The trusses, joists and beams in a structure form a network of bearing relationships. Figure 1 shows an example of this. Only members not acting as girders can be analyzed in isolation. Members carrying other members must be analyzed in careful order1.
This is further complicated by the fact that each multi-span member is analyzed in several ways based on different patterns of live/snow load on its spans (e.g. every 2nd span loaded with snow). A consequence of this is that any member acting as a girder might also need to be analyzed in several ways, because a multi-span member exists “downstream” from it and produced multiple possible reactions. We will look at how design software considers different ways of loading a member, as well as which possible reaction(s) it passes on to carrying members.
With respect to loading the member itself, the now-defunct Keymark aka CS-Build software would run the member loaded with only positive live loads, then with only negative loads, and finally with both positive and negative loads (dead load was of course always on). At each of these stages, it would do a pattern loading analysis with the live load present on all spans, on only even spans, on only odd spans, and finally on all pairs of adjacent spans and turned off for all others2. Appendix A illustrates this process. For snow load, CS-Build would carry out the pattern loading check, except that instead of removing loads on certain spans it would only reduce them by half. It would only do this in its calculation of reactions to pass on to carrying members; in the factored calculation for sizing the member itself, done separately, no pattern loading was done for snow.
The iStruct software analyzes in a similar fashion to CS-Build, except that the pattern loading checks all possible combinations of loaded and un-loaded spans. Mitek's Sapphire software also uses pattern loading, and Engineering does so whenever enabled in the program settings.
Clearly this pattern loading will produce multiple possible reactions, of which there will a high-end worst case and a low-end worst-case3. We will now look at if, and how, programs pass these reaction pairs on to carrying members.
In iStruct as well as Mitek Sapphire and Engineering, both reactions are passed on, but only if the high-end is positive and the low-end is negative.
CS-Build did not transfer both reactions to carrying members. A single load of each component type, that with the highest absolute value, is tranferred4. The pattern loading described above does offer a weak approximation of passing dual reactions. If a high-end or low-end reaction is around zero, it will be accounted for in the analysis of the carrying member in those patterns where the carrying span has its live load turned off.
1 In design software bearing relationships are tracked using a Directed Acyclic Graph. A member can only be analyzed once all “downstream” members have been analyzed.
2 The rationale for this approach is that when only positive loads are being considered, one of the patterns listed is guaranteed to produce the worst-case downward reaction at each bearing (this is dictated by the bearing’s influence line graph). Likewise, with only negative loads one of the patterns will produce the worst-case uplift. However, one might observe that a more conservative approach would be to run the analysis in the same way, except on spans where the load is turned off, instead enable any loads present with the opposite magnitude (negative or positive) to the already-loaded spans.
3 In a factored reaction, where components are multiplied by different coefficients and added together in various ways prior to analyzing the member, pattern loading alone does not decide the high- and low-end reaction.
4 This is despite the fact that the member report will show both a positive and negative component reaction whenever both exist, with a note saying that these should be transferred to carrying members. A further warning regarding this note is that it only lists component loads that happen to be present in the load combination of the factored reaction calculated in the analysis of the member itself. All component reactions should be passed on as they could play a governing role in the analysis of carrying members, even if they don't for the carried member.
The following pages show a CS-Beam analysis for a joist with two spans, with both a positive and negative point load on the first span, and only a negative point load on the second span. The results we will show will be the same if the joist is converted to a girder or beam.
The markup throughout will demonstrate that the analysis has the following sections.