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Elongation of Truncated Conical Rod due to Self Weight Formula

GoElongation due to Self Weight in Prismatic Bar Formula

GoElongation due to Self Weight in Prismatic Bar using Applied Load Formula

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Elongation is defined as the length at breaking point expressed as a percentage of its original length (i.e. length at rest). Check FAQs

δl = \frac{(γ Rod \cdot l^{2}) \cdot (d 1 + d 2)}{6 \cdot E \cdot (d 1 - d 2)}

δl - Elongation?γ_Rod - Specific Weight of Rod?l - Length of Tapered Bar?d₁ - Diameter1?d₂ - Diameter2?E - Young's Modulus?

Elongation of Truncated Conical Rod due to Self Weight Example

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Here is how the Elongation of Truncated Conical Rod due to Self Weight equation looks like with Values.

Here is how the Elongation of Truncated Conical Rod due to Self Weight equation looks like with Units.

Here is how the Elongation of Truncated Conical Rod due to Self Weight equation looks like.

0.02 = \frac{(4930.96 \cdot {7.8}^{2}) \cdot (0.045 + 0.035)}{6 \cdot 20000 \cdot (0.045 - 0.035)}

0.02m = \frac{(4930.96kN/m³ \cdot {7.8m}^{2}) \cdot (0.045m + 0.035m)}{6 \cdot 20000MPa \cdot (0.045m - 0.035m)}

0.02 = \frac{(4930.96 \cdot {7.8}^{2}) \cdot (0.045 + 0.035)}{6 \cdot 20000 \cdot (0.045 - 0.035)}

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Strength of Materials » fx Elongation of Truncated Conical Rod due to Self Weight

Elongation of Truncated Conical Rod due to Self Weight Solution

Follow our step by step solution on how to calculate Elongation of Truncated Conical Rod due to Self Weight?

FIRST Step Consider the formula

δl = \frac{(γ Rod \cdot l^{2}) \cdot (d 1 + d 2)}{6 \cdot E \cdot (d 1 - d 2)}

Next Step Substitute values of Variables

∴

δl = \frac{(4930.96kN/m³ \cdot {7.8m}^{2}) \cdot (0.045m + 0.035m)}{6 \cdot 20000MPa \cdot (0.045m - 0.035m)}

Next Step Convert Units

∴

δl = \frac{(4.9E+6N/m³ \cdot {7.8m}^{2}) \cdot (0.045m + 0.035m)}{6 \cdot 2E+10Pa \cdot (0.045m - 0.035m)}

Next Step Prepare to Evaluate

∴

δl = \frac{(4.9E+6 \cdot {7.8}^{2}) \cdot (0.045 + 0.035)}{6 \cdot 2E+10 \cdot (0.045 - 0.035)}

Next Step Evaluate

∴

δl = 0.01999997376m

LAST Step Rounding Answer

∴

δl = 0.02m

Elongation of Truncated Conical Rod due to Self Weight Formula Elements

Variables

Elongation

Elongation is defined as the length at breaking point expressed as a percentage of its original length (i.e. length at rest).

Symbol: δl

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Elongation

Specific Weight of Rod

Specific Weight of Rod is defined as weight per unit volume of the rod.

Symbol: γ_Rod

Measurement: Specific WeightUnit: kN/m³

Note: Value can be positive or negative.

Formulas to find Specific Weight of Rod

Length of Tapered Bar

The Length of Tapered Bar is defined as the total length of the Bar.

Symbol: l

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Length of Tapered Bar

Diameter1

Diameter1 is the diameter on one side of the rod.

Symbol: d₁

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Diameter1

Diameter2

Diameter2 is the length of the diameter on 2nd side.

Symbol: d₂

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diameter2

Young's Modulus

Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.

Symbol: E

Measurement: StressUnit: MPa

Note: Value can be positive or negative.

Formulas to find Young's Modulus

Other Formulas to find Elongation

Go Elongation due to Self Weight in Prismatic Bar

δl = γ Rod \cdot L \cdot \frac{L}{E \cdot 2}

Go Elongation due to Self Weight in Prismatic Bar using Applied Load

δl = W Load \cdot \frac{L}{2 \cdot A \cdot E}

Other formulas in Elongation due to Self weight category

Go Specific weight of Truncated Conical Rod using its elongation due to Self Weight

γ Rod = \frac{δl}{\frac{(l^{2}) \cdot (d 1 + d 2)}{6 \cdot E \cdot (d 1 - d 2)}}

Go Length of Rod of Truncated Conical Section

l = \sqrt{\frac{δl}{\frac{(γ Rod) \cdot (d 1 + d 2)}{6 \cdot E \cdot (d 1 - d 2)}}}

Go Modulus of Elasticity of Rod using Extension of Truncated Conical Rod due to Self Weight

E = \frac{(γ Rod \cdot l^{2}) \cdot (d 1 + d 2)}{6 \cdot δl \cdot (d 1 - d 2)}

Go Modulus of Elasticity of Bar with known elongation of Truncated Conical Rod due to Self Weight

E = \frac{(γ Rod \cdot l^{2}) \cdot (d 1 + d 2)}{6 \cdot δl \cdot (d 1 - d 2)}

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

Elongation of Truncated Conical Rod due to Self Weight evaluator uses Elongation = ((Specific Weight of Rod*Length of Tapered Bar^2)*(Diameter1+Diameter2))/(6*Young's Modulus*(Diameter1-Diameter2)) to evaluate 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 evaluate Elongation of Truncated Conical Rod due to Self Weight using this online evaluator? To use this online evaluator for Elongation of Truncated Conical Rod due to Self Weight, enter Specific Weight of Rod (γ_Rod), Length of Tapered Bar (l), Diameter1 (d₁), Diameter2 (d₂) & Young's Modulus (E) and hit the calculate button.

FAQs on Elongation of Truncated Conical Rod due to Self Weight

What is the formula to find Elongation of Truncated Conical Rod due to Self Weight?

The formula of Elongation of Truncated Conical Rod due to Self Weight is expressed as Elongation = ((Specific Weight of Rod*Length of Tapered Bar^2)*(Diameter1+Diameter2))/(6*Young's Modulus*(Diameter1-Diameter2)). Here is an example- 0.000284 = ((4930960*7.8^2)*(0.045+0.035))/(6*20000000000*(0.045-0.035)).

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

With Specific Weight of Rod (γ_Rod), Length of Tapered Bar (l), Diameter1 (d₁), Diameter2 (d₂) & Young's Modulus (E) we can find Elongation of Truncated Conical Rod due to Self Weight using the formula - Elongation = ((Specific Weight of Rod*Length of Tapered Bar^2)*(Diameter1+Diameter2))/(6*Young's Modulus*(Diameter1-Diameter2)).

What are the other ways to Calculate Elongation?

Here are the different ways to Calculate Elongation-

Elongation=Specific Weight of Rod*Length*Length/(Young's Modulus*2)
Elongation=Applied Load SOM*Length/(2*Area of Cross-Section*Young's Modulus)

Can the Elongation of Truncated Conical Rod due to Self Weight be negative?

Yes, the Elongation of Truncated Conical Rod due to Self Weight, measured in Length can be negative.

Which unit is used to measure Elongation of Truncated Conical Rod due to Self Weight?

Elongation of Truncated Conical Rod due to Self Weight is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Elongation of Truncated Conical Rod due to Self Weight can be measured.

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Elongation of Truncated Conical Rod due to Self Weight Formula

​GoElongation due to Self Weight in Prismatic Bar Formula

​GoElongation due to Self Weight in Prismatic Bar using Applied Load Formula

Elongation of Truncated Conical Rod due to Self Weight Example

Elongation of Truncated Conical Rod due to Self Weight Solution

Elongation of Truncated Conical Rod due to Self Weight Formula Elements

Other Formulas to find Elongation

Other formulas in Elongation due to Self weight category

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

FAQs on Elongation of Truncated Conical Rod due to Self Weight

Variable Name

GoElongation due to Self Weight in Prismatic Bar Formula

GoElongation due to Self Weight in Prismatic Bar using Applied Load Formula