Hi Ricardo,
For lifting analysis, you should use Non-linear cable analysis. Also you have used ground supports for frame which I removed as while lifting the only support should be the crane hook point. I have used the member truss command for the angle sections to simulate their pinned end connections. Please find attached the modified model. You can now match your hand calculations with considering the self weight of the structure.
regards,
Madhan(Please visit the site to view this file)