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Elongation of Circular Tapering Rod 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 = 4 \cdot W Applied load \cdot \frac{L}{π \cdot E \cdot d 1 \cdot d 2}

δl - Elongation?W_{Applied load} - Applied Load?L - Length?E - Young's Modulus?d₁ - Diameter1?d₂ - Diameter2?π - Archimedes' constant?

Elongation of Circular Tapering Rod Example

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Here is how the Elongation of Circular Tapering Rod equation looks like with Values.

Here is how the Elongation of Circular Tapering Rod equation looks like with Units.

Here is how the Elongation of Circular Tapering Rod equation looks like.

0.0182 = 4 \cdot 150 \cdot \frac{3}{3.1416 \cdot 20000 \cdot 0.045 \cdot 0.035}

0.0182m = 4 \cdot 150kN \cdot \frac{3m}{3.1416 \cdot 20000MPa \cdot 0.045m \cdot 0.035m}

0.0182 = 4 \cdot 150 \cdot \frac{3}{3.1416 \cdot 20000 \cdot 0.045 \cdot 0.035}

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Home » Engineering » Civil » Strength of Materials » Elongation of Circular Tapering Rod

Elongation of Circular Tapering Rod Solution

Follow our step by step solution on how to calculate Elongation of Circular Tapering Rod?

FIRST Step Consider the formula

δl = 4 \cdot W Applied load \cdot \frac{L}{π \cdot E \cdot d 1 \cdot d 2}

Next Step Substitute values of Variables

∴

δl = 4 \cdot 150kN \cdot \frac{3m}{π \cdot 20000MPa \cdot 0.045m \cdot 0.035m}

Next Step Substitute values of Constants

∴

δl = 4 \cdot 150kN \cdot \frac{3m}{3.1416 \cdot 20000MPa \cdot 0.045m \cdot 0.035m}

Next Step Convert Units

∴

δl = 4 \cdot 150000N \cdot \frac{3m}{3.1416 \cdot 2E+10Pa \cdot 0.045m \cdot 0.035m}

Next Step Prepare to Evaluate

∴

δl = 4 \cdot 150000 \cdot \frac{3}{3.1416 \cdot 2E+10 \cdot 0.045 \cdot 0.035}

Next Step Evaluate

∴

δl = 0.0181891363533595m

LAST Step Rounding Answer

∴

δl = 0.0182m

Elongation of Circular Tapering Rod Formula Elements

Variables

Constants

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.

Applied Load

Applied Load is a force imposed on an object by a person or another object.

Symbol: W_{Applied load}

Measurement: ForceUnit: kN

Note: Value can be positive or negative.

Length

Length is the measurement or extent of something from end to end.

Symbol: L

Measurement: LengthUnit: m

Note: Value should be greater than 0.

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.

Diameter1

Diameter1 is the diameter on one side of the rod.

Symbol: d₁

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Diameter2

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

Symbol: d₂

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Credits

Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

Rithik Agrawal has created this Formula and 1300+ more formulas!

Verified by M Naveen

National Institute of Technology (NIT), Warangal

M Naveen has verified this Formula and 900+ more formulas!

Other Formulas to find Elongation

Go Elongation of Prismatic Rod

δl = 4 \cdot W Applied load \cdot \frac{L}{π \cdot E \cdot (d^{2})}

Other formulas in Circular Tapering Rod category

Go Load at End with known Extension of Circular Tapering Rod

W Applied load = \frac{δl}{4 \cdot \frac{L}{π \cdot E \cdot d 1 \cdot d 2}}

Go Length of Circular Tapering rod

L = \frac{δl}{4 \cdot \frac{W Applied load}{π \cdot E \cdot d 1 \cdot d 2}}

Go Diameter at One End of Circular Tapering Rod

d 2 = 4 \cdot W Applied load \cdot \frac{L}{π \cdot E \cdot δl \cdot d 1}

Go Diameter at Other End of Circular Tapering Rod

d 1 = 4 \cdot W Applied load \cdot \frac{L}{π \cdot E \cdot δl \cdot d 2}

How to Evaluate Elongation of Circular Tapering Rod?

Elongation of Circular Tapering Rod evaluator uses Elongation = 4*Applied Load*Length/(pi*Young's Modulus*Diameter1*Diameter2) to evaluate the Elongation, The Elongation of Circular Tapering Rod is defined as the amount of length changed on applied load from initial length. Elongation is denoted by δl symbol.

How to evaluate Elongation of Circular Tapering Rod using this online evaluator? To use this online evaluator for Elongation of Circular Tapering Rod, enter Applied Load (W_{Applied load}), Length (L), Young's Modulus (E), Diameter1 (d₁) & Diameter2 (d₂) and hit the calculate button.

FAQs on Elongation of Circular Tapering Rod

What is the formula to find Elongation of Circular Tapering Rod?

The formula of Elongation of Circular Tapering Rod is expressed as Elongation = 4*Applied Load*Length/(pi*Young's Modulus*Diameter1*Diameter2). Here is an example- 0.018189 = 4*150000*3/(pi*20000000000*0.045*0.035).

How to calculate Elongation of Circular Tapering Rod?

With Applied Load (W_{Applied load}), Length (L), Young's Modulus (E), Diameter1 (d₁) & Diameter2 (d₂) we can find Elongation of Circular Tapering Rod using the formula - Elongation = 4*Applied Load*Length/(pi*Young's Modulus*Diameter1*Diameter2). This formula also uses Archimedes' constant .

What are the other ways to Calculate Elongation?

Here are the different ways to Calculate Elongation-

Elongation=4*Applied Load*Length/(pi*Young's Modulus*(Diameter of Shaft^2))

Can the Elongation of Circular Tapering Rod be negative?

Yes, the Elongation of Circular Tapering Rod, measured in Length can be negative.

Which unit is used to measure Elongation of Circular Tapering Rod?

Elongation of Circular Tapering Rod is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Elongation of Circular Tapering Rod can be measured.