Avoid Combination of combinations in Etabs Design

Load combination U1= 1.2DEAD+1.6LL , where DEAD is defined as a combination of SW+WALL+SDL

Load combination U2= 1.2SW+1.2WALL+1.2SDL+1.6LL (Loads are individually added)

Design Using load combination U1

Design Using load combination U2

The minor axis bending moment is zero. So the minimum eccentricity moment is considered for both the load combos U1 and U2. In both cases the minimum eccentricity moment is 35.952 kN-m (M2,min). Then for the second order effect this moment is amplified by the Delta_ns factor. For the case of U1, this factor is 1.585. This leads to a design moment of 35.952 kN-m X 1.585 = 56.965 kN-m. For the case of U2, this factor is 3.145. This leads to a design moment of 35.952 kN-m X 4.145 = 113.070 kN-m.

Now the question arises, why the Delta_ns factor is different for cases U1 and U2 even though both have apparently the same original loading. U1 is a combo of combo. It has 1.2DEAD+1.6LL in it, where DEAD = Combo(SW+WALL+SDL). The DEAD consists of some permanent dead load and some superimposed dead load. On the other hand, U2=1.2(SW+WALL+SDL) + 1.6LL. The total moment diagrams and axial force diagram for U1 are the same as those for U2. However, for case U1 program cannot distinguish between the permanent dead load and superimposed load correctly. This causes the beta_d factors to be different for the two cases resulting in different EI and Pe values. Eventually the Delta_ns factors are different.

It is recommended to avoid using a combination of combinations for the purpose of design. While a combination of combinations is not a problem for enveloping analysis results, it is not appropriate for design. This is because some of the design parameters are invariably dependent on the type of loading and this information is lost when combos are used within a combination.