Length of Rod of Truncated Conical Section Calculator

✖Elongation is defined as the length at breaking point expressed as a percentage of its original length (i.e. length at rest).ⓘ Elongation [δl]			+10% -10%
✖Specific Weight of Rod is defined as weight per unit volume of the rod.ⓘ Specific Weight of Rod [γ_Rod]			+10% -10%
✖Diameter1 is the diameter on one side of the rod.ⓘ Diameter1 [d₁]			+10% -10%
✖Diameter2 is the length of the diameter on 2nd side.ⓘ Diameter2 [d₂]			+10% -10%
✖Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.ⓘ Young's Modulus [E]			+10% -10%

✖The Length of Tapered Bar is defined as the total length of the Bar.ⓘ Length of Rod of Truncated Conical Section [l]

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Formula

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Length of Rod of Truncated Conical Section

Formula

`"l" = sqrt("δl"/((("γ"_{"Rod"})*("d"_{"1"}+"d"_{"2"}))/(6*"E"*("d"_{"1"}-"d"_{"2"}))))`

Example

`"7.800005m"=sqrt("0.020m"/((("4930.96kN/m³")*("0.045m"+"0.035m"))/(6*"20000MPa"*("0.045m"-"0.035m"))))`

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Length of Rod of Truncated Conical Section Solution

STEP 0: Pre-Calculation Summary

Formula Used

Length of Tapered Bar = sqrt(Elongation/(((Specific Weight of Rod)*(Diameter1+Diameter2))/(6*Young's Modulus*(Diameter1-Diameter2))))
l = sqrt(δl/(((γ_Rod)*(d₁+d₂))/(6*E*(d₁-d₂))))
This formula uses 1 Functions, 6 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

Length of Tapered Bar - (Measured in Meter) - The Length of Tapered Bar is defined as the total length of the Bar.
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.
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

Elongation: 0.02 Meter --> 0.02 Meter No Conversion Required
Specific Weight of Rod: 4930.96 Kilonewton per Cubic Meter --> 4930960 Newton per Cubic Meter (Check conversion here)
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

l = sqrt(δl/(((γ_Rod)*(d₁+d₂))/(6*E*(d₁-d₂)))) --> sqrt(0.02/(((4930960)*(0.045+0.035))/(6*20000000000*(0.045-0.035))))

Evaluating ... ...

l = 7.80000511680503

STEP 3: Convert Result to Output's Unit

7.80000511680503 Meter --> No Conversion Required

FINAL ANSWER

7.80000511680503 ≈ 7.800005 Meter <-- Length of Tapered Bar

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Strength of Materials » Stress and Strain » Elongation due to Self weight » Length of Rod of Truncated Conical Section

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

Rithik Agrawal has created this Calculator and 1300+ more calculators!

Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

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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)

Length of Rod of Truncated Conical Section Formula

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

What is Strain in Bar?

Strain is the response of a system to an applied stress. When a material is loaded with a force, it produces a stress, which then causes a material to deform. For example, the strain in a bar that is being stretched in tension is the amount of elongation or change in length divided by its original length. ...

How to Calculate Length of Rod of Truncated Conical Section?

Length of Rod of Truncated Conical Section calculator uses Length of Tapered Bar = sqrt(Elongation/(((Specific Weight of Rod)*(Diameter1+Diameter2))/(6*Young's Modulus*(Diameter1-Diameter2)))) to calculate the Length of Tapered Bar, Length of Rod of Truncated Conical Section is defined as the length of the bar under which pull is applied. Here, the pull is due to self-weight of the structute. Note Diameter1 > diamter2. Length of Tapered Bar is denoted by l symbol.

How to calculate Length of Rod of Truncated Conical Section using this online calculator? To use this online calculator for Length of Rod of Truncated Conical Section, enter Elongation (δl), Specific Weight of Rod (γ_Rod), Diameter1 (d₁), Diameter2 (d₂) & Young's Modulus (E) and hit the calculate button. Here is how the Length of Rod of Truncated Conical Section calculation can be explained with given input values -> 65.46537 = sqrt(0.02/(((4930960)*(0.045+0.035))/(6*20000000000*(0.045-0.035)))).

FAQ

What is Length of Rod of Truncated Conical Section?

Length of Rod of Truncated Conical Section is defined as the length of the bar under which pull is applied. Here, the pull is due to self-weight of the structute. Note Diameter1 > diamter2 and is represented as l = sqrt(δl/(((γ_Rod)*(d₁+d₂))/(6*E*(d₁-d₂)))) or Length of Tapered Bar = sqrt(Elongation/(((Specific Weight of Rod)*(Diameter1+Diameter2))/(6*Young's Modulus*(Diameter1-Diameter2)))). 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 is defined as weight per unit volume of the rod, 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 Length of Rod of Truncated Conical Section?

Length of Rod of Truncated Conical Section is defined as the length of the bar under which pull is applied. Here, the pull is due to self-weight of the structute. Note Diameter1 > diamter2 is calculated using Length of Tapered Bar = sqrt(Elongation/(((Specific Weight of Rod)*(Diameter1+Diameter2))/(6*Young's Modulus*(Diameter1-Diameter2)))). To calculate Length of Rod of Truncated Conical Section, you need Elongation (δl), Specific Weight of Rod (γ_Rod), Diameter1 (d₁), Diameter2 (d₂) & Young's Modulus (E). With our tool, you need to enter the respective value for Elongation, Specific Weight of Rod, 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.

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