# Combination of Permanent and Variable Load Is Dependent
## 4 Discussion  
The basic assumption of the ILC is that the combination load is constructed from independent and uncorrelated load pairs of permanent and variable loads. However, the loads are correlated as the ILC contradicts the physics and should be combined dependently as explained in Section 3.1. The physics demand that the loads must be combined as if the loads have a full correlation. _The current hypothesis is, that the variable load in the structural design is random. However, the maximum variable load is the 50-year load as this load strikes all structures and all load combinations,_ i.e., _this load is not random, and the load reduction is not acceptable._ The current calculation applies a load reduction to this load and erroneously uses the 5-year load in the load combination. When the 50-year variable load and the random permanent load is combined independently the result is almost the same as the DLC and only 0-6% lower as  
Figure 4: Same as Figure 1 with different scale. Figure 3: Cumulative load distributions for 50-year variable load and group of permanent loads with 1, 50, 500, and 5000 permanent loads, thin solid line, dashed line dash-dotted line and dotted line, 50-year variable load and one permanent load with the DLC is shown with thick solid line. seen in Figure 2. This combination will be even closer to the DLC when the group effect is considered. If the load group is 50 with the same variable load and multiple permanent loads about one half of the load reduction is removed as disclosed in Section 3.5. It is feasible to assume that the 50-year variable load is constant and that is combined with the random permanent load. Such assumption almost fully equals the DLC as seen in Figure 2.  
One variable load occurring simultaneously with multiple permanent loads induces correlation and load increase regarding the ILC. It is possible that the load group includes 5000 permanent loads meaning that no load reduction can be applied as explained in Section 3.5. It is also feasible to set the design criterion in such a way that the criterion must be fulfilled in all cases the design applies to, which would demand the DLC for load groups with the same variable load. Finally, the basic assumption of the ILC is incorrect. Namely, the load pairs are not independent as the variable load may be the same in adjacent load pairs. The motivation for using the ILC is that it reduces the design loads and the material costs. However, compared with the DLC approach, the ILC leads some amount of to load vanishing in the combination process and the failure probability exceeds, thus, the target reliability as laid down in the codes. As suggested by the numerical evaluation of this study, a total of 0-20% of the load can vanish in the ILC process, meaning that the failure probability is about ten times that of the DLC approach. The intended target reliability of the Eurocodes is \(\beta_{50}=3.8\), but the ILC can result in a reliability value as low as about \(\beta_{50}=3.2\). In the current codes, the ILC is normally implemented by two permanent load factors greater than unity. However, the correct load combination may include only one permanent load factor greater than unity. The Eurocodes include three combination rules. One of these (8.12), i.e., 1.35G + 1.5Q utilizes the DLC and the other two (8.13a,b), max(1.15G + 1.5Q, 1.35G + 1.05Q) and (8.14a,b), max(1.35G, 1.15G + 1.5Q) correspond to the ILC. The combination rule (8.12) of the Eurocodes is correct, but the safety factors and the failure probably are calculated erroneously. Namely the variable loads are calculated for five-year loads only [16] whereas they should be calculated for 50-year loads. The current Eurocodes in unclear regarding the load combination as both the ILC and the DLC are applied. The present calculation suggests that the variable load safety factor \(\gamma_{\text{Q}}=1.5\) of the Eurocodes should be increased by about 20% if the target reliability is kept unchanged, \(\beta_{50}=3.83\).