Goodman Line Amplitude Stress Calculator

✖The Endurance Limit of a material is defined as the stress below which a material can endure an infinite number of repeated load cycles without exhibiting failure.ⓘ Endurance Limit [S_e]			+10% -10%
✖Mean Stress for Fluctuating Load is defined as the amount of mean stress acting when a material or component is subjected to fluctuating stress.ⓘ Mean Stress for Fluctuating Load [σ_m]			+10% -10%
✖Ultimate Tensile Strength (UTS) is the maximum stress that a material can withstand while being stretched or pulled.ⓘ Ultimate Tensile strength [σ_ut]			+10% -10%

✖Stress amplitude for fluctuating load is defined as the amount of stress deviation from the mean stress and is also called the alternating component of stress in fluctuating loads.ⓘ Goodman Line Amplitude Stress [σ_a]

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Formula

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Goodman Line Amplitude Stress

Formula

`"σ"_{"a"} = "S"_{"e"}*(1-"σ"_{"m"}/"σ"_{"ut"})`

Example

`"45.20455N/mm²"="51N/mm²"*(1-"50N/mm²"/"440N/mm²")`

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Goodman Line Amplitude Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Stress Amplitude for Fluctuating Load = Endurance Limit*(1-Mean Stress for Fluctuating Load/Ultimate Tensile strength)
σ_a = S_e*(1-σ_m/σ_ut)
This formula uses 4 Variables

Variables Used

Stress Amplitude for Fluctuating Load - (Measured in Pascal) - Stress amplitude for fluctuating load is defined as the amount of stress deviation from the mean stress and is also called the alternating component of stress in fluctuating loads.
Endurance Limit - (Measured in Pascal) - The Endurance Limit of a material is defined as the stress below which a material can endure an infinite number of repeated load cycles without exhibiting failure.
Mean Stress for Fluctuating Load - (Measured in Pascal) - Mean Stress for Fluctuating Load is defined as the amount of mean stress acting when a material or component is subjected to fluctuating stress.
Ultimate Tensile strength - (Measured in Pascal) - Ultimate Tensile Strength (UTS) is the maximum stress that a material can withstand while being stretched or pulled.

STEP 1: Convert Input(s) to Base Unit

Endurance Limit: 51 Newton per Square Millimeter --> 51000000 Pascal (Check conversion here)
Mean Stress for Fluctuating Load: 50 Newton per Square Millimeter --> 50000000 Pascal (Check conversion here)
Ultimate Tensile strength: 440 Newton per Square Millimeter --> 440000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_a = S_e*(1-σ_m/σ_ut) --> 51000000*(1-50000000/440000000)

Evaluating ... ...

σ_a = 45204545.4545455

STEP 3: Convert Result to Output's Unit

45204545.4545455 Pascal -->45.2045454545455 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

45.2045454545455 ≈ 45.20455 Newton per Square Millimeter <-- Stress Amplitude for Fluctuating Load

(Calculation completed in 00.004 seconds)

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Home » Engineering » Mechanical » Machine Design » Design against Fluctuating Load » Soderberg and Goodman Lines » Goodman Line Amplitude Stress

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Created by Vaibhav Malani

National Institute of Technology (NIT), Tiruchirapalli

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Institute of Aeronautical Engineering (IARE), Hyderabad

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< 15 Soderberg and Goodman Lines Calculators

Soderberg Line Tensile Yield Strength

Go Tensile Yield Strength for Fluctuating load = Mean Stress for Fluctuating Load/(1-Stress Amplitude for Fluctuating Load/Endurance Limit)

Soderberg Line Amplitude Stress

Go Stress Amplitude for Fluctuating Load = Endurance Limit*(1-Mean Stress for Fluctuating Load/Tensile Yield Strength for Fluctuating load)

Soderberg Line Endurance Limit

Go Endurance Limit = Stress Amplitude for Fluctuating Load/(1-Mean Stress for Fluctuating Load/Tensile Yield Strength for Fluctuating load)

Soderberg Line Mean stress

Go Mean Stress for Fluctuating Load = Tensile Yield Strength for Fluctuating load*(1-Stress Amplitude for Fluctuating Load/Endurance Limit)

Goodman Line Ultimate Tensile Strength

Go Ultimate Tensile strength = Mean Stress for Fluctuating Load/(1-Stress Amplitude for Fluctuating Load/Endurance Limit)

Goodman Line Amplitude Stress

Go Stress Amplitude for Fluctuating Load = Endurance Limit*(1-Mean Stress for Fluctuating Load/Ultimate Tensile strength)

Goodman Line Endurance Limit

Go Endurance Limit = Stress Amplitude for Fluctuating Load/(1-Mean Stress for Fluctuating Load/Ultimate Tensile strength)

Goodman Line Mean Stress

Go Mean Stress for Fluctuating Load = Ultimate Tensile strength*(1-Stress Amplitude for Fluctuating Load/Endurance Limit)

Slope of Line OE in Modified Goodman Diagram given Force Amplitude and Mean Force

Go Slope of modified Goodman Line = Force Amplitude for Fluctuating Stress/Mean Force for Fluctuating Stress

Slope of Line OE in Modified Goodman Diagram given Stress Amplitude and Mean Stress

Go Slope of modified Goodman Line = Stress Amplitude for Fluctuating Load/Mean Stress for Fluctuating Load

Permissible Stress Amplitude for Fluctuating Load

Go Stress Amplitude for Fluctuating Load = Limiting Value of Stress Amplitude/Design Factor of Safety

Limiting Value of Stress Amplitude

Go Limiting Value of Stress Amplitude = Design Factor of Safety*Stress Amplitude for Fluctuating Load

Permissible Mean Stress for Fluctuating Load

Go Mean Stress for Fluctuating Load = Limiting Value of Mean Stress/Design Factor of Safety

Limiting Value of Mean Stress

Go Limiting Value of Mean Stress = Design Factor of Safety*Mean Stress for Fluctuating Load

Slope of Line OE in Modified Goodman Diagram given Bending Amplitude and Mean Bending Moment

Go Slope of modified Goodman Line = Bending Moment Amplitude/Mean Bending Moment

Goodman Line Amplitude Stress Formula

Stress Amplitude for Fluctuating Load = Endurance Limit*(1-Mean Stress for Fluctuating Load/Ultimate Tensile strength)
σ_a = S_e*(1-σ_m/σ_ut)

What is endurance limit?

The fatigue or endurance limit of a material is defined as the maximum amplitude of completely reversed stress that the standard specimen can sustain for an unlimited number of cycles without fatigue failure.

How to Calculate Goodman Line Amplitude Stress?

Goodman Line Amplitude Stress calculator uses Stress Amplitude for Fluctuating Load = Endurance Limit*(1-Mean Stress for Fluctuating Load/Ultimate Tensile strength) to calculate the Stress Amplitude for Fluctuating Load, Goodman Line Amplitude Stress is defined as the stress amplitude (the maximum or the peak value of the alternating stress) of the specimen calculated from the Goodman line diagram. Stress Amplitude for Fluctuating Load is denoted by σ_a symbol.

How to calculate Goodman Line Amplitude Stress using this online calculator? To use this online calculator for Goodman Line Amplitude Stress, enter Endurance Limit (S_e), Mean Stress for Fluctuating Load (σ_m) & Ultimate Tensile strength (σ_ut) and hit the calculate button. Here is how the Goodman Line Amplitude Stress calculation can be explained with given input values -> 4.5E-5 = 51000000*(1-50000000/440000000).

FAQ

What is Goodman Line Amplitude Stress?

Goodman Line Amplitude Stress is defined as the stress amplitude (the maximum or the peak value of the alternating stress) of the specimen calculated from the Goodman line diagram and is represented as σ_a = S_e*(1-σ_m/σ_ut) or Stress Amplitude for Fluctuating Load = Endurance Limit*(1-Mean Stress for Fluctuating Load/Ultimate Tensile strength). The Endurance Limit of a material is defined as the stress below which a material can endure an infinite number of repeated load cycles without exhibiting failure, Mean Stress for Fluctuating Load is defined as the amount of mean stress acting when a material or component is subjected to fluctuating stress & Ultimate Tensile Strength (UTS) is the maximum stress that a material can withstand while being stretched or pulled.

How to calculate Goodman Line Amplitude Stress?

Goodman Line Amplitude Stress is defined as the stress amplitude (the maximum or the peak value of the alternating stress) of the specimen calculated from the Goodman line diagram is calculated using Stress Amplitude for Fluctuating Load = Endurance Limit*(1-Mean Stress for Fluctuating Load/Ultimate Tensile strength). To calculate Goodman Line Amplitude Stress, you need Endurance Limit (S_e), Mean Stress for Fluctuating Load (σ_m) & Ultimate Tensile strength (σ_ut). With our tool, you need to enter the respective value for Endurance Limit, Mean Stress for Fluctuating Load & Ultimate Tensile strength 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 Stress Amplitude for Fluctuating Load?

In this formula, Stress Amplitude for Fluctuating Load uses Endurance Limit, Mean Stress for Fluctuating Load & Ultimate Tensile strength. We can use 2 other way(s) to calculate the same, which is/are as follows -

Stress Amplitude for Fluctuating Load = Endurance Limit*(1-Mean Stress for Fluctuating Load/Tensile Yield Strength for Fluctuating load)
Stress Amplitude for Fluctuating Load = Limiting Value of Stress Amplitude/Design Factor of Safety

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