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Cross-sectional Area of Rod When Strain Energy stored in a Rod is Given Solution

STEP 0: Pre-Calculation Summary
Formula Used
cross_sectional_area = Axial Force^2*Length of Rod/2*Strain Energy*Modulus Of Elasticity
A = P^2*l/2*U*E
This formula uses 4 Variables
Variables Used
Axial Force - The Axial Force value/ axial force (Measured in Newton)
Length of Rod - The length of the rod is defined as the total length of the conducting rod. (Measured in Meter)
Strain Energy - The Strain energy is defined as the energy stored in a body due to deformation. (Measured in Joule)
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)
STEP 1: Convert Input(s) to Base Unit
Axial Force: 10 Newton --> 10 Newton No Conversion Required
Length of Rod: 2 Meter --> 2 Meter No Conversion Required
Strain Energy: 50 Joule --> 50 Joule No Conversion Required
Modulus Of Elasticity: 10 Kilonewton per Square Meter --> 10000 Pascal (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
A = P^2*l/2*U*E --> 10^2*2/2*50*10000
Evaluating ... ...
A = 50000000
STEP 3: Convert Result to Output's Unit
50000000 Square Meter --> No Conversion Required
FINAL ANSWER
50000000 Square Meter <-- Cross sectional area
(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

Cross-sectional Area of Rod When Strain Energy stored in a Rod is Given Formula

cross_sectional_area = Axial Force^2*Length of Rod/2*Strain Energy*Modulus Of Elasticity
A = P^2*l/2*U*E

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 Cross-sectional Area of Rod When Strain Energy stored in a Rod is Given?

Cross-sectional Area of Rod When Strain Energy stored in a Rod is Given calculator uses cross_sectional_area = Axial Force^2*Length of Rod/2*Strain Energy*Modulus Of Elasticity to calculate the Cross sectional area, The Cross-sectional Area of Rod When Strain Energy stored in a Rod is Given formula is defined as the representation of the intersection of an object by a plane along its axis. A cross-section is a shape that is yielded from a solid, when intersected by a plane. Cross sectional area and is denoted by A symbol.

How to calculate Cross-sectional Area of Rod When Strain Energy stored in a Rod is Given using this online calculator? To use this online calculator for Cross-sectional Area of Rod When Strain Energy stored in a Rod is Given, enter Axial Force (P), Length of Rod (l), Strain Energy (U) and Modulus Of Elasticity (E) and hit the calculate button. Here is how the Cross-sectional Area of Rod When Strain Energy stored in a Rod is Given calculation can be explained with given input values -> 5.000E+7 = 10^2*2/2*50*10000.

FAQ

What is Cross-sectional Area of Rod When Strain Energy stored in a Rod is Given?
The Cross-sectional Area of Rod When Strain Energy stored in a Rod is Given formula is defined as the representation of the intersection of an object by a plane along its axis. A cross-section is a shape that is yielded from a solid, when intersected by a plane and is represented as A = P^2*l/2*U*E or cross_sectional_area = Axial Force^2*Length of Rod/2*Strain Energy*Modulus Of Elasticity. The Axial Force value/ axial force, The length of the rod is defined as the total length of the conducting rod, The Strain energy is defined as the energy stored in a body due to deformation and 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.
How to calculate Cross-sectional Area of Rod When Strain Energy stored in a Rod is Given?
The Cross-sectional Area of Rod When Strain Energy stored in a Rod is Given formula is defined as the representation of the intersection of an object by a plane along its axis. A cross-section is a shape that is yielded from a solid, when intersected by a plane is calculated using cross_sectional_area = Axial Force^2*Length of Rod/2*Strain Energy*Modulus Of Elasticity. To calculate Cross-sectional Area of Rod When Strain Energy stored in a Rod is Given, you need Axial Force (P), Length of Rod (l), Strain Energy (U) and Modulus Of Elasticity (E). With our tool, you need to enter the respective value for Axial Force, Length of Rod, Strain Energy and Modulus Of Elasticity 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 Cross sectional area?
In this formula, Cross sectional area uses Axial Force, Length of Rod, Strain Energy and Modulus Of Elasticity. 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 Cross-sectional Area of Rod When Strain Energy stored in a Rod is Given calculator used?
Among many, Cross-sectional Area of Rod When Strain Energy stored in a Rod is Given calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
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