Why we are getting opposite sign bending moments in the external and the internal longitudinal members due to Heating?

Answer:
Let me explain with the 'Heating' load case. 
I removed all the transverse members connected to the main girders and after running the analysis the moments are almost zero for all four girders as expected.

And the center of all girders are moving upward as shown below.

If you check the rotations about the global Y axis (RY), we can see that the rotations are larger in the external girder than the internal girder. In the grillage model, the main girders are connected to the transverse members. Thus, the difference of rotations between the internal girder and external girder is restrained by each other. Therefore, the rotations of the external girder are decreased, which leads to sagging moments. The rotations of the internal girder are increased, which leads to hogging moments.
Creation date: 8/15/2018 8:47 PM      Updated: 5/16/2023 3:05 PM
Files   
DataImage70.jpeg
23 KB
DataImage90.jpeg
75 KB
DataImage45.jpeg
52 KB
DataImage43.png
22 KB
DataImage71.png
16 KB
Stage_2 - GAST3 LC 28 Cooling.pdf
83 KB
Stage_2 - GAST3 LC 27 Heating.pdf
83 KB
Stage_2 - GAST3.mcb
2 MB