Finding maximum allowable alternating stress using goodmans relation

• mammal
In summary, the conversation is about using the Goodman method with a factor of safety of 1.5 to determine the maximum allowable alternating stress for a steel alloy with an ultimate tensile strength of 820MN/m2 and a fatigue endurance limit of 390MN/m2. The formula used is σa = σfat x (σm/σts) where σa is the alternating stress, σm is the mean stress, σfat is the fatigue endurance limit, and σts is the ultimate tensile stress. The person is having trouble rearranging the formula and is seeking help before the assignment is due on Monday.
mammal

Homework Statement

(b) A steel alloy has an ultimate tensile strength of 820MN/m2 and a fatigue endurance limit of 390MN/m2. The steel is used in a fatigue application in which the alternating stress is 0.3 times the mean stress. Using the Goodman method with a factor of safety of 1.5 applied determine the maximum allowable alternating stress that will allow safe operation

Homework Equations

σa = σfat x (σm/σts)
Where σa is the alternating stress, σm is the mean stress, σfat is the fatigue endurance limit and σts is the ultimate tensile stress.

The Attempt at a Solution

So far I have substituted σa for 0.3 x σm and tried to rearrange this formula, I have however run into problems and am doubting this is the correct method.

Any ideas? The entire assignment is due in on monday and this is all I'm having problems with.

What is Goodman's relation and how is it used in finding maximum allowable alternating stress?

Goodman's relation is a mechanical engineering concept that relates the mean stress and the alternating stress to the endurance limit of a material. It is used to determine the maximum allowable alternating stress that a material can withstand without failing due to fatigue.

Why is it important to consider alternating stress when designing a component?

Alternating stress is important to consider because it can cause fatigue failure in a component over time. By using Goodman's relation to find the maximum allowable alternating stress, engineers can design components that will have a longer lifespan and reduce the risk of failure.

What factors can affect the maximum allowable alternating stress of a material?

The maximum allowable alternating stress of a material can be affected by factors such as the material's strength, ductility, and surface finish. It can also be influenced by environmental factors such as temperature and corrosion.

How can Goodman's relation be used to compare different materials for a specific component?

Goodman's relation can be used to compare different materials for a specific component by calculating the maximum allowable alternating stress for each material and selecting the one with the highest value. This ensures that the chosen material will have the best chance of withstanding the expected alternating stress in the component.

Are there any limitations to using Goodman's relation in designing components?

Yes, there are limitations to using Goodman's relation. It assumes that the material is homogenous, isotropic, and has a constant endurance limit. It also does not take into account factors such as stress concentrations and variable loading conditions, which can affect the actual fatigue life of a component.

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