Elongation of Truncated Conical Rod due to Self Weight Solution

STEP 0: Pre-Calculation Summary
Formula Used
Elongation = ((Specific Weight of Rod*Length of Tapered Bar^2)*(Diameter1+Diameter2))/(6*Young's Modulus*(Diameter1-Diameter2))
δl = ((γRod*l^2)*(d1+d2))/(6*E*(d1-d2))
This formula uses 6 Variables
Variables Used
Elongation - (Measured in Meter) - Elongation is defined as the length at breaking point expressed as a percentage of its original length (i.e. length at rest).
Specific Weight of Rod - (Measured in Newton per Cubic Meter) - Specific Weight of Rod is defined as weight per unit volume of the rod.
Length of Tapered Bar - (Measured in Meter) - The Length of Tapered Bar is defined as the total length of the Bar.
Diameter1 - (Measured in Meter) - Diameter1 is the diameter on one side of the rod.
Diameter2 - (Measured in Meter) - Diameter2 is the length of the diameter on 2nd side.
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.
STEP 1: Convert Input(s) to Base Unit
Specific Weight of Rod: 4930.96 Kilonewton per Cubic Meter --> 4930960 Newton per Cubic Meter (Check conversion here)
Length of Tapered Bar: 7.8 Meter --> 7.8 Meter No Conversion Required
Diameter1: 0.045 Meter --> 0.045 Meter No Conversion Required
Diameter2: 0.035 Meter --> 0.035 Meter No Conversion Required
Young's Modulus: 20000 Megapascal --> 20000000000 Pascal (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
δl = ((γRod*l^2)*(d1+d2))/(6*E*(d1-d2)) --> ((4930960*7.8^2)*(0.045+0.035))/(6*20000000000*(0.045-0.035))
Evaluating ... ...
δl = 0.01999997376
STEP 3: Convert Result to Output's Unit
0.01999997376 Meter --> No Conversion Required
FINAL ANSWER
0.01999997376 0.02 Meter <-- Elongation
(Calculation completed in 00.004 seconds)

Credits

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National Institute of Technology Karnataka (NITK), Surathkal
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11 Elongation due to Self weight Calculators

Length of Rod of Truncated Conical Section
Go Length of Tapered Bar = sqrt(Elongation/(((Specific Weight of Rod)*(Diameter1+Diameter2))/(6*Young's Modulus*(Diameter1-Diameter2))))
Specific weight of Truncated Conical Rod using its elongation due to Self Weight
Go Specific Weight of Rod = Elongation/(((Length of Tapered Bar^2)*(Diameter1+Diameter2))/(6*Young's Modulus*(Diameter1-Diameter2)))
Modulus of Elasticity of Bar with known elongation of Truncated Conical Rod due to Self Weight
Go Young's Modulus = ((Specific Weight of Rod*Length of Tapered Bar^2)*(Diameter1+Diameter2))/(6*Elongation*(Diameter1-Diameter2))
Modulus of Elasticity of Rod using Extension of Truncated Conical Rod due to Self Weight
Go Young's Modulus = ((Specific Weight of Rod*Length of Tapered Bar^2)*(Diameter1+Diameter2))/(6*Elongation*(Diameter1-Diameter2))
Elongation of Truncated Conical Rod due to Self Weight
Go Elongation = ((Specific Weight of Rod*Length of Tapered Bar^2)*(Diameter1+Diameter2))/(6*Young's Modulus*(Diameter1-Diameter2))
Length of Bar using its Uniform Strength
Go Length = (2.303*log10(Area 1/Area 2))*(Uniform Stress/Specific Weight of Rod)
Uniform Stress on Bar due to Self-Weight
Go Uniform Stress = Length/((2.303*log10(Area 1/Area 2))/Specific Weight of Rod)
Cross Sectional Area with known Elongation of Tapering Bar due to Self Weight
Go Area of Cross-Section = Applied Load SOM*Length/(6*Elongation*Young's Modulus)
Elongation due to Self Weight in Prismatic Bar using Applied Load
Go Elongation = Applied Load SOM*Length/(2*Area of Cross-Section*Young's Modulus)
Length of Bar using Elongation due to Self Weight in Prismatic bar
Go Length = sqrt(Elongation/(Specific Weight of Rod/(Young's Modulus*2)))
Elongation due to Self Weight in Prismatic Bar
Go Elongation = Specific Weight of Rod*Length*Length/(Young's Modulus*2)

Elongation of Truncated Conical Rod due to Self Weight Formula

Elongation = ((Specific Weight of Rod*Length of Tapered Bar^2)*(Diameter1+Diameter2))/(6*Young's Modulus*(Diameter1-Diameter2))
δl = ((γRod*l^2)*(d1+d2))/(6*E*(d1-d2))

What is Strain in Conical Rod?

The rod elongates under this tension to a new length, and the normal strain is a ratio of this small deformation to the rod's original length. Strain is a unitless measure of how much an object gets bigger or smaller from an applied load.

How to Calculate Elongation of Truncated Conical Rod due to Self Weight?

Elongation of Truncated Conical Rod due to Self Weight calculator uses Elongation = ((Specific Weight of Rod*Length of Tapered Bar^2)*(Diameter1+Diameter2))/(6*Young's Modulus*(Diameter1-Diameter2)) to calculate the Elongation, The Elongation of Truncated Conical Rod due to Self Weight is defined as change in length of bar at the conical rod. Elongation is denoted by δl symbol.

How to calculate Elongation of Truncated Conical Rod due to Self Weight using this online calculator? To use this online calculator for Elongation of Truncated Conical Rod due to Self Weight, enter Specific Weight of Rod Rod), Length of Tapered Bar (l), Diameter1 (d1), Diameter2 (d2) & Young's Modulus (E) and hit the calculate button. Here is how the Elongation of Truncated Conical Rod due to Self Weight calculation can be explained with given input values -> 0.000284 = ((4930960*7.8^2)*(0.045+0.035))/(6*20000000000*(0.045-0.035)).

FAQ

What is Elongation of Truncated Conical Rod due to Self Weight?
The Elongation of Truncated Conical Rod due to Self Weight is defined as change in length of bar at the conical rod and is represented as δl = ((γRod*l^2)*(d1+d2))/(6*E*(d1-d2)) or Elongation = ((Specific Weight of Rod*Length of Tapered Bar^2)*(Diameter1+Diameter2))/(6*Young's Modulus*(Diameter1-Diameter2)). Specific Weight of Rod is defined as weight per unit volume of the rod, The Length of Tapered Bar is defined as the total length of the Bar, Diameter1 is the diameter on one side of the rod, Diameter2 is the length of the diameter on 2nd side & Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.
How to calculate Elongation of Truncated Conical Rod due to Self Weight?
The Elongation of Truncated Conical Rod due to Self Weight is defined as change in length of bar at the conical rod is calculated using Elongation = ((Specific Weight of Rod*Length of Tapered Bar^2)*(Diameter1+Diameter2))/(6*Young's Modulus*(Diameter1-Diameter2)). To calculate Elongation of Truncated Conical Rod due to Self Weight, you need Specific Weight of Rod Rod), Length of Tapered Bar (l), Diameter1 (d1), Diameter2 (d2) & Young's Modulus (E). With our tool, you need to enter the respective value for Specific Weight of Rod, Length of Tapered Bar, Diameter1, Diameter2 & Young's Modulus 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 Elongation?
In this formula, Elongation uses Specific Weight of Rod, Length of Tapered Bar, Diameter1, Diameter2 & Young's Modulus. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Elongation = Specific Weight of Rod*Length*Length/(Young's Modulus*2)
  • Elongation = Applied Load SOM*Length/(2*Area of Cross-Section*Young's Modulus)
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