Final answer:
The factor of safety using the modified Goodman criterion is 2. The factor of safety for the structural member under fatigue loading using the Modified Goodman criterion is calculated to be 7, considering the given material properties and stresses.
Step-by-step explanation:
The factor of safety using the modified Goodman criterion can be calculated by dividing the endurance strength of the material by the alternating stress at the critical point. The modified Goodman criterion is given by the equation:
Factor of Safety = Endurance Strength / (Maximum Stress - Minimum Stress)
In this case, the endurance strength is 200 MPa, the maximum stress is 150 MPa, and the minimum stress is 50 MPa. Plugging in these values, we get:
Factor of Safety = 200 MPa / (150 MPa - 50 MPa) = 200 MPa / 100 MPa = 2
Therefore, the factor of safety using the modified Goodman criterion is 2.
The factor of safety for the structural member under fatigue loading using the Modified Goodman criterion is calculated to be 7, considering the given material properties and stresses.
The Modified Goodman criterion is an engineering formula used to predict the safety factor of a material under fatigue loading conditions. The criterion takes into account the endurance limit, the yield strength, the minimum and maximum stress experienced by the material, and the ultimate tensile strength. The endurance strength of a material is the stress below which it would withstand an effectively infinite number of stress cycles without failure. The yield strength is the stress at which a material begins to deform plastically. Ultimate tensile strength (UTS) is the maximum stress that a material can withstand while being stretched or pulled before necking, which is when the specimen's cross-section starts to significantly contract.
The formula for the Modified Goodman criterion is:
Factor of Safety (n) = \( \frac{ Se }{ Sa } + \frac{ Sy }{ Smax - Sa } \)
Where:
\(Se\) = Endurance Limit
\(Sa\) = Alternating Stress (\(Smax - Smin\)/2)
\(Sy\) = Yield Strength
\(Smax\) = Maximum stress
For the case provided:
\(Se\) = 200 MPa
\(Smin\) = 50 MPa
\(Smax\) = 150 MPa
\(Sy\) = 300 MPa
Alternating stress (\(Sa\)) = \(\frac{150 - 50}{2}\) = 50 MPa
Substituting the values into the formula:
Factor of Safety (n) = \( \frac{200}{50} \) + \( \frac{300}{150 - 50} \) = \( \frac{200}{50} \) + \( \frac{300}{100} \) = 4 + 3 = 7
Therefore, the factor of safety using the Modified Goodman criterion is 7.