Question
Why is the sign of Zg negative in the calculation of the critical moment Mcr for beams, even when [TOP] is selected for the point of load application?
Please find the clause of Eurocode
And member design report showing Zg as negative.
Answer
The sign of Zg is determined by three factors:
- The direction of the bending moment
- The location of the compressive flange (whether it’s at the top or bottom of the section)
- The point where the load is applied
The software calculates the bending moment of the member, which indicates the direction of the load and the location of the compression flange. This, combined with the load application point, determines the sign of Zg.
According to Eurocode, the following applies:
"zg = (za - zs), where za and zs are the coordinates of the point of load application and the shear center, relative to the centroid of the cross-section. These quantities are positive if located in the compressed part and negative if located in the tension part."
Therefore, the software determines whether the coordinates of the load application point (za) and shear center (zs) are positive or negative, based on whether they are located in the compression or tension parts of the section.