Force Applied on Rod given Strain Energy Stored in Tension Rod Solution

STEP 0: Pre-Calculation Summary
Formula Used
Axial Force on Beam = sqrt(Strain Energy in Rod or Shaft*2*Cross Sectional Area of Rod*Modulus of elasticity of rod or shaft/Length of Rod or Shaft)
P = sqrt(U*2*A*E/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
Axial Force on Beam - (Measured in Newton) - Axial Force on Beam is defined as the compression or tension force acting on a beam, rod, or shaft.
Strain Energy in Rod or Shaft - (Measured in Joule) - Strain Energy in Rod or Shaft is defined as the energy stored in a rod or a shaft due to deformation.
Cross Sectional Area of Rod - (Measured in Square Meter) - Cross Sectional Area of Rod is the area of a two-dimensional shape that is obtained when a three-dimensional rod is sliced perpendicular to some specified axis at a point.
Modulus of elasticity of rod or shaft - (Measured in Pascal) - Modulus of elasticity of rod or shaft is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.
Length of Rod or Shaft - (Measured in Meter) - Length of Rod or Shaft is defined as the total length of the rod or the shaft according to Castiglano's theorom.
STEP 1: Convert Input(s) to Base Unit
Strain Energy in Rod or Shaft: 40 Joule --> 40 Joule No Conversion Required
Cross Sectional Area of Rod: 513.34 Square Millimeter --> 0.00051334 Square Meter (Check conversion here)
Modulus of elasticity of rod or shaft: 98000 Newton per Square Millimeter --> 98000000000 Pascal (Check conversion here)
Length of Rod or Shaft: 1330 Millimeter --> 1.33 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
P = sqrt(U*2*A*E/L) --> sqrt(40*2*0.00051334*98000000000/1.33)
Evaluating ... ...
P = 55009.1284290736
STEP 3: Convert Result to Output's Unit
55009.1284290736 Newton --> No Conversion Required
FINAL ANSWER
55009.1284290736 55009.13 Newton <-- Axial Force on Beam
(Calculation completed in 00.004 seconds)

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Created by Kethavath Srinath
Osmania University (OU), Hyderabad
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Vishwakarma Government Engineering College (VGEC), Ahmedabad
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14 Castigliano's Theorem for Deflection in Complex Structures Calculators

Torque given Strain Energy in Rod Subjected to External Torque
Go Torque on Rod or Shaft = sqrt(2*Strain Energy in Rod or Shaft*Polar Moment of Inertia of rod or shaft*Modulus of rigidity of rod or shaft/Length of Rod or Shaft)
Force Applied on Rod given Strain Energy Stored in Tension Rod
Go Axial Force on Beam = sqrt(Strain Energy in Rod or Shaft*2*Cross Sectional Area of Rod*Modulus of elasticity of rod or shaft/Length of Rod or Shaft)
Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment
Go Area Moment of Inertia of rod or shaft = (Bending Moment in Shaft or Beam^2)*Length of Rod or Shaft/(2*Modulus of elasticity of rod or shaft*Strain Energy in Rod or Shaft)
Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment
Go Modulus of elasticity of rod or shaft = (Bending Moment in Shaft or Beam^2)*Length of Rod or Shaft/(2*Strain Energy in Rod or Shaft*Area Moment of Inertia of rod or shaft)
Strain Energy Stored in Rod Subjected to Bending Moment
Go Strain Energy in Rod or Shaft = (Bending Moment in Shaft or Beam^2)*Length of Rod or Shaft/(2*Modulus of elasticity of rod or shaft*Area Moment of Inertia of rod or shaft)
Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment
Go Length of Rod or Shaft = 2*Strain Energy in Rod or Shaft*Modulus of elasticity of rod or shaft*Area Moment of Inertia of rod or shaft/(Bending Moment in Shaft or Beam^2)
Length of Shaft when Strain Energy in Shaft Subjected to External Torque
Go Length of Rod or Shaft = (2*Strain Energy in Rod or Shaft*Polar Moment of Inertia of rod or shaft*Modulus of rigidity of rod or shaft)/(Torque on Rod or Shaft^2)
Strain Energy in Rod when it is Subjected to External Torque
Go Strain Energy in Rod or Shaft = (Torque on Rod or Shaft^2)*Length of Rod or Shaft/(2*Polar Moment of Inertia of rod or shaft*Modulus of rigidity of rod or shaft)
Polar Moment of Inertia of Rod given Strain Energy in Rod
Go Polar Moment of Inertia of rod or shaft = (Torque on Rod or Shaft^2)*Length of Rod or Shaft/(2*Strain Energy in Rod or Shaft*Modulus of rigidity of rod or shaft)
Modulus of Rigidity of Rod given Strain Energy in Rod
Go Modulus of rigidity of rod or shaft = (Torque on Rod or Shaft^2)*Length of Rod or Shaft/(2*Polar Moment of Inertia of rod or shaft*Strain Energy in Rod or Shaft)
Strain Energy Stored in Tension Rod
Go Strain Energy in Rod or Shaft = ((Axial Force on Beam^2)*Length of Rod or Shaft)/(2*Cross Sectional Area of Rod*Modulus of elasticity of rod or shaft)
Cross-sectional Area of Rod given Strain Energy stored in Rod
Go Cross Sectional Area of Rod = Axial Force on Beam^2*Length of Rod or Shaft/(2*Strain Energy in Rod or Shaft*Modulus of elasticity of rod or shaft)
Modulus of Elasticity of Rod given Strain Energy Stored
Go Modulus of elasticity of rod or shaft = Axial Force on Beam^2*Length of Rod or Shaft/(2*Cross Sectional Area of Rod*Strain Energy in Rod or Shaft)
Length of Rod given Strain Energy Stored
Go Length of Rod or Shaft = Strain Energy in Rod or Shaft*2*Cross Sectional Area of Rod*Modulus of elasticity of rod or shaft/Axial Force on Beam^2

Force Applied on Rod given Strain Energy Stored in Tension Rod Formula

Axial Force on Beam = sqrt(Strain Energy in Rod or Shaft*2*Cross Sectional Area of Rod*Modulus of elasticity of rod or shaft/Length of Rod or Shaft)
P = sqrt(U*2*A*E/L)

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 Force Applied on Rod given Strain Energy Stored in Tension Rod?

Force Applied on Rod given Strain Energy Stored in Tension Rod calculator uses Axial Force on Beam = sqrt(Strain Energy in Rod or Shaft*2*Cross Sectional Area of Rod*Modulus of elasticity of rod or shaft/Length of Rod or Shaft) to calculate the Axial Force on Beam, The Force Applied on Rod given Strain Energy Stored in Tension Rod formula is defined as the total amount of force applied on the rod . Axial Force on Beam is denoted by P symbol.

How to calculate Force Applied on Rod given Strain Energy Stored in Tension Rod using this online calculator? To use this online calculator for Force Applied on Rod given Strain Energy Stored in Tension Rod, enter Strain Energy in Rod or Shaft (U), Cross Sectional Area of Rod (A), Modulus of elasticity of rod or shaft (E) & Length of Rod or Shaft (L) and hit the calculate button. Here is how the Force Applied on Rod given Strain Energy Stored in Tension Rod calculation can be explained with given input values -> 55009.13 = sqrt(40*2*0.00051334*98000000000/1.33).

FAQ

What is Force Applied on Rod given Strain Energy Stored in Tension Rod?
The Force Applied on Rod given Strain Energy Stored in Tension Rod formula is defined as the total amount of force applied on the rod and is represented as P = sqrt(U*2*A*E/L) or Axial Force on Beam = sqrt(Strain Energy in Rod or Shaft*2*Cross Sectional Area of Rod*Modulus of elasticity of rod or shaft/Length of Rod or Shaft). Strain Energy in Rod or Shaft is defined as the energy stored in a rod or a shaft due to deformation, Cross Sectional Area of Rod is the area of a two-dimensional shape that is obtained when a three-dimensional rod is sliced perpendicular to some specified axis at a point, Modulus of elasticity of rod or shaft is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it & Length of Rod or Shaft is defined as the total length of the rod or the shaft according to Castiglano's theorom.
How to calculate Force Applied on Rod given Strain Energy Stored in Tension Rod?
The Force Applied on Rod given Strain Energy Stored in Tension Rod formula is defined as the total amount of force applied on the rod is calculated using Axial Force on Beam = sqrt(Strain Energy in Rod or Shaft*2*Cross Sectional Area of Rod*Modulus of elasticity of rod or shaft/Length of Rod or Shaft). To calculate Force Applied on Rod given Strain Energy Stored in Tension Rod, you need Strain Energy in Rod or Shaft (U), Cross Sectional Area of Rod (A), Modulus of elasticity of rod or shaft (E) & Length of Rod or Shaft (L). With our tool, you need to enter the respective value for Strain Energy in Rod or Shaft, Cross Sectional Area of Rod, Modulus of elasticity of rod or shaft & Length of Rod or Shaft 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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