Seismic Design of Coupled Frame-Wall Structures

The methodology emphasizes capacity design principles to ensure that inelastic behavior (plasticity) is confined to specifically designed hinge zones in beams and at the base of structural walls. This controlled yielding is intended to dissipate seismic energy primarily through flexural yielding, minimizing damage to other parts of the structure. The design aims to create a predictable failure mechanism, focusing energy dissipation in predetermined areas. The careful detailing of these hinge zones is crucial to the success of this approach, allowing for significant inelastic rotations without compromising the overall structural integrity. This strategy contrasts with approaches that allow for more widespread yielding throughout the structure.

Numerous inelastic time history analyses were performed on simplified 6- and 12-story buildings to evaluate the proposed design methodology under simulated earthquake conditions. These analyses used accelerograms to generate realistic inertia loading histories. Key variables considered included the relative stiffness of the frame and wall components, the fixity (degree of constraint) at the base of the walls, and the overall height of the walls. By varying these parameters, the researchers aimed to understand their influence on the overall seismic response of the structures and refine the design approach for optimal performance under seismic loads. The results provided valuable insights into the behavior of frame-wall structures under various conditions.

A computer program was used to simulate the incremental loading of the structure, tracking its response until a collapse mechanism formed. The program utilized simplified yield surface envelopes for structural members with bilinear hysteresis rules, a model that captures the non-linear behavior of materials under cyclic loading. The load-displacement curves obtained from these analyses revealed approximately linear behavior until wall hinge formation, after which the frame absorbed a significant portion of the load, resulting in a stiffness reduction of 60%. The sequential formation of beam and column hinges, with base-level column hinges forming last, indicated the effectiveness of the wall in controlling deflections. The analyses provided detailed information on displacement, base shear forces and moments, and plastic rotations in the beam hinges, which were compared against existing building codes.

The study also references an alternative iterative procedure using inelastic analyses to refine the design of a 31-story frame-coupled wall building, where plasticity was restricted to main and coupling beams. While such iterative approaches using inelastic analysis are becoming more common, the report indicates that current practice typically employs dynamic analyses as a design-checking tool rather than a direct design tool. This highlights the ongoing challenge of determining a suitable preliminary design before undertaking more sophisticated analyses, emphasizing the importance of the proposed methodology in establishing this initial, crucial step. This is particularly pertinent given that the reliability of preliminary designs directly influences the efficiency of subsequent inelastic analysis.

The research leveraged two distinct computer programs, RUAUMOKO and DRAIN-2D, for the dynamic analyses. Both programs modeled the force-deformation response of planar structural systems under simulated seismic loading. A direct stiffness formulation of the equations of motion was employed and solved for nodal displacements using time-wise step-by-step numerical integration. RUAUMOKO, developed at the University of Canterbury, offered a linear damping model, while DRAIN-2D, originating from the Earthquake Engineering Research Center (EERC) at Berkeley, was noted as a widely accepted package. The choice of these programs, and their inherent characteristics, influenced the analysis results and overall interpretations. The characteristics of each program’s damping model (Rayleigh vs. Linear) is considered, and the differences in computational stability discussed.

The research highlights the critical importance of shear design in structural walls, noting that while shear failures are relatively rare, they often occur after other mechanisms (bond failure, foundation failure) have initiated. This suggests that existing shear design practices may be inadequate. The study emphasizes the need to prevent shear failure in structural walls as a primary design objective. A re-examination of shear design practices is conducted, focusing on fundamental lateral load-resisting elements. The analysis explores how shear design practices are magnified for coupled structural walls within a frame-wall system in contrast to uncoupled cantilever walls, a key design consideration to avoid undesirable failure modes.

A significant portion of the research focuses on the phenomenon of dynamic magnification of shear forces in structural walls during seismic events. This magnification, exceeding the forces specified in building codes, is a key concern. The investigation seeks to understand the extent of this magnification and its implications for design. The study analyzed the effects of factors such as wall height, wall stiffness, and base fixity on this magnification. The work uses dynamic analysis time history programs and historical accelerograms (such as El Centro) to simulate realistic seismic loading, thus providing empirical data to assess the validity of code-specified shear forces and their potential for underestimation in actual seismic scenarios.

The study considers the influence of higher modes of vibration (beyond the first mode) on the seismic response of structural walls. It's noted that codified shear force distributions often represent only the first mode of vibration. The inclusion of higher modes significantly affects the distribution of inertia forces within the wall, lowering the centroid of these forces. This in turn leads to a higher moment gradient and consequently, a higher base shear than predicted by first-mode analysis alone. This highlights the importance of accounting for higher mode effects in accurate seismic design. The increased complexity necessitates modification of design approaches to accommodate the influence of these higher modes, which are not fully captured by simplified analytical models.

The research examines the impact of wall cracking on the seismic performance of the structures. The influence of different cracking distributions, including variations in the second moment of area and gross section properties for a 12-story rectangular walled structure subjected to the El Centro accelerogram, was investigated. The findings are particularly focused on how the assumed degree of cracking affects various parameters. The analysis correlates the first mode period with the second moment of area to inform refinement of structural models. This investigation suggests that accounting for cracking patterns in structural walls is crucial for accurate prediction of seismic behavior and suggests further improvement in modeling techniques.

The study compares the proposed design methodology with existing approaches, specifically mentioning a PCA (Portland Cement Association) method. A direct comparison with the New Zealand code is deemed impossible due to differences in methodological structuring. However, a sample calculation from the PCA is presented, highlighting differences in the required flexural strength and design shear force relative to the base moment. These comparisons serve to demonstrate the unique aspects and potential improvements offered by the proposed methodology over established design practices. The significant discrepancies noted underscore the need for a more refined method that better accounts for the complex dynamic forces involved during seismic events. The differences in calculated flexural strength and design shear force between different methods are a major point of this section.

The study examined the influence of wall base fixity on displacement response using time histories of horizontal deflections. Analyses subjected 2m and 4m walled structures to El Centro and Pacoima Dam excitations. The El Centro results showed predominantly first-mode response, while the Pacoima Dam excitation produced larger deformations, as expected. For the 4m walled structure, no 'locked-in' displacement (permanent deformation) was observed, whereas the 2m walled structure exhibited only slight permanent plastic displacement. The normalized top-level displacements were recorded, revealing the control exerted by the wall on the overall displacement response. These observations highlighted the significance of wall base fixity on the overall structural displacement and the importance of using appropriate accelerograms to represent realistic seismic events. The comparison between the two accelerograms demonstrated the differential response that might be expected depending on the specific characteristics of the earthquake.

The analysis investigated the impact of wall base fixity on wall bending moments and shear forces. It was found that wall bending moments were strongly influenced by base fixity, particularly in the bottom storey. While a transition from fixed to pinned base conditions resulted in only a 25% reduction in moment demand at the first storey level, the point of zero moment was slightly lowered with increased wall foundation compliance. Beam end moments increased modestly (15%) with this transition. Column shear forces, however, showed a strong dependence on wall base fixity, particularly at the bottom level. Bottom storey column shear forces for the pinned wall case were approximately 2.5 times greater than those for the fixed base wall, demonstrating a critical dependence on the support conditions at the base. This analysis highlights that while the upper floors show a relatively low sensitivity to variations in base fixity, the bottom floor and columns experience much greater change, influencing the design considerations.

The study examined column actions (bending moments and axial forces) under different wall base conditions. Extreme column axial forces were very similar for both pinned and fixed wall structures, suggesting adequate estimation of design forces. Column bending moments, however, were significantly affected by the change in wall base fixity, particularly at the bottom level where demands were substantially higher for the pinned wall structure. Despite this, protection ratios (flexural strength capacity exceeding demands) generally remained high. The analysis indicates that while yielding should be anticipated at ground and top floor levels, adequate transverse reinforcement is required to ensure full hinge detailing and prevent excessive column yielding. This highlights the interaction between wall behavior, column design, and the importance of considering base fixity in overall structural design.

The influence of wall base fixity was investigated using 12-story structures, focusing on the correlation between wall size and the magnitude of alterations in member actions due to base deformations. Larger walls showed a greater sensitivity to base fixity changes. Interstorey drifts, beam moments, and aggregated beam moments were impacted. While drifts for the pinned 7.0m walled building compared more favorably under dynamic loading than under static loading, the overall response was considerably affected. The findings emphasize the importance of considering base fixity in the design of taller buildings and the need for careful analysis to account for its significant influence on structural performance. This section stresses the significant impact of wall base fixity, especially in the context of higher-mode responses and the differences between static and dynamic loading conditions.

The study directly compared structural responses for both fully fixed and pinned base wall conditions. The same lateral loading was applied to both building types, facilitating a clear comparison of member actions. While the overall structural response of the 4m walled building to the Bucharest excitation was notably worse with the pinned base condition due to a period shift making the structure more susceptible to severe excitation. This was attributed to the increased structural flexibility and higher first-mode periods associated with the pinned base. Although wall actions were low for the pinned wall case, beam and column inelastic demands were substantially greater. This indicates that the assumption of fixed base conditions, typically used in design analyses, may lead to inaccurate predictions and potentially unsafe designs if the actual base conditions are different.

The research included a comparative analysis of a 'frame-only' structure, designed according to codified procedures for ductile multi-story frames, assuming a one-way frame configuration. This structure was designed using a structural type factor (S) of 0.8, reflecting the pure moment-resisting frame configuration (compared to S=1.0 for the hybrid frame-wall structures). A dynamic magnification factor (w) of 1.8 was used for column design, as recommended for this type of building. Although some column reinforcement requirements were relatively high (up to 2.7%), and might necessitate increased member sizes in practice, the same structural geometry as the frame component of the frame-wall buildings was retained to ensure consistency across the comparisons. The consistent geometry allowed for a direct comparison of the frame-only structural behavior with the frame-wall systems under identical simulated seismic loading.

A key aspect of the comparison involved analyzing member actions (forces and moments) in the frame-only structure and frame-wall structures. Both fixed and pinned base conditions were considered for the frame-wall structures. The same lateral loading was applied to both frame-only and frame-wall buildings, despite a 20% lower allowable loading for the pure moment resisting frame according to NZS 4203. This uniform loading enabled a meaningful comparison of member actions, providing insights into the relative performance of each structural system. The analysis revealed significant differences in the behavior, especially concerning column forces and moments, highlighting the effectiveness of the structural walls in mitigating seismic loads. The results are essential in evaluating the additional benefits of incorporating structural walls into building design for improved seismic performance.

The influence of wall height and base fixity was investigated in the frame-wall structures by modeling structures with 9, 4, and 1-story walls and a frame-only structure for comparison. This also included structures with varying wall heights. The analysis showed that for the fixed-base wall structures, the 9-story wall envelope was similar to that of the full-height wall, suggesting a limit to the beneficial effects of increased wall height. For structures with shorter walls (3 and 6 stories), column shear force envelopes followed the frame-only patterns until the wall top. Then, a sudden decrease occurred because the lateral load was transferred to the wall. The findings showed that the trends observed in the structures with 7m pinned walls were similar to those with 3m pinned walls, illustrating that the wall's height and base conditions play a significant role in determining overall structural behavior under seismic loads. The comparative analysis allowed researchers to understand the effect of wall presence, its height, and foundation conditions on the overall response, assisting in optimal design strategies for frame-wall structures.

The study analyzed column moments, comparing the maximum column moment demands and probable section capacities in frame-only and frame-wall structures. Columns at least one story below the wall top were well protected against yielding in the frame-wall structures, except at the base level. However, columns above the wall top and in the uppermost story (with a wall present) had less reserve strength, and their capacity was often less than the dynamic analysis demands. This deficiency was somewhat mitigated in the pinned wall structures. In the frame-only structure, a dynamic magnification factor (w) of 1.8 was used, while 1.2 was deemed suitable for frame-wall configurations. The study explored the rationale behind the difference in w-values and the implications for column design in different structural systems. The comparison demonstrated the enhanced seismic protection offered by the frame-wall systems, specifically highlighting the significance of appropriate dynamic magnification factors in the design process.

The experimental validation involved testing six approximately one-third scale models of prototype walls. These models comprised four barbell-shaped and two rectangular sections. High-strength steel (nominally 414 MPa) was used for both vertical and transverse reinforcement, with concrete compression strengths of approximately 35 MPa. The three-story walls were subjected to a constant axial load of approximately 0.07f'A (where f' is the concrete compressive strength and A is the cross-sectional area). The consistent scaling and material properties ensured that the experimental results could be reasonably extrapolated to full-scale structures, providing valuable empirical data to support the findings from the numerical analyses. The choice of materials and scaling reflects standard practice in experimental structural engineering research, facilitating meaningful comparisons and validating theoretical predictions.

While the specific testing procedure isn't fully detailed, the text indicates that the walls were loaded to elicit a response representative of seismic conditions. The goal was to observe the structural wall's behavior under load, to provide experimental evidence supporting the analytical findings. The text mentions that the tests were conducted to assess the behavior of the walls. This involved subjecting the scaled models to a controlled loading regime that simulates the type of stresses a wall in a building might encounter during a seismic event. The resulting data were likely used to assess the accuracy and reliability of the numerical models employed and provide empirical verification of the theoretical predictions on structural wall performance under seismic loading. Information about the type of loading protocol employed, the measurement techniques used and the criteria for defining failure are missing and further data is needed.