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)
Sure. It is the calculation of normal stress for 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).
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
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.