strain energy stored in it.

How to Calculate Length of the Rod When Strain Energy Stored is Given?

Length of the Rod When Strain Energy Stored is Given calculator uses length_of_rod = Strain Energy*2*Cross sectional area*Modulus Of Elasticity/Axial Force^2 to calculate the Length of Rod, The Length of the Rod When Strain Energy Stored is Given formula is defined as the total length of the rod on which the force is applied and that force applied is converted to strain energy. Length of Rod and is denoted by l symbol.

How to calculate Length of the Rod When Strain Energy Stored is Given using this online calculator? To use this online calculator for Length of the Rod When Strain Energy Stored is Given, enter Strain Energy (U), Cross sectional area (A), Modulus Of Elasticity (E) and Axial Force (P) and hit the calculate button. Here is how the Length of the Rod When Strain Energy Stored is Given calculation can be explained with given input values -> 100000 = 50*2*10*10000/10^2.

FAQ

What is Length of the Rod When Strain Energy Stored is Given?
The Length of the Rod When Strain Energy Stored is Given formula is defined as the total length of the rod on which the force is applied and that force applied is converted to strain energy and is represented as l = U*2*A*E/P^2 or length_of_rod = Strain Energy*2*Cross sectional area*Modulus Of Elasticity/Axial Force^2. The Strain energy is defined as the energy stored in a body due to deformation, Cross sectional area is the area of a two-dimensional shape that is obtained when a three dimensional shape is sliced perpendicular to some specifies axis at a point, Modulus Of Elasticity is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it and The Axial Force value/ axial force.
How to calculate Length of the Rod When Strain Energy Stored is Given?
The Length of the Rod When Strain Energy Stored is Given formula is defined as the total length of the rod on which the force is applied and that force applied is converted to strain energy is calculated using length_of_rod = Strain Energy*2*Cross sectional area*Modulus Of Elasticity/Axial Force^2. To calculate Length of the Rod When Strain Energy Stored is Given, you need Strain Energy (U), Cross sectional area (A), Modulus Of Elasticity (E) and Axial Force (P). With our tool, you need to enter the respective value for Strain Energy, Cross sectional area, Modulus Of Elasticity and Axial Force and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Length of Rod?
In this formula, Length of Rod uses Strain Energy, Cross sectional area, Modulus Of Elasticity and Axial Force. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • strain_energy = Axial Force^2*Length of Rod/2*Cross sectional area*Modulus Of Elasticity
  • axial_force = sqrt(Strain Energy*2*Cross sectional area*Modulus Of Elasticity/Length of Rod)
  • length_of_rod = Strain Energy*2*Cross sectional area*Modulus Of Elasticity/Axial Force^2
  • modulus_of_elasticity = Axial Force^2*Length of Rod/2*Cross sectional area*Strain Energy
  • strain_energy = (Torque^2)*Length of Shaft/Polar moment of Inertia*Modulus of rigidity
  • torque = sqrt(Strain Energy*Polar moment of Inertia*Modulus of rigidity/Length of Shaft)
  • length_of_shaft = Strain Energy*Polar moment of Inertia*Modulus of rigidity/(Torque^2)
  • modulus_of_rigidity = (Torque^2)*Length of Shaft/Polar moment of Inertia*Strain Energy
  • polar_moment_of_inertia = (Torque^2)*Length of Shaft/Strain Energy*Modulus of rigidity
  • strain_energy = (Bending moment^2)*Length of Shaft/Modulus Of Elasticity*Moment of Inertia
Where is the Length of the Rod When Strain Energy Stored is Given calculator used?
Among many, Length of the Rod When Strain Energy Stored is Given calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
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