Abaqus will solve the problem incrementally and at each increment you should be able to extract the amplitude of the UDL and a sample displacement. You can then plot your load displacement graph.
Create a set of the area/point of your load application and load the beam with prescribed displacement. In your history output request, request the reaction force and displacement at that set in desired direction. After the simulation, these responses can be saved and combined in XY data to get Load-displacement curve.