Friday, 31 July 2015
Damping Strategies for Structural Systems
The direction of the evolution of tall building structural
systems, based on new structural concepts with newly adopted
high-strength materials and construction methods, has been
towards augmented efficiency. Consequently, tall building
structural systems have become much lighter than earlier ones. This
direction of the structural evolution toward lightness, however,
often causes serious structural motion problems – primarily due
to wind-induced motion.
From the viewpoint of structural material’s properties, due to
the lag in material stiffness compared with material strength, the
serviceability of the structure potentially becomes a governing factor
in tall building design when high strength material is used. For
instance, today, structural steel is available from 170 to 690 MPa
(24 to 100 ksi). However, its modulus of elasticity remains nearly
the same without regard to the change in its strength. The change
of production process or heat treatment influences its strength
but not the modulus of elasticity. Regarding concrete, increase
in its strength results in increase in its modulus of elasticity, albeit
increasing its brittleness. However, this increase in the modulus of
elasticity is relatively small compared with the increase in strength.
Thus, the lighter structures produced by high-strength materials
can cause motion problems.
The control of this structural motion should be considered
with regard to static loads as well as dynamic loads. Against the
static effect of wind loads, stiffer structures produce less lateral
displacement. With regard to the dynamic effect of wind loads,
not only the windward response but also the across-wind response
of the structure should be considered. Generally, in tall buildings,
the lateral vibration in the across-wind direction induced by vortex
shedding is more critical than that in the windward direction.Regarding both directions, structures with more damping
reduce the magnitude of vibration and dissipate the
vibration more quickly. With regard to the vibration in
the across-wind direction, a stiffer structure reduces the
probability of lock-in condition because as a structure’s
fundamental frequency increases, wind velocity that
causes the lock-in condition also increases. Since the
natural direction of structural evolution towards lightness
is not likely to be reversed in the future, more stiffness
and damping characteristics should be achieved with a
minimum amount of material (Moon, 2005).
Achievement of more stiffness in tall buildings is related
to the configuration of primary structural systems, which
were discussed in previous sections. For example, more
recent structural trends such as tubes, diagrids and coresupported
outrigger structures in general achieve much
higher stiffness than traditional rigid frame structures.
Obtaining more damping is also related to the choice
of primary structural systems and materials. However,
the damping achieved by the primary
structure is quite uncertain until the
building construction is completed.
A more rigorous and reliable increase
in damping, to resolve tall building
motion problems, could be achieved
by installing auxiliary damping
devices within the primary structural
system. The effect of such damping
can be estimated relatively accurately.
Thus, when severe wind-induced
vibration problems are expected,Premium for Height
The primary structural skeleton of a tall building can be visualized
as a vertical cantilever beam with its base fixed in the ground. The
structure has to carry the vertical gravity loads and the lateral wind
and earthquake loads. Gravity loads are caused by dead and live
loads. Lateral loads tend to snap the building or topple it. The
building must therefore have adequate shear and bending resistance
and must not lose its vertical load-carrying capability.
Fazlur Khan realized for the first time that as buildings became
taller, there is a “premium for height” due to lateral loads and the
demand on the structural system dramatically increased, and as a
result, the total structural material consumption increases drastically
(Ali, 2001). If there would be no lateral forces on the building such
as wind or earthquake, any high-rise building could be designed just
for gravity loads. The floor framing system usually carries almost
the same gravity loads at each floor, although the girders along
the column lines need to be progressively heavier towards the base
of the building to carry increasing lateral forces and to augment
the building’s stiffness. The column sizes increase progressively
towards the base of the building due to the accumulated increase
in the gravity loads transmitted from the floors above.
If we assume the same bay sizes, the material quantities required for floor framing is almost the same regardless of the number of stories. The material needed for floor framing depends upon the span of the framing elements, that is, column-to-column distance and not on the building height. The quantity of materials required for resisting lateral loads, on the other hand, is even more increased and would begin to exceed other structural costs if a rigid-frame system is used for very tall structures. This calls for a structural system that goes well beyond the simple rigid frame concept. Based on his investigations Khan argued that as the height increases beyond 10 stories, the lateral drift starts controlling the design, the stiffness rather than strength becomes the dominant factor, and the premium for height increases rapidly with the number of stories. Following this line of reasoning, Khan recognized that a hierarchy of structural systems could be categorized with respect to relative effectiveness in resisting lateral loads for buildings beyond the 20- to 30-story range (Khan, 1969).
If we assume the same bay sizes, the material quantities required for floor framing is almost the same regardless of the number of stories. The material needed for floor framing depends upon the span of the framing elements, that is, column-to-column distance and not on the building height. The quantity of materials required for resisting lateral loads, on the other hand, is even more increased and would begin to exceed other structural costs if a rigid-frame system is used for very tall structures. This calls for a structural system that goes well beyond the simple rigid frame concept. Based on his investigations Khan argued that as the height increases beyond 10 stories, the lateral drift starts controlling the design, the stiffness rather than strength becomes the dominant factor, and the premium for height increases rapidly with the number of stories. Following this line of reasoning, Khan recognized that a hierarchy of structural systems could be categorized with respect to relative effectiveness in resisting lateral loads for buildings beyond the 20- to 30-story range (Khan, 1969).
Preface
In recent years the subject of computer programming has been recognized as a discipline whose mastery
is fundamental and crucial to the success of many engineering projects and which is amenable to
scientific treatement and presentation. It has advanced from a craft to an academic discipline. The initial
outstanding contributions toward this development were made by E.W. Dijkstra and C.A.R. Hoare.
Dijkstra's Notes on Structured Programming [1] opened a new view of programming as a scientific
subject and intellectual challenge, and it coined the title for a "revolution" in programming. Hoare's
Axiomatic Basis of Computer Programming [2] showed in a lucid manner that programs are amenable to
an exacting analysis based on mathematical reasoning. Both these papers argue convincingly that many
programmming errors can be prevented by making programmers aware of the methods and techniques
which they hitherto applied intuitively and often unconsciously. These papers focused their attention on
the aspects of composition and analysis of programs, or more explicitly, on the structure of algorithms
represented by program texts. Yet, it is abundantly clear that a systematic and scientific approach to
program construction primarily has a bearing in the case of large, complex programs which involve
complicated sets of data. Hence, a methodology of programming is also bound to include all aspects of
data structuring. Programs, after all, are concrete formulations of abstract algorithms based on particular
representations and structures of data. An outstanding contribution to bring order into the bewildering
variety of terminology and concepts on data structures was made by Hoare through his Notes on Data
Structuring [3]. It made clear that decisions about structuring data cannot be made without knowledge of
the algorithms applied to the data and that, vice versa, the structure and choice of algorithms often
depend strongly on the structure of the underlying data. In short, the subjects of program composition
and data structures are inseparably interwined.
Yet, this book starts with a chapter on data structure for two reasons. First, one has an intuitive feeling
that data precede algorithms: you must have some objects before you can perform operations on them.
Second, and this is the more immediate reason, this book assumes that the reader is familiar with the
basic notions of computer programming. Traditionally and sensibly, however, introductory programming
courses concentrate on algorithms operating on relatively simple structures of data. Hence, an
introductory chapter on data structures seems appropriate.
Throughout the book, and particularly in Chap. 1, we follow the theory and terminology expounded by
Hoare and realized in the programming language Pascal [4]. The essence of this theory is that data in the
first instance represent abstractions of real phenomena and are preferably formulated as abstract
structures not necessarily realized in common programming languages. In the process of program
construction the data representation is gradually refined -- in step with the refinement of the algorithm --
to comply more and more with the constraints imposed by an available programming system [5]. We
therefore postulate a number of basic building principles of data structures, called the fundamental
structures. It is most important that they are constructs that are known to be quite easily implementable
on actual computers, for only in this case can they be considered the true elements of an actual data
representation, as the molecules emerging from the final step of refinements of the data description. They
are the record, the array (with fixed size), and the set. Not surprisingly, these basic building principles
correspond to mathematical notions that are fundamental as well.
A cornerstone of this theory of data structures is the distinction between fundamental and "advanced"
structures. The former are the molecules -- themselves built out of atoms -- that are the components of
the latter. Variables of a fundamental structure change only their value, but never their structure and
never the set of values they can assume. As a consequence, the size of the store they occupy remains
constant. "Advanced" structures, however, are characterized by their change of value and structure during
the execution of a program. More sophisticated techniques are therefore needed for their implementation.
The sequence appears as a hybrid in this classification. It certainly varies its length; but that change in
structure is of a trivial nature. Since the sequence plays a truly fundamental role in practically all
computer systems, its treatment is included in Chap.13 structural steel buildings that dazzle
The winning projects and their respective team members were recognized on April 17 during 2013 NASCC: The Steel Conference in St. Louis. Each year, awards for each winning project are presented to the project team members involved in the design and construction of the structural framing system, including the architect, structural engineer, general contractor, detailer, fabricator, erector and owner. A panel of design and construction industry professionals identified National and Merit winners in three categories, based on constructed value: projects less than $15 million; projects $15 million to $75 million; and projects greater than $75 million. In addition, the panel awarded a Presidential Award of Excellence in Engineering to one project for structural engineering accomplishment. The 2013 award-winning projects are (photos and project descriptions courtesy
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