Behavior and Capacity of Headed Reinforcement

ACI Structural Journal, Jul/Aug 2006 by Thompson, M Keith, Jirsa, James O, Breen, John E

DISCUSSION

Importance of anchorage length

The proposed model was inaccurate for the beam-column tests and stub-beam pullout tests because the anchorage length of the headed bars was not accounted for in the calculation of bond contribution or to determine the applicability of the model for head bearing. These results indicate the importance of anchorage length in the proposed model. Anchorage length L^sub a^ is measured from the bearing face of the head, the outside bend of a hook, or the end of a straight bar to the point of peak bar stress. When a strut-and-tie model is considered, the point of peak bar stress coincides approximately with the intersection of the tie bar with the leading edges of the compression struts anchored by the tie bar (the end of the extended nodal zone). Strut-and-tie modeling is the best approach to determine anchorage length.

The recommendation of strut-and-tie modeling to determine anchorage length is a departure from conventional treatments of anchorage that use the splice length or embedment length to characterize capacity. The language and figures used in ACI 318-02, Chapter 12 ("Development and Splices of Reinforcement") recognize the critical section for development of reinforcement as that corresponding to maximum moment at a beam's midspan or at a joint. Thus, the development length expressions for straight bars and hooks are derived with a beam theory approach in mind. With a strut-and-tie approach, however, the strut-and-tie model will indicate, in many cases, that the critical section occurs at a different location. This is particularly true for joints.

As an example, consider the joint illustrated in Fig. R12.12(a) of ACI 318-02 (a representation of which is shown in Fig. 12(a)). The figure in the code shows the critical section to occur at the face of the column. The development length L^sub dh^ is compared to the embedment length of the bar into the column. Now consider a strut-and-tie model of the same joint as shown in Fig. 12(b). The tension in the hooked bar is balanced by compression Struts AB and AC (shown as dashed lines). Struts AB and AC occupy some height and width within the joint (Fig. 12(c)). Under the strut-and-tie model, the critical section of the hooked bar occurs where it intersects the leading edge of these struts. The resulting anchorage length is much shorter than the embedment length that is generally used to compare against development length.

Another example of the importance of this issue is provided by the failure of the original gravity-based support for the Sleipner A offshore oil platform.8,9 The main report of the failure9 concluded that failure was a result of inadequate design of the tricell joints formed at the intersections of adjacent caisson walls. Two primary flaws were cited: 1) errors in the finite element analysis used to calculate shear at the joint; and 2) failure to provide adequate embedment for doubleheaded tension ties at the joint. The report also cited a need for the use of rational design checks for the joint. Strut-andtie modeling would have provided a rational procedure for checking the detailing of the joint. If a strut-and-tie model had been applied to the joint, the inadequate anchorage of the double-headed tie reinforcement would have become apparent (Fig. 13(b)). Test specimens of the tricell joint revealed a mode of failure in which shear cracks in the walls of the joint bypassed the ends of the double-headed tie bars (Fig. 13(a)). In redesign details, the length of the double headed ties was increased by 500 mm, shifting the termination Fig. 10-Results from proposed model for beam-column and point of the ties into the compression zone of the joint walls (additionally, much more stirrup reinforcement was provided in the region of the joint to carry recalculated shear forces). Improvements to the detailing of the joint specimens provided as much as a 70% increase in capacity.