05 end 2009 taranath reinforced concrete design of tall buildings

Wind Loads 345 which is apparently in reasonable agreement with many field measurements However, this value is not in good agreement with the generally accepted eigenvalue analyses It is not known if this observed discrepancy is due to Errors in the field measurements Computer modeling inaccuracies and oversimplified modeling assumptions Wind-tunnel engineers are typically hesitant to “outguess” the design engineer or substitute their own estimate of the structure’s period They are most likely to produce loads consistent with the modal properties provided the engineer So, this is an issue worthy of further research Until then, it is appropriate for discussion between the wind-tunnel engineer and design engineer Another consideration that goes hand-in-hand with the determination of building periods is the value of damping for the structure Damping for buildings is any effect that reduces its amplitude of vibrations It results from many conditions ranging from the presence of interior partition walls, to concrete cracking, to deliberately engineered damping devices While for seismic design, 5% of critical damping is typically assumed for systems without engineered damping devices, the corresponding values for wind design are much lower as buildings subject to wind loads generally respond within the elastic range as opposed to inelastic range for seismic loading The additional damping for seismic design is assumed to come from severe concrete cracking and plastic hinging The ASCE 7-05 Commentary suggests a damping value of 1% for steel buildings and 2% for concrete buildings These wind damping values are typically associated with determining wind loads for serviceability check Without recommending specific values, the commentary implicitly suggests that higher values may be appropriate for checking the survivability states So, what design values are engineers supposed to use for ultimate level (1.6W) wind loads? Several resources are available as for example, the references cited in the ASCE 7-05 Commentary, but the values vary greatly depending upon which reference, is used The type of lateral force resisting system influences the damping value that may vary from a low of 0.5% to a high of 10% or more Although the level of damping has only a minor effect on the overall base shear for wind design for a large majority of low- and mid-rise buildings, for tall buildings, a more in-depth study of damping criteria is typically warranted While the use of the fundamental building period for seismic design calculations is well established, the parameters used for wind design have not been as clear For wind design, the building period is only relevant for those buildings designated as “flexible” (having a fundamental building period exceeding s) When a building is designated as flexible, the natural frequency (inverse of the building’s fundamental period) is introduced into the gust-effect factor, G f Prior to ASCE 7-05, designers typically used either the approximate equations within the seismic section or the values provided by a computer eigenvalue analysis The first can actually be unconservative because the approximate seismic equations are intentionally skewed toward shorter building periods Thus for wind design, where longer periods equate to higher base shears, their use can provide potentially unconservative results Also, the results of an eigenvalue analysis can yield building periods much longer than those observed in actual tests, thus providing potentially overly conservative results The period determination for wind analysis is therefore, a point at issue worthy of further research In summary, the choice of building period and damping for initial design continues to be a subject of discussion for building engineers This choice is compounded by our increasing complexity of structures, including buildings linked at top For many of these projects there may be no way around performing an initial Finite Element Analysis, FEA, to obtain a starting point for wind load determination Ongoing research into damping mechanisms combined with an increase in buildings with monitoring systems will help the design community make more informed decisions regarding the value of damping to use in design Seismic Design Although structural design for seismic loading is primarily concerned with structural safety during major earthquakes, serviceability and the potential for economic loss are also of concern As such, seismic design requires an understanding of the structural behavior under large inelastic, cyclic deformations Behavior under this loading is fundamentally different from wind or gravity loading It requires a more detailed analysis, and the application of a number of stringent detailing requirements to assure acceptable seismic performance beyond the elastic range Some structural damage can be expected when the building experiences design ground motions because almost all building codes allow inelastic energy dissipation in structural systems The seismic analysis and design of buildings has traditionally focused on reducing the risk of the loss of life in the largest expected earthquake Building codes base their provisions on the historic performance of buildings and their deficiencies and have developed provisions around life-safety concerns by focusing their attention to prevent collapse under the most intense earthquake expected at a site during the life of a structure These provisions are based on the concept that the successful performance of buildings in areas of high seismicity depends on a combination of strength; ductility manifested in the details of construction; and the presence of a fully interconnected, balanced, and complete lateral force–resisting system In regions of low seismicity, the need for ductility reduces substantially And in fact, strength may even substitute for a lack of ductility Very brittle lateral force–resisting systems can be excellent performers as long as they are never pushed beyond their elastic strength Seismic provisions typically specify criteria for the design and construction of new structures subjected to earthquake ground motions with three goals: (1) minimize the hazard to life from all structures, (2) increase the expected performance of structures having a substantial public hazard due to occupancy or use, and (3) improve the capability of essential facilities to function after an earthquake Some structural damage can be expected as a result of design ground motion because the codes allow inelastic energy dissipation in the structural system For ground motions in excess of the design levels, the intent of the codes is for structures to have a low likelihood of collapse In most structures that are subjected to moderate-to-strong earthquakes, economical earthquake resistance is achieved by allowing yielding to take place in some structural members It is generally impractical as well as uneconomical to design a structure to respond in the elastic range to the maximum expected earthquake-induced inertia forces Therefore, in seismic design, yielding is permitted in predetermined structural members or locations, with the provision that the vertical load-carrying capacity of the structure is maintained even after strong earthquakes However, for certain types of structures such as nuclear facilities, yielding cannot be tolerated and as such, the design needs to be elastic Structures that contain facilities critical to post-earthquake operations—such as hospitals, fire stations, power plants, and communication centers—must not only survive without collapse, but must also remain operational after an earthquake Therefore, in addition to life safety, damage control is an important design consideration for structures deemed vital to post-earthquake functions In general, most earthquake code provisions implicitly require that structures be able to resist Minor earthquakes without any damage Moderate earthquakes with negligible structural damage and some nonstructural damage Major earthquakes with some structural and nonstructural damage but without collapse The structure is expected to undergo fairly large deformations by yielding in some structural members 347 348 Reinforced Concrete Design of Tall Buildings Seismic waves (a) Original static position before earthquake Deflected shape of building due to dynamic effects caused by rapid ground displacement Seismic waves (b) FIGURE 5.1 Building behavior during earthquakes An idea of the behavior of a building during an earthquake may be grasped by considering the simplified response shape shown in Figure 5.1 As the ground on which the building rests is displaced, the base of the building moves with it However, the building above the base is reluctant to move with it because the inertia of the building mass resists motion and causes the building to distort This distortion wave travels along the height of the structure, and with continued shaking of the base, causes the building to undergo a complex series of oscillations Although both wind and seismic forces are essentially dynamic, there is a fundamental difference in the manner in which they are induced in a structure Wind loads, applied as external loads, are characteristically proportional to the exposed surface of a structure, while the earthquake forces are principally internal forces resulting from the distortion produced by the inertial resistance of the structure to earthquake motions The magnitude of earthquake forces is a function of the mass of the structure rather than its exposed surface Whereas in wind design, one would feel greater assurance about the safety of a structure made up of heavy sections, in seismic design, this does not necessarily produce a safer design Seismic Design 349 5.1 BUILDING BEHAVIOR The behavior of a building during an earthquake is a vibration problem The seismic motions of the ground not damage a building by impact, as does a wrecker’s ball, or by externally applied pressure such as wind, but by internally generated inertial forces caused by the vibration of the building mass An increase in mass has two undesirable effects on the earthquake design First, it results in an increase in the force, and second, it can cause buckling or crushing of columns and walls when the mass pushes down on a member bent or moved out of plumb by the lateral forces This effect is known as the PΔ effect and the greater the vertical forces, the greater the movement due to PΔ It is almost always the vertical load that causes buildings to collapse; in earthquakes, buildings very rarely fall over—they fall down The distribution of dynamic deformations caused by the ground motions and the duration of motion are of concern in seismic design Although the duration of strong motion is an important design issue, it is not presently (2009) explicitly accounted for in design In general, tall buildings respond to seismic motion differently than low-rise buildings The magnitude of inertia forces induced in an earthquake depends on the building mass, ground acceleration, the nature of the foundation, and the dynamic characteristics of the structure (Figure 5.2) If a building and its foundation were infinitely rigid, it would have the same acceleration as the ground, resulting in an inertia force F = ma, for a given ground acceleration, a However, because buildings have certain flexibility, the force tends to be less than the product of buildings mass and acceleration Tall buildings are invariably more flexible than low-rise buildings, and in general, they experience much lower accelerations than low-rise buildings But a flexible building subjected to ground motions for a prolonged period may experience much larger forces if its natural period is near that of the ground waves Thus, the magnitude of lateral force is not a function of the acceleration of the ground alone, but is influenced to a great extent by the type of response of the structure itself and its foundation as well This interrelationship of building behavior and seismic ground motion also depends on the building period as formulated in the so-called response spectrum, explained later in this chapter 5.1.1 INFLUENCE OF SOIL The intensity of ground motion reduces with the distance from the epicenter of the earthquake The reduction, called attenuation, occurs at a faster rate for higher frequency (short-period) components F = Ma FIGURE 5.2 F < Ma Schematic representation of seismic forces F > Ma 350 Reinforced Concrete Design of Tall Buildings than for lower frequency (long-period) components The cause of the change in attenuation rate is not understood, but its existence is certain This is a significant factor in the design of tall buildings, because a tall building, although situated farther from a causative fault than a low-rise building, may experience greater seismic loads because long-period components are not attenuated as fast as the short-period components Therefore, the area influenced by ground shaking potentially damaging to, say, a 50-story building is much greater than for a 1-story building As a building vibrates due to ground motion, its acceleration will be amplified if the fundamental period of the building coincides with the period of vibrations being transmitted through the soil This amplified response is called resonance Natural periods of soil are in the range of 0.5–1.0 s Therefore, it is entirely possible for the building and ground it rests upon to have the same fundamental period This was the case for many 5- to 10-story buildings in the September 1985 earthquake in Mexico City An obvious design strategy is to ensure that buildings have a natural period different from that of the expected ground vibration to prevent amplification 5.1.2 DAMPING Buildings not resonate with the purity of a tuning fork because they are damped; the extent of damping depends upon the construction materials, the type of connections, and the influence of nonstructural elements on the stiffness characteristics of the building Damping is measured as a percentage of critical damping In a dynamic system, critical damping is defined as the minimum amount of damping necessary to prevent oscillation altogether To visualize critical damping, imagine a tensioned string immersed in water When the string is plucked, it oscillates about its rest position several times before stopping If we replace water with a liquid of higher viscosity, the string will oscillate, but certainly not as many times as it did in water By progressively increasing the viscosity of the liquid, it is easy to visualize that a state can be reached where the string, once plucked, will return to its neutral position without ever crossing it The minimum viscosity of the liquid that prevents the vibration of the string altogether can be considered equivalent to the critical damping The damping of structures is influenced by a number of external and internal sources Chief among them are External viscous damping caused by air surrounding the building Since the viscosity of air is low, this effect is negligible in comparison to other types of damping Internal viscous damping associated with the material viscosity This is proportional to velocity and increases in proportion to the natural frequency of the structure Friction damping, also called Coulomb damping, occurring at connections and support points of the structure It is a constant, irrespective of the velocity or amount of displacement Hysteretic damping that contributes to a major portion of the energy absorbed in ductile structures For analytical purposes, it is a common practice to lump different sources of damping into a single viscous damping For nonbase-isolated buildings, analyzed for code-prescribed loads, the damping ratios used in practice vary anywhere from 1% to 10% of critical The low-end values are for wind, while those of the upper end are for seismic design The damping ratio used in the analysis of seismic base-isolated buildings is rather large compared to values used for nonisolated buildings, and varies from about 0.20 to 0.35 (20% to 35% of critical damping) Base isolation, discussed in Chapter 8, consists of mounting a building on an isolation system to prevent horizontal seismic ground motions from entering the building This strategy results in significant reductions in interstory drifts and floor accelerations, thereby protecting the building and its contents from earthquake damage Seismic Design 351 F1 F2 FR F1 + F2 + FR = W = building weight FIGURE 5.3 Concept of 100%g (1g) K x Kx M Mx Damping force fD cx Damping force c FIGURE 5.4 Linear viscous damper A level of ground acceleration on the order of 0.1g, where g is the acceleration due to gravity, is often sufficient to produce some damage to weak construction An acceleration of 1.0g, or 100% of gravity, is analytically equivalent, in the static sense, to a building that cantilevers horizontally from a vertical surface (Figure 5.3) As stated previously, the process by which free vibration steadily diminishes in amplitude is called damping In damping, the energy of the vibrating system is dissipated by various mechanisms, and often more than one mechanism may be present at the same time In simple laboratory models, most of the energy dissipation arises from the thermal effect of the repeated elastic straining of the material and from the internal friction In actual structures, however, many other mechanisms also contribute to the energy dissipation In a vibrating concrete building, these include the opening and closing of microcracks in concrete, friction between the structure itself and nonstructural elements such as partition walls Invariably, it is impossible to identify or describe mathematically each of these energy-dissipating mechanisms in an actual building Therefore, the damping in actual structures is usually represented in a highly idealized manner For many purposes, the actual damping in structures can be idealized satisfactorily by a linear viscous damper or dashpot The damping coefficient is selected so that the vibrational energy that dissipates is equivalent to the energy dissipated in all the damping mechanisms This idealization is called equivalent viscous damping Figure 5.4 shows a linear viscous damper subjected to a force, f D The damping force, f D, is related to the velocity u· across the linear viscous damper by fD = cu⋅ where the constant c is the viscous damping coefficient; it has units of force × time/length Unlike the stiffness of a structure, the damping coefficient cannot be calculated from the dimensions of the structure and the sizes of the structural elements This is understandable because it is not feasible to identify all the mechanisms that dissipate the vibrational energy of actual structures 352 Reinforced Concrete Design of Tall Buildings Force Fy Hysteresis loop Kp Q Ke Dy FIGURE 5.5 Displacement Bilinear force–displacement hysteresis loop Thus, vibration experiments on actual structures provide the data for evaluating the damping coefficient These may be free-vibration experiments that lead to measured rate at which motion decays in free vibration The damping property may also be determined from forced-vibration experiments The equivalent viscous damper is intended to model the energy dissipation at deformation amplitudes within the linear elastic limit of the overall structure Over this range of deformations, the damping coefficient c determined from experiments may vary with the deformation amplitude This nonlinearity of the damping property is usually not considered explicitly in dynamic analyses It may be handled indirectly by selecting a value for the damping coefficient that is appropriate for the expected deformation amplitude, usually taken as the deformation associated with the linearly elastic limit of the structure Additional energy is dissipated due to the inelastic behavior of the structure at larger deformations Under cyclic forces or deformations, this behavior implies the formation of a force–displacement hysteresis loop (Figure 5.5) The damping energy dissipated during one deformation cycle between deformation limits ±uo is given by the area within the hysteresis loop abcda (Figure 5.5) This energy dissipation is usually not modeled by a viscous damper, especially if the excitation is earthquake ground motion Instead, the most common and direct approach to account for the energy dissipation through inelastic behavior is to recognize the inelastic relationship between resisting force and deformation Such force–deformation relationships are obtained from experiments on structures or structural components at slow rates of deformation, thus excluding any energy dissipation arising from rate-dependent effects 5.1.3 BUILDING MOTIONS AND DEFLECTIONS Earthquake-induced motions, even when they are more violent than those induced by wind, evoke a totally different human response—first, because earthquakes occur much less frequently than windstorms, and second, because the duration of motion caused by an earthquake is generally short People who experience earthquakes are grateful that they have survived the trauma and are less inclined to be critical of the building motion Earthquake-induced motions are, therefore, a safety rather than a human discomfort issue Lateral deflections that occur during earthquakes should be limited to prevent distress in structural members and architectural components Nonload-bearing in-fills, external wall panels, and window glazing should be designed with sufficient clearance or with flexible supports to accommodate the anticipated movements 5.1.4 BUILDING DRIFT AND SEPARATION Drift is generally defined as the lateral displacement of one floor relative to the floor below Drift control is necessary to limit damage to interior partitions, elevator and stair enclosures, glass, and cladding Seismic Design 353 systems Stress or strength limitations in ductile materials not always provide adequate drift control, especially for tall buildings with relatively flexible moment-resisting frames or narrow shear walls Total building drift is the absolute displacement of any point relative to the base Adjoining buildings or adjoining sections of the same building may not have identical modes of response, and therefore may have a tendency to pound against one another Building separations or joints must be provided to permit adjoining buildings to respond independently to earthquake ground motion 5.2 SEISMIC DESIGN CONCEPT An effective seismic design generally includes Selecting an overall structural concept including layout of a lateral force–resisting system that is appropriate to the anticipated level of ground shaking This includes providing a redundant and continuous load path to ensure that a building responds as a unit when subjected to ground motion Determining code-prescribed forces and deformations generated by the ground motion, and distributing the forces vertically to the lateral force–resisting system The structural system, configuration, and site characteristics are all considered when determining these forces Analyzing the building for the combined effects of gravity and seismic loads to verify that adequate vertical and lateral strengths and stiffnesses are achieved to satisfy the structural performance and acceptable deformation levels prescribed in the governing building code Providing details to assure that the structure has sufficient inelastic deformability to undergo large deformations when subjected to a major earthquake Appropriately detailed members possess the necessary characteristics to dissipate energy by inelastic deformations 5.2.1 STRUCTURAL RESPONSE If the base of a structure is suddenly moved, as in a seismic event, the upper part of the structure will not respond instantaneously, but will lag because of the inertial resistance and flexibility of the structure The resulting stresses and distortions in the building are the same as if the base of the structure were to remain stationary while time-varying horizontal forces are applied to the upper part of the building These forces, called inertia forces, are equal to the product of the mass of the structure times acceleration, that is, F = ma (the mass m is equal to weight divided by the acceleration of gravity, i.e., m = w/g) Because earthquake ground motion is three-dimensional (3D; one vertical and two horizontal), the structure, in general, deforms in a 3D manner Generally, the inertia forces generated by the horizontal components of ground motion require greater consideration for seismic design since adequate resistance to vertical seismic loads is usually provided by the member capacities required for gravity load design In the equivalent static procedure, the inertia forces are represented by equivalent static forces 5.2.2 LOAD PATH Buildings typically consist of vertical and horizontal structural elements The vertical elements that transfer lateral and gravity loads are the shear walls and columns The horizontal elements such as floor and roof slabs distribute lateral forces to the vertical elements acting as horizontal diaphragms In special situations, horizontal bracing may be required in the diaphragms to transfer large shears from discontinuous walls or braces The inertia forces proportional to the mass and acceleration of the building elements must be transmitted to the lateral force–resisting elements, through the diaphragms and then to the base of the structure and into the ground, via the vertical lateral load– resisting elements 354 Reinforced Concrete Design of Tall Buildings A complete load path is a basic requirement There must be a complete gravity and lateral force–resisting system that forms a continuous load path between the foundation and all portions of the building The general load path is as follows Seismic forces originating throughout the building are delivered through connections to horizontal diaphragms; the diaphragms distribute these forces to lateral force–resisting elements such as shear walls and frames; the vertical elements transfer the forces into the foundation; and the foundation transfers the forces into the supporting soil If there is a discontinuity in the load path, the building is unable to resist seismic forces regardless of the strength of the elements Interconnecting the elements needed to complete the load path is necessary to achieve the required seismic performance Examples of gaps in the load path would include a shear wall that does not extend to the foundation, a missing shear transfer connection between a diaphragm and vertical elements, a discontinuous chord at a diaphragm’s notch, or a missing collector A good way to remember this important design strategy is to ask yourself the question, “How does the inertia load get from here (meaning the point at which it originates) to there (meaning the shear base of the structure, typically the foundations)?” Seismic loads result directly from the distortions induced in the structure by the motion of the ground on which it rests Base motion is characterized by displacements, velocities, and accelerations that are erratic in direction, magnitude, duration, and sequence Earthquake loads are inertia forces related to the mass, stiffness, and energy-absorbing (e.g., damping and ductility) characteristics of the structure During its life, a building located in a seismically active zone is generally expected to go through many small, some moderate, one or more large, and possibly one very severe earthquakes As stated previously, in general, it is uneconomical or impractical to design buildings to resist the forces resulting from large or severe earthquakes within the elastic range of stress In severe earthquakes, most buildings are designed to experience yielding in at least some of their members The energy-absorption capacity of yielding will limit the damage to properly designed and detailed buildings These can survive earthquake forces substantially greater than the design forces determined from an elastic analysis 5.2.3 RESPONSE OF ELEMENTS ATTACHED TO BUILDINGS Elements attached to the floors of buildings (e.g., mechanical equipment, ornamentation, piping, and nonstructural partitions) respond to floor motion in much the same manner as the building responds to ground motion However, the floor motion may vary substantially from the ground motion The high-frequency components of the ground motion tend to be filtered out at the higher levels in the building, whereas the components of ground motion that correspond to the natural periods of vibrations of the building tend to be magnified If the elements are rigid and are rigidly attached to the structure, the forces on the elements will be in the same proportion to the mass as the forces on the structure But elements that are flexible and have periods of vibration close to any of the predominant modes of the building vibration will experience forces in proportion substantially greater than the forces on the structure 5.2.4 ADJACENT BUILDINGS Buildings are often built right up to property lines in order to make the maximum use of space Historically, buildings have been built as if the adjacent structures not exist As a result, the buildings may pound during an earthquake Building pounding can alter the dynamic response of both buildings, and impart additional inertial loads to them Buildings that are the same height and have matching floors are likely to exhibit similar dynamic behavior If the buildings pound, floors will impact other floors, so damage usually will be limited to nonstructural components When floors of adjacent buildings are at different elevations, the floors Mandarin Oriental, Miami, Florida A hotel tower, this building’s roofline is gradually terraced to abstractly resemble the company’s Mandarin sampan logo The complex’s concrete structure utilizes both conventional and post-tensioned slabs and shear walls for lateral support A pile foundation was required for support as the building is located on reclaimed land Marquis, Tampa Bay, Florida The Marquis is a residential tower standing 700 ft tall in a hurricane prone area Wind tunnel analysis was performed and the structure was designed to withstand wind speeds up to 146 mph The structural system consists of concrete shear walls and post-tensioned flat plate slabs with columns The foundation utilized grade 75 steel to reduce rebar congestion where localized shear reinforcing was required Millennium Place, Boston, Massachusetts This project is a steel framed tower with a low-rise podium and a concreteframed below-grade parking garage The top-down construction method allowed construction to proceed downward while the steel superstructure framing proceeded upward simultaneously Transfer level for the towers consisted of 56 intersecting trusses and 30 transfer girders Forty fluid viscous dampers controls the building acceleration 301 Mission Street, San Francisco, California A 59-story residential tower, 301 Mission is one of the tallest reinforced concrete structures in the Western United States Outrigger trusses at three intermediate levels help in controlling lateral deflection A dynamic time-history analysis and a nonlinear push-over analysis were performed to better quantify the building performance and to validate the designed procedure Mohegan Sun Phase II, Uncasville, Connecticut A large private gaming and hospitality development that includes a 35-story tower and a 2-story low rise housing entertainment, retail, meeting, and convention space One Bayfront Plaza, Miami, Florida The project comprises of two towers sitting atop a 22-story podium building Tower one is 61 stories tall and tower two is 70 stories tall Our Lucaya Beach & Golf Resort, Grand Bahama Island An extensive renovation and upgrade of this resort complex included the renovation of an existing hotel into a convention center Extensive concrete repairs and strengthening were performed on the existing structure Several one-story concrete and masonry buildings were constructed, including four new restaurants Peter B Lewis Building, Cleveland, Ohio The building is a composite structure of concrete and steel Cast-in-place concrete flat-slab construction with a 36 in concrete transfer slab and ft deep, curved concrete beams were utilized to transfer gravity forces to the columns The building features a steel clad roof framed using in standard pipe steel Residential Tower Conceptual Design, Las Vegas, Nevada The architect shows a superstructure that requires bridging to transfer the gravity and lateral loads to the foundation Steel trusses are used to act as a support spanning from concrete core to concrete core Ritz-Carlton Downtown, New York This 40-story mixed-use tower comprises of reinforced concrete walls and columns supporting flat-plate construction Shear walls are coupled to improve resistance to high wind loading Flushing Metro Center, Flushing, New York A mixed-use facility situated above a manufacturing/warehouse facility located on a 14 acre site in Queens The Standard, New York A 22-story boutique hotel erected over the Highline, a historic elevated railroad landmark in the heart of Manhattan’s Meat Packing district The building’s structure consists of cast-in-place concrete A transfer system spanning 80 ft allocated at the fifth floor enables the upper levels of the building to span over the existing Highline Poor soil conditions and a high ground water line required a deep foundation system with the implementation of a heavily reinforced bathtub-type foundation Vdara Tower, City Center, Las Vegas, Nevada A 57-story concrete condominium and hotel tower located at City Center, Block B The floor system is posttensioned flat plate and the lateral system consists of reinforced concrete shear walls Westin Diplomat Resort & Spa, Hollywood, Florida A 41-story conventional reinforced concrete structure sits on top of two discrete structures A 15 ft deep composite truss connects the two legs at the 10th floor, supporting the single tower above Where the building is dramatically sloped back from the perimeter, sloped columns are used to pick up long cantilevers created by the step backs