# Combination of Variable Loads in Structural Design
## 4 Discussion
* Most variable load pairs involve loads of different magnitudes, typically with load proportions \(\alpha<\approx\)0.3. In these cases, the reliability advantage ranges from 0 to 7% for the variable loads. Without applying combination factors, the potential reliability gains indicated by the light grey area above the dash-dotted line cannot be realized. The dash-dotted line dropping below the dashed line indicates a margin of 2% unsafety, represented by the dark grey area. Unsafe errors are more detrimental than safe ones. The light grey area is approximately three times larger than the dark grey area, implying that if code writers consider unsafe errors three times more harmful than safe ones, the combination factor calculation becomes almost unfeasible due to the unsafe errors it introduces. * Assuming loads \(\alpha=\) 0-0.5 have equal occurrence and disregarding the unsafe error at \(\alpha<\approx\)0.3, the overall reliability gain obtained by combination factors is 3-5%. Estimation of the overall gain due to combination factors is difficult. The unsafe error in the combination factor model, though disregarded here, should somehow be considered. The prevalence of variable load cases is unknown; the high prevalence of unequal loads is apparent. The above calculation applies to a rare case of the highest combination factor gain \(\psi_{\text{code}}=0.75\) for wind-imposed load and loads \(V_{\text{Q}}=0.4\) (loads \(V_{\text{Q}}<0.4\) result in higher factors). Other combination factors are higher (\(\psi_{\text{code}}=0.8\)-1) with lower gain. The combination factors are meaningful in structures with low permanent load, i.e., in timber and steel structures, and the meaning is negligible in concrete structures. The combination factors are meaningless in cases of different load magnitudes, including a little unsafe error. Virtually, the combination factors are meaningful in one case only, i.e., in the ULS design of light roofs with about equal snow and wind. However, it can be assumed that the overall reliability gain obtained from the combination factors is about 2-3% in the ULS with an ultimate highest gain of 8% in rare cases (light roof with equal wind and snow). A gain of similar magnitude likely applies in the SLS as well. Thus, the meaning of the combination factor is negligible. Besides reliability, there are points which must be considered in the evaluation of the combination factors. Next, six points support the removal of the combination factors from codes:  
* Removing combination factors would simplify the structural codes, making them easier to understand and apply. * The elimination of combination factors lessens the workload for engineers, streamlining the design process. * When combination factors are included, the outcomes are approximate, encompassing both safe and unsafe cases. * In most cases, the impact of combination factors is negligible, with clear benefit gained virtually in one load case only, such as a steel or timber roof loaded with approximately equal snow and wind. * In the current Eurocodes, the reliability in cases dominated by variable loads is significantly below the target. Removing combination factors reduces this discrepancy and improves reliability. * If combination factors are removed from codes, the resulting error is always safe and negligible compared to other unavoidable errors and approximations inherent in structural design. These issues are further discussed next.