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Thickness of Tapered Bar using Temperature Stress Formula

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Section Thickness is the dimension through an object, as opposed to length or width. Check FAQs

t = \frac{σ}{E \cdot α \cdot Δt \cdot \frac{D 2 - h 1}{\ln (\frac{D 2}{h 1})}}

t - Section Thickness?σ - Thermal Stress?E - Young's Modulus?α - Coefficient of Linear Thermal Expansion?Δt - Change in Temperature?D₂ - Depth of Point 2?h ₁ - Depth of Point 1?

Thickness of Tapered Bar using Temperature Stress Example

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Here is how the Thickness of Tapered Bar using Temperature Stress equation looks like with Values.

Here is how the Thickness of Tapered Bar using Temperature Stress equation looks like with Units.

Here is how the Thickness of Tapered Bar using Temperature Stress equation looks like.

0.0065 = \frac{20}{20000 \cdot 0.001 \cdot 12.5 \cdot \frac{15 - 10}{\ln (\frac{15}{10})}}

0.0065m = \frac{20MPa}{20000MPa \cdot 0.001°C⁻¹ \cdot 12.5°C \cdot \frac{15m - 10m}{\ln (\frac{15m}{10m})}}

0.0065 = \frac{20}{20000 \cdot 0.001 \cdot 12.5 \cdot \frac{15 - 10}{\ln (\frac{15}{10})}}

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Thickness of Tapered Bar using Temperature Stress Solution

Follow our step by step solution on how to calculate Thickness of Tapered Bar using Temperature Stress?

FIRST Step Consider the formula

t = \frac{σ}{E \cdot α \cdot Δt \cdot \frac{D 2 - h 1}{\ln (\frac{D 2}{h 1})}}

Next Step Substitute values of Variables

∴

t = \frac{20MPa}{20000MPa \cdot 0.001°C⁻¹ \cdot 12.5°C \cdot \frac{15m - 10m}{\ln (\frac{15m}{10m})}}

Next Step Convert Units

∴

t = \frac{2E+7Pa}{2E+10Pa \cdot 0.0011/K \cdot 12.5K \cdot \frac{15m - 10m}{\ln (\frac{15m}{10m})}}

Next Step Prepare to Evaluate

∴

t = \frac{2E+7}{2E+10 \cdot 0.001 \cdot 12.5 \cdot \frac{15 - 10}{\ln (\frac{15}{10})}}

Next Step Evaluate

∴

t = 0.00648744172973063m

LAST Step Rounding Answer

∴

t = 0.0065m

Thickness of Tapered Bar using Temperature Stress Formula Elements

Variables

Functions

Section Thickness

Section Thickness is the dimension through an object, as opposed to length or width.

Symbol: t

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Section Thickness

Thermal Stress

Thermal Stress is the stress produced by any change in the temperature of the material.

Symbol: σ

Measurement: StressUnit: MPa

Note: Value can be positive or negative.

Formulas to find Thermal Stress

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

Coefficient of Linear Thermal Expansion

The Coefficient of Linear Thermal Expansion is a material property that characterizes the ability of a plastic to expand under the effect of temperature elevation.

Symbol: α

Measurement: Temperature Coefficient of ResistanceUnit: °C⁻¹

Note: Value can be positive or negative.

Formulas to find Coefficient of Linear Thermal Expansion

Change in Temperature

Change in temperature is the change in final and intial temperatures.

Symbol: Δt

Measurement: Temperature DifferenceUnit: °C

Note: Value can be positive or negative.

Formulas to find Change in Temperature

Depth of Point 2

Depth of Point 2 is the depth of point below the free surface in a static mass of liquid.

Symbol: D₂

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Depth of Point 2

Depth of Point 1

Depth of Point 1 is the depth of point below the free surface in a static mass of liquid.

Symbol: h ₁

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Depth of Point 1

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 Temperature Stresses and Strains category

Go Temperature Strain

ε = (\frac{D wheel - d tyre}{d tyre})

Go Change in Temperature using Temperature Stress for Tapering Rod

Δt = \frac{σ}{t \cdot E \cdot α \cdot \frac{D 2 - h 1}{\ln (\frac{D 2}{h 1})}}

How to Evaluate Thickness of Tapered Bar using Temperature Stress?

Thickness of Tapered Bar using Temperature Stress evaluator uses Section Thickness = Thermal Stress/(Young's Modulus*Coefficient of Linear Thermal Expansion*Change in Temperature*(Depth of Point 2-Depth of Point 1)/(ln(Depth of Point 2/Depth of Point 1))) to evaluate the Section Thickness, The Thickness of Tapered Bar using Temperature Stress is defined as constant for stress acting on the section. Section Thickness is denoted by t symbol.

How to evaluate Thickness of Tapered Bar using Temperature Stress using this online evaluator? To use this online evaluator for Thickness of Tapered Bar using Temperature Stress, enter Thermal Stress (σ), Young's Modulus (E), Coefficient of Linear Thermal Expansion (α), Change in Temperature (Δt), Depth of Point 2 (D₂) & Depth of Point 1 (h ₁) and hit the calculate button.

FAQs on Thickness of Tapered Bar using Temperature Stress

What is the formula to find Thickness of Tapered Bar using Temperature Stress?

The formula of Thickness of Tapered Bar using Temperature Stress is expressed as Section Thickness = Thermal Stress/(Young's Modulus*Coefficient of Linear Thermal Expansion*Change in Temperature*(Depth of Point 2-Depth of Point 1)/(ln(Depth of Point 2/Depth of Point 1))). Here is an example- 0.006487 = 20000000/(20000000000*0.001*12.5*(15-10)/(ln(15/10))).

How to calculate Thickness of Tapered Bar using Temperature Stress?

With Thermal Stress (σ), Young's Modulus (E), Coefficient of Linear Thermal Expansion (α), Change in Temperature (Δt), Depth of Point 2 (D₂) & Depth of Point 1 (h ₁) we can find Thickness of Tapered Bar using Temperature Stress using the formula - Section Thickness = Thermal Stress/(Young's Modulus*Coefficient of Linear Thermal Expansion*Change in Temperature*(Depth of Point 2-Depth of Point 1)/(ln(Depth of Point 2/Depth of Point 1))). This formula also uses Natural Logarithm (ln) function(s).

Can the Thickness of Tapered Bar using Temperature Stress be negative?

Yes, the Thickness of Tapered Bar using Temperature Stress, measured in Length can be negative.

Which unit is used to measure Thickness of Tapered Bar using Temperature Stress?

Thickness of Tapered Bar using Temperature Stress is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Thickness of Tapered Bar using Temperature Stress can be measured.

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Thickness of Tapered Bar using Temperature Stress Formula

Thickness of Tapered Bar using Temperature Stress Example

Thickness of Tapered Bar using Temperature Stress Solution

Thickness of Tapered Bar using Temperature Stress Formula Elements

Other formulas in Temperature Stresses and Strains category

How to Evaluate Thickness of Tapered Bar using Temperature Stress?

FAQs on Thickness of Tapered Bar using Temperature Stress

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