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45 (a) Moment-Curvature Response (b) Axial Load-Moment Interaction Figure 28. Representative responses. 2.7.2 Spacing of Spiral Reinforcement was reviewed to determine whether it accurately describes the confining ability of high-strength transverse steel. For cases that are not controlled by seismic requirements, the volumetric ratio of spiral reinforcement must satisfy AASHTO Equation 5.7.4.6-1, that is 2.7.2.1 Formulation Ag fc The axial load before spalling of cover (Po) and the capacity s 0.45 -1 Ac f yh after spalling of cover (P) can be computed from the follow- ing equations: Additionally, according to 5.10.6.2, the center-to-center spacing shall not exceed six times the diameter of the longitu- Po = fc( Ag - As ) + As f y dinal bar or 6 in. From a practical point of view, the clear ( Ac - As ) + As f y P = fcc spacing of spirals cannot be less than 1 in. or 1.33 times the maximum size of the aggregate (AASHTO 5.10.6.2). The Where: basis of AASHTO Equation 5.7.4.6-1 is to ensure that the axial Ag = gross column area; load capacity of columns after spalling of the concrete cover is As = area of longitudinal bar; at least equal to the capacity before spalling. This provision fy = yield strength of longitudinal bars;

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46 fc = unconfined concrete strength; and Table 24a. Spacing of spiral (#4 Spiral, fyh 60 ksi). c = confined concrete strength, which is a function of fc co =5 ksi f' f' co =10 ksi f' co =15 ksi spacing of spiral(s). D (in.) Model Model Model AASHTO AASHTO AASHTO The provided spiral should be sufficient such that Po and P R-S R-S R-S 18 3.12 2.24 1.56 1.29 1.04 0.93 are equal to each other, as follows: 20 3.17 2.4 1.59 1.38 1.06 0.99 f c( Ag - As ) = f cc ( Ac - As ) 22 3.21 2.55 1.6 1.46 1.07 1.06 24 3.24 2.83 1.62 1.62 1.08 1.17 26 3.27 3.09 1.63 1.77 1.09 1.22 For a given concrete compressive strength, column size, 28 3.29 3.35 1.64 1.92 1.1 1.25 cover, longitudinal reinforcement ratio, longitudinal bar size, 30 3.31 3.72 1.65 2.07 1.1 1.27 spiral size, yield strength of spiral, and modulus of elasticity, 32 3.32 3.97 1.66 2.11 1.11 1.3 34 3.34 4.32 1.67 2.15 1.11 1.32 iterate the value of the spiral spacing such that this equality is 36 3.35 4.56 1.67 2.19 1.12 1.34 satisfied. The Razvi and Saatcioglu (1999) model was used to 38 3.36 4.89 1.68 2.22 1.12 1.36 compute f c c. Additional details, including the use of another 40 3.37 5.19 1.69 2.25 1.12 1.38 42 3.38 5.26 1.69 2.28 1.13 1.4 confined concrete model, are provided in Appendix G. 44 3.39 5.33 1.69 2.31 1.13 1.42 46 3.4 5.39 1.7 2.34 1.13 1.43 48 3.4 5.45 1.7 2.37 1.13 1.45 2.7.2.2 Parametric Study 50 3.41 5.51 1.7 2.39 1.14 1.47 52 3.41 5.57 1.71 2.41 1.14 1.48 Using the AASHTO provision and the aforementioned for- 54 3.42 5.62 1.71 2.44 1.14 1.5 mulation, the required spiral spacing was computed for a num- 56 3.43 5.67 1.71 2.46 1.14 1.51 ber of columns with the parameters listed in Table 23. All of 58 3.43 5.72 1.71 2.48 1.14 1.52 60 3.43 5.77 1.72 2.5 1.14 1.54 the columns were reinforced with #9 longitudinal bars, and the 62 3.44 5.82 1.72 2.53 1.15 1.55 longitudinal reinforcement ratio was set equal to 1.5%. The 64 3.44 5.87 1.72 2.54 1.15 1.56 cover to the spiral was taken as 1.5 in. The aim of this study was 66 3.45 5.91 1.72 2.56 1.15 1.57 to evaluate the spacing of high-strength spiral reinforcement. 68 3.45 5.95 1.72 2.58 1.15 1.58 70 3.45 6 1.73 2.6 1.15 1.6 72 3.45 6.04 1.73 2.62 1.15 1.61 74 3.46 6.08 1.73 2.64 1.15 1.62 2.7.2.3 Results and Discussions 76 3.46 6.12 1.73 2.65 1.15 1.63 78 3.46 6.15 1.73 2.67 1.15 1.64 The calculated required spacings for a representative case 80 3.46 6.19 1.73 2.69 1.15 1.65 are summarized in Table 24. The results for the other cases Notes: are provided in Appendix G. For a given concrete strength, Shaded cells indicate where calculated spacings exceed the maximum limit of the calculated spacing using any of the methods increases 6 in. The tabulated values of spacings are in inches. Method R-S is based on the confined model proposed by Razvi and Saatcioglu (1999 and 2002). as the yield strength of the spiral increases. In terms of reduc- ing the spiral spacing in columns cast with high-strength con- crete, the use of larger, high-strength spirals is more efficient. unity and spirals can be placed at larger spacings. From a con- For a number of cases (shaded in Table 24), the calculated finement point of view, for an "infinitely" large column, the spacings exceed the maximum limit of 6 in. These cases spiral spacing is expected to become "infinitely large." The involve columns using 5-ksi concrete. The calculated spacings formulation presented in Section 2.7.2.1 accurately replicates in columns with a concrete strength of 15 ksi are below the this trend. The difference between the spacings based on cur- maximum limit for all steel strengths. rent AASHTO requirements (Equation 5.7.4.6-1) and more The trend of the computed spacings is expected. That is, rational methodology presented in Section 2.7.2.1 becomes as the column diameter becomes larger, the difference between more pronounced as the column diameter increases. Unfor- the core and gross areas diminishes; hence, the ratio of axial tunately, the available test data do not include test results for load capacity before and after spalling of cover approaches columns larger than 24 in. because of the large amount of axial force required to test such large columns. Table 23. Parameters for transverse spacing study. The level of axial load in most bridge columns is relatively small (on the order of 0.05f cAg) and is appreciably less than Variable Value/Description the axial load capacity. Therefore, the capacity after the loss Concrete Compressive Strength* 5, 10, 15 ksi Spiral Yield Strength 60 ksi, 100 ksi, 120 ksi of cover will be above the normal loads that typical bridge Column Diameter 18-80 in. (2-in. increments) columns are expected to experience. This point is evident Spiral Bar Size #3, #4, #5 from Figure 29 in which the ratio of the axial load capacity Note: *The strain at peak stress ( co) was taken as 0.0025. (taken as 0.85f cAc, where f c = unconfined concrete strength,

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47 Table 24b. Spacing of spiral (#4 Spiral, fyh 100 ksi). Table 24c. Spacing of spiral (#4 Spiral, fyh 120 ksi). f' co =5 ksi f' co =10 ksi f' co =15 ksi co = 5 ksi f' f' co =10 ksi f' co =15 ksi D D (in.) Model Model Model (in.) Model Model Model AASHTO AASHTO AASHTO AASHTO AASHTO AASHTO R-S R-S R-S R-S R-S R-S 18 5.21 3.15 2.6 1.81 1.74 1.31 18 6.25 3.56 3.12 2.04 2.08 1.47 20 5.29 3.38 2.64 1.94 1.76 1.4 20 6.34 3.82 3.17 2.19 2.11 1.58 22 5.35 3.59 2.67 2.06 1.78 1.48 22 6.42 4.05 3.21 2.32 2.14 1.68 24 5.4 3.97 2.7 2.28 1.8 1.64 24 6.48 4.45 3.24 2.57 2.16 1.86 26 5.44 4.35 2.72 2.49 1.81 1.8 26 6.53 4.83 3.27 2.8 2.18 2.03 28 5.48 4.72 2.74 2.7 1.83 1.95 28 6.57 5.2 3.29 3.01 2.19 2.19 30 5.51 5.23 2.76 3 1.84 2.12 30 6.61 5.72 3.31 3.31 2.2 2.41 32 5.54 5.58 2.77 3.2 1.85 2.16 32 6.64 6.07 3.32 3.51 2.21 2.51 34 5.56 6.07 2.78 3.48 1.85 2.2 34 6.67 6.56 3.34 3.8 2.22 2.53 36 5.58 6.41 2.79 3.65 1.86 2.24 36 6.7 6.89 3.35 3.99 2.23 2.55 38 5.6 6.88 2.8 3.7 1.87 2.27 38 6.72 7.35 3.36 4.15 2.24 2.57 40 5.62 7.33 2.81 3.75 1.87 2.3 40 6.74 7.8 3.37 4.18 2.25 2.59 42 5.63 7.78 2.82 3.8 1.88 2.33 42 6.76 8.24 3.38 4.2 2.25 2.6 44 5.65 8.21 2.82 3.85 1.88 2.36 44 6.78 8.66 3.39 4.23 2.26 2.62 46 5.66 8.64 2.83 3.9 1.89 2.39 46 6.79 9.08 3.4 4.26 2.26 2.63 48 5.67 9.07 2.84 3.94 1.89 2.42 48 6.81 9.49 3.4 4.28 2.27 2.65 50 5.68 9.19 2.84 3.99 1.89 2.45 50 6.82 9.79 3.41 4.3 2.27 2.66 52 5.69 9.28 2.85 4.02 1.9 2.47 52 6.83 9.83 3.41 4.32 2.28 2.68 54 5.7 9.37 2.85 4.06 1.9 2.49 54 6.84 9.88 3.42 4.35 2.28 2.69 56 5.71 9.45 2.85 4.1 1.9 2.52 56 6.85 9.93 3.43 4.37 2.28 2.7 58 5.72 9.54 2.86 4.14 1.91 2.54 58 6.86 9.97 3.43 4.39 2.29 2.71 60 5.72 9.62 2.86 4.17 1.91 2.56 60 6.87 10.02 3.43 4.41 2.29 2.72 62 5.73 9.7 2.87 4.21 1.91 2.58 62 6.88 10.06 3.44 4.42 2.29 2.74 64 5.74 9.78 2.87 4.24 1.91 2.6 64 6.88 10.11 3.44 4.44 2.29 2.75 66 5.74 9.85 2.87 4.27 1.91 2.62 66 6.89 10.15 3.45 4.46 2.3 2.76 68 5.75 9.92 2.87 4.31 1.92 2.64 68 6.9 10.19 3.45 4.48 2.3 2.77 70 5.75 9.99 2.88 4.33 1.92 2.66 70 6.9 10.22 3.45 4.49 2.3 2.78 72 5.76 10.06 2.88 4.37 1.92 2.68 72 6.91 10.26 3.45 4.51 2.3 2.79 74 5.76 10.13 2.88 4.39 1.92 2.7 74 6.91 10.29 3.46 4.52 2.3 2.8 76 5.77 10.19 2.88 4.42 1.92 2.71 76 6.92 10.33 3.46 4.54 2.31 2.81 78 5.77 10.26 2.89 4.45 1.92 2.73 78 6.93 10.37 3.46 4.55 2.31 2.81 80 5.77 10.32 2.89 4.48 1.92 2.75 80 6.93 10.4 3.46 4.57 2.31 2.82 Notes: Notes: Shaded cells indicate where calculated spacings exceed the maximum limit of Shaded cells indicate where calculated spacings exceed the maximum limit of 6 in. The tabulated values of spacings are in inches. Method R-S is based on 6 in. The tabulated values of spacings are in inches. Method R-S is based on the confined model proposed by Razvi and Saatcioglu (1999 and 2002). the confined model proposed by Razvi and Saatcioglu (1999 and 2002). Figure 29. Ratio of core axial load capacity to axial load demands.