Hi Mustafa,
I'm sorry for not being able to give you detailed reply faster but my knowledge of ACI is limited and I needed to reach out for assistance 
1. My understanding is that you imported simple load cases but you used manually defined combinations in your hand calculations

2. My understanding is that you defined your own combination 1.0D + 0.5LL and you assumed is as long term (ACI: dead + sustained live load)

In Robot this is not possible to assign which combination is of which type.
3. In RSA sustained load is defined by its ratio to the entire load and it is only possible in the stand alone mode of RC Beam design. If imported from a model all live loads are treated as long term.

4. There is difference in the formulas for fr between RSA and your hand calculations


5. RSA calculates Ie from the middle of the beam rather than as the cleavage value which as far as I can read is 'considered satisfactory'.

6. For calculating cracked deflection Robot uses linear scaling u*E’I’/EI where E’I’ is the stiffness calculated with ACI formulas whwrwas you replaced EI with this value in the model and calculated the deflection running its static analysis. This may be difficult to be done for a large models and poses a question shall the change be done for the actually designed beam of all elements of a structure?
I hope this helps.
If you find your post answered press the Accept as Solution button please. This will help other users to find solutions much faster. Thank you.
P.S. I'll be travelling for the next 3 weeks so I have to postpone the analysis of your DAM topic till I'm back 

Artur Kosakowski