In cases where STAAD does not have a code that you want to design your structure with, you can use STAAD for the analysis part. Analysis is the process for obtaining results such as joint displacements, member forces, plate and solid element stresses, support reactions, etc. Example problem 10 in Help-Contents-APplication Examples shows a method for analysing these structures. The various loading conditions you mention can be simulated through positive/negative pressure loads (trapezoidal & uniform) on the appropriate elements.
You can then take those results and perform the design to your desired code either through hand calculations or through an OpenSTAAD Macro that you will have to create. The macro can be constructed to automatically fetch the results from the STAAD analysis.