Negative Moment

Not sure what your program is doing, but if the beam to column connections are rigid, that is a primary determinative of the negative moments in the beams.

OP says "STAAD Pro" (which doesn't impress me much !?).

would the loading (not shown) have an impact ?

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

Loading must be considered to determine the magnitude and direction of all moments.

To understand it better, read about the Moment Distribution method of analysis in which each member has a Fixed End Moment as a result of the loads, then joints are released, one at a time and moments are distributed according to each member's stiffness. There is a carry over factor between nodes, which requires additional cycles of moment distribution which terminate when the moment becomes small enough to ignore.

Also, sizes of members will also play into any answers. But Hokie pretty well nailed it. If the beam to column connection is detailed as rigid, then it will create negative moments at the supports. Whether that is correct or not depends on your detailing of that connection.

The relative size of the column and beam also will play into how much moment you can adequately transfer through that joint.

Some numbers might help. But I don't know why one would be surprised by high negative moments in a framing plan like that.