承受竖向荷载和不平衡弯矩的板柱节点受冲切计算方法

A calculation method for punching failure of slab-column connections subjected to vertical loads and unbalanced bending moments

摘要:

GB 50010—2010《混凝土结构设计规范》验算有不平衡弯矩的板柱节点受冲切时,基于弹性理论计算等效集中反力,将其按仅承受竖向荷载作用的板柱节点进行受冲切承载力验算。但已有研究表明,有不平衡弯矩的板柱节点达到受冲切承载力极限状态时,其临界截面上的剪应力具有塑性特征。为解决弹性理论未考虑板柱节点塑性行为的问题,提出考虑塑性对剪应力影响的有不平衡弯矩板柱节点受冲切承载力计算方法。首先,为衡量有不平衡弯矩板柱节点发生冲切破坏时的临界截面剪应力的塑性发展程度,将按弹性方法计算得到的有不平衡弯矩板柱节点发生冲切破坏时的临界截面最大剪应力与仅竖向荷载作用板柱节点发生冲切破坏时的临界截面极限剪应力之比定义为塑性发展系数。然后,通过分析收集到的76组竖向荷载和不平衡弯矩共同作用下的板柱节点冲切试验数据,发现塑性发展系数随混凝土轴心抗拉强度的提高呈下降趋势,而随不平衡弯矩产生的偏心剪应力与竖向荷载产生平均剪应力之比的增大呈上升趋势。并以混凝土轴心抗拉强度和剪应力之比为两个横坐标,以塑性发展系数为纵坐标,拟合得到了三者的关系。最后,根据拟合得到的塑性发展系数计算公式,将有不平衡弯矩板柱节点的等效集中反力计算方法过渡到塑性理论。

Abstract:

According to China′s code for design of concrete structures (GB 50010—2010), the punching calculation for slabs with unbalanced bending moments is currently based on elastic theory to calculate the equivalent concentrated reaction force. This force is then used to evaluate the punching shear capacity of the plate-column joint under the action of vertical loads only. However, previous studies have revealed that the shear stress along the control perimeter exhibits plastic characteristics when the slab with unbalanced bending moments reaches its ultimate state. Therefore, to address the limitation of elastic methods in neglecting the plastic behavior of slabs, this paper presents a formula for calculating the punching of slabs with unbalanced bending moments, considering the influence of plasticity on shear stress. Initially, to assess the plastic development of shear stress along the control perimeter when slabs with unbalanced bending moments undergo shear failure, the ratio of the maximum shear stress along the control perimeter calculated by elastic methods in slabs with vertical loads and unbalanced bending moments to the ultimate shear stress along the control perimeter in slabs with vertical loads only is defined as the plastic development coefficient. Subsequently, through analysis of 76 sets of punching test data of slabs under the combined action of vertical load and unbalanced bending moment, it was observed that the plastic development coefficient decreases with the increase of concrete tensile strength, while the ratio of the eccentric shear stress induced by unbalanced bending moment to the average shear stress induced by vertical load increases. Consequently, by considering concrete tensile strength and shear stress ratio as the two horizontal coordinates and the plastic development coefficient as the vertical axis, the relationship between the three was fitted. Finally, the method for calculating the equivalent concentrated reaction force for slabs with unbalanced bending moments is revised to plastic theory, utilizing the derived formula for calculating the plastic development coefficient.