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Change in length of Tapered Bar Formula

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Change in Length of Tapered Bar is defined as change in length due to applied force. Check FAQs

ΔL = (F a \cdot \frac{l}{t \cdot E \cdot (L Right - L Left)}) \cdot \frac{\ln (\frac{L Right}{L Left})}{1000000}

ΔL - Change in Length of Tapered Bar?F_a - Applied Force?l - Length of Tapered Bar?t - Thickness?E - Young's Modulus Bar?L^Right - Length of Tapered Bar on Right?L_Left - Length of Tapered Bar on Left?

Change in length of Tapered Bar Example

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Here is how the Change in length of Tapered Bar equation looks like with Values.

Here is how the Change in length of Tapered Bar equation looks like with Units.

Here is how the Change in length of Tapered Bar equation looks like.

0.0084 = (2500 \cdot \frac{7800}{1200 \cdot 0.023 \cdot (70 - 100)}) \cdot \frac{\ln (\frac{70}{100})}{1000000}

0.0084mm = (2500N \cdot \frac{7800mm}{1200mm \cdot 0.023MPa \cdot (70mm - 100mm)}) \cdot \frac{\ln (\frac{70mm}{100mm})}{1000000}

0.0084 = (2500 \cdot \frac{7800}{1200 \cdot 0.023 \cdot (70 - 100)}) \cdot \frac{\ln (\frac{70}{100})}{1000000}

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Change in length of Tapered Bar Solution

Follow our step by step solution on how to calculate Change in length of Tapered Bar?

FIRST Step Consider the formula

ΔL = (F a \cdot \frac{l}{t \cdot E \cdot (L Right - L Left)}) \cdot \frac{\ln (\frac{L Right}{L Left})}{1000000}

Next Step Substitute values of Variables

∴

ΔL = (2500N \cdot \frac{7800mm}{1200mm \cdot 0.023MPa \cdot (70mm - 100mm)}) \cdot \frac{\ln (\frac{70mm}{100mm})}{1000000}

Next Step Convert Units

∴

ΔL = (2500N \cdot \frac{7.8m}{1.2m \cdot 23000Pa \cdot (0.07m - 0.1m)}) \cdot \frac{\ln (\frac{0.07m}{0.1m})}{1000000}

Next Step Prepare to Evaluate

∴

ΔL = (2500 \cdot \frac{7.8}{1.2 \cdot 23000 \cdot (0.07 - 0.1)}) \cdot \frac{\ln (\frac{0.07}{0.1})}{1000000}

Next Step Evaluate

∴

ΔL = 8.39995338986145E-06m

Next Step Convert to Output's Unit

∴

ΔL = 0.00839995338986145mm

LAST Step Rounding Answer

∴

ΔL = 0.0084mm

Change in length of Tapered Bar Formula Elements

Variables

Functions

Change in Length of Tapered Bar

Change in Length of Tapered Bar is defined as change in length due to applied force.

Symbol: ΔL

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Change in Length of Tapered Bar

Applied Force

Applied force is a force that is applied to an object by a person or another object.

Symbol: F_a

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Applied Force

Length of Tapered Bar

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

Symbol: l

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Length of Tapered Bar

Thickness

The Thickness refers to the distance through an object.

Symbol: t

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Thickness

Young's Modulus Bar

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

Symbol: E

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Young's Modulus Bar

Length of Tapered Bar on Right

Length of Tapered Bar on Right is the length of the tapered bar on the right side.

Symbol: L^Right

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Tapered Bar on Right

Length of Tapered Bar on Left

Length of Tapered Bar on Left is the length of the tapered bar on the left side.

Symbol: L_Left

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Tapered Bar on Left

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

Other formulas in Strain in Bar category

Go Longitudinal Strain using Poisson's Ratio

ε ln = - (\frac{ε L}{𝛎})

Go Elongation of bar given applied tensile load, area and length

∆ = P \cdot \frac{L 0}{A cs \cdot E}

How to Evaluate Change in length of Tapered Bar?

Change in length of Tapered Bar evaluator uses Change in Length of Tapered Bar = (Applied Force*Length of Tapered Bar/(Thickness*Young's Modulus Bar*(Length of Tapered Bar on Right-Length of Tapered Bar on Left)))*ln(Length of Tapered Bar on Right/Length of Tapered Bar on Left)/1000000 to evaluate the Change in Length of Tapered Bar, Change in length of Tapered Bar formula is defined as a method to quantify the deformation experienced by a tapered bar under applied force. It accounts for the bar's dimensions and material properties, providing insight into how the structure responds to mechanical stress. Change in Length of Tapered Bar is denoted by ΔL symbol.

How to evaluate Change in length of Tapered Bar using this online evaluator? To use this online evaluator for Change in length of Tapered Bar, enter Applied Force (F_a), Length of Tapered Bar (l), Thickness (t), Young's Modulus Bar (E), Length of Tapered Bar on Right (L^Right) & Length of Tapered Bar on Left (L_Left) and hit the calculate button.

FAQs on Change in length of Tapered Bar

What is the formula to find Change in length of Tapered Bar?

The formula of Change in length of Tapered Bar is expressed as Change in Length of Tapered Bar = (Applied Force*Length of Tapered Bar/(Thickness*Young's Modulus Bar*(Length of Tapered Bar on Right-Length of Tapered Bar on Left)))*ln(Length of Tapered Bar on Right/Length of Tapered Bar on Left)/1000000. Here is an example- 8.399953 = (2500*7.8/(1.2*23000*(0.07-0.1)))*ln(0.07/0.1)/1000000.

How to calculate Change in length of Tapered Bar?

With Applied Force (F_a), Length of Tapered Bar (l), Thickness (t), Young's Modulus Bar (E), Length of Tapered Bar on Right (L^Right) & Length of Tapered Bar on Left (L_Left) we can find Change in length of Tapered Bar using the formula - Change in Length of Tapered Bar = (Applied Force*Length of Tapered Bar/(Thickness*Young's Modulus Bar*(Length of Tapered Bar on Right-Length of Tapered Bar on Left)))*ln(Length of Tapered Bar on Right/Length of Tapered Bar on Left)/1000000. This formula also uses Natural Logarithm (ln) function(s).

Can the Change in length of Tapered Bar be negative?

Yes, the Change in length of Tapered Bar, measured in Length can be negative.

Which unit is used to measure Change in length of Tapered Bar?

Change in length of Tapered Bar is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Change in length of Tapered Bar can be measured.

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Change in length of Tapered Bar Formula

Change in length of Tapered Bar Example

Change in length of Tapered Bar Solution

Change in length of Tapered Bar Formula Elements

Other formulas in Strain in Bar category

How to Evaluate Change in length of Tapered Bar?

FAQs on Change in length of Tapered Bar

Variable Name