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6.1.2.1 Application of Stage 1 Hold-Down

In order to prevent possible cracking of the column, the following loading protocol was followed when applying the Stage 1 hold-down force: 30% of the total load was applied to the North span; 70% of the total load was applied to the South span; 100% of the total load was then applied to the North span; and finally, 100% of the total load was applied to the South span.

6.1.2.2 Application of Stage 2 Hold-Down

Though cracking of the column was not as great of a concern during the application of the Stage 2 hold-down force, as the increase in moment was less than that which was needed to cause flexural cracking within the column, the following load protocol was followed simply out of precaution: 50% of the total load was applied to the North span; 100% of the total load was applied to the South span; and 100% of the total load was finally applied to the North span.

6.1.2.3 Horizontal Actuator Protocol

As mentioned previously, the test unit was cycled though a number of progressively increasing displacement targets during Phase 1 of testing. Initially, the test unit was subjected to low-level elastic displacements, during which the specimen was cycled through a force of positive and negative 0.25F’y, 0.5F’y, and 0.75F’y, where F’y corresponded to the condition at

which the reinforcement within the plastic hinge region of the column was expected to yield first. Following the aforementioned preliminary cycles, the test unit was cycled through the following levels of displacement ductility, µΔ, within the column plastic hinges: ±1, ±1.5, ±2, ±3, ±4, and ±6. In order to more accurately capture the cyclic behavior of the structure, including any possible strength degradation, each level of displacement ductility was subjected to three cycles. Since the maximum expected displacement ductility was approximately 5.4, the actual condition of the specimen at a displacement ductility level of 6 was not well known. It is likely that the plastic hinges within the column could achieve a ductility level higher than what was predicted, given the various assumptions that were made for material properties, especially the confined concrete behavior, which were used in

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obtaining the expected maximum ductility. Therefore, provided that the column were not near the point of failure at a ductility level of 6, an additional three cycles at a ductility level of 7.5 was planned. Table 6.1 provides the expected displacements and the corresponding lateral force resistance, as obtained from the SAP2000 grillage model, at each force and ductility level during testing.

Table 6.1: Preliminary Horizontal Testing Protocol Established for Phase 1 Testing Expected

Cycle Level Δabsolute

(in)

Absolute Actuator Force (kips) 0.25F’y 0.14 40 0.5F’y 0.30 80 0.75F’y 0.46 120 µΔ = ±1 0.94 198 µΔ = ±1.5 1.41 225 µΔ = ±2 1.89 235 µΔ = ±3 2.83 247 µΔ = ±4 3.77 257 µΔ = ±6 5.66 270 µΔ = ±7.5 7.07 278

6.1.2.4 Vertical Actuator Protocol

In order to ensure that the vertical actuators maintained stability in the system, without introducing any extraneous loads into the column, it was important to program the vertical actuators to accommodate any growth within the column. Therefore, at various horizontal displacement levels, the column growth was approximated per the procedure outlined in (Holombo, Priestley, & Seible, 1998).

The column was divided into three sections as shown in Figure 6.2, consisting of two inelastic sections, defined by the respective plastic hinge lengths at the top and bottom of the column, and the elastic portion of the column, located between the plastic hinges. Within the plastic hinge regions, the curvature was assumed to be constant, while it varied linearly over the elastic region of the column. The corresponding axial strains within each section were obtained by using the curvature, φ, to calculate the strain at the centerline of the column, εcl,

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per Equation 6.1, where D and yN.A. corresponded to the column diameter and neutral axis

depth of the column cross-section, respectively.

Figure 6.2: Estimating Column Growth in the Vertical Direction

(6.1)

The curvature and neutral axis depths were obtained via the moment curvature analysis of the column section within each plastic hinge region. However, for the elastic portion of the column, an average curvature was calculated via Equation 6.2, where Icr represented the

cracked moment of inertia of the column at first yield and an average absolute moment along the length of the column, Mave, was computed per Equation 6.3.As stated, both the moment

and curvature was assumed to vary linearly along the elastic portion of the column; therefore, an average moment and curvature was used to calculate the growth of the elastic portion of the column, which simplified the integration of growth over the region. The values MT and

MB in Equation 6.3 represent the moments in the top and bottom column hinges, respectively

and were obtained via the SAP2000 grillage analysis at the corresponding level of horizontal displacement. Additionally, the value for the neutral axis depth over the elastic portion of the column was approximated as a value of D/4.

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(6.2)

(6.3)

Once the strain at the centerline of the column was obtained for each section, it was multiplied by the length of the respective section, LT, LB, and LElastic, in order to obtain the

column growth for the section, per Equation 6.4. The values for LT and LB were calculated

per Equation 4.5. The sum of the growth over each section was then taken as the overall growth of the column.

(6.4)

It should be noted however, that Equation 6.4 is only valid in the inelastic regions after the hinges have experienced inelastic behavior, as the equation for the plastic hinge length accounted for both elastic and plastic strain penetration into the column-to-cap and column- to-footing joint regions. Therefore, for displacement levels less than the expected first yield condition, the value of L’sp was used for the length of each hinge, as it only accounted for the

elastic penetration effects into the joint region, per Equation 4.4.

Since the superstructure flexibility varied between the as-built and improved connection sides, it was appropriate to calculate a horizontal displacement vs. column growth curve for each displacement direction, pushing to the South to active the as-built positive moment connection or pulling to the North to active the improved positive moment connection detail. The resulting horizontal displacement vs. column growth curves are shown below in Figure 6.3. It should be noted that when one positive moment connection was tested in a given loading direction, the other side’s negative moment connection was also tested. For example, both the positive moment connection on the as-built side and the negative moment connection on the improved side were tested simultaneously when the superstructure was pushed to the South.

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Figure 6.3: Horizontal Actuator Displacement vs. Column Growth

The aforementioned growth curves were used to program the vertical actuators using the best fit equations included in Figure 6.3, in conjunction with active feed back from the external instrumentation, in order to maintain vertical stability within the system.