The redistribution of moment within a statically indeterminate reinforced concrete beam at the ultimate limit state occurs through variations in the flexural rigidities and through the formation of hinges. The phenomena of moment redistribution (MR) is used to increase the efficiency of reinforced concrete design by allowing moments to be transferred away from critical cross sections thereby resulting in lower design moments. To allow for this effect in design, two main approaches are adopted. The first is to perform an elastic analysis and then to adjust the resulting distribution of moment using a codified MR factor. The second is to apply a plastic analysis allowing for the formation of hinges, and to calculate the rotational requirements at the hinges from first principles. This paper uses fundamental plastic analyses to derive closed‐form expressions for the hinge rotational requirements for full MR (that required to achieve the theoretical maximum applied load within the beam based on the moment capacity of sections within the beam). These closed‐form solutions are then used to quantify the maximum load on a beam when the rotational capacities at a hinge are less than the rotational requirements for full MR (partial MR). Closed‐form solutions are then used to derive MR factors which do not require semimechanical calibration.

中文翻译：

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预测钢筋混凝土梁弯矩再分布的闭式表达式，并应用于常规混凝土和超高性能纤维增强混凝土

在极限状态下，超静定钢筋混凝土梁中弯矩的重新分布是通过抗弯刚度的变化和铰链的形成而发生的。弯矩重新分布（MR）现象通过允许弯矩从临界截面转移开来提高钢筋混凝土设计的效率，从而降低了设计弯矩。为了在设计中达到这种效果，采用了两种主要方法。首先是执行弹性分析，然后使用编码的MR系数调整力矩的最终分布。第二个步骤是应用塑性分析以允许形成铰链，并根据第一个原理计算铰链处的旋转要求。本文使用基本的塑性分析来得出全MR的铰链旋转要求的闭式表达式（根据梁内各部分的抗弯承载力，达到理论上梁内的最大施加载荷所需）。当铰链处的旋转能力小于完全MR（部分MR）的旋转要求时，这些封闭形式的解决方案然后用于量化梁上的最大载荷。然后使用闭式解导出不需要半机械校准的MR因子。当铰链处的旋转能力小于完全MR（部分MR）的旋转要求时，这些封闭形式的解决方案然后用于量化梁上的最大载荷。然后使用闭式解导出不需要半机械校准的MR因子。当铰链处的旋转能力小于完全MR（部分MR）的旋转要求时，这些封闭形式的解决方案然后用于量化梁上的最大载荷。然后使用闭式解导出不需要半机械校准的MR因子。