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Modulus of Elasticity given Temperature Stress for Tapering Rod Section Formula

GoModulus of Elasticity using Hoop Stress due to Temperature Fall Formula

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

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

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

Modulus of Elasticity given Temperature Stress for Tapering Rod Section Example

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Here is how the Modulus of Elasticity given Temperature Stress for Tapering Rod Section equation looks like with Values.

Here is how the Modulus of Elasticity given Temperature Stress for Tapering Rod Section equation looks like with Units.

Here is how the Modulus of Elasticity given Temperature Stress for Tapering Rod Section equation looks like.

21624.8058 = \frac{20}{0.006 \cdot 0.001 \cdot 12.5 \cdot \frac{15 - 10}{\ln (\frac{15}{10})}}

21624.8058MPa = \frac{20MPa}{0.006m \cdot 0.001°C⁻¹ \cdot 12.5°C \cdot \frac{15m - 10m}{\ln (\frac{15m}{10m})}}

21624.8058 = \frac{20}{0.006 \cdot 0.001 \cdot 12.5 \cdot \frac{15 - 10}{\ln (\frac{15}{10})}}

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Modulus of Elasticity given Temperature Stress for Tapering Rod Section Solution

Follow our step by step solution on how to calculate Modulus of Elasticity given Temperature Stress for Tapering Rod Section?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

E = \frac{20MPa}{0.006m \cdot 0.001°C⁻¹ \cdot 12.5°C \cdot \frac{15m - 10m}{\ln (\frac{15m}{10m})}}

Next Step Convert Units

∴

E = \frac{2E+7Pa}{0.006m \cdot 0.0011/K \cdot 12.5K \cdot \frac{15m - 10m}{\ln (\frac{15m}{10m})}}

Next Step Prepare to Evaluate

∴

E = \frac{2E+7}{0.006 \cdot 0.001 \cdot 12.5 \cdot \frac{15 - 10}{\ln (\frac{15}{10})}}

Next Step Evaluate

∴

E = 21624805765.7688Pa

Next Step Convert to Output's Unit

∴

E = 21624.8057657688MPa

LAST Step Rounding Answer

∴

E = 21624.8058MPa

Modulus of Elasticity given Temperature Stress for Tapering Rod Section Formula Elements

Variables

Functions

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

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

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

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 to find Young's Modulus

Go Modulus of Elasticity using Hoop Stress due to Temperature Fall

E = \frac{σ h \cdot d tyre}{D wheel - d tyre}

Other formulas in Temperature Stresses and Strains category

Go Temperature Strain

ε = (\frac{D wheel - d tyre}{d tyre})

Go Thickness of Tapered Bar using Temperature Stress

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

How to Evaluate Modulus of Elasticity given Temperature Stress for Tapering Rod Section?

Modulus of Elasticity given Temperature Stress for Tapering Rod Section evaluator uses Young's Modulus = Thermal Stress/(Section Thickness*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 Young's Modulus, Modulus of Elasticity given Temperature Stress for Tapering Rod Section is defined as ratio of stress to strain in bar. Young's Modulus is denoted by E symbol.

How to evaluate Modulus of Elasticity given Temperature Stress for Tapering Rod Section using this online evaluator? To use this online evaluator for Modulus of Elasticity given Temperature Stress for Tapering Rod Section, enter Thermal Stress (σ), Section Thickness (t), 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 Modulus of Elasticity given Temperature Stress for Tapering Rod Section

What is the formula to find Modulus of Elasticity given Temperature Stress for Tapering Rod Section?

The formula of Modulus of Elasticity given Temperature Stress for Tapering Rod Section is expressed as Young's Modulus = Thermal Stress/(Section Thickness*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- 0.021625 = 20000000/(0.006*0.001*12.5*(15-10)/(ln(15/10))).

How to calculate Modulus of Elasticity given Temperature Stress for Tapering Rod Section?

With Thermal Stress (σ), Section Thickness (t), Coefficient of Linear Thermal Expansion (α), Change in Temperature (Δt), Depth of Point 2 (D₂) & Depth of Point 1 (h ₁) we can find Modulus of Elasticity given Temperature Stress for Tapering Rod Section using the formula - Young's Modulus = Thermal Stress/(Section Thickness*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).

What are the other ways to Calculate Young's Modulus?

Here are the different ways to Calculate Young's Modulus-

Young's Modulus=(Hoop Stress SOM*Diameter of Tyre)/(Wheel Diameter-Diameter of Tyre)

Can the Modulus of Elasticity given Temperature Stress for Tapering Rod Section be negative?

Yes, the Modulus of Elasticity given Temperature Stress for Tapering Rod Section, measured in Stress can be negative.

Which unit is used to measure Modulus of Elasticity given Temperature Stress for Tapering Rod Section?

Modulus of Elasticity given Temperature Stress for Tapering Rod Section is usually measured using the Megapascal[MPa] for Stress. Pascal[MPa], Newton per Square Meter[MPa], Newton per Square Millimeter[MPa] are the few other units in which Modulus of Elasticity given Temperature Stress for Tapering Rod Section can be measured.

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Modulus of Elasticity given Temperature Stress for Tapering Rod Section Formula

​GoModulus of Elasticity using Hoop Stress due to Temperature Fall Formula

Modulus of Elasticity given Temperature Stress for Tapering Rod Section Example

Modulus of Elasticity given Temperature Stress for Tapering Rod Section Solution

Modulus of Elasticity given Temperature Stress for Tapering Rod Section Formula Elements

Other Formulas to find Young's Modulus

Other formulas in Temperature Stresses and Strains category

How to Evaluate Modulus of Elasticity given Temperature Stress for Tapering Rod Section?

FAQs on Modulus of Elasticity given Temperature Stress for Tapering Rod Section

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GoModulus of Elasticity using Hoop Stress due to Temperature Fall Formula