✖The Coefficient of Linear Expansion is a material property that measures the rate of change of the material's linear dimensions in response to a change in temperature.ⓘ Coefficient of Linear Expansion [α_L]			+10% -10%
✖Change in Temperature is the difference between the final and initial temperature.ⓘ Change in Temperature [ΔT]			+10% -10%
✖Length of Bar typically refers to the physical measurement of the bar along its longest dimension.ⓘ Length of Bar [L_bar]			+10% -10%
✖Yield Amount (Length) is the amount of plastic deformation that the material has undergone when under stress.ⓘ Yield Amount (Length) [δ]			+10% -10%
✖Modulus of Elasticity of Bar is a quantity that measures bar's resistance to being deformed elastically when a stress is applied to it.ⓘ Modulus of Elasticity of Bar [E_bar]			+10% -10%

✖Actual Stress with Support Yield is the stress experienced by a material when there is some yielding or deformation in the supports holding the material.ⓘ Actual Stress when Support Yields [σ_a']

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Formula

✖

Actual Stress when Support Yields

Formula

`"σ"_{"a'"} = (("α"_{"L"}*"ΔT"*"L"_{"bar"}-"δ")*"E"_{"bar"})/"L"_{"bar"}`

Example

`"0.63MPa"=(("0.0005K⁻¹"*"10K"*"2000mm"-"4mm")*"210MPa")/"2000mm"`

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Actual Stress when Support Yields Solution

STEP 0: Pre-Calculation Summary

Formula Used

Actual Stress with Support Yield = ((Coefficient of Linear Expansion*Change in Temperature*Length of Bar-Yield Amount (Length))*Modulus of Elasticity of Bar)/Length of Bar
σ_a' = ((α_L*ΔT*L_bar-δ)*E_bar)/L_bar
This formula uses 6 Variables

Variables Used

Actual Stress with Support Yield - (Measured in Pascal) - Actual Stress with Support Yield is the stress experienced by a material when there is some yielding or deformation in the supports holding the material.
Coefficient of Linear Expansion - (Measured in Per Kelvin) - The Coefficient of Linear Expansion is a material property that measures the rate of change of the material's linear dimensions in response to a change in temperature.
Change in Temperature - (Measured in Kelvin) - Change in Temperature is the difference between the final and initial temperature.
Length of Bar - (Measured in Meter) - Length of Bar typically refers to the physical measurement of the bar along its longest dimension.
Yield Amount (Length) - (Measured in Meter) - Yield Amount (Length) is the amount of plastic deformation that the material has undergone when under stress.
Modulus of Elasticity of Bar - (Measured in Pascal) - Modulus of Elasticity of Bar is a quantity that measures bar's resistance to being deformed elastically when a stress is applied to it.

STEP 1: Convert Input(s) to Base Unit

Coefficient of Linear Expansion: 0.0005 Per Kelvin --> 0.0005 Per Kelvin No Conversion Required
Change in Temperature: 10 Kelvin --> 10 Kelvin No Conversion Required
Length of Bar: 2000 Millimeter --> 2 Meter (Check conversion here)
Yield Amount (Length): 4 Millimeter --> 0.004 Meter (Check conversion here)
Modulus of Elasticity of Bar: 210 Megapascal --> 210000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_a' = ((α_L*ΔT*L_bar-δ)*E_bar)/L_bar --> ((0.0005*10*2-0.004)*210000000)/2

Evaluating ... ...

σ_a' = 630000

STEP 3: Convert Result to Output's Unit

630000 Pascal -->0.63 Megapascal (Check conversion here)

FINAL ANSWER

0.63 Megapascal <-- Actual Stress with Support Yield

(Calculation completed in 00.004 seconds)

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< 11 Thermal Stress Calculators

Actual Stress when Support Yields

Go Actual Stress with Support Yield = ((Coefficient of Linear Expansion*Change in Temperature*Length of Bar-Yield Amount (Length))*Modulus of Elasticity of Bar)/Length of Bar

Actual Strain when Support Yields

Go Actual Strain = (Coefficient of Linear Expansion*Change in Temperature*Length of Bar-Yield Amount (Length))/Length of Bar

Actual Expansion when Support Yields

Go Actual Expansion = Coefficient of Linear Expansion*Length of Bar*Change in Temperature-Yield Amount (Length)

Thermal Stress given Coefficient of Linear Expansion

Go Thermal Stress given Coef. of Linear Expansion = Coefficient of Linear Expansion*Temperature Rise*Young's Modulus Bar

Extension of Rod if Rod is Free to Extend

Go Increase in Bar Length = Initial Length*Coefficient of Thermal Expansion*Temperature Rise

Thermal Strain given Coefficient of Linear Expansion

Go Thermal Strain given Coef. of Linear Expansion = Coefficient of Linear Expansion*Temperature Rise

Actual Stress given Support Yields for Value of Actual Strain

Go Actual Stress with Support Yield = Actual Strain*Modulus of Elasticity of Bar

Thermal Strain given Thermal Stress

Go Thermal Strain given Thermal Stress = Thermal Stress/Young's Modulus Bar

Thermal Stress given Thermal Strain

Go Thermal Stress given Thermal Strain = Thermal Strain*Young's Modulus Bar

Thermal Strain

Go Thermal Strain = Prevented Extension/Initial Length

Actual Strain given Support Yields for Value of Actual Expansion

Go Actual Strain = Actual Expansion/Length of Bar

< 4 Actual Stress and Strain Calculators

Actual Stress when Support Yields

Go Actual Stress with Support Yield = ((Coefficient of Linear Expansion*Change in Temperature*Length of Bar-Yield Amount (Length))*Modulus of Elasticity of Bar)/Length of Bar

Actual Strain when Support Yields

Go Actual Strain = (Coefficient of Linear Expansion*Change in Temperature*Length of Bar-Yield Amount (Length))/Length of Bar

Actual Stress given Support Yields for Value of Actual Strain

Go Actual Stress with Support Yield = Actual Strain*Modulus of Elasticity of Bar

Actual Strain given Support Yields for Value of Actual Expansion

Go Actual Strain = Actual Expansion/Length of Bar

Actual Stress when Support Yields Formula

What is coefficient of linear expansion?

The coefficient of linear expansion can be defined as the increase in length per unit length when the temperature is raised by 1°C.

How to Calculate Actual Stress when Support Yields?

Actual Stress when Support Yields calculator uses Actual Stress with Support Yield = ((Coefficient of Linear Expansion*Change in Temperature*Length of Bar-Yield Amount (Length))*Modulus of Elasticity of Bar)/Length of Bar to calculate the Actual Stress with Support Yield, The Actual Stress when Support Yields formula is defined as the stress experienced by a material when the support holding the material gives way or deforms. In structural analysis and strength of materials, this stress is significant because it represents the point at which the support no longer provides adequate resistance to the applied load, leading to additional deformation or potential failure of the structure or component. Actual Stress with Support Yield is denoted by σ_a' symbol.

How to calculate Actual Stress when Support Yields using this online calculator? To use this online calculator for Actual Stress when Support Yields, enter Coefficient of Linear Expansion (α_L), Change in Temperature (ΔT), Length of Bar (L_bar), Yield Amount (Length) (δ) & Modulus of Elasticity of Bar (E_bar) and hit the calculate button. Here is how the Actual Stress when Support Yields calculation can be explained with given input values -> 6.3E-7 = ((0.0005*10*2-0.004)*210000000)/2.

FAQ

What is Actual Stress when Support Yields?

The Actual Stress when Support Yields formula is defined as the stress experienced by a material when the support holding the material gives way or deforms. In structural analysis and strength of materials, this stress is significant because it represents the point at which the support no longer provides adequate resistance to the applied load, leading to additional deformation or potential failure of the structure or component and is represented as σ_a' = ((α_L*ΔT*L_bar-δ)*E_bar)/L_bar or Actual Stress with Support Yield = ((Coefficient of Linear Expansion*Change in Temperature*Length of Bar-Yield Amount (Length))*Modulus of Elasticity of Bar)/Length of Bar. The Coefficient of Linear Expansion is a material property that measures the rate of change of the material's linear dimensions in response to a change in temperature, Change in Temperature is the difference between the final and initial temperature, Length of Bar typically refers to the physical measurement of the bar along its longest dimension, Yield Amount (Length) is the amount of plastic deformation that the material has undergone when under stress & Modulus of Elasticity of Bar is a quantity that measures bar's resistance to being deformed elastically when a stress is applied to it.

How to calculate Actual Stress when Support Yields?

The Actual Stress when Support Yields formula is defined as the stress experienced by a material when the support holding the material gives way or deforms. In structural analysis and strength of materials, this stress is significant because it represents the point at which the support no longer provides adequate resistance to the applied load, leading to additional deformation or potential failure of the structure or component is calculated using Actual Stress with Support Yield = ((Coefficient of Linear Expansion*Change in Temperature*Length of Bar-Yield Amount (Length))*Modulus of Elasticity of Bar)/Length of Bar. To calculate Actual Stress when Support Yields, you need Coefficient of Linear Expansion (α_L), Change in Temperature (ΔT), Length of Bar (L_bar), Yield Amount (Length) (δ) & Modulus of Elasticity of Bar (E_bar). With our tool, you need to enter the respective value for Coefficient of Linear Expansion, Change in Temperature, Length of Bar, Yield Amount (Length) & Modulus of Elasticity of Bar 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 Actual Stress with Support Yield?

In this formula, Actual Stress with Support Yield uses Coefficient of Linear Expansion, Change in Temperature, Length of Bar, Yield Amount (Length) & Modulus of Elasticity of Bar. We can use 2 other way(s) to calculate the same, which is/are as follows -

Actual Stress with Support Yield = Actual Strain*Modulus of Elasticity of Bar
Actual Stress with Support Yield = Actual Strain*Modulus of Elasticity of Bar

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