Should I take into account the weight of the support that is provided to the piping model? for e.g a u bolt with a plate and I beam used to support a pipeline vertically?

Also, is it advisable to give vertical thermal displacement in anchors when modeling nozzles as terminal points because doing so would render most of the supports in effective. In such a case should one resort to the method of modeling the vessels with the nozzle?

What are the shortcomings of modeling terminal vessels nozzle as anchors and should one use the thermal growth of the nozzle? would this be a conservative design or insufficient design?

appreciate your help

Support weights are typically not included - you need to evaluate your specific conditions though.

It is far easier to model the vessel, and include the nozzle flexibilities then to second guess things by modeling anchors or computing displacements. If you change the temperature you have to recalculate (and input) the displacements - a procedure susceptible to making a mistake.