Performance-Based Seismic Bridge Design (2013)

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68 CHAPTER TEN SUMMARY OF ORGANIZATION AND PROJECT-SPECIFIC CRITERIA This chapter summarizes the organization- and project- specific criteria reviewed and discussed in chapters eight and nine. Criteria will be compared for trends, consensus, and differences. Summary tables of material strain lim- its used in bridge and waterfront structure performance- based guidelines and codes also will be are provided and discussed. SUMMARY OF CRITERIA Table 23 provides summary information for the organiza- tional criteria that have been reviewed in chapter eight, and Table 24 provides information for specific projects discussed in chapter nine. The narrative on seismic hazard and performance objec- tives and the summary tables make it clear that no general consensus exists regarding criteria. One reason for the apparent lack of consensus is that AASHTO criteria were changing and improving during the years that are covered by the tables. The AASHTO seismic criteria evolution started in 1990 with a single-level 500-year return period. Then, a 2,500- year ground motion was proposed by the MCEER/ATC 49 project, which first included a two-level approach (includ- ing a 108-year lower level), but the final product contained only a single-level hazard at 2,500 years. Finally, in the late 2000s AASHTO settled upon a single-level, 1,000-year seis- mic hazard. When comparing the entries in the tables, the trends that somewhat follow what AASHTO was using or considering at a given time are evident. This lack of consensus is also caused by the fact that no single solution is best for all projects. This leads to agencies such as Caltrans using a peer review process to develop appro- priate criteria for each major project. This process develops performance criteria on factors such as ground motion haz- ard, bridge type, bridge use, local emergency needs, avail- ability of alternate routes, and the local or regional economy. The data in the preceding tables has been further sum- marized and combined with other metrics discussed earlier in the report in Table 25. This table provides a compre- TABLE 23 SEISMIC DESIGN CRITERIA FOR AGENCIES/ORGANIZATIONS Organization Year Ground Motion1 Damage Performance Ground Motion2 Damage Performance Caltrans Ordinary 2010 NA NA NA SEE Maximum of 5% in 50 yr (1,000-yr RP) and deter- ministic ground motion Significant, no collapse Impaired Caltrans Important 2010 FEE project-specific defined by peer review panel Minimal Immediate SEE project-specific defined by peer review panel Repairable Limited SCDOT Operational Class I 2008 FEE 15% in 75 yr (500-yr RP) Minimal Immediate SEE 3% in 75 yr (2,500-yr RP) Repairable Maintained SCDOT Operational Class II 2008 FEE 15% in 75 yr (500-yr RP) Repair- able Maintained SEE 3% in 75 yr (2,500-yr RP) Significant Impaired SCDOT Operational Class III 2008 NA NA NA SEE 3% in 75 yr (2,500-yr RP) Significant Impaired ODOT 2011 15% in 75 yr (500-yr RP) Minimal Open in 72 hours 7% in 75 yr (1,000-yr RP) Significant Impaired Notes: 1. Return periods shown are approximate. 2. If no percent exceedance is provided, then none was provided in the source data. FEE = Ffunctional Eevaluation Eearthquake; SEE = Ssafety Eevaluation Eearthquake. Terms are those used by the agencies. NA = not available.

69 hensive summary of the data presented in this synthesis, organized by damage descriptors along the top and seismic hazard (in terms of return period) down the side. The dam- age descriptors were taken from visual catalog developed by Caltrans (2006b) and Hose and Seible (1999), which were discussed in the Damage States section of chapter six. Additionally, stated damage descriptors in the criteria source documents have been included in the table, although some interpretation was required to place the information in the cells. There is some ambiguity in this process in terms of where one level or definition stops and the other begins. The performance in terms of damage, reparability, and operational are actually continua, not discrete steps that can be absolutely put into definitive cells. This table melds many descriptors in order to develop a perspective on performance objectives used by different agencies and on different major projects. No effort has been made to bring in international data, such as Japan’s data, because of dif- ficulties in assigning return periods. The damage descriptors in the table are intended to apply at a system level for a bridge, although the detailed descrip- tions of damage are keyed to the ductile (energy-dissipating) elements in a conventional RC substructure. For ordinary bridges, most criteria permit damage in the upper-level event to approach, but not extend into, the collapse region (DL V). In this table, the line between DLs IV and V represents the transition in the strength-degrading region of performance that would precede collapse. This would physically corre- spond to buckling and fracture of bars and loss of confine- ment as a result of the rupture of transverse reinforcement. Several trends are evident in the table and in the descrip- tion of its development. The general trend of increasing rigor or improvement in response for more important struc- tures is similar to the conceptual layout of Figure 6 that was developed by SEAOC in the Vision 2000 document. For a given structure, the diagonal down and to the right repre- sents more damage in larger earthquakes, and the diagonal down and to the left represents increases in design controls to minimize damage for more important structures. Also evident is a convergence of criteria toward the 1,000-year return period for either the single-level criteria or the upper level of two-level criteria. Two-level criteria are common for more important structures, but also for the FHWA Retrofit- ting Manual, SCDOT, and ODOT. One can also see a trend toward the use of longer return periods for those geographic locations where the seismic hazard at 2,500 years is much higher than that at 500 or 1,000 years (i.e., the central and eastern United States). TABLE 24 SEISMIC DESIGN CRITERIA FOR VARIOUS PROJECTS Project and Agency Year Ground Motion1 Damage Performance Ground Motion2 Damage Performance Cooper River Bridge SCDOT Critical Access Path 2000 FEE 15% in 75 yr (500-yr RP) Minimal Immediate SEE 3% in 75 yr (2,500- yr RP) Repairable Functional; emer- gency vehicles SR 520 Floating Bridge WSDOT 2011 NA NA NA 7% in 75 yr (1,000-yr RP) Repairable Maintained West Approach SFOBB Caltrans 2002 FEE 40% in Life (300-yr RP) Minimal Immediate to all vehicles SEE 1,000– 2,000-yr RP Repairable Immediate; emer- gency vehicles Antioch Toll Bridge Retrofit Caltrans 2010 N/A (Low ADT) NA NA SEE 1,000-yr RP Significant, No collapse Impaired Vincent Thomas Bridge Retrofit Caltrans 1996 FEE 40% in 150 yr (285-yr RP) Repairable Immediate SEE 16% in 150 yr (950-yr RP) Significant Emergency vehi- cles within days Columbia River Crossing, ODOT & WSDOT 2008 FEE 15% in 75 yr (500-yr RP) Minimal NR SEE 3% in 75 yr (2.500-yr RP) Significant No collapse NR I-40 Bridge, Mississippi River TDOT 1992 NA NA NA 2% in 50 yr (2,500-yr RP) Minimal Serviceable Notes: 1 Return periods shown are approximate. 2 If no percent exceedance is provided, then none was provided in the source data. FEE = functional evaluation earthquake; SEE = safety evaluation earthquake. Terms are those used by the agencies. NA = not available, NR = not reported.

70 It is difficult to put all the damage descriptors and criteria together in one table without some ambiguity or inconsisten- cies. This is because the terminology used in various criteria and reconnaissance and laboratory work is not always consis- tent; nor are the statements of performance objectives. There- fore, an effort to develop a consistent description of these terms on a national level would be useful. A large amount of data are already available, but what remains to be done is a synthesis of those data into a document that could be used consistently by the U.S. bridge engineering community as a whole. Such a project is beyond the scope of this synthesis. MATERIAL STRAIN LIMITS Earlier in this synthesis, the use of material strain limits to determine flexural damage limit states was discussed. Following is a summary of strain limits specified for new design in bridge and marine/waterfront performance-based codes and guidelines. This summary provides a brief sur- vey documenting which flexural damage states have been incorporated and the specific strain values associated with each. The following tables address strain limits for tension in A706 mild reinforcement (Table 26), tension in prestress- TABLE 25 COMBINED PERFORMANCE, DAMAGE, AND HAZARD FOR SELECTED AGENCY- AND PROJECT-SPECIFIC CRITERIA D am ag e D es cr ip to rs Damage Level I II III IV V Classification None Minor Moderate Life safety Collapse Damage Description None Minimal Repairable Significant Collapse Physical Description (Reinforced Concrete Elements) Hairline cracks First yield of ten- sile reinforcement Onset of spalling Wide cracks extended spalling Bar buckling bar fracture confined concrete crushing Displacement Ductility μ∆ ≤ 1 μ∆ = 2 μ∆ = 4 to 6 μ∆ = 8 to 12 Repair Reparability None/no interruption Minor repair/ no closure Repair/limited closure Repair/weeks to months closure Replacement P er fo rm an ce D es cr ip to rs Availability Immediate open to all traffic Open to emergency vehicles only Closed Performance Level Fully operational Operational Life safety Collapse Retrofit Manual PL3 PL2 PL1 NA Agency or project-specific criteria are shown below S ei sm ic H az ar d R et ur n P er io d 100-yr RP RM-E RM-S 300-yr RP VTR SFOBB-WA 500-yr RP SC-OC I SC-OCII ODOT CRC 1,000-yr RP LRFD-C LRFD-E SGS B/C* RM-E LRFD-O SGS-D RM-S CA-SDC ODOT* VTR Antioch SR520* SFOBB-WA* 2,500-yr RP I-40 MR (isolated) LRFD-C SC-OC I SC-OC II SC-OCI II CRC Key: LRFD-O—AASHTO LRFD Spec Ordinary. SC-OC1—SCDOT Operational Class I also Cooper River CAP structures. LRFD-C—AASHTO LRFD Spec Critical. SC-OCII—SCDOT Operational Class II. LRFD-E—AASHTO LRFD Spec Essential. SC-OCIII—SCDOT Operational Class III. SGS-D—AASHTO SGS SDC D also Caltrans SDC. ODOT—Oregon BDM. SGS-B/C—AASHTO SGS SDC B&C Implicit Eqns. VTR—Vincent Thomas Bridge retrofit LA River, CA. CA-SDC—Caltrans Seismic Design Criteria. SFOBB-WA San Francisco Oakland Bay Bridge West Approach retrofit. RM-S—FHWA Retrofit Manual Standard >50 yr. Antioch—Antioch Bridge San Joaquin River, CA. RM-E—FHWA Retrofit Manual Essential >50 yr. I-40 MR—I-40 retrofit Mississippi River, TN. CRC—Columbia River Crossing WA/OR. Damage Descriptors—Caltrans (2006b), Hose and Seible (1999), and cited agency/project-specific criteria. Note that the Life-Safety classification and performance level have been moved to correspond to Damage Level IV to match actual practice. Note: “ * ” indicates that the stated criteria would lie between delineations in table. For instance, SGS C would lie between B and D, and the ODOT, SR-520, and SFOBB-WA criteria would lie on the lower end of the Damage Level within which they are shown within (e.g., DL III.5).

71 ing steel (Table 27), compressive concrete strain (Table 28), and structural steel pipe piles (Table 29). These four material categories are used in the codes and guidelines to determine the flexural deformation limits for reinforced and prestressed concrete, and structural steel (pipe pile) beam-columns. Within each table are columns listing the agency produc- ing the code or guideline, the year of publication, the seis- mic hazard in terms of probability of exceedance and return period, the structural component, and location of plastic hinging. There are also columns showing whether the code or guideline explicitly relates the strain limit to a specific damage level (yes or no), then a column describing the asso- ciated damage state. If the code or guideline associates an explicit damage state to the strain limit, then the damage state is provided. In cases where the code or guideline does not explicitly relate the strain limit and damage state, the authors have provided an inferred damage state based on the overall intent of seismic design philosophy described in the code or guideline, related research, and engineering judgment. In some cases it was difficult to infer the intended damage state. Several observations can be made regarding the strain limit tables. First, most of the codes and guidelines surveyed do not explicitly relate the strain limit to the specific dam- age state the strain limit is intended to prevent. For example, the strain limits for steel pipe piles do not have clear links between strain and damage. Do the limits prevent pipe bulg- ing, buckling, or tearing? Damage can only be inferred with the information provided within the code or guideline. If a damage state is not linked to the strain, it is difficult for TABLE 26 TENSION STRAIN LIMITS—MILD REINFORCING STEEL (A706 - GRADE 60) Agency Year Ground Motion Component and Location Explicit Dam- age State? Damage State Strain Limit (in./in.) AASHTO SGS 2011 7% in 75 yr (1,000-yr RP) RC column plastic hinge No Bar fracture #4 - #10 0.090 #11 - #18 0.060 SCDOT 2008 3% in 75 yr (2,500-yr RP) RC column plastic hinge No Bar fracture #4 - #10 0.090 #11 - #18 0.060 Caltrans 2010 5% in 50 yr (1,000-yr RP) RC column plastic hinge No Bar fracture #4 - #10 0.090 #11 - #18 0.060 Priestley et al. 2007 Serviceability RC column plastic hinge Yes Crack control (< 1.0 mm) 0.010–0.015 Damage Control Yes Bar fracture 0.6 su 0.06 Kowalsky 2000 Serviceability RC column plastic hinge Yes Crack control (< 1.0 mm) 0.015 Damage Control Yes Bar fracture 0.060 POLA/POLB 2010/ 2009 50% in 50 yr (72-yr RP) Solid concrete pile-to- deck plastic hinge No Crack control 0.015 10% in 50 yr (475-yr RP) No Bar fracture 2/3 of 2% in 50 yrs (2/3 of 2,475-yr RP) No ? POLA/POLB 2010/ 2009 50% in 50 yr (72-yr RP) Hollow concrete pile-to- deck plastic hinge No Crack control 0.015 10% in 50 yr (475-yr RP) No ? 2/3 of 2% in 50 yrs (2/3 of 2, 475-yr RP) No Bar fracture POLA/POLB 2010/ 2009 50% in 50 yr (72-yr RP) Concrete plug in steel pipe pile-to-deck plastic hinge No Crack control 0.015 10% in 50 yr (475-yr RP) No Bar fracture 2/3 of 2% in 50 yr (2/3 of 2, 475-yr RP) No ? MOTEMS 2011 50% in 50 yr (72-yr RP) Pile-to-deck plastic hinge No Crack control 0.010 10% in 50 yr (475-yr RP) No Bar fracture 0.050 MOTEMS 2011 50% in 50 yr (72-yr RP) RC drilled shaft or pre- stressed concrete pile In-ground plastic hinge No Crack control 0.010 10% in 50 yr (475-yr RP) No ? 0.025 su = ultimate tensile strain of reinforcing steel.

72 engineers to know what performance is intended (i.e., what damage is prevented) by adherence to the strain limit. If the engineers do not know this information, then it is impos- sible for the owner/stakeholder to know what the level of increased performance is intended by performance-based design other than the often succinct description provided within the design philosophy of the code or guideline. These descriptions typically discuss damage in terms of “no dam- age,” “minimal damage,” “repairable damage,” or “signifi- cant damage,” with no quantification of specific damage levels, such as crack width, depth of spalling, or onset of bar buckling or bar fracture. Second, the strain limits for specific damage states are gen- erally in agreement between different codes and guidelines. This is likely more a function of the heavy influence of Cal- trans, M .J. N Priestley, and others in the development of per- formance-based guidelines for bridges and marine structures than of separate organizations coming to the same conclusions. Although some variations do exist, the difference likely results from the objectives of the performance criteria. For example, the strain at concrete cover spalling is often set at 0.008 in./in. for deep in-ground plastic hinges, while 0.004 or 0.005 in./in. is used for plastic hinges above or near the surface of the ground (i.e., plastic hinges forming less than 10 pile diameters below ground). Although this may appear to be a discrepancy at a cursory glance, the increased strain at spalling for in-ground plastic hinges is a result of the increased confinement of the cover concrete provided by the surrounding soil. An exception to the congruency between codes and guidelines is the ulti- mate strain allowed for prestressing strands, where strain lim- its range from 0.025 to 0.05 in./in. Under monotonic loading, prestressing strands can generally withstand strains up to 0.05 to 0.07 in./in.; however, the effects of low-cycle fatigue and buckling are poorly documented. Furthermore, none of the codes or guidelines provides justification or references for the strain limit adopted. It can only be assumed that the published strain limits represent conservative best estimates to safeguard against strand fracture. Finally, the strain limits are generally based on conser- vative rule-of-thumb estimates of the strain at the initiation of damage. For example, strain limits for mild (A706) rein- forcing steel typically use 60% to 70% of the ultimate strain under monotonic loading ( ) to establish a reduced ultimate strain under cyclic loading resulting from low-cycle fatigue and buckling. Although the use of such rules of thumb provides a deterministic link between strain and damage, they cannot provide a uniform and consistent level of pro- tection against the onset of damage resulting from load his- tory effects. However, this represents the most justifiable and accurate method currently available to the profession, as the mechanics controlling some damage limit states (such as bar buckling) are complex and not entirely understood. TABLE 27 TENSION STRAIN LIMITS—PRESTRESSING STEEL Agency Year Ground Motion Component and Location Explicit Damage State? Damage State Strain Limit (in./in.) AASHTO SGS 2011 7% in 75 yr (1,000-yr RP) Column/pile plastic hinge No Strand fracture 0.030 SCDOT 2008 3% in 75 yr (2,500-yr RP) Column/pile plastic hinge No Strand fracture 0.035 Caltrans 2010 5% in 50 yr (1,000-yr RP) Column/pile plastic hinge No Strand fracture 0.030 POLA/POLB 2010/2009 50% in 50 yr (72-yr RP) Solid concrete in-ground plastic hinge (depth <10 diameter of pile) No Crack control 0.015 10% in 50 yr (475-yr RP) No Strand fracture? 0.025 2/3 of 2% in 50 yr (2/3 of 2, 475-yr RP) No Strand fracture? 0.035 POLA/POLB 2010/2009 50% in 50 yr (72-yr RP) Solid concrete deep in- ground plastic hinge (depth >10 diameter of pile) No Crack control 0.015 10% in 50 yr (475-yr RP) No Strand fracture 0.025 2/3 of 2% in 50 yr (2/3 of 2, 475-yr RP) No ? 0.050 POLA/POLB 2010/2009 50% in 50 yr (72-yr RP) Hollow concrete in-ground plastic hinge (depth <10 diameter of pile) No Crack control 0.015 10% in 50 yr (475-yr RP) No Strand fracture 0.025 2/3 of 2% in 50 yr (2/3 of 2, 475-yr RP) No Strand fracture 0.025 POLA/POLB 2010/2009 50% in 50 yr (72-yr RP) Hollow concrete deep in- ground plastic hinge (depth >10 diameter of pile) No Crack control 0.015 10% in 50 yr (475-yr RP) No Strand fracture 0.025 2/3 of 2% in 50 yr (2/3 of 2, 475-yr RP) No ? 0.050 MOTEMS 2011 50% in 50 yr (72-yr RP) Prestressed concrete pile in-ground plastic hinge No Crack control 0.005 (incremental) 10% in 50 yr (475-yr RP) No Strand fracture 0.025 (total)

73 TABLE 28 COMPRESSION STRAIN LIMITS—CONCRETE Agency Year Ground Motion Component and Location Explicit Damage State? Damage State Strain Limit (in./in.) AASHTO SGS 2011 7% in 75 yr (1,000-yr RP) Column plastic hinge con- fined concrete No Transverse reinforce- ment fracture/core crushing Column/pile in-ground plas- tic hinge confined concrete No Transverse reinforce- ment fracture/core crushing 0.020 SCDOT 2008 3% in 75 yr (1,000-yr RP) Column plastic hinge con- fined concrete No Transverse reinforce- ment fracture/core crushing Note: Omission of in the source may be a typographical error Caltrans 2010 5% in 50 yr (1,000-yr RP) Column plastic hinge con- fined concrete No Transverse reinforce- ment fracture/core crushing Priestley et al. 2007 Serviceability Column plastic hinge uncon- fined concrete Yes Cover spalling 0.004 Damage control Column plastic hinge con- fined concrete Yes Transverse reinforce- ment fracture/core crushing Kowalsky 2000 Serviceability Column plastic hinge uncon- fined concrete Yes Cover spalling 0.004 Damage control Column plastic hinge con- fined concrete Yes Transverse reinforce- ment fracture/core crushing 0.018 POLA/POLB 2010/2009 50% in 50 yr (72-yr RP) Solid concrete pile-to-deck plastic hinge extreme fiber concrete compression strain No Cover spalling 0.005 (cover concrete)* 10% in 50 yr (475-yr RP) No Transverse reinforce- ment fracture/core crushing (core concrete)* 2/3 of 2% in 50 yr (2/3 of 2, 475-yr RP) No NA No limit POLA/POLB 2010/2009 50% in 50 yr (72-yr RP) Solid concrete in-ground plastic hinge Extreme fiber concrete com- pression strain No Cover spalling 0.005 (cover concrete)* 10% in 50 yr (475-yr RP) No Core spalling (core concrete)* 2/3 of 2% in 50 yr (2/3 of 2, 475-yr RP) No Transverse reinforce- ment fracture/core crushing (core concrete)* POLA/POLB 2010/2009 50% in 50 yr (72-yr RP) Solid concrete deep in-ground plastic hinge (depth > 10 diameter of pile) extreme fiber concrete compression strain No Cover spalling 0.008 (cover concrete)* 10% in 50 yr (475-yr RP) No ? 0.012 (cover concrete)* 2/3 of 2% in 50yr (2/3 of 2, 475-yr RP) No NA No Limit POLA/POLB 2010/2009 50% in 50 yr (72-yr RP) Concrete filled steel pipe pile-to-deck plastic hinge extreme fiber concrete com- pression strain No Concrete spalling 0.010 (cover concrete)* 10% in 50 yr (475-yr RP) No Concrete crushing 0.025 (core concrete)* 2/3 of 2% in 50 yr (2/3 of 2, 475-yr RP) No NA No Limit Table 28 continued on p.74

74 To put strain limit data into a probabilistic PBSD for- mat will require the use of distribution functions using a central tendency (mean or median value) and a dispersion measure, as has been discussed previously. If this format is implemented, the judgment-based strain limits will give way to more objective data. However, a consensus within the design community must still be achieved for a uniform damage definition. An example of such consensus may be illustrated by consideration of how damage states and performance levels might be linked. Consider the generic fragility or probability of occurrence curves shown in Figure 20. If performance lev- els, such as those shown in Table 25, are mapped onto these same fragilities, the break points between performance lev- els must be positioned relative to the damage state fragilities. A logical and conservative way to do this may be to set the break points such that 90% or 95% of the occurrences of the various damage states lie to the right or above the break point. This approach would then result in a 5% or 10% probability of bar buckling at the collapse performance-level break point, as illustrated in Figure 26. Alternatively, this conservatism might only apply at the life safety/collapse break point, and less conservatism might be chosen for the lower break points. Agency Year Ground Motion Component and Location Explicit Damage State? Damage State Strain Limit (in./in.) POLA/POLB 2010/2009 50% in 50 yr (72-yr RP) Hollow concrete pile-to-deck plastic hinge extreme fiber concrete compression strain No Cover spalling 0.004 (cover concrete)* 10% in 50 yr (475-yr RP) No Prevent pile implosion? 0.006 (cover concrete)* 2/3 of 2% in 50yr (2/3 of 2, 475-yr RP) No ? 0.008 (cover concrete)* POLA/POLB 2010/2009 50% in 50 yr (72-yr RP) Hollow concrete in-ground plastic hinge extreme fiber concrete compression strain No Cover spalling 0.004 (cover concrete)* 10% in 50 yr (475-yr RP) No Prevent pile implosion? 0.006 (cover concrete)* 2/3 of 2% in 50 yr (2/3 of 2, 475-yr RP) No ? 0.008 (cover concrete)* POLA/POLB 2010/2009 50% in 50 yr (72-yr RP) Hollow concrete deep in- ground plastic hinge Extreme fiber concrete com- pression strain No Cover spalling 0.004 (cover concrete)* No Prevent pile implosion? 0.006 (cover concrete)* No ? 0.008 (cover concrete)* MOTEMS 2011 50% in 50 yr (72-yr RP) Pile-to-deck plastic hinge maximum concrete compres- sion strain No Cover spalling 0.004 (cover concrete)* 10% in 50 yr (475-yr RP) No Transverse reinforce- ment fracture/core crushing (core concrete)* MOTEMS 2011 50% in 50 yr (72-yr RP) In-ground plastic hinge Maximum concrete compres- sion strain No Cover spalling 0.004 (cover concrete)* 10% in 50 yr (475-yr RP) No Transverse reinforce- ment fracture/core crushing (core concrete)* * The POLA/POLB Seismic Codes and MOTEMS do not explicitly state whether the strain limits apply to the unconfined cover, or the confined core concrete, but only refer to the “extreme fiber concrete compression strain” or the “maximum concrete compression strain” for POLA/POLB and MOTEMS, respectively. Below the strain limit given, the authors have included a remark clarifying what they believe is the intended “extreme fiber,” whether it belongs to the unconfined cover or the confined core concrete. The clarification was based on research reports and commonly used strain limits within bridge practice and their applicable fiber location. v = confining transverse steel volumetric ratio. fyh = nominal yield stress of transverse reinforcing steel. su = ultimate tensile strain of transverse reinforcing steel. f’cc = confined concrete compressive strength. suR = reduced ultimate tensile strain of reinforcing steel to account for buckling and low-cycle fatigue. s = confining spiral volumetric ratio. NA = not available. Table 28 continued from p.73

75 TABLE 29 COMPRESSION AND TENSION STRAIN LIMITS—STRUCTURAL STEEL Agency Year Ground Motion Component Explicit Damage State? Damage State Strain Limit POLA/POLB 2010/2009 50% in 50 yr (72-yr RP) Steel pipe pile in-ground plastic hinge—extreme strain No Local bulging? 0.010 10% in 50 yr (475-yr RP) No Local buckling? 0.025 2/3 of 2% in 50 yr (2/3 of 2, 475-yr RP) No Tearing? 0.035 POLA/POLB 2010/2009 50% in 50 yr (72-yr RP) Steel pipe pile filled with concrete in-ground plastic hinge—extreme strain No Local bulging? 0.010 10% in 50 yr (475-yr RP) No Local buckling? 0.035 2/3 of 2% in 50 yr (2/3 of 2, 475-yr RP) No Pipe tearing? 0.050 POLA/POLB 2010/2009 50% in 50 yr (72-yr RP) Steel pipe pile deep in- ground plastic hinge— extreme strain (depth > 10 diameter of pile) No Local bulging? 0.010 10% in 50 yr (475-yr RP) No Local buckling? 0.035 2/3 of 2% in 50 yr (2/3 of 2, 475-yr RP) No Pipe tearing? 0.050 POLA/POLB 2010/ 2009 50% in 50 yr (72-yr RP) Steel pipe pile filled with concrete in-ground deep plas- tic hinge—extreme strain (depth > 10 diameter of pile) No Local bulging? 0.010 10% in 50 yr (475-yr RP) No Local buckling? 0.035 2/3 of 2% in 50 yr (2/3 of 2, 475-yr RP) No Pipe tearing? 0.050 MOTEMS 2011 50% in 50 yr (72-yr RP) Steel pipe pile plastic hinge—extreme strain No Local bulging? 0.008 10% in 50 yr (475-yr RP) No Pipe tearing? 0.025 MOTEMS 2011 50% in 50 yr (72-yr RP) Steel pipe pile filled with concrete plastic hinge— extreme strain No Local bulging? 0.008 10% in 50 yr (475-yr RP) No Pipe tearing? 0.030 FIGURE 26 Relationship between probability of damage and performance level.