Curved-Bar Nodes

Headnote

A detailing tool for strut-and-tie models

(ProQuest: ... denotes formulae omitted.)

Since reinforcing bars were first used in concrete, they have been designed with bends for anchorage and transfer of forces in connection regions. Examples include beam-column and wall-slab junctions, where bent bars at the outside of a frame corner resist closing moments.

The forces in these corners can be modeled using the strut-and-tie model (STM) shown in Fig. 1. In this example, the curved region of the bar is modeled as a series of segments with tension forces opposed by a series of fan-shaped compression struts. In this article, I'll explain how this curved region can be modeled as a curved-bar node. In the general case, a curved-bar node is the bend region of a continuous reinforcing bar (or bars) where two tension ties are in equilibrium with a compression strut in an STM. Specific recommendations for design and detailing using STMs with curved-bar nodes in frame corners and dapped-end beams are offered.

STRUT-AND-TIE MODEL

The tie forces at a curved-bar node must be equilibrated by one or more struts. In most cases, the intersection of two ties and a strut at the curved-bar node form a compression-tension-tension (C-T-T) node. Several additional examples of curved-bar nodes in concrete connection regions, or so-called D-regions, are shown in Fig. 2. To simplify analyses of C-T-T nodes such as shown in Fig. 1, 2(a), or 2(b), the curved region can be modeled as a single node at the intersection of the centerlines of the straight ties (Point a in Fig. 1).

As shown by the example C-T-T node in Fig. 3, nodal zones are generally too small to allow development of tie forces through bond alone. If conservative design guidelines for the use of curved-bar nodes in D-regions are developed, curved-bar nodes can provide a cost-effective, simpler alternative to separate mechanical anchorages. Although Appendix A of ACI 318-081 does not yet recognize curved-bar nodes, its provisions can be used to develop design recommendations.

COMPRESSIVE STRESS AT CURVED-BAR NODES

In a typical case, a strut bisects the angle formed by the ties extending from the curved-bar node. For 90-degree corners with equal tie forces, the strut angle is 45 degrees, and, using a pressure vessel analogy, the...