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

✖Change in temperature is the change in final and intial temperatures.ⓘ Change in Temperature using Temperature Stress for Tapering Rod [Δt]

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Change in Temperature using Temperature Stress for Tapering Rod

Formula

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

Example

`"13.5155°C"="20MPa"/("0.006m"*"20000MPa"*"0.001°C⁻¹"*("15m"-"10m")/(ln("15m"/"10m")))`

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Change in Temperature using Temperature Stress for Tapering Rod Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
Δt = σ/(t*E*α*(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

Change in Temperature - (Measured in Kelvin) - Change in temperature is the change in final and intial temperatures.
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.
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.
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.
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
Young's Modulus: 20000 Megapascal --> 20000000000 Pascal (Check conversion here)
Coefficient of Linear Thermal Expansion: 0.001 Per Degree Celsius --> 0.001 Per 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

Δt = σ/(t*E*α*(D₂-h ₁)/(ln(D₂/h ₁))) --> 20000000/(0.006*20000000000*0.001*(15-10)/(ln(15/10)))

Evaluating ... ...

Δt = 13.5155036036055

STEP 3: Convert Result to Output's Unit

13.5155036036055 Kelvin -->13.5155036036055 Degree Celsius (Check conversion here)

FINAL ANSWER

13.5155036036055 ≈ 13.5155 Degree Celsius <-- Change in Temperature

(Calculation completed in 00.007 seconds)

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Home » Engineering » Civil » Strength of Materials » Stress and Strain » Temperature Stresses and Strains » Change in Temperature using Temperature Stress for Tapering Rod

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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Verified by M Naveen

National Institute of Technology (NIT), Warangal

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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)

Change in Temperature using Temperature Stress for Tapering Rod 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 Change in Temperature using Temperature Stress for Tapering Rod?

Change in Temperature using Temperature Stress for Tapering Rod calculator uses 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))) to calculate the Change in Temperature, Change in Temperature using Temperature Stress for Tapering Rod formula is defined as variation of temperature in bar. Change in Temperature is denoted by Δt symbol.

How to calculate Change in Temperature using Temperature Stress for Tapering Rod using this online calculator? To use this online calculator for Change in Temperature using Temperature Stress for Tapering Rod, enter Thermal Stress (σ), Section Thickness (t), Young's Modulus (E), Coefficient of Linear Thermal Expansion (α), Depth of Point 2 (D₂) & Depth of Point 1 (h ₁) and hit the calculate button. Here is how the Change in Temperature using Temperature Stress for Tapering Rod calculation can be explained with given input values -> 13.5155 = 20000000/(0.006*20000000000*0.001*(15-10)/(ln(15/10))).

FAQ

What is Change in Temperature using Temperature Stress for Tapering Rod?

Change in Temperature using Temperature Stress for Tapering Rod formula is defined as variation of temperature in bar and is represented as Δt = σ/(t*E*α*(D₂-h ₁)/(ln(D₂/h ₁))) or 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))). 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, Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain, 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, 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 Change in Temperature using Temperature Stress for Tapering Rod?

Change in Temperature using Temperature Stress for Tapering Rod formula is defined as variation of temperature in bar is calculated using 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))). To calculate Change in Temperature using Temperature Stress for Tapering Rod, you need Thermal Stress (σ), Section Thickness (t), Young's Modulus (E), Coefficient of Linear Thermal Expansion (α), 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, Young's Modulus, Coefficient of Linear Thermal Expansion, 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.

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