Goodman Line Mean Stress Solution

STEP 0: Pre-Calculation Summary
Formula Used
Mean Stress for Fluctuating Load = Ultimate Tensile strength*(1-Stress Amplitude for Fluctuating Load/Endurance Limit)
σm = σut*(1-σa/Se)
This formula uses 4 Variables
Variables Used
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.
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.
STEP 1: Convert Input(s) to Base Unit
Ultimate Tensile strength: 440 Newton per Square Millimeter --> 440000000 Pascal (Check conversion here)
Stress Amplitude for Fluctuating Load: 30 Newton per Square Millimeter --> 30000000 Pascal (Check conversion here)
Endurance Limit: 51 Newton per Square Millimeter --> 51000000 Pascal (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
σm = σut*(1-σa/Se) --> 440000000*(1-30000000/51000000)
Evaluating ... ...
σm = 181176470.588235
STEP 3: Convert Result to Output's Unit
181176470.588235 Pascal -->181.176470588235 Newton per Square Millimeter (Check conversion here)
FINAL ANSWER
181.176470588235 181.1765 Newton per Square Millimeter <-- Mean Stress for Fluctuating Load
(Calculation completed in 00.004 seconds)

Credits

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 Mean Stress Formula

Mean Stress for Fluctuating Load = Ultimate Tensile strength*(1-Stress Amplitude for Fluctuating Load/Endurance Limit)
σm = σut*(1-σa/Se)

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 Mean Stress?

Goodman Line Mean Stress calculator uses Mean Stress for Fluctuating Load = Ultimate Tensile strength*(1-Stress Amplitude for Fluctuating Load/Endurance Limit) to calculate the Mean Stress for Fluctuating Load, Goodman Line Mean Stress is defined as the amount of mean stress acting on a material when the material is subjected to fluctuating stress or under fatigue loading and this value is obtained using Goodman line diagram. Mean Stress for Fluctuating Load is denoted by σm symbol.

How to calculate Goodman Line Mean Stress using this online calculator? To use this online calculator for Goodman Line Mean Stress, enter Ultimate Tensile strength ut), Stress Amplitude for Fluctuating Load a) & Endurance Limit (Se) and hit the calculate button. Here is how the Goodman Line Mean Stress calculation can be explained with given input values -> 0.000181 = 440000000*(1-30000000/51000000).

FAQ

What is Goodman Line Mean Stress?
Goodman Line Mean Stress is defined as the amount of mean stress acting on a material when the material is subjected to fluctuating stress or under fatigue loading and this value is obtained using Goodman line diagram and is represented as σm = σut*(1-σa/Se) or Mean Stress for Fluctuating Load = Ultimate Tensile strength*(1-Stress Amplitude for Fluctuating Load/Endurance Limit). Ultimate Tensile Strength (UTS) is the maximum stress that a material can withstand while being stretched or pulled, 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 & 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.
How to calculate Goodman Line Mean Stress?
Goodman Line Mean Stress is defined as the amount of mean stress acting on a material when the material is subjected to fluctuating stress or under fatigue loading and this value is obtained using Goodman line diagram is calculated using Mean Stress for Fluctuating Load = Ultimate Tensile strength*(1-Stress Amplitude for Fluctuating Load/Endurance Limit). To calculate Goodman Line Mean Stress, you need Ultimate Tensile strength ut), Stress Amplitude for Fluctuating Load a) & Endurance Limit (Se). With our tool, you need to enter the respective value for Ultimate Tensile strength, Stress Amplitude for Fluctuating Load & Endurance Limit 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 Mean Stress for Fluctuating Load?
In this formula, Mean Stress for Fluctuating Load uses Ultimate Tensile strength, Stress Amplitude for Fluctuating Load & Endurance Limit. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Mean Stress for Fluctuating Load = Tensile Yield Strength for Fluctuating load*(1-Stress Amplitude for Fluctuating Load/Endurance Limit)
  • Mean Stress for Fluctuating Load = Limiting Value of Mean Stress/Design Factor of Safety
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