Structural engineering is generally regarded as a specialized subdiscipline of civil. It’s an important part of civil engineering – but it’s not the whole thing.
For example, you say you want to design buildings and bridges. That’s “structural engineering”. OK, in that case, UCSD should be fine.
But – you also mentioned “roads”. That’s “transportation engineering”, and it probably isn’t available at UCSD. How about water supply systems? That’s “water resource engineering”, and it probably isn’t available at UCSD either.
The UCSD program specializes in one particular branch of civil engineering. There’s nothing wrong with that, as long as you are interested in that speciality. However, you probably won’t get the same exposure to the different branches of civil engineering, and have as many different options, as you would in a traditional civil department.