Load cases, combinations and envelopes
Real beams often carry multiple loads from different sources, and a design must be based on the most onerous combination of loads likely to act on the structure. In this step, we'll arrange step 4's loads into load cases - the dead (or permanent) load and the imposed (or variable) load. We'll treat these loads as characteristic loads and multiply them by load factors. Then we'll combine them into load combinations, and read the results envelopes that take the worst of the combinations at every point along the structure.
1.0 The idea
A load case is a set of loads that act together. The solver solves each case individually. If a linear solution is performed, the structure's response to a factored combination of loads (a load combination) is just the sum of the factored results from individual load cases - thanks to the principle of superposition.
You are free to specify whatever load factors are appropriate for your analysis; typical Eurocode ultimate limit state load factors for permanent and variable loads are 1.35 and 1.5, respectively. Serviceability limit state factors are usually 1.
For a structure where it cannot be assumed that the load applies in all locations simultaneously, we need to consider loading patterns to ensure we identify the most onerous load combination to design against. On a continuous beam, for example, the worst-case sagging moment typically occurs when the maximum loading is applied to one span, and the minimum is applied to the other.
One source of loading that can vary across the structure is the imposed or variable load. Therefore, the imposed load goes into one case per span. Then we can build individual load patterns to evaluate when we build our load combinations - we'll see this below.
Finally, an envelope is a set of combinations read together: at every position along the structure, an envelope presents the largest and smallest value across all load combinations and identifies the governing combination at each location.