Stress Fields for Nodes of Strut‐and‐Tie Models

Truss models have been developed and applied to the ultimate strength design and detailing of two‐dimensional reinforced concrete members loaded in their plane. Such a truss is composed of struts and ties which represent one‐dimensional stress fields. The nodes, however, form two‐dimensional stress fields whose bearing capacity also needs to be checked. The geometry of the nodes is only limited by the existing boundary of the plate, and not by the area formed by the intersection of the stress fields reaching the node. This makes it possible to show that for any node with an arbitrary number of struts of equal stress intensity, a stress field can be found that satisfies the lower bound theorem of plasticity. This stress field consists of several triangular and rectangular areas, which are separated by lines of stress discontinuity. The stress state inside each of these areas is homogeneous, either one‐dimensional or “pseudo‐hydrostatic.” An algorithm for the automatic generation of such stress fields is presented. It will further be shown that even if there are stress fields of different intensities, nodes as described can be formed. This is made possible by the introduction of “transition stress fields” and by exploiting the concrete tensile strength.