Semi-probabilistic methods are widely used for structural engineering design and assessment. In such methods, the safety and performance adequacy of structures are typically tied to partial safety factors for load and resistance, and load combination factors. There exist some heuristic strategies for estimating these partial factors, such as the design value method and first order reliability coefficient method. However, when adopted for the estimation of load combination factors, these strategies are either inaccurate or have non-unique estimates. Excessive conservatism in factor estimates is not desirable, particularly for the performance assessment of existing structures. In this study we propose a method for estimating load combination factors using a matrix linear algebra approach. Specifically, we develop a closed-form analytical expression to estimate unique load combination factors for typical code calibration problems. A comparative study of the existing heuristic approaches with the new approach is presented and demonstrated on two case studies. It is shown that the proposed method offers a valuable means of deriving load combination factors: one that avoids hueristics, and conservatism.

半概率方法广泛应用于结构工程设计和评估。在此类方法中，结构的安全性和性能充足性通常与载荷和阻力的部分安全系数以及载荷组合系数相关。存在一些用于估计这些部分因素的启发式策略，例如设计值法和一阶可靠性系数法。然而，当采用这些策略来估计负荷组合因子时，这些策略要么不准确，要么具有不唯一的估计。因素估计中过度保守是不可取的，特别是对于现有结构的绩效评估。在本研究中，我们提出了一种使用矩阵线性代数方法估计荷载组合系数的方法。具体来说，我们开发了一个封闭式分析表达式来估计典型代码校准问题的独特负载组合因子。对现有启发式方法与新方法进行了比较研究，并通过两个案例研究进行了论证。结果表明，所提出的方法提供了一种导出荷载组合因子的有价值的方法：避免色彩学和保守主义的方法。