Modulus of Elasticity given Temperature Stress for Tapering Rod Section Calculator

✖Thermal Stress is the stress produced by any change in the temperature of the material.ⓘ Thermal Stress [σ]			+10% -10%
✖Section Thickness is the dimension through an object, as opposed to length or width.ⓘ Section Thickness [t]			+10% -10%
✖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.ⓘ Coefficient of Linear Thermal Expansion [α]			+10% -10%
✖Change in temperature is the change in final and intial temperatures.ⓘ Change in Temperature [Δt]			+10% -10%
✖Depth of Point 2 is the depth of point below the free surface in a static mass of liquid.ⓘ Depth of Point 2 [D₂]			+10% -10%
✖Depth of Point 1 is the depth of point below the free surface in a static mass of liquid.ⓘ Depth of Point 1 [h ₁]			+10% -10%

✖Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.ⓘ Modulus of Elasticity given Temperature Stress for Tapering Rod Section [E]

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Formula

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Modulus of Elasticity given Temperature Stress for Tapering Rod Section

Formula

`"E" = "σ"/("t"*"α"*"Δt"*("D"_{"2"}-"h "_{"1"})/(ln("D"_{"2"}/"h "_{"1"})))`

Example

`"21624.81MPa"="20MPa"/("0.006m"*"0.001°C⁻¹"*"12.5°C"*("15m"-"10m")/(ln("15m"/"10m")))`

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Modulus of Elasticity given Temperature Stress for Tapering Rod Section Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
E = σ/(t*α*Δt*(D₂-h ₁)/(ln(D₂/h ₁)))
This formula uses 1 Functions, 7 Variables

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

Young's Modulus - (Measured in Pascal) - Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.
Thermal Stress - (Measured in Pascal) - Thermal Stress is the stress produced by any change in the temperature of the material.
Section Thickness - (Measured in Meter) - Section Thickness is the dimension through an object, as opposed to length or width.
Coefficient of Linear Thermal Expansion - (Measured in Per Kelvin) - 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.
Change in Temperature - (Measured in Kelvin) - Change in temperature is the change in final and intial temperatures.
Depth of Point 2 - (Measured in Meter) - Depth of Point 2 is the depth of point below the free surface in a static mass of liquid.
Depth of Point 1 - (Measured in Meter) - Depth of Point 1 is the depth of point below the free surface in a static mass of liquid.

STEP 1: Convert Input(s) to Base Unit

Thermal Stress: 20 Megapascal --> 20000000 Pascal (Check conversion here)
Section Thickness: 0.006 Meter --> 0.006 Meter No Conversion Required
Coefficient of Linear Thermal Expansion: 0.001 Per Degree Celsius --> 0.001 Per Kelvin (Check conversion here)
Change in Temperature: 12.5 Degree Celsius --> 12.5 Kelvin (Check conversion here)
Depth of Point 2: 15 Meter --> 15 Meter No Conversion Required
Depth of Point 1: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E = σ/(t*α*Δt*(D₂-h ₁)/(ln(D₂/h ₁))) --> 20000000/(0.006*0.001*12.5*(15-10)/(ln(15/10)))

Evaluating ... ...

E = 21624805765.7688

STEP 3: Convert Result to Output's Unit

21624805765.7688 Pascal -->21624.8057657688 Megapascal (Check conversion here)

FINAL ANSWER

21624.8057657688 ≈ 21624.81 Megapascal <-- Young's Modulus

(Calculation completed in 00.021 seconds)

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Home » Engineering » Civil » Strength of Materials » Stress and Strain » Temperature Stresses and Strains » Modulus of Elasticity given Temperature Stress for Tapering Rod Section

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< 9 Temperature Stresses and Strains Calculators

Coefficient of Thermal Expansion given Temperature Stress for Tapering Rod Section

Go Coefficient of Linear Thermal Expansion = Load Applied KN/(Section Thickness*Young's Modulus*Change in Temperature*(Depth of Point 2-Depth of Point 1)/(ln(Depth of Point 2/Depth of Point 1)))

Modulus of Elasticity given Temperature Stress for Tapering Rod Section

Go 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)))

Change in Temperature using Temperature Stress for Tapering Rod

Go Change in Temperature = Thermal Stress/(Section Thickness*Young's Modulus*Coefficient of Linear Thermal Expansion*(Depth of Point 2-Depth of Point 1)/(ln(Depth of Point 2/Depth of Point 1)))

Thickness of Tapered Bar using Temperature Stress

Go 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)))

Temperature Stress for Tapering Rod Section

Go Load Applied KN = Section Thickness*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))

Modulus of Elasticity using Hoop Stress due to Temperature Fall

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

Temperature Strain

Go Strain = ((Wheel Diameter-Diameter of Tyre)/Diameter of Tyre)

Diameter of Tyre given Temperature Strain

Go Diameter of Tyre = (Wheel Diameter/(Strain+1))

Diameter of Wheel given Temperature Strain

Go Wheel Diameter = Diameter of Tyre*(Strain+1)

Modulus of Elasticity given Temperature Stress for Tapering Rod Section Formula

What is Temperature Stresses?

Thermal stress is mechanical stress created by any change in temperature of a material. These stresses can lead to fracturing or plastic deformation depending on the other variables of heating, which include material types and constraints.

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

Modulus of Elasticity given Temperature Stress for Tapering Rod Section calculator 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 calculate 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 calculate Modulus of Elasticity given Temperature Stress for Tapering Rod Section using this online calculator? To use this online calculator 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. Here is how the Modulus of Elasticity given Temperature Stress for Tapering Rod Section calculation can be explained with given input values -> 0.021625 = 20000000/(0.006*0.001*12.5*(15-10)/(ln(15/10))).

FAQ

What is Modulus of Elasticity given Temperature Stress for Tapering Rod Section?

Modulus of Elasticity given Temperature Stress for Tapering Rod Section is defined as ratio of stress to strain in bar and is represented as E = σ/(t*α*Δt*(D₂-h ₁)/(ln(D₂/h ₁))) or 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))). Thermal Stress is the stress produced by any change in the temperature of the material, Section Thickness is the dimension through an object, as opposed to length or width, 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, Change in temperature is the change in final and intial temperatures, Depth of Point 2 is the depth of point below the free surface in a static mass of liquid & Depth of Point 1 is the depth of point below the free surface in a static mass of liquid.

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

Modulus of Elasticity given Temperature Stress for Tapering Rod Section is defined as ratio of stress to strain in bar is calculated using 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 calculate Modulus of Elasticity given Temperature Stress for Tapering Rod Section, you need 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). With our tool, you need to enter the respective value for Thermal Stress, Section Thickness, Coefficient of Linear Thermal Expansion, Change in Temperature, Depth of Point 2 & Depth of Point 1 and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Young's Modulus?

In this formula, Young's Modulus uses Thermal Stress, Section Thickness, Coefficient of Linear Thermal Expansion, Change in Temperature, Depth of Point 2 & Depth of Point 1. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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