Green's Theorem Part 2: Calculating Normal Stress for Asymmetric Cross-Sections

January 11, 2024

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2. Normal stress for Asymmetric section

   We have discussed the process of calculating cross-sectional properties using "Green's theorem."

   So what are some useful ways to apply this knowledge?


Figure 8. An Image from Sample Calculation Sheet (Green’s theorem)

Figure 8. An Image from Sample Calculation Sheet (Green’s theorem)


   Sure. It is the calculation of normal stress for an asymmetric cross-section.


(1) Vertical Stress of an Asymmetric Cross Section

   Let's express the symmetric cross-section that we commonly refer to with a number. The fact is that the bending moment at the neutral axis of such a cross-section is zero (0). If only one of the two axes is symmetric, the bending moment at the neutral axis will still be zero (0).


Calculation 0.

   Does this mean that all asymmetric cross-sections have non-zero bending moments at the neutral axis? Not necessarily. We can still find an axis where the bending moment is zero (0) in asymmetric cross-sections (refer to Mohr's circle).

For the cross-sections where the bending moment at the neutral axis is not zero (0), the mechanics of materials textbook explains the vertical stress as follows."


Figure 9. Asymmetric section

Figure 9. Asymmetric section


Calculation 1-1.Calculation 1-2.


Let's convert the formulas according to our needs to calculate the stress.
- Coordinate axis change for using the sectional force of MIDAS Civil
- Consideration of stress for axial force
   Let's verify the converted formulas through example calculations.


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You can check more of these details in the download file.


(2) Example

(3) Conclusion

Sources and References

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About the Author
Jay.J | Structural Engineer | MIDAS IT HQ

I executed bridge (rail, road) projects over ten years as a structural engineer. I mainly did overseas projects in Kuwait, Indonesia, Malaysia, the Philippines, the U.K., etc. You know what? I've never been to the places on a business trip, even after completing construction. I have experienced national design-build projects twice and have done almost every shape of bridge project except wire bridges.

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