The live load duration refers to the period when the live load is larger than a given threshold in the reference period. The smallest threshold that allows the duration to be shorter than the required length is employed as the design live load for serviceability limit states. However, the traditional method only considers the mean duration and the probability that the duration exceeds the required length is unknown. This study proposes a new algorithm to determine the probability distributions of the live load duration. A sustained or extraordinary load process is transformed into a random variable set based on the stochastic harmonic functions. Subsequently, the duration distributions can be derived by employing the load coincidence principle and probability density evolution method. Three numerical examples including one sustained load and multiple extraordinary loads are provided and the results of the proposed algorithm are compared with those of Monte Carlo simulation. The proposed algorithm allows the exact determination of design live loads based on a predefined exceeding probability. As an application, the quasi-permanent and frequent values of seven user categories are calculated when the exceeding probabilities are taken as 10%, 5% and 2%, respectively. It is found that the quasi-permanent values can increase with increasing area and the differences between the frequent and quasi-permanent values can be more than 20 times.

活荷载持续时间是指参考期内活荷载大于给定阈值的时间段。采用允许持续时间短于所需长度的最小阈值作为可使用性的设计活荷载限制状态。然而，传统方法仅考虑平均持续时间，并且持续时间超过所需长度的概率是未知的。本研究提出了一种新算法来确定活荷载持续时间的概率分布。将持续或异常载荷过程转化为基于随机调和函数的随机变量集。随后，可以利用载荷符合原理和概率密度演化方法导出持续时间分布。提供了包括一个持续载荷和多个异常载荷在内的三个数值算例，并将该算法的结果与蒙特卡罗模拟的结果进行了比较。所提出的算法允许根据预定义的超出概率准确确定设计活荷载。作为一个应用，分别计算超出概率为10%、5%和2%时7个用户类别的准常值和频繁值。研究发现，准永久值会随着面积的增加而增加，频繁值与准永久值之间的差异可达20倍以上。