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 00.004 seconds)

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National Institute of Technology Karnataka (NITK), Surathkal
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Temperature Stresses and Strains Calculators

Change in Temperature using Temperature Stress for Tapering Rod
​ LaTeX ​ 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
​ LaTeX ​ 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
​ LaTeX ​ 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))
Temperature Strain
​ LaTeX ​ Go Strain = ((Wheel Diameter-Diameter of Tyre)/Diameter of Tyre)

Modulus of Elasticity given Temperature Stress for Tapering Rod Section Formula

​LaTeX ​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)))
E = σ/(t*α*Δt*(D2-h 1)/(ln(D2/h 1)))

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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