# Combination of Variable Loads in Structural Design
## 2 Materials and Methods
### Independent vs. Dependent Load Combination  
Load combinations in structural design can be approached independently or dependently, with no intermediate method available. The dominant approach is that variable loads are independently and stochastically combined [1; 2; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24]. However, this load combination method is inconsistent with structural probability theory. In the ULS, permanent loads and variable loads are combined independently with a load reduction, whereas in the SLS, they are combined dependently and deterministically without a load reduction for single variable loads, and with a reduction for multiple variable loads. Imposed loadson multi-storey buildings are combined independently, while corresponding permanent loads are combined dependently. Nonetheless, most loads are combined dependently. The article in [29] presents five arguments supporting that permanent and variable loads should be combined dependently. Another article [30] addresses the issue further, summarizing current load combination procedures and explaining that the 50-year variable load impacts every structure and permanent load within the design domain. The independent combination of the 50-year variable load and the permanent load yields virtually identical results to those obtained through dependent combination methods. If we recognize that structures are designed for 50-year loads, the independent-dependent problem almost vanishes. However, the current calculation with a 5-year variable load results in approximately 10% lower load. The independent combination is virtually always unsafe, except for wind loads; the dependent combination is always safe, usually fully correct, and sometimes excessively safe. Two arguments are further presented here for the dependent combination: permanent and variable loads are not independent in the combination, and the variable load simultaneously impacts all permanent loads within the failure domain. * The current practice of combining loads independently in structural design is based on the combination of a random permanent load with a random variable load. This approach, however, does not capture the non-random nature of actual load combinations in real-world scenarios. In practical design, one combination load in design is applied to multiple actual combinations. For example, the design of one roof girder applies to multiple roof girders and various actual load combinations. Every actual variable load, including the maximum value in the variable load domain, has a simultaneous impact on multiple permanent loads. This includes a randomly selected permanent load, its adjacent loads, and typically the maximum load in the permanent load domain. For design purposes, the highest actual loads in the design domain are simultaneous and must be added up without any reduction. This indicates that the highest variable loads and the highest permanent loads coincide and should thus be considered together. The possibility of high variable loads coinciding with low permanent loads or vice versa cannot be utilized because the design must account for the highest combination load. * In the Eurocodes, the highest variable load in each design is the service time load, specifically the 50-year load with an occurrence probability \(P_{t,50}=1/15,000\). The permanent load failure domain encompasses an area that includes structures with 15,000 failure options, typically much smaller than 1 km\({}^{2}\). Within this domain, only one failure is permitted in 50 years. It is normal for each variable load to have a uniform and simultaneous impact on all permanent loads within the domain. As a result, the maximum loads, the next highest loads, and so on, occur concurrently. Consequently, the combination load distribution must be constructed as if the loads were fully correlated to accurately reflect their simultaneous nature.