Headed Studs in Concrete: State of the Art. Paper by Amin Ghali and Samer A. Youakim/AUTHORS' CLOSURE

Discussion by M. Keith Thompson, James O. Jirsa, and John E. Breen

Assistant Professor, University of Wisconsin-Platteville, Platteville, Wisc.; FACI, Janet S. Cockrell Centennial Chair in Engineering, University of Texas at Austin, Austin, Tex.; and ACI Honorary Member, Nasser I. Al-Rashid Chair in Civil Engineering, University of Texas at Austin.

The authors have compiled a valuable summary of headed bar research and usage. Particularly, the use of doubleheaded studs as confinement for compression members or as shear reinforcement for flat plates presents many advantages over conventional hooked ties or stirrups both in terms of constructibility and structural performance. However, the discussers would like to address some important concepts that were omitted from the paper:

1. The cover dimension c^sub 1^, as used in Eq. (2) and (3) of the paper and originally presented by Thompson,20 follows the same definition for c^sub b^ used for the straight bar development length equations presented in ACI 318-05, Section 12.2.21 That is, the cover dimension is defined as the smaller of (a) the distance from the center of a bar to the nearest concrete surface; or (b) one-half the center-to-center spacing of bars being developed. Thus, when the authors state that "splitting of the cover need not be a concern when [the cover] c ≥ 3d^sub b^," they should note that the center-to-center bar spacing must also not be less than 7d^sub b^ according to the second condition in the definition for cover dimension. Furthermore, for edge bars that run parallel and close to only one exterior surface, if half the center-to-center spacing does not control c^sub 1^, then the second cover dimension c^sub 2^ will be limited to this condition. Thus, ψ (the radial disturbance factor defined by Eq. (3)) may be less than 2.0 for an edge bar. The authors' conclusions that spalling of cover is not a concern when c ≥ 3d^sub b^ lacks this essential caveat;

2. The research by Thompson20 also concluded that strut-and-tie modeling (STM) is an important condition for use of Eq. (2) and (3) of the paper. Whereas it is true that the bar may be fully developed at the head if the cover c^sub 1^ and head area A^sub nh^ are large enough and the concrete strength f'^sub c^ is high, this does not imply that the development length of the bar is zero. Consider the joint shown in Fig. A. Because the conventional interpretation for the critical section based on maximum moment occurs at the joint face, if the head is sufficient to develop the bar at the head, it may be interpreted that the headed bar requires only a minimal embedment into the joint. If STM is applied to the joint as in Fig. B(a), however, it can be shown that such embedment is clearly insufficient because the bar does not intersect the critical CCT node of the strut-and-tie model. The correct way to embed the headed bar is shown Fig. B(b), where the headed bar engages the CCT node. Based on the limitations of his test data, Thompson20 recommends that the bar should be embedded at least 6d^sub b^ into the node, hence the lower bound presented for Eq. (4) of the paper. This limit is not so much a lower bound on anchorage length L^sub a^, as it is a lower bound for the size of the extended nodal zone;

3. On Page 665 of the paper, the authors stated that the head area used in tests conducted by Thompson20 in which headed bars were used as ties in CCT nodes was "ten times the cross-sectional area of the stud." This was incorrect. The relative head area (net head area divided by the bar area) varied from 0.0 (corresponding to non-headed bars) to 10.4. The smallest heads used in those tests were 2.2 times the area of the bar (or a relative head area of 1.2). Furthermore, those test results indicated that it was not always necessary to have a head area 10 times the bar area for a bar to develop its yield strength;

4. In the review of the research of double-headed studs as shear reinforcement in concrete I-beams, the authors cited Berner and Hoff's6 conclusions that "ACI unnecessarily limited f^sub y^ for the shear reinforcement to 413 MPa (60 ksi) and its contribution to the shear strength to (2/3)[radical]f'^sub c^ MPa (8[radical]f'^sub c^ psi)." This conclusion was based on the extraordinary capacity achieved by Berner and Hoff's test beams. The high end limit for shear capacity from stirrups (which is set in ACI 318-05, Section 11.5.6.921) derives from serviceability conditions, not ultimate strength. The limit of (2/3)[radical]f'^sub c^ MPa (8[radical]f'^sub c^ psi) is defined to prevent excessive widths in shear cracks at service loads. MacGregor et al.40 discusses this issue in his text on reinforced concrete design and the original recommendation for this limit was provided by ACI Committee 426.41 Furthermore, fulfillment of the necessary V^sub s^ by using less stirrup area A^sub v^ and higher yield stress f^sub y^ may again result in excessive shear crack widths at service loads due to the loss of stiffness in the stirrups. Berner and Hoff use the wrong basis for their conclusion that the shear contribution from stirrups is unnecessarily limited when headed bars are used. Without evidence showing improvement in service level performance, the limits for f^sub y^ and V^sub s^ should remain. Because of the superior anchorage of headed studs, testing may indeed reveal that they produce lower shear crack widths at service loads when used as shear reinforcement in I-beams than analogous I-beams reinforced with conventional stirrups. However, such data has not yet been presented; and