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8. Refer to the figure below. Even though the cyclic loading accidentally caused the stresses to exceed the levels at point A slightly (as marked by the red arrow), the machine part may not break instantly according to the Modified Goodman fatigue failure criterion. True_ or False Alternating stress a S Yield (Langer) line Soderberg line! A Gerber line Sm Midrange stress om Load line, slope r = SalSm Modified Goodman line -ASME-elliptic line Sut

8. Refer to the figure below. Even though the cyclic loading accidentally caused the stresses to exceed the levels at point A slightly (as marked by the red arrow), the machine part may not break instantly according to the Modified Goodman fatigue failure criterion. True_ or False Alternating stress a S Yield (Langer) line Soderberg line! A Gerber line Sm Midrange stress om Load line, slope r = SalSm Modified Goodman line -ASME-elliptic line Sut

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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### Question 8. Refer to the figure below. Even though the cyclic loading accidentally caused the stresses to exceed the levels at point A slightly (as marked by the red arrow), the machine part may not break instantly according to the Modified Goodman fatigue failure criterion. True _____ or False _____. ### Diagram Explanation The graph is a plot of alternating stress (\( \sigma_a \)) against midrange stress (\( \sigma_m \)). **Key Elements of the Graph:** 1. **Yield (Langer) Line:** A dashed line starting from \( S_y \) on the \( \sigma_m \) axis and following a negative slope, indicating the yield strength. 2. **Gerber Line:** A curving solid line that depicts the relationship between the alternating and midrange stresses, based on Gerber's equation. 3. **Modified Goodman Line:** A straight solid line starting at \( S_e \) on the \( \sigma_a \) axis and \( S_{ut} \) on the \( \sigma_m \) axis, depicting the Modified Goodman failure criterion. 4. **ASME-elliptic Line:** Another curve similar to the Gerber line, indicating the ASME's elliptical criterion for fatigue failure. 5. **Soderberg Line:** A straight solid line from \( S_e \) on the \( \sigma_a \) axis to \( S_y \) on the \( \sigma_m \) axis. 6. **Load Line:** A line with slope \( r = S_a / S_m \). 7. **Important Points on Axes:** - \( S_e \): Endurance limit on the \( \sigma_a \) axis. - \( S_a \): Alternating stress level as dashed line. - \( S_m \): Midrange stress level. - \( S_y \): Yield strength on the \( \sigma_m \) axis. - \( S_{ut} \): Ultimate tensile strength on the \( \sigma_m \) axis. **Point A:** The red arrow indicates point A, where the stresses exceed limits slightly. The question requires evaluating whether the machine part might not fail instantly according to the Modified Goodman fatigue criterion.
Transcribed Image Text:### Question 8. Refer to the figure below. Even though the cyclic loading accidentally caused the stresses to exceed the levels at point A slightly (as marked by the red arrow), the machine part may not break instantly according to the Modified Goodman fatigue failure criterion. True _____ or False _____. ### Diagram Explanation The graph is a plot of alternating stress (\( \sigma_a \)) against midrange stress (\( \sigma_m \)). **Key Elements of the Graph:** 1. **Yield (Langer) Line:** A dashed line starting from \( S_y \) on the \( \sigma_m \) axis and following a negative slope, indicating the yield strength. 2. **Gerber Line:** A curving solid line that depicts the relationship between the alternating and midrange stresses, based on Gerber's equation. 3. **Modified Goodman Line:** A straight solid line starting at \( S_e \) on the \( \sigma_a \) axis and \( S_{ut} \) on the \( \sigma_m \) axis, depicting the Modified Goodman failure criterion. 4. **ASME-elliptic Line:** Another curve similar to the Gerber line, indicating the ASME's elliptical criterion for fatigue failure. 5. **Soderberg Line:** A straight solid line from \( S_e \) on the \( \sigma_a \) axis to \( S_y \) on the \( \sigma_m \) axis. 6. **Load Line:** A line with slope \( r = S_a / S_m \). 7. **Important Points on Axes:** - \( S_e \): Endurance limit on the \( \sigma_a \) axis. - \( S_a \): Alternating stress level as dashed line. - \( S_m \): Midrange stress level. - \( S_y \): Yield strength on the \( \sigma_m \) axis. - \( S_{ut} \): Ultimate tensile strength on the \( \sigma_m \) axis. **Point A:** The red arrow indicates point A, where the stresses exceed limits slightly. The question requires evaluating whether the machine part might not fail instantly according to the Modified Goodman fatigue criterion.
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