Actually calculating something like the critical load strength of a column or the load a beam could carry would have to wait long after the Romans: it would wait until algebra, wait for Newton, wait until Euler and Bernoulli in the mid-18th c. Materials science, strength of materials, would be even later: it actually would not be much more than compiled results from testing machines until the 20th c., when researchers with scanning electron microscopes actually could look at atomic structures under stress and understand why a steel girder was stronger than glass one.

So, if a Roman was building a limestone wall, it would still be a craft. Vitruvius , in his De Architectura, would be thinking of an architect less as master builder than as a master of the various craftspeople doing the building, and though his text does have some basic geometry when it comes to surveying and laying out a town, for building it is much more about using craft knowledge, with geometry being employed for making all the proportions harmonious. Craftspeople would work from a knowledge base of previous experience, and have rules of thumb, and Vitruvius simply says that a foundation should be of the right form and that mortar should be of the proper type....in other words, the masons working for the architect should know what they're doing and do it. Depending on the height and the ground, a mason would have an idea of what kind of a foundation to put under the wall , and how thick the wall should be, and the proper recipe for the lime mortar, how the stones should fit. It may seem rather counter intuitive, that the Romans could achieve some very impressive structures that still survive without knowing anything about finite element analysis, but trial and error over a long time can produce a very impressive knowledge base: after 200 years of violin building in Cremona, Italy, there was enough knowledge in place there for Stradivari and the Amati family to be able to build some very nice fiddles, and Roman empire lasted much longer than that. And that survivor bias is not rubbish. We know that the Romans built things that fell down quite a lot and of course they don't survive. Failure is educational, if a very unappreciated part of the learning process. If one mason built five walls 10 meters high, and three fell and two did not, if he'd been making notes as to what he'd done each time, that mason would have learned something important (as would, perhaps, the unfortunate residents of that apartment building) and if several masons had walls collapse and talked together they would have learned even more.

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John Gray Landels' Engineering in the Ancient World is a still a decent intro to the subject, and is over on Google books..

J.E. Gordon's The New Science of Strong Materials, or Why You Don't Fall Through the Floor is a both a classic ( and lively ) account of the beginnings of materials science and a great introduction to it.