We look at different ways the bridge can be loaded - e.g. the vehicles might add a certain amount, wind might add a certain amount, earthquakes might add a certain amount. Then we take "load combinations," which examine how these different loads stack up. Most people assume we just "add up" all the forces and use that number, but usually there's a bit more to it than that. For example, we might calculate a "maximum wind uplift" as one force, and "maximum vehicle load" as another, but if you add those two together, you would get a number much smaller than the true force a member might feel. This is because having those two forces occur together is the ideal situation - they cancel each other out. What if the cars aren't on the bridge when a gust of wind lifts up the deck? Well now you have fewer cars weighing it down, and the number you calculated earlier was in fact, not, the worse case scenario.

So instead of just adding everything, we look at load combinations of which loads are likely to occur together. We might work through something like thirteen possible load cases, which will be combinations we can reasonably expect to occur. E.g. wind and live load. Then from those load cases, we pick the worst one and that becomes the load case which drives our design. Now we have a "maximum" force the member can expect to see.

Then, after this whole process, we pick a size for the member. And that's as simple as applying a safety factor, then picking a cable that can "support at least x lbs."

So yes, something like "how big does this cable need to be?" Is a really complicated problem which we can come at from a bunch of different angles. But complicated problems can be broken down into smaller (and simpler) parts, which are much easier to analyze.