Factors affecting the seismic behavior of segmental precast bridge columns

Abstract

This manuscript discusses the design parameters that potentially affect the lateral seismic response of segmental precast post-tensioned bridge piers. The piers consist of precast circular cross section segments stacked one on top of the other with concentric tendons passing through ducts made in the segments during casting. The bottommost segments of the piers were encased in steel tubes to enhance ductility and minimize damage. An FE model was used to investigate different design parameters and how they influence the lateral force – displacement response of the piers. Design parameters investigated included the initial post-tensioning stress as a percentage of the tendon yield stress, the applied axial stresses on concrete due to post-tensioning, pier aspect ratios, construction details, steel tube thicknesses, and internal mild steel rebar added as energy dissipaters. Based on the data presented, an initial tendon stress in the range of 40%-60% of its yield stress and initial axial stress on concrete of approximately 20% of the concrete’s characteristic strength is appropriate for most typical designs. These design values will prevent tendon yielding until lateral drift angle reaches approximately 4.5%. Changing the steel tube thickness, height, or a combination of both proved to be an effective parameter that may be used to reach a target performance level at a specific seismic zone.

Keywords

finite element analysis / concrete / precast units / bridges

Introduction

The Federal Highway Administration (FHWA) and the States Departments of Transportation are in urgent need to address the challenge of aging bridges, which need rehabilitation or replacement. In addition, in the last few decades, traffic demand has grown tremendously with a limited increase in highway capacity. This resulted in surging demand on improving existing highways and constructing new highways including bridges. However, large construction projects resulted in high level of congestion during lengthy construction periods. Hence, there is strong momentum to develop technology to expedite bridge construction and different transportation agencies adopted the mantra “get in, get out, stay out.” Growing number of States employ prefabricated bridge elements and systems to accelerate bridge construction. The use of precast for construction of bridge piers and abutments can have tremendous impacts on construction schedules through time saved in establishing a work zone, forming, placing reinforcement, pouring concrete, stripping formwork and curing, all of which can be accomplished offsite and in parallel with other construction operations [ 1].

The use of precast concrete bridge piers and abutments is not a new concept. Precast post-tensioned (PPT) piers has been used in Long Key Bridge (Florida), Seven Mile Bridge (Florida), John T. Collinson Rail Bridge (Florida), Sunshine Skyway Bridge (Florida), Dauphin Island Bridge (Alabama), Neches River Bridge (Texas), Louetta Road Overpass (Texas), Linn Cove Viaduct (North Carolina), and Chesapeake and Delaware Canal Bridge (Delaware), Varina-Enon Bridge (Virginia), West Gate Free Way Viaduct (Australia) [ 2, 3]. In these projects, bonded post-tensioning tendons were used and the construction of the precast piers emulated the conventional cast in place monolithic reinforced concrete piers.

Unbonded segmental precast post-tensioned (SPPT) pier system has been evolved over the past two decades for accelerating bridge construction. In addition, unbonded SPPT piers have inherent self-centering features, which reduce residual displacement at the conclusion of an earthquake. Past research, also, showed that unbonded SPPT piers suffered less damage compared to counterpart monolithic reinforced concrete piers. Both conventional reinforced concrete (i.e., including vertical rebar and steel stirrups) and concrete encased in steel or fiber reinforced polymer tubes were used for construction of the segments [ 4– 15].

For piers having circular cross sections, past research experimentally investigated the effects of pier aspect ratio, applied initial post-tensioning stress, and confinement thickness (i.e., thickness of the steel tube). This paper used a detailed 3D finite element model, which was developed and presented in [ 11] to study the effects of tendon initial post-tensioning stress level (PT), initial concrete compressive stress due to post-tensioning (IS), pier aspect ratio (AR), different construction details of the system (CON), confinement thickness at the pier’s base (CTh), and internal energy dissipating bars (IED) on the force-displacement response of SPPT piers.

Standard SPPT Pier

The standard pier investigated in this paper (see Fig. 1(a)) was similar in dimensions to a 40% scale model namely pier JH11 tested by Hewes [ 4]. The pier consisted of four concrete segments placed on top of each other and structurally connected using a concentric unbonded tendon comprised of 27 – 12.7 mm [0.5 in] diameter ASTM A779 [ 16] Grade 270 (1860 MPa [270 ksi]) low-relaxation steel strands with a total cross-sectional area of 2665 mm² [4.13 in²]. The pier was circular in cross-section with diameter of 610 mm [24 in]. The pier has an aspect ratio (AR) of 6, where aspect ratio is defined as the distance between point of application of lateral loading and pier base divided by pier diameter. The unbonded tendon length was L_t = 4953 mm [195 in]. During the experimental work, the pier was subjected to an initial post tensioning stress corresponding to approximately 45% of the yield strength of the tendons.

The bottommost segment of the pier utilized a 6.0 mm [0.24 in] thick, ASTM A569 [ 17], A36 steel jacket to provide the relatively high level of lateral confinement which is required due to the high compressive strains associated with a pier rocking about its base. The steel jacket started from the top of the bottommost segment and terminated approximately 25.4 mm [1.0 in] above its bottom to prevent the jacket from bearing on the footing during testing. This resulted in a jacket height of approximately 585 mm [23 in] or approximately 17% of the pier height. The steel used in jacketing the segment had yield and ultimate strengths of 317 [46 ksi] and 460 MPa [67 ksi], respectively. The jacketed segment did not contain any longitudinal reinforcement other than the post-tensioning tendons. Segments two through four (i.e., the three non-jacketed segments) had 8 #4 (Gr. 60) as longitudinal rebar spaced evenly around the perimeter of the section. This corresponds to a longitudinal non-prestressed reinforcement ratio of 0.35%. These bars were used to position the stirrups and hence were not continued between segments. The characteristic concrete compressive strength (f′_c) used was 41.4 MPa [6000 psi]. All other segments above the bottommost segment were constructed as conventional reinforced concrete segments having transverse spiral of #3 of Grade 60 spaced at 75 mm [3.0 in] for lateral confinement. The upper non-jacketed segments had a concrete cover of 25.4 mm [1.0 in]. The pier cross section was selected to be circular since jacket confinement is very effective for circular cross sections compared to rectangular ones.

Throughout this manuscript the standard pier was used for the analysis. However, to evaluate the effect of pier aspect ratio on pier response, a squat pier – namely “Pier B” – was also used in the investigation. The pier characteristics are identical to the standard pier in this manuscript but with an aspect ratio of 3. It consisted of only two segments resulting in a clear height of 1524 mm [60 in] instead of 3354 mm [132 in] for the standard pier.

Summary of the 3D finite element model

ABAQUS/Standard version 6.8-2 [ 18], a general-purpose finite element code, was selected as a basic platform for developing a 3D detailed finite element (FE) model during this study. The model was built up using 3D continuum elements for concrete and fiber components and 3D beam elements for the post-tensioning tendons (Fig. 2). The detailed description and validation of the model are given by [ 11].

The concrete damaged plasticity model [ 19, 20] was used to model the concrete material behavior while the classic metal plasticity model was used for the tendon’s material. The fiber tube was modeled as an elastic orthotropic material. The ends of the tendon were embedded in the loading stub (that represents the superstructure) and the foundation to simulate the tendon’s anchorage. The tendon was subjected to a stress type initial condition to simulate its post-tensioning. By neglecting the sliding of the foundation and by assuming a rigid soil underneath the foundation, the bottom surface of the foundation was constrained in the three motional directions. A typical pier loading stages were: a) tendon’s post-tensioning; b) application of a vertical external gravity load; and c) application of a monolithically increasing lateral displacement.

Figure 2 shows a summary of the detailed finite element pier model. This model was used to study the effects of six parameters on the force-displacement response of SPPT piers. The effects of tendon initial post-tensioning stress level (PT), initial concrete compressive stress due to post-tensioning (IS), pier aspect ratio (AR), different construction details of the system (CON), confinement thickness at the pier’s base (CTh), and internal energy dissipating bars (IED) on the overall behavior of the system were investigated. Table 1 summarizes the different values assigned for each parameter. The range of these parameters was selected to investigate a wide spectrum of values and does not necessarily reflect typical values to be used in practice.

Results and discussions

Effects of initial post-tensioning level in the tendon

The first parameter investigated in this study – the PT series – was the level of initial tendon stress. The initial post-tensioning stress ranged from 30% to 90% of the yield strength of the tendons while changing the cross sectional area from 4000 mm² [6.2 in²] to 1300 mm² [2.0 in²], respectively, to maintain the axial stresses on the concrete invariant at 7.17 MPa [1040 psi] which corresponds to 17% of f′_c. Figure 3 shows the lateral drift at the loading point (middle of the loading stub) versus the measured the lateral resistance of the different piers. The lateral drift was defined as the ratio of the measured lateral displacement divided by the height of the loading point above the pier base. As shown in the figure, all the piers reached their ultimate strengths at a lateral drift angle of approximately 3%. Beyond that, a gradual degradation in the strength occurred and the analysis ended at a lateral drift angle of 5%. At this drift level, a reduction of approximately 14% occurred in the strengths of the piers. The analysis truncated due to stress concentrations occurred at the bottom of the second segment. Similar stress concentrations occurred at the top and bottom of the bottommost segment. However, since the bottommost segment was confined using the steel jacket, the segment was able to reach high strains without any potential concrete crushing. However, the second segment was a conventional RC segment and the strains in the concrete cover exceeded a potential spalling strain of 0.003 mm/mm.

Figure 3 shows that changing the initial post tensioning stress in the tendon while maintaining constant initial axial stress on the concrete segments does not have a major effect on the backbone curve of the system. Surprisingly, in no case yielding of the tendon was observed. Since the post-tensioning tendon was placed in the geometric centroid of the pier, the increase in the tendon stress due to interface joints opening initiated after significant drift of the pier took place. Figure 4 shows the lateral drift vs. the peak stress in the tendon for each pier. As shown in the figure, the increase in the tendon stress started at a lateral drift angle of approximately 1% and beyond that the increases in the post-tensioning stresses were quite small. The post-tensioning stresses reached their peak values at a lateral drift of 3% when the piers reached their peak strength. As explained earlier the tendons did not reach their yield strength. Beyond 3% drift, both the strengths of the piers and the stresses in the tendons started to decrease due to damage at the bottom of the second segments.

A second reason for the elastic response of the tendon was the relatively long unbonded length of the tendon. For a squat pier, the unbonded tendon length is relatively small and thus larger incremental tendon strains occur with increasing the applied lateral displacement, resulting in potential yielding of the tendon if it was initially stressed to high initial stress levels. Figure 5 shows the effects of the level of the initial post-tensioning stresses on the response of Pier B. Only three levels of initial post-tensioning stresses were investigated namely, 40%, 60%, and 80% of the yield stress of the tendon. Figure 6 shows the peak stresses in the tendons versus the lateral drifts of Pier B.

As shown in Figs. 5 and 6, increasing the initial post-tensioning stresses to 60% and 80% of the tendon yield stresses resulted in yielding of the tendon at lateral drift angles of 5.5%, and 2.5%, respectively. In addition, Fig. 6 shows that the increase in the tendon stresses started at small lateral drifts of approximately 0.2% which is significantly smaller than in the case of the more slender standard pier. Moreover, the rate of the strain increase in the post-tensioning is higher in the case of the squat piers compared to the slender piers. For small initial stresses of 40% of the yield stress, no yielding of the tendon was observed and the tendon reached a peak stress of approximately 82% of its yield stress followed by concrete crushing and the analysis stopped. Such crushing at high drift angle of 7% led to brittle failure as indicated in Fig. 5.

For initial tendon stresses of 40% of the yield stress (Fig. 5), the pier was able to develop peak strength of 650 kN [146 kips] at a lateral drift angle of 7% where the concrete started to crush and the analysis stopped at a lateral drift angle of 8%. However, such drift angle is beyond the anticipated level of drift angle for a typical bridge. Priestley et al. [ 21] recommended a drift angle of 4.5% for a bridge at the collapse prevention limit state. For high initial stress in the tendons, the piers reached lateral strengths of 580 kN [130 kips] and 480 kN [108 kips] at lateral drift angles of 5.5% and 2.5% for initial post-tensioning stresses of 60 and 80% of the yield stress. Once the tendon yielded, the pier reached its peak strength and substantial decrease in the tangent stiffness of the system occurred. Based on these analyses and within the scope of this study it appears that an initial post-tensioning stress in the tendon that range from 40 to 60% of the tendon yield stress is suitable for design. A squat pier (AR= 3) with an initial post-tensioning stress of 60% of the tendon yield stress would reach yielding of the tendon at a lateral drift of 5.5%. It should be noted that this drift value significantly depends on the provided confinement at the bottom segment.

Effects of initial stresses (IS) on the concrete

The second parameter investigated in this study – the IS series – was the level of the initial axial compressive stress imposed on the concrete due to post-tensioning forces. This was achieved by maintaining the tendon’s post-tensioning stress constant at 45% of its yield stress while changing the tendon cross-sectional area from 1980 mm² to 4990 mm² [3.07 in² to 7.73 in²]. This resulted in axial stresses in the concrete ranging from 5.38 MPa [780 psi] to 12.83 MPa [1860 psi] which corresponds to 13% to 31% of f′_c.

Figure 7 shows the lateral drift angle versus the lateral resistance of the piers with different initial stresses on the concrete. Increasing the applied axial stresses on the piers increased the nominal strengths, the ultimate strengths, and the post-elastic stiffness of the piers. However, the increase in the applied initial post-tensioning stress on the concrete resulted in a reduction in the ultimate drift angles and the drift angle at the maximum lateral load. For small axial stresses on the concrete segments, the geometric nonlinearity, i.e., the rocking mechanism was predominant, while for the case of high axial stresses the material nonlinearity was dominant leading to concrete crushing at smaller drift angles. This resulted in two features in the backbone curves (Fig. 7): 1) the transition between the initial and post-elastic stiffness is abrupt for small axial stresses compared to high initial stresses; and 2) the slope of the lateral resistance—drift curves beyond the peak strength is relatively sharper for higher concrete initial axial stress resulting in small ultimate drift angles. This is attributed to the high stresses accumulated by the rigid body rocking that result in more brittle failure. Finally, the change in the areas of post-tensioning tendons did not change the initial stiffness of the investigated columns. However, the post-elastic stiffness of specimens having higher areas of post-tensioning tendons is slightly higher than those with smaller areas of post-tensioning tendons.

Figure 8 shows the peak stress in the post-tensioning tendon normalized by its yield stress vs. the lateral drift of the standard piers. As shown in the figure, in no case did tendon yielding occur. In addition, the rate of increase in the post-tensioning stress was slightly higher for piers having smaller axial stress on the concrete since piers that were subjected to small axial stress due to post-tensioning were able to reach deformation higher than other piers subjected to higher post-tensioning forces (Fig. 7). Decreasing the applied axial stress due to post-tensioning made the rocking response and geometric nonlinearity more dominant compared to the deformation in the case of high applied axial stress due to post-tensioning.

Based on these analyses, it seems an initial concrete axial stress of approximately 20%f′_c is reasonable for design of piers similar to those examined in this manuscript. The slender piers that were subjected to axial concrete stresses of approximately 20% of f′_c or less were able to reach an ultimate drift angle of 4.5% or larger.

To investigate this recommendation for a squat pier, Pier B was analyzed under different axial concrete stresses ranging from 19 to 31% f′_c. Figure 9 shows the effects of the applied axial stresses on the concrete on the backbone curves of Piers B. As shown in the figure and similar to the case of the standard pier, increasing the applied axial stress due to post-tensioning slightly increased the strength of the piers; however, it significantly increased the post-elastic stiffness and decreased the ultimate drift angle. Piers that were subjected to an axial stress of approximately 22% of f′_c or less were able to reach an ultimate drift angle of 5% or greater.

Figure 10 shows the variation of peak stresses in the tendons versus the lateral drift for Pier B for the different applied axial stresses on the concrete segments. As shown in the figure, in no case did yielding of the tendon occur.

Effects of pier aspect ratio

The third parameter investigated in this manuscript was the effects of increasing the aspect ratio – AR series – of the piers from 3 to 9 by adding one more segment from one pier to the other as shown in Fig. 11. Figure 12 shows the lateral resistance of the different piers versus the lateral drift angle measured at the loading point. Increasing the aspect ratio of the piers from 3 to 9 decreased the initial stiffness and the ultimate drift angle (Fig. 12(a)) but increased, to a lesser extent, the ultimate displacement (Fig. 12(b)). Failure of squat piers was more abrupt compared to slender piers since in the squat piers more stress concentration and damage occurred at the bottom of the second segment compared to slender piers. The slope of the post-elastic stiffness increased with decreasing the pier aspect ratio. Figure 13 shows an approximate mechanism for the rotation of two piers having two different aspect ratios, assuming rigid rotations of the segments over each other and also assuming that only the interface joint between the bottommost segment and foundation will open. For both piers to reach the same displacement, the ratio of the rotation of the squat piers (θ_squat) to the rotation of the slender piers (θ_slender) i.e., (θ_squat/θ_slender) should be approximately equal to H/h where h, H, θ_squat and θ_slender are shown on Fig. 13. Because the rotation in the squat pier is higher, the elongation of the tendon in the squat pier is higher. Additionally, for the squat pier the unbonded tendon length is shorter than in the case of the slender pier, resulting in higher incremental strains and higher incremental post-tensioning stresses. Such increases led to an increase in the slope of the post-elastic stiffness. It is worth noting that in no case did the tendon reach its yield strain and in all cases the analysis stopped due to concrete crushing at the bottom of the second segment which was not confined with a steel jacket.

Effects of construction details

The fourth parameter investigated – CON series – was the effect of different construction details on the behavior of the pier system. As shown in Fig. 14, case CON-1 was a pier constructed similar to the standard pier with steel tube confining 17% of the pier height. Pier CON-2 represents a different construction scenario where the bottommost two segments in the pier CON-1 were replaced by a single segment cast monolithically while maintaining the steel confinement height and thickness unchanged from those used for pier CON-1. In the case of pier CON-3, the three lowest segments were cast monolithically while maintaining the same steel confinement configuration. Pier CON-4 had construction details similar to pier CON-1 except that the two lower segments of pier CON-4 were both confined by steel tubes having a thickness of 6 mm [0.24 in] i.e., the confinement was extending over 45% of the pier height. In Fig. 14, the hatched areas represent segments confined by external steel tubes. The joints between segments were dry joints i.e., neither epoxy nor shear keys were used and shear transferred between different segments by friction. The surface between any two concrete segments was modeled using standard hard contact with finite sliding formulation and node to surface discretization with a coefficient of friction of 0.5. The normal component of contact between concrete segments was modeled using standard hard contact with no penetration.

Figure 15 represents the backbone curves for the different piers of series CON. As shown in the figure, the ultimate displacement of the pier CON-2 is approximately 140% of that of the pier CON-1. In the case of pier CON-1, the pier failed due to stress concentration at the interface between the lowest two segments resulting in spalling and crushing of the concrete at the second segment. The concrete of the second segment was less ductile than that of the bottommost segment due to the confining steel tube. Pier CON-2 has the advantage of the continuation of stresses between the first two segments (no interface joint opening), and consequently concentrated the stresses at the interface joint between the foundation and the bottommost segment. The high confinement of the lower segment prevented the premature failure of the pier due to high stress concentrations that happened in the case of pier CON-1.

Removing the interface joint between the second and the third segments in the case of pier CON-3 had minor effects on the ultimate drift angle. Since the joint opening at this interface in pier CON-2 was minimal, removal of the joint for CON-3 had little influence on response.

Another option to prevent premature failure due to stress concentration at the interface joint between the first and second segment was to encase the second segment in a steel tube as shown for pier CON-4 in Fig. 14. As expected, in the case of pier CON-4, the ultimate drift angle increased to approximately 160% and 115% of the ultimate drift angles of the piers CON-1 and CON-2, respectively. This indicated the importance of designing the confinement of each segment to obtain the optimum performance of the pier from structural and economical point of views. This analysis showed an important conclusion that a design engineer can achieve a target displacement performance point using either an appropriate segment height, appropriate confinement configuration, or a combination of the two.

Effects of confinement thickness

The fifth parameter investigated in this study – series CTh – was the effect of changing the confinement ratio of the bottommost segment on the backbone behavior of the system. The volumetric reinforcement ratios chosen ranged from 3.9% to 1% which corresponds to a steel tube thickness of 6.0 mm [0.24 in] to 1.5 mm [0.06 in]. These thicknesses were used for confinement in two different scenarios: the first scenario (Fig. 16(a)) where only the bottommost segment was confined; the second scenario where the two bottommost segments (Fig. 16(b)) were confined. As shown in the figure, the confinement volumetric reinforcement ratio had minimal effect in the case of confining only the lower segment since failure occurred mainly at the second segment due to concrete cover spalling. On the other hand, increasing the confinement thickness of the two bottommost segments enhanced the ductility and increased the ultimate displacement by approximately 100% when the confinement thickness increased from 1.5 mm [0.06 in] to 6.0 mm [0.24 in]. Increasing the confinement thickness had no effect on the nominal lateral strength but slightly increased the post yield stiffness. This shows that the confinement volumetric reinforcement ratio and height are very important parameters to fulfill the required performance level in a given seismic zone.

Effects of adding internal energy dissipaters

The last parameter investigated in this study was the effect of adding ten mild steel rebar as internal energy dissipaters (IED) to the interface joint between the base and the bottommost segment as well as at the interface between the bottommost segment and the second segment. During earthquake ground motion such mild steel bars would yield increasing the energy dissipation of the system. The rebar had nominal diameters of 0 (i.e., no IED), 10 mm [#3], 13 mm [#4], 22 mm [#7], and 25 mm [#8] corresponding to reinforcement ratios of 0, 0.2%, 0.4%, 1.3%, and 1.7%, respectively. Each rebar extended 305mm [12 in] on each side of the interface joints which representing one-half the height of the bottommost segment. Figure 17 shows the backbone curves for the different piers having the internal rebar. As shown in the figure, adding internal mild steel rebar, as energy dissipaters, increased the ultimate strength. However, failure of the piers having such rebar was quite brittle with limited drift angle capacity. Adding the rebar changed the mode of failure from compression controlled, for pier IED#0—without internal rebar, to anchorage failure in the rebar due to the limited development length (Fig. 18). In general, increasing the rebar size decreased the ultimate drift angle but increased the ultimate strength of the piers. Figure 19 shows the relationship between pier lateral drift angle versus the normalized tensile stress in the rebar located at the extreme tension side of the pier. The normalized tensile stress is defined as the stress in the rebar normalized by its yield stress. The figure shows that in the case of small rebar diameters, i.e., #3 (i.e., reinforcement ratio of 0.2%), and #4 (i.e., reinforcement ratio of 0.4%), the mild bars reached their yield strength before the failure of the pier occurs. However, the rebar were not able to develop their complete over-strength stresses. For large rebar diameters i.e., #7 and #8 the mild rebar didn’t reach their yield stress and the use of large rebar diameter led to a high tensile stress concentration at the ends of the rebar causing truncation of the analysis. Such stress concentration would lead to anchorage failure in real applications. Yielding of the rebar potentially will lead to higher energy dissipation, high residual displacement, and more concrete damage. However, the rebar should be well designed to avoid brittle anchorage failure. Wang et al. [ 22] used a proprietary nuts and plates to prevent this type of failure. Using small rebar diameters such as #3 and #4 as well as using appropriate heights for the segments will reduce the potential of anchorage failure. In addition to avoiding anchorage failure, the design engineer should design a clear unbonded length of the rebar that extend between two segments to reduce potential low cycle fatigue rupture. Finally, it should be noted that the maximum amount of energy dissipater bars should be proportional to the axial loads to ensure closure of the segment joints at the conclusion of an earthquake.

Findings and conclusions

This paper discusses the seismic behavior of the SPPT bridge pier system. The piers examined in this article consisted of precast segments stacked on each other and sandwiched between a reinforced concrete foundation and the bridge superstructure. The system was connected by unbonded post-tensioning tendons passing through ducts created in the segments during casting. The bottommost segments of the piers were encased in steel tubes to enhance its ductility. An FE model was used to investigate different design parameters and how they affect the backbone curves of a given pier. Different parameters including: initial post-tensioning stresses as a percentage of the tendon yield stress, the applied axial stresses on concrete due to post-tensioning, the piers aspect ratios, construction details, confinement thicknesses, and adding internal mild steel rebar as energy dissipaters are discussed in this manuscript. The analyses revealed that:

1) Increasing the post-tensioning stresses in the tendon by decreasing its cross sectional area while keeping the same axial stress on the concrete did not have significant effects on pier having aspect ratio of 6. In this case tendons will not likely yield. On the other hand, increasing the initial post-tensioning stresses in the tendons of pier having an aspect ratio of 3 led to yielding of the tendons at large drifts which decreased both the pier’s tangent stiffness and the ultimate strength. Based on the data analyzed in this manuscript, it seems that an initial tendon stress of 40-60% of its yield stress will be appropriate for design purposes. Using this initial post-tensioning stress will not lead to yielding of the tendon until a lateral drift angle of approximately 4.5% which has been recommended as collapse prevention limit state for concrete bridges. Using initial post-tensioning less than 40% may result in uneconomical design.

2) Increasing the initial axial stresses on concrete segments by increasing the post-tensioning forces significantly increased the nominal and ultimate strengths, but reduced the ultimate drift angles due to concrete compression failure at the toe of the segment joint. Based on the data analyzed in this manuscript, an initial axial stress on the concrete of approximately 20% of f′_c seems appropriate for design purposes.

3) Increasing the aspect ratio of the piers led to a decrease of the initial stiffness and post-elastic stiffness as well as the nominal lateral load. On the other hand, increasing the aspect ratio led to a less brittle descending branch of the backbone curves and increased displacement capacity.

4) Encasing the concrete segments in steel tubes significantly increased the ductility of the SPPT piers. However, However, the volumetric confinement ratio and height of the steel tubes are critical are critical parameters that can be tailored to fit different seismic demands.

5) Adding internal energy dissipaters to the piers led to an increase in the ultimate strength and post elastic stiffness. Using small reinforcement ratios resulted in yielding of the rebar potentially leading to high energy dissipation and residual displacement. On the other hand, using high reinforcement ratios resulted in elastic response of the rebar potentially leading to small energy dissipation and residual displacements. However, adequate development length should be provided to avoid concrete brittle failure.

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