# Perry Erwin Adebar

#### Relevant Thesis-Based Degree Programs

## Graduate Student Supervision

##### Doctoral Student Supervision

Dissertations completed in 2010 or later are listed below. Please note that there is a 6-12 month delay to add the latest dissertations.

State-of-the-art nonlinear analysis was used to investigate three different types of irregularities or discontinuities in high-rise concrete shear wall buildings. The objective was to develop knowledge that will assist practicing engineers who design buildings.Overhanging wall discontinuity due to the wall above being longer than the wall below creates significant amplification of concrete compression strains immediately below the overhang. While the strains are highly nonlinear, the results of the current study were used to develop simple amplification factors for estimating the nonlinear strain increases from the results of linear finite element analysis, which can be done by practicing engineers. A simple safe limit for the maximum compression strain in a wall below an overhang determined from linear analysis is 0.001 in order to limit the nonlinear vertical compression strain in the zone below the overhang to 0.004. A discontinuity in lateral stiffness of building occurs at grade level where the concrete diaphragms connect tower walls to foundation walls or at the top of podium levels. In design practice, these diaphragms are usually modelled as linear elastic members, and the choice of effective stiffness significantly influences how much force will go into the backstay force path. The effect of membrane forces on the flexibility of concrete diaphragms was investigated and a range of simplified models was presented. The nonlinear models provide a more accurate estimate of the diaphragm stiffness, while the simple upper and lower-bound (constant) stiffness models are much easier to use in practice. The influence of out-of-plane bending of the diaphragms on reducing membrane stiffness of the diaphragms was also investigated.Sloped-column Irregularity is a new type of irregularity defined in the 2020 National Building Code of Canada for the seismic design of buildings as an outcome of the current study. Nonlinear time history analysis was used to investigate how the differential horizontal movement at the top and bottom of sloped columns causes vertical accelerations of the building mass. A simplified procedure was developed to account for the possible range of member stiffnesses and to account for vertical ground motions in a simplified way.

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In shear wall buildings, walls serve as the seismic force resisting system while the gravity-load system consists of columns that are primarily designed to carry the weight of the building through frame action and are not detailed for seismic ductility. Design codes require the gravity-load system to be checked for deformation compatibility as the building deforms laterally. The process of checking the columns for adequate deformability still requires more work.In addition to flexural deformations, components such as shear strain and rotation of the foundation contribute significantly to lateral deformations in the wall plastic hinge zone. Shear strains in flexural shear walls are analytically shown to be a result of large vertical tensile strains in areas with inclined cracks. Based on this theory, a simple design-oriented method for estimating shear strain profile of flexural shear walls is formulated, the accuracy of which is verified against experimental results from works of other researchers.Rotation of shear wall foundations is studied through performing about 2000 Nonlinear Time-History Analysis (NTHA) considering the nonlinear interaction between the foundation and the underlying soil. Behaviour of shear walls accounting for foundation rotation is explained with emphasis on relative wall to foundation strengths. A simple method for obtaining the monotonic foundation moment-rotation response is formulated which is then used in a simple step-by-step method for estimating foundation rotation in a given shear wall building.Curvature demand on columns pushed to a given wall deformation profile is studied using a structural analysis algorithm specifically designed for the task. In the absence of wall shear strain or significant foundation rotation, column curvature demand is found to remain close to the wall maximum curvature. Wall shear strain and foundation rotation are found to cause severe increase to column curvature demand. In a parametric study on column curvature demand, parameters including wall length, column length, height of column plastic hinge zone, first storey height, fixity of the column at grade level, and the effect of members framing into the column are studied. Several simple expressions for estimating column curvature demand are derived that can be implemented in design.

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Nonlinear time history analysis was carried out in order to estimate the demands on cantilever shear wall buildings due to the design level earthquakes. A hysteretic bending moment - curvature relationship was developed and implemented into computer program OpenSees. The study included 15 different shear wall buildings that ranged in height from 10 to 50 stories with a range of elastic bending moment demand at the base as a ratio of bending moment capacity from 1.3 to 3.7.The influence of ground motion selection and scaling on different structural response quantities was studied. The input ground motions were scaled to uniform hazard spectrum (UHS) and conditional mean spectrum (CMS). It was observed that a fewer number of spectrum matched ground motions can be used to establish the mean response, while a reasonable similarity was found between the mean demand parameters from spectrum matched and the envelope of CMS ground motions.Mean roof displacements from nonlinear time history analysis were used to determine appropriate effective stiffness values to be used in response spectrum analysis to accurately predict the maximum roof displacement. It was observed that stiffness reduction factor reduced from 1.0 to about 0.5 as the ratio of elastic bending moment demand at the base to the wall flexural capacity increased from 1.3 to 3.7. In addition, models were proposed for the complete envelopes of curvature demand and interstory drift demand over the wall height, including an accurate estimate of the maximum curvature demand at the wall base, midheight curvature demand, and maximum interstory drift at the roof. The developed models for base curvature and roof interstory drift demands were expressed in term of roof displacement demand. The midheight curvature demand was found to be less than the recommended values for yield curvature. Lastly, the results of nonlinear time history analysis were used to determine an expression for estimating base shear force demands. The shear amplification factor, defined as the ratio that the design base shear force needs to be increased, was found to be independent of the building height and to have a maximum value of 2.0.

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Concrete shear walls are used as the seismic force resisting system in many high-rise buildings in Western Canada. During earthquake, the response of a high-rise concrete wall as it undergoes severe cracking of concrete and yielding of reinforcement is very complex. In particular, the nonlinear shear behaviour of concrete shear walls is not well known; therefore available analysis programs generally use very primitive models for nonlinear shear behaviour. Gérin and Adebar (2004) quantified the observed experimental results on reinforced concrete membrane elements and presented a simple nonlinear shear model that included the influence of concrete diagonal cracking, yielding of horizontal reinforcement and ultimate shear capacity. There are a number of important issues in the design of high-rise concrete shear walls where shear deformations play a very important role and hence nonlinear shear behaviour will have a significant influence. In this dissertation, three different seismic design issues where nonlinear shear response plays a significant role are investigated. The first issue which is of considerable concern to designers is the large reverse shear force in high-rise concrete walls due to rigid diaphragms below the flexural plastic hinge. The nonlinear analyses that were carried out in this study show that diagonal cracking and yielding of horizontal reinforcement significantly reduce the magnitude of reverse shear force compared to what is predicted by using linear analysis procedures. A second issue where nonlinear shear behaviour has a significant influence is associated with the shear force distribution between inter-connected high-rise walls of different lengths. The results presented in this work, show that when diagonal cracking is included in the analysis, significant redistribution of shear forces takes place between walls and all walls do not necessarily yield at the same displacement.The third issue is related to the dynamic shear demand caused by influence of higher modes and the corresponding nonlinear action that takes place in tall cantilever walls. According to the nonlinear dynamic analyses that were performed, the influence of hysteretic shear response on the seismic demand of high-rise concrete walls was investigated.

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The simplest shear problem involves a two-dimensional rectangular element with uniformly distributed reinforcement parallel to the element sides, and subjected to uniform normal stresses and shear stress. Such a uniform shear element will have uniform average stresses in reinforcement and concrete. The simplest model for elements subjected to shear force and bending moment that leads to code provisions uses one uniform shear element. Shear force is assumed to be resisted by a central portion of the cross-section acting as a uniform shear element, while bending moment is assumed to be resisted by the flexural tension reinforcement and concrete compression zone at the cross-section ends. In this thesis, the shear strength of bridge girders and squat shear walls are evaluated using a uniform shear element approach.Current code shear design provisions for beams are necessarily simplified procedures that are generally conservative. While the extra costs are small for new design, it may lead to unnecessary load restrictions on bridges or unnecessary retrofitting when used for shear strength evaluation. A new shear strength evaluation procedure for structural concrete girders is proposed. The procedure accounts for the influence of more parameters and provides more insight into the failure mode than code design methods. To verify the procedure, predicted trends are compared with Modified Compression Field theory (MCFT) for uniform shear elements, and Response-2000 for beam elements subjected to combined shear and bending moment. Shear strength predictions are also compared with results from strength tests on reinforced and prestressed concrete beams, together with predictions from current code shear design provisions. The current Canadian building code CSA A23.3 2004 contains new provisions for the seismic design of squat walls that were developed using a uniform shear element approach. These new code provisions are rigorously evaluated for the first time in this study. A new method to account for the flexure-shear interaction at the base of squat shear walls is proposed as well as refinements to the 2004 CSA A23.3 shear strength provisions for squat shear walls. These are verified by comparing the predicted trends with the predictions of MCFT-based nonlinear finite element program VecTor 2.

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##### Master's Student Supervision

Theses completed in 2010 or later are listed below. Please note that there is a 6-12 month delay to add the latest theses.

This thesis focuses on the behaviour of thin and lightly-reinforced concrete walls subjected to axial and lateral in-plane force and displacement demands within high-rise cantilever and coupled shear wall type buildings. Many older and some new high-rise buildings employ thin wall elements of this type as a part of the main gravity system. A brief case study of a fictitious sample building is used to identify some shortcomings of these elements in design practice.Current North American design codes employ two main design methods to determine the in-plane, uni-axial capacity of thin bearing walls. Results of past wall tests are aggregated and compared to the empirical method and rational "moment magnifier" method of slender wall design. Comparisons of the design methods show that significantly different design axial load capacities are possible within the same design code. The results of this comparison are used to derive a new empirical bearing wall design formula which better corresponds with the results and design input parameters of the rational "moment magnifier" design method.Recent seismic events have also shown that these thin walls are subject to sudden compression failures when subjected large in plane lateral displacements. A database analysis of past wall tests is used to identify parameters which influence the drift capacity of these elements, and a new empirical relationship of overall wall drift capacity based on shear height and compression zone slenderness is derived. The database results are used to identify several low drift capacity elements for further analysis. An analysis of several previous wall tests and non-linear finite element models is used to determine the sectional and global response characteristics of these members. The results of this test specimen analysis shows that thin and lightly-reinforced wall elements show very little vertical spread of plasticity resulting in smaller than anticipated plastic hinge lengths, however sectional analysis methods produce good estimates of overall sectional properties. Finally, a model of in-plane shear displacements based on measured average vertical strains in the plastic hinge zone is validated for these types of elements.

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In residential high-rise buildings, flat plate slabs and columns are two of the primary structural member types. While codes provide prescriptive measures for their design, many decisions are still required by the design engineers. There are three primary objectives of this study. First, this study will discuss our current knowledge of construction practices, concrete material properties, and environmental conditions that impact slab design and deflections. Next, several current methods of estimating slab deflections will be reviewed, and the estimates will be compared with survey results from an actual high-rise. Finally, this study will identify optimum configurations of slabs and columns in residential high-rise buildings, in terms of cost.Through the review of the current literature and practice, it was found that there are many parameters that impact slab deflection and consideration must be taken to ensure that slabs do not have excessive deflection. This is especially true with residential towers with compressed construction schedules. The current finite element analysis programs are powerful tools but also can have significant drawbacks. The designer should understand the advantages and disadvantages of each method to ensure meaningful results. Several methods may need to be used to get an accurate understanding of a slab’s deflection behaviour. Through the cost analysis, it was determined that square columns with higher concrete strength and lower reinforcing ratios were the most cost effective. Moreover, for residential tower slab and column configurations, a layout that reduced the slab thickness with well distributed and smaller columns was found to be the most cost effective in the majority of circumstances.

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Reinforced concrete shear wall core structures are very common among high-rise buildings in Vancouver, and increasingly so elsewhere. While the flexural behaviour of these structures is well understood, the shear behaviour is not. Much of the research regarding the shear behaviour is related to the amplifications of demands due to higher mode seismic shear, however, there has been little research regarding the resistance of these structures to higher mode seismic shear demands. It is theorized that due to the lack of experimental data on which more complex shear models could be based on, structural engineers have resorted to using building models with complex non-linear fibre section flexural stiffness, but a linear elastic shear stiffness. Which may have lead to higher mode shear demands to be overestimated.Therefore, the goal of this thesis is to complete an experimental program in which scaled shear wall core specimens are tested under higher mode demands in the cantilevered direction. Through the experimental program, topics that are investigated include: the effect of the rate of loading on the shear resistance, the effect of existing flexural base yielding on the shear resistance, and the presence of a plastic hinge at the base on the shear resistance.In addition to the experimental program, a series of dynamic analyses were completed on a simplified model, in order to better understand the behaviour of a high-rise reinforced concrete shear wall structure to higher mode effects, and the results of the experimental program are also compared to predictions made using common analytical tools.

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The current research investigates the performance of commonly-used non-code-compliant stirrup detailing in concrete I-girder bridges, specifically when the lower hooks on the stirrups are oriented parallel to the longitudinal prestressing strands and are not bent around any longitudinal bars. Such detailing does not meet the specifications in the Canadian Highway Bridge Design Code CSA S6-06. An experimental investigation was conducted on full-scale partial sections of a concrete I-girder to evaluate the performance of such non-code-compliant stirrup anchorages by comparing their performance to the performance of code-compliant stirrup anchorages. An analysis of an example concrete I-girder bridge was conducted to determine the demands on the stirrup anchorage during the tests. In the tests, the flexural tension force was applied to the prestressing strand while a diagonal force was applied to the web of the test specimens at approximately 30° to the longitudinal axis of the specimen. Two pairs of stirrups were fixed to a support as the diagonal force was applied. The ratio of the slip of the stirrup to the strain along the exposed length of the stirrup, which equals to the debonded length, was monitored in order to observe the performance of the stirrup anchorage. After applying many cycles of the diagonal force, including about 100 cycles after yielding of the stirrups, the non-code-compliant hooks were found to perform adequately.

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The bending displacement capacity of elongated wall-like gravity-load columns subjected to lateral displacements due to earthquake demands on a high-rise building is of considerable concern. The long cross-sectional dimension makes these members much less flexible compared to square columns. Elongated gravity-load columns are popular because they can be hidden in walls and because they reduce the span of floor slabs, which means the thickness of the floor slabs can be reduced. No previous tests have been done on elongated gravity-load columns subjected to simulated earthquake loading. In the current study, five half-scale specimens including four column specimens and one wall specimen were subjected to constant axial compression and reverse cyclic lateral load to determine the displacement capacity of the members. The cross-sectional width-to-length ratios of the four columns were 1:1 (square), 1:2, 1:4, 1:8 and the wall specimen was 1:8. The load-deformation responses of the specimens were predicted using two nonlinear programs Response2000 and VecTor2, as well as hand calculation procedures. The predictions were used to design the test setup and were compared with the test results in order to better understand the significance of the test results. The predicted load capacities of all specimens were found to be similar to the observed maximum loads; but the displacement capacities of all specimens were significantly higher than predicted. Slip of the vertical reinforcing bars from the column foundations contributed to a large part of the increased displacement capacity of the columns. Only the elongated columns with a cross-sectional width-to-length ratios of 1:4 and 1:8 and the wall specimen suffered complete collapse during the test.

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The experimental research was completed to investigate the strain capacity of thin concretewalls. 45 wall elements that were either 24 in. (610 mm) or 36 in. (914 mm) high had 5.5 in.(140 mm),6 in. (152 mm), 8 in. (203 mm) or 10 in. (254 mm) thickness and variousreinforcement arrangements. The concrete wall elements were subjected to concentric axialcompression load. The strain capacity of the wall elements was measured. In many of thetests the strain was kept uniform and in some of the testing no effort was made to keep strainequable. The test results and observations indicated that the strain capacity of thin concretewalls could be as low as 0.0015. Low strain capacity was observed when the slenderspecimens (with height-to-thickness ratio of 4.5) did not contain lateral confinement. Inslender specimens that had straight horizontal reinforcement and no lateral ties, concretecover tended to separate. Moreover, diagonal cracks were formed through the location oflateral reinforcement. In some cases the cracks coalesced at the middle section of thespecimen into a larger crack and split the specimen in the middle. An analytical study wasconducted to investigate how the compression strain capacity could influence the axial loadcapacity of bearing walls. Maximum compression axial load was calculated for variousbearing wall lengths of 2 to 60 ft while keeping the strain demand on the bearing walls withincertain limits.

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The nonlinear shear behaviour of cantilever reinforced concrete shear walls is complex and not fully understood. Design assumptions often oversimplify the wall response and can yield results which do not reflect the true response of the shear wall. One such assumption is analyzing the wall ignoring the effects from multiple floor slabs connected to the wall over its height. Floor slabs can provide a significant increase in wall shear capacity. This thesis examines the nonlinear shear response of walls, including the effect of floor slabs as a wall-slab system, through state-of-the-art nonlinear finite element analysis. Finite element slab models were developed to emulate the 3D slab effect within a 2D analysis environment: a high-end pseudo 3D model for in-depth slab analysis and a simple 2D slab layer model for typical wall analysis. The slab effects are explored through a parametric study varying the wall size, concrete strength, axial load, horizontal steel ratio and the slab dimensions parallel and perpendicular to the wall. The slabs were found to act like large external stirrups which provide additional tension capacity for the slab and limit shear cracking and failure. The slabs can significantly increase the shear capacity of lightly-reinforced walls. Using the developed slab models, the bounds of the slab effect were investigated by a parametric study with lightly to heavily-reinforced walls, with and without axial load, as well as varying the slab spacing. Within this study, the nonlinear response of isolated walls is compared to nonlinear uniformly-loaded membrane models. It is determined that although code-based shear capacity equations are fairly accurate, the membrane models can underestimate the shear stiffness and over predict the ductility. This study also reveals that tightly spaced slabs can increase up to 3 times the isolated wall capacity for walls with minimum horizontal steel, whereas there is little effect for walls with horizontal steel above 1%. Finally, methods were developed to predict the nonlinear shear stress-strain response of isolated walls and the peak shear capacity of wall-slab systems.

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This thesis addresses the issue of seismic shear force demand in reinforced concrete cantilever walls, and specifically the dynamic amplification of shear force due to higher mode effects. Current design codes either do not account for this phenomenon, or vary considerably in the approach they take. In order to determine the reason for the variation, previous research is first examined, and it is found that the conclusions reached are not consistent with each other. It is identified that a major source of the problem is a lack of a comprehensive analysis of the problem.To attempt to address this issue, the analysis portion of the thesis starts by performing response spectrum analysis on structures with heights ranging from 5 to 70 storeys. It is shown that when a pin is placed at the bottom of the structure to simulate yielding, the moment is limited but the shear can still increase. A simple relationship between the fixed base and pinned base shear is found. Reduction in the shear stiffness, possible yielding higher in the structure, and the effect of the spectrum are also issues examined.The next two chapters deal with both linear and nonlinear time history analyses performed using OpenSees. Linear time history analysis is used to demonstrate the issues with ground motion scaling in tall structures. It is then shown that the shear at the base of the structure from a nonlinear analysis is more than the code predicts, as is the moment higher up in the structure. Furthermore, the shear at the base of the structure remains relatively constant no matter how the rest of the structure yields. A possible model is then proposed which adds the pinned response spectrum analysis results to the reduced shear. This model is compared to the nonlinear results and it is found to agree well.Finally, a chapter is devoted to factors which may complicate the results. They are separated into two sections: choice of hysteretic model, and the influence of the shear capacity on the demand. It is determined that further research is needed in these areas.

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