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## Seismic Performance Assessment and Probabilistic Repair Cost Analysis of Precast Concrete Cladding Systems for Multistory Buildings

- Author(s): Hunt, Jeffrey Patrick
- Advisor(s): Stojadinovic, Bozidar
- et al.

## Abstract

Analytical and experimental tests have shown that the seismic response of multistory moment-frame structures with precast concrete cladding in moderate to severe earthquakes is significantly influenced by the cladding system. Moreover, considerable damage to the cladding system components from recent earthquakes has been reported. The cladding system can account for a significant portion of the initial cost of a building, often as much as 20%. However, in seismic analysis and design, engineers typically ignore the additional stiffness and damping that the cladding system may provide, which could prove to be beneficial or detrimental to the building's seismic performance. Most of the efforts in nonlinear dynamic modeling focus on representing the behavior of structural elements and do not include the effects of non-structural elements such as cladding systems. The purpose of the research discussed in this dissertation is to study the effect that the cladding system has on the structural response of multistory buildings, to develop analytical equations to estimate the seismic demands in the cladding connections, to calculate the probability of failure of typical cladding connections, and to determine the post-earthquake repair costs and repair times of typical cladding systems.

The nine-story LA SAC steel moment-frame building is selected as the study building, and a two-dimensional, nonlinear model is developed of the bare-frame structure in OpenSees. The steel moment-resisting frame of the bare-frame structure is modeled using nonlinear force beam-column line elements capable of representing distributed plasticity along their length. The frame connections are reduced-beam section (RBS) moment connections, and their modeled cyclic moment-rotation behavior is based on experimental test results of the connection. Analytical models of three different precast cladding designs are applied to the bare-frame structure to study their effect on the building's seismic response. The three cladding designs represent common systems used in regular multistory buildings in modern construction. The first cladding design, cladding type C1, consists of alternating horizontal bands of spandrel panels (covering the exterior floor beams) and glazing. The spandrel panels extend the full width of the bay. The second cladding design, cladding type C2, consists of spandrel panels that extend the full height of the story with rectangular window openings "punched" into their surface. The third cladding design, cladding type C3, consists of the same spandrel panels as in type C1 with column cover panels spanning between adjacent spandrel panels. The force-deformation curves of the connections used in the model are obtained from experimental tests of push-pull connections and column cover connections. The total seismic mass of the models with the cladding systems is the same as the total seismic mass of the bare-frame model. However; in the models with cladding, the seismic mass is distributed between the beam-column nodes and the nodes of the cladding system according to their respective tributary weights.

The effects of the cladding on the seismic response of the bare-frame structure are studied by performing modal analyses, nonlinear static pushover analyses, and nonlinear dynamic time-history analyses of the analytical models. The inclusion of cladding decreases the fundamental period of the building by only 4%; however, the effects of the cladding on the maximum interstory drifts, floor accelerations, and plastic hinge rotations are significant. Time-history analyses of each model are performed using 140 ground motions. The ground motions in each bin are scaled by a common factor (cloud method with constant scaling) to ensure nonlinear response was captured. The time-history results are plotted in log-log space, and a linear trend line is fitted to the data to represent the mean maximum response values. The time-history results reveal that the addition of cladding reduces the mean maximum interstory drift ratios in the bare-frame model by up to 22%, 28%, and 33% for the 50%-, 10%-, and 2%-in-50 year probability of exceedance levels, respectively. The reductions in interstory drift are the largest for cladding type C3 and smallest for cladding type C1. The mean residual interstory drifts are small for all levels of intensity and were not significantly affected by the cladding. The mean maximum floor accelerations are not significantly affected by cladding types C1 and C2: the mean values of maximum floor accelerations in the bare frame structure are reduced by only 8% for these two cladding types. On the other hand, the mean values of the maximum acceleration at the roof level in the model with cladding type C3 are up to 35%, 63%, and 97% larger than the values in the bare frame structure for the 50%-, 10%-, and 2%-in-50 year probability of exceedance level, respectively.

The finite-element models of structures with cladding are time-consuming to create and computationally demanding to analyze. Thus, analytical equations are derived to describe the mechanisms for deformation in the cladding connectors. The equations are used to estimate the maximum deformations in the push-pull and column cover connectors. The maximum deformations estimated from the equations are compared to the maximum deformations recorded from the time-history analyses. The comparisons of the median values of maximum deformation between the two approaches show that the analytical equations provide good estimates of the maximum deformations up the height of the building. The analytical equations can be used as conservative estimates of deformation for the seismic design of similar cladding connectors.

The time-history analysis results show that significant deformations develop in the column cover connections in moderate earthquakes. The deformations exceed the life-safety, and in some cases, the collapse prevention performance criteria. Thus, the failure probabilities of the column cover connections subject to multiple hazard levels are investigated using structural reliability theory. The analytical equations for estimating the deformations in the column cover connectors are used to construct the limit-state function describing the structural reliability of the connectors. The random variables consist of the maximum interstory drift, the gap width in the slotted connections, and the failure shear deformation in the connectors. The deterministic parameters in the limit-state functions are the panel dimensions and the story height. The correlation coefficients are calculated for the maximum interstory drifts between different stories. The components of the column covers consist of four connectors (one in each corner). The component failure probabilities (calculated using FORM) are as high as 44.2%, 70.0%, and 100% for the 50%-, 10%-, and 2%-in-50 year probability of exceedance levels, respectively. The maximum interstory drift is found to be the most important (has the largest effect on the results) random variable, and the gap width is the most important capacity or design variable. Regarding the deterministic parameters, decreasing the panel width has the largest effect on decreasing the probability of failure of one panel. The probability of failure can also be decreased by increasing the panel height or increasing the story height. Story system reliability analyses are performed to investigate the probability of failure of multiple panels per story. For each story, the total probability theorem is used to calculate the total probability of failure of 2 panels in the low hazard event, 4 panels in the moderate hazard event, and 8 panels in the high hazard event. The total probability of failure is as high as 48.4% for a lifetime of 50 years of the building, with the largest probabilities at the top three stories of the building.

To gain additional insight on the seismic performance of multistory buildings with cladding, post-earthquake repair cost analyses are performed on the analytical models using the performance-based earthquake engineering (PBEE) methodology developed by the Pacific Engineering Earthquake Research (PEER) Center. The total repair costs of the cladding system represent up to 5%, 26%, and 66% of the replacement cost of the cladding for the 50%-, 10%-, and 2%-in-50 year probability of exceedance levels, respectively. At the 2%-in-50 year probability of exceedance level, the repair costs of the cladding system are up to 30-50% of the repair costs of the complete building and up to 14% of the replacement cost of the complete building. Using the repair cost results, the mean annual total repair costs of the cladding systems are $39,563, $16,213, and $40,824 for cladding types C1, C2, and C3, respectively. Based on the repair cost analyses, it is apparent that cladding type C2 is the most cost-effective cladding design. Because the cladding panels have window punch-outs, the window panes are protected from damage due to interstory drift. In addition, cladding type C2 does not use the highly damageable column cover connections that are expensive to repair.

The results of this research highlight several important issues in cladding design. First, the cladding system should be carefully designed in consultation with the structural engineer to ensure that the cladding system does not significantly impact the structural response of the building structure. As shown by the results of the time-history analyses, the selected cladding type determines how much the cladding affects the structural response of the building. The analysis of the code equations for window glazing systems reveal that windows with narrow aspect ratios (height greater than width) and generous clearances between the glass and surrounding window framing provide significantly better seismic drift capacity before cracking and glass fallout occurs. The results of the post-earthquake repair cost analyses show that the repair costs of the cladding system have a significant contribution to the repair costs of the complete building. Of the three typical cladding types analyzed in this research, the full-story height cladding system with window punchouts (cladding type C2) incurs the lowest repair costs.