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					               Proposal
Structures: Form, Function and Failure
                  Danielle Cove
               December 11, 2001
    Professor Shilepsky and Professor Stiadle
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Table of Contents
1       EXECUTIVE SUMMARY................................................................................................................. 3

2       INTRODUCTION............................................................................................................................... 4

3       STRUCTURES .................................................................................................................................... 5
    3.1     FUNCTION AND STRUCTURE.............................................................................................................. 5
    3.2     ARCHITECTS AND ENGINEERS ........................................................................................................... 5
4       BUILDING CODES ............................................................................................................................ 5

5       LOADS ................................................................................................................................................. 5
    5.1 STATIC LOADS .................................................................................................................................. 5
       5.1.1 Dead Loads ............................................................................................................................. 5
       5.1.2 Live Loads .............................................................................................................................. 6
    5.2 DYNAMIC LOADS .............................................................................................................................. 6
       5.2.1 Impact Loads .......................................................................................................................... 6
       5.2.2 Earthquake Loads ................................................................................................................... 6
            5.2.2.1       Richter Scale ..................................................................................................................................... 6
       5.2.3 Thermal and Settlement Loads ............................................................................................... 6
       5.2.4 Resonance ............................................................................................................................... 7
    5.3 WIND LOADS .................................................................................................................................... 7
       5.3.1 Wind Drift ............................................................................................................................... 8
6       MATERIALS ...................................................................................................................................... 8
    6.1 STEEL................................................................................................................................................ 8
    6.2 REINFORCED CONCRETE ................................................................................................................... 8
    6.3 PLASTICS .......................................................................................................................................... 9
    6.4 FORCES ON MATERIALS .................................................................................................................... 9
       6.4.1 Tension and Compression....................................................................................................... 9
            6.4.1.1       Yield Stress ....................................................................................................................................... 9
            6.4.1.2       The Law of Least Work..................................................................................................................... 9
        6.4.2        Elasticity and Plasticity .......................................................................................................... 9
            6.4.2.1 Elasticity............................................................................................................................................ 9
            6.4.2.2 Linearly Elastic ............................................................................................................................... 10
            6.4.2.3 Plasticity .......................................................................................................................................... 10
               6.4.2.3.1 Brittle ......................................................................................................................................... 10
               6.4.2.3.2 Temperature ............................................................................................................................... 10
        6.4.3        Safety .....................................................................................................................................10
            6.4.3.1       Safety Factors .................................................................................................................................. 11
7       BEAMS AND COLUMNS ................................................................................................................11
    7.1 NEWTON’S LAWS .............................................................................................................................11
       7.1.1 Equilibrium ............................................................................................................................11
    7.2 TRANSLATIONAL EQUILIBRIUM .......................................................................................................11
    7.3 ROTATIONAL EQUILIBRIUM .............................................................................................................11
    7.4 BEAM ACTION .................................................................................................................................12
       7.4.1 Moment if Inertia ...................................................................................................................12
    7.5 SHEAR ..............................................................................................................................................12
    7.6 BUCKLING........................................................................................................................................13
8       DOMES AND DISHES ......................................................................................................................13
    8.1     STRUCTURE OF DOME ......................................................................................................................13
    8.2     MODERN DOMES..............................................................................................................................13
    8.3     HANGING DISH ................................................................................................................................13
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9        FORM-RESISTANT STRUCTURES ..............................................................................................14
     9.1     GRIDS AND FLAT SLABS ..................................................................................................................14
     9.2     STRENGTH THROUGH FORM ............................................................................................................14
     9.3     CURVED SURFACES ..........................................................................................................................14
     9.4     BARREL ROOFS AND FOLDED PLATES..............................................................................................15
     9.5     SADDLE ROOFS ................................................................................................................................15
     9.6     COMPLEX ROOFS .............................................................................................................................15
10       SKYSCRAPERS ................................................................................................................................15
     10.1 HIGH-RISE ........................................................................................................................................15
     10.2 STRUCTURE OF A SKYSCRAPER ........................................................................................................15
11       PROPOSAL ........................................................................................................................................17
     11.1 APPROACH .......................................................................................................................................17
     11.2 TASK LIST ........................................................................................................................................17
        11.2.1 Decide What Buildings to Research ......................................................................................17
             11.2.1.1 Criteria ............................................................................................................................................ 17
             11.2.1.2 Deciding Building Failure ............................................................................................................... 17
             11.2.1.3 Deciding on the Buildings ............................................................................................................... 17
         11.2.2       Research on Individual Buildings ..........................................................................................17
             11.2.2.1      Research Codes of Time Period and Area ....................................................................................... 17
             11.2.2.2      Research Material’s Strengths/Weaknesses .................................................................................... 18
             11.2.2.3      Research Design Process ................................................................................................................. 18
             11.2.2.4      Successful Use of Architectural Feature/Design ............................................................................. 18
             11.2.2.5      Myths .............................................................................................................................................. 18
             11.2.2.6      Math ................................................................................................................................................ 18
         11.2.3       Analyze Findings ...................................................................................................................18
             11.2.3.1 Expert’s Findings ............................................................................................................................ 18
             11.2.3.2 Evaluation of Structural Failure ...................................................................................................... 18
         11.2.4       Compare my Analysis to Expert’s Findings ..........................................................................19
             11.2.4.1 Differences ...................................................................................................................................... 19
        11.2.5 Presentation ...........................................................................................................................19
        11.2.6 Write and Hand in Paper .......................................................................................................19
     11.3 GANTT CHART .................................................................................................................................19
12       APPENDIX I: VOCABULARY........................................................................................................20

13       BIBLIOGRAPHY ..............................................................................................................................22
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1   EXECUTIVE SUMMARY
        Since before the recent events of September 11th I have had an interest in why
buildings fail as well as the ever-changing conditions surrounding building structures.
The need to evaluate and improve modern builds is a driving force in today’s
architectural and structural world. I wish to explore this in depth by examining two
modern buildings that had structural failure.

        In this proposal, I explain many of the concepts needed to begin to understand the
physics behind the modern building. Structure, essentially the skeleton of a building, is
analyzed via loads, function, and materials. Furthermore, the many types of loads, the
forces that act on the structure of a building, are discussed at length. Materials, building
codes, beams, columns, domes, dishes, form resistant structures, and skyscrapers all have
sections dedicated to them.

        Therefore, for my thesis I plan to physically and mathematically evaluate two
modern buildings that have failed using the knowledge a gained this semester. I will
investigate the structures that have failed and try to understand what happened. Then I
will examine the engineer’s evaluation of these buildings and compare my findings to
those of experts. This will help me to understand the concepts behind the failure, the
process used to evaluate it, and the work that goes into creating a building. Doing this
will give me a better awareness of the structural integrity of modern buildings.
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2   INTRODUCTION
        The need for shelter is one of the driving forces of the human condition. From the
first days of civilization, humans have strove to build better, bigger, and more efficient
houses and work places. In the beginning, trial and error was the method of choice. For
example, say a new idea was tried on a cathedral. If it stood up, then it was used again, if
not, the idea was scrapped or revised (Salvadori 19). Eventually, this expensive and time
consuming process was replaced by a more scientific method of applying equations and
even modeling the building in certain situations, wind tunnels for instance. The invention
of new materials brought about new approaches to constructing buildings. However,
innovation does not come without a price and so not all buildings will be successful. The
best architects and engineers admit that they cannot see every possible disaster and keep
an open and suspicious mind. Thomas Edison once said to a man that he fired from his
laboratory, “I don’t mind the fact that you don’t know much, yet. The trouble is you
don’t even suspect” (Salvadori 66).

        The ever-changing conditions surrounding a building structure have always
intrigued me. By studying the forces that act on buildings, I hope to gain a better
understanding of what work goes into creating a building. Then, I will examine
structures that have failed and try to understand what happened. Finally, I will compare
my findings to those of experts. Doing this will give me a better understanding of the
structural integrity of modern buildings.

In chapter 1, I will explain what a structure is and who creates and designs buildings.

I explain what building codes are in chapter 2.

In chapter 3, I go over the different types of loads that act on buildings.

Chapter 4 examines the materials used in structures and the unique properties they have
as well as some general properties a structural element must have.

Chapters 5 and chapter 6 take an in-depth look at beams and columns and domes and
dishes while chapter 7 takes a general look at some other structural elements.

Finally, chapter 8 looks at some ideas behind the skyscraper.
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3     STRUCTURES
3.1   FUNCTION AND STRUCTURE
        A structure is the skeleton of a building. It holds up the weight of the building
and withstands any other force acting on it, such as wind or the weight of the furniture.
Structural elements such as columns, floors, beams, and walls carry and protect against
the loads, or forces, that act on the building. The idea of a structure for buildings has
been around since the creation of permanent dwellings and developed through the ages.
From the very first huts to medieval cathedrals to the modern skyscrapers of day,
structure has undergone momentous changes. These revolutions have made the modern
skyline possible (Salvadori 19).

3.2   ARCHITECTS AND ENGINEERS
       While architects are the imagination behind today’s buildings, engineers are the
workhorses. Engineers work with architects to make the creative process of designing a
building reality. Architects are concerned with the function and purpose of a building but
they are also concerned with the aesthetic value, or the visual appeal of a building.
Engineers calculate and adapt the architect’s view so that it will be safe and affordable,
and withstand the necessary forces. The architect then revises this and the cycle
continues until both are sufficiently happy (Salvadori 25).

4     BUILDING CODES
       Building codes are rules and regulations that deal with the safety and aesthetic
value of a building. Veteran engineers create building codes and cities, states, and
countries publish them (Salvadori 44). Each area has variations in the codes so, for
example, it is impossible for a building designed under the codes for St. Paul, MN to
undergo construction in Bakersfield, CA.
5     LOADS
       Engineers and architects must analyze the loads, or forces, associated with a
climate and building type before beginning the design of the actual building.

5.1  STATIC LOADS
      Static loads are permanent or semi-permanent loads. When calculated, there is an
amount of certainty to how well the building will withstand the loads because they are
permanent or change very slowly over time (Salvadori 45).

5.1.1 Dead Loads
       A dead load is the weight of a building or its individual parts. This load stays the
same throughout the lifetime of the structure. One can calculate this by multiplying the
volume of the object or objects by its specific weight (Salvadori 43).
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5.1.2 Live Loads
        The live load of a building includes all of the other objects, such as people,
furniture, and machines. These loads are movable and may be spread out over the entire
floor space or rest in the center of the room. Yet, this changes slowly over time. Basing
the live load calculations on the worst possible scenario over the structure life guaranties
safety. This is where building codes come into play (Salvadori 44). The values for the
live load limitations change with location, building type, and function. For example, the
floors of a warehouse, an office building, and a house all have vary different maximum
weight requirements. The calculations for live loads are complicated and time
consuming; most engineers use computers to do them now (Salvadori 45).

5.2   DYNAMIC LOADS
        A dynamic load can change suddenly and rapidly. These include forces received
from earthquakes, some wind gusts, dropping something on the floor, or pounding on a
wall, as well as many others. These forces are unpredictable and vary unexpectedly.
Therefore, these are the forces that can be the most destructive and the hardest to guard
against (Salvadori 45).

5.2.1 Impact Loads
        Impact loads account for the forces exerted on a building by an object that has
fallen, dropped, or crashed into a part of the building. Since the object has a velocity at
the time of impact, and may even be accelerating, the force it puts on the building is
much greater than its static equivalent, or weight (Salvadori 46).

5.2.2 Earthquake Loads
        Only buildings constructed in the last 20-40 years reaped the benefits of this
knowledge. In fact, in 1967, over 265,000 people died in two separate earthquakes.
However, most of the dynamic impact forces of earthquakes are horizontal so the same
theories and techniques used with wind loads apply (Salvadori 53).

5.2.2.1   Richter Scale
        The Richter scale is a measurement of earthquake energy. A relatively harmless
earthquake is three or four on the scale; however, earthquakes of magnitude eight or
greater causes buildings to collapse and deaths. Fortunately, we know where these types
of earthquakes occur and only at these locations do earthquake load apply (Salvadori 54).

5.2.3 Thermal and Settlement Loads
        Daily and seasonal changes in air temperature cause thermal loads. Soil
settlement under a structure causes settlement load. These loads are locked-in, or hidden
loads, because they are invisible to the eye (Salvadori 54).

        Thermal expansion happens when the temperature of the surrounding air causes
the structure to shrink or expand in size. An example, bridges experience thermal
expansion. Consider a steel bridge 400 feet long built in the summer at a temperature of
80 degrees. In winter, the bridge shrinks 2 inches. Since steel beams are very rigid, the
expansion of the bridge uses up ½ of the strength of the steel. To avoid this, one of the
ends of the bridge must be movable, allowing the thermal expansion to occur (Salvadori
                                                                                            7


55). Domes provide another example of thermal expansion. The base of a dome will
crack due to thermal expansion unless reinforced with a steel ring (Salvadori 56).

       Moreover, buildings usually maintain a constant indoor air temperature while the
air temperature outside changes constantly. Therefore, the outside of a building will
expand and contract while the inside of the building does not. This can damage the
building if the beams are not hinged (Salvadori 56).

        Uneven soil settlement under a building also causes bending in beams. A fine
example of this is the Leaning Tower of Pisa. The soil under this building started settling
during construction. The Pisans thought that they could stop this by building the upper
part vertically; however, it is still falling at a rate of 1 inch per 8 years. Now it is 16 ft
from plumb (Salvadori 57).

       Yet, despite all of the above examples, foundation problems cause most damage
done to buildings (Salvadori 57).

5.2.4 Resonance
       Although this type of load is dynamic, it does not happen suddenly like other
dynamic loads. Rather, resonance happens gradually over time. Wind gusts that push on
the building in time with its natural oscillation create this kind of load. In order to
understand this one could think of the rope and church bell, a child pumping her legs on a
swing, or the Tacoma Narrows Bridge in Washington. Pulling on the rope at the right
times causes the bell to gradually swing wider and wider (Salvadori 47). The other
examples illustrate the same idea. When resonance happens for a long enough time, it
could cause a building to collapse (Salvadori 48).

5.3    WIND LOADS
        Wind loads can be either dynamic or static, depending on the type of building that
the wind acts on. In order to understand this, one must look at the natural period of
oscillation of a building (Salvadori 49).

        The materials buildings are composed of are not completely rigid, even steel
bends. The taller the building, the more bending, or sway, it will have. However, this is
not always noticeable to the eye or other senses. The natural period of oscillation is the
time it takes for the building to complete one oscillation, or for it to move back and forth
once. For instance, the World Trade Centers, which were 1,350 feet high, had a period of
oscillation of 10 seconds (Salvadori 48).

        If the wind gust lasts for a much shorter time than the period of oscillation then
the force exerted is dynamic. For example, the World Trade Center experienced a wind
gust lasting 3 seconds. A building only 20 stories high, with a period of 1 second,
experienced the same gust. Then for the WTC, the force would be dynamic and for the
shorter building, the force would be static (Salvadori 47).
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        Wind speed increases with height and wind pressure increases as the square of
wind speed. In effect the taller the building the more the engineers and architects must
pay attention to the wind load (Salvadori 48).

5.3.1 Wind Drift
       The wind drift of a building is the lateral displacement of the top of the building
from equilibrium, or plumb (Salvadori 52).

6     MATERIALS
       Not every material can be used in the structure of a building. They must be able
to withstand the tension and compression associated with the building as well as

6.1    STEEL
        Steel is a very affordable and strong material. There are many different types of
steel; however, all are composed of iron and carbon with small amounts of other metals
in it that give it specific qualities. The production of steel in mass quantity has two
different strengths. Regular structural steel has a yielding strength of 36,000 pounds per
square inch and high-strength steel has a yielding strength of 50,000 pounds per square
inch (Salvadori 64). However, steel can theoretically have a yielding strength of 4
million pounds per square inch. Right now, we have steel cables that have an ultimate
strength of 300,000 pounds per square inch with an allowable stress of 150,000 pounds
per square inch. This is strong enough to suspend the Leaning Tower of Pisa from a
cable that is 1.1 inches in diameter (Salvadori 65).

        However, there are some downsides to steel. It melts at relatively low
temperatures, around 1200 degrees F, and becomes brittle at relatively high temperatures,
around 30 degrees F. Without proper treatments, steel becomes useless and dangerous
(Salvadori 65). In addition, if treated improperly, steel in a high building slices into
pastry thin layers. This phenomenon is called lamination stress. Improperly welded
joints cause similar stresses. Finally, repeated compression and tension fatigue steel
(Salvadori 66).

6.2   REINFORCED CONCRETE
        Reinforced concrete is composed of concrete (a mixture of sand, pebbles, water,
and cement) and steel and was originally invented in 19th century France (Salvadori 68).
When hardened it becomes a very strong material. Portland cement is a particularly
strong combination of limestone and clay. It is impermeable to water and actually grows
in stronger if placed in water after solidifying (Salvadori 67). In concrete, the
compression strength is much larger than the tensile strength. However, placing steel
rods inside the concrete, where tension will be present, results in a material that is strong
in both stresses, called reinforced concrete. The unfortunate part about reinforced
concrete is that it cracks if it dries too fast. Furthermore, even 3 to 4 years after
hardening it can experience lengthening or shortening when under a constant load
(Salvadori 68). Fortunately this can be countered used a process called prestressing
(Salvadori 69).
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6.3   PLASTICS
       Plastics can be as strong as steel in tension and compression, are very rugged, and
can be elastic and plastic. Fiberglas, a plastic strengthened with glass particles, is the
most prevalent plastic used in buildings (Salvadori 70). However, no one uses plastic in
the structure of buildings for two reasons. Firstly, plastics deform more than the
materials used now. Secondly, they are too pricey (Salvadori 71).

6.4 FORCES ON MATERIALS
6.4.1 Tension and Compression
        “The purpose of a structure is to channel the loads on the building to the ground.”
Furthermore, loads either pull (stretch) or push (squeeze). Therefore, loads stress a
structure and structures strain under a load. An “overstressed” load on a material “breaks
down” or “buckles” and eventually damages it (Salvadori 59). When pulled, a structure
is in tension. One can recognize tension by increased lengths in the material. A good
example of this is the rubber band. When pushed, a structure is in compression, or
decreases in length (Salvadori 60).

        Both tension and compression happen to every material although we cannot
always see it. As a high rise building is under construction, the lower columns compress
as it gets taller and taller. However, this is never noticeable since a building 1000 feet
high only compress by 1 inch (Salvadori 60).

        The strain is the change in length divided by the original length. Since all
structures have loads acting on them, they all have tension and/or compression. So all
materials used to build buildings must be able to withstand one or both of these forces
(Salvadori 60).

6.4.1.1   Yield Stress
        The weight at which a material changes from elastic to plastic behavior is called
the yield stress (Salvadori 63).

6.4.1.2   The Law of Least Work
        The law of least work states that a load on a building will find the easiest path in a
structure to the ground. This path is one that demands the minimum amount of work on
the structural materials (Salvadori 59).

6.4.2 Elasticity and Plasticity
6.4.2.1    Elasticity
        We need materials that stretch or contract when a load is applied and then return
to their normal lengths after the load disappears. This is called elasticity. However, the
material must not stretch or contract too much. If this happens, the material might break
or deform permanently under the load. For example, if a high rise building did not
recover from a wind load then it would eventually look like the Leaning Tower of Pisa.
“A material whose change in shape vanishes rapidly when the loads on it disappear is
said to behave elastically (Salvadori 61).” All materials used in building are elastic to a
                                                                                           10


point; however, with large loads the materials sometimes deform permanently (Salvadori
61).

6.4.2.2     Linearly Elastic
        Material can be linearly elastic, or have elasticity. For example, when one applies
double the load to a material the stretching or bending doubles as well. In other words,
the graphed loads verses stretching, is a straight line (Salvadori 61).

6.4.2.3     Plasticity
        If a load on a material is so great that it causes deformation even when unloaded,
the material behaves plastically. “Materials under relatively small loads behave
elastically and plastically under higher loads” are good for use in buildings (Salvadori
62). The reason behind this is that these materials do not break or give-out suddenly.
They give “warning” signs when things begin to get dangerous. When the material is
weighted heavily enough it not only deforms but “the material keeps stretching under a
constant load” (Salvadori 62).

6.4.2.3.1    Brittle
       The materials that are not plastic are called brittle. If used in the structure of a
building, they will stretch without deformation until their breaking point. They break
suddenly. For example, glass is stronger than steel under tension and compression;
however, it is not plastic so it could never be used in the structure of a building (Salvadori
62).

6.4.2.3.2    Temperature
        The point at which the structure starts behaving plastically rely on a variety of
variables, the most significant being temperature. For example, steel fails at 1,200
degrees F and at 30 degrees F it becomes brittle. Therefore, fireproofing steel as well as
heating it maintains strength (Salvadori 63).

6.4.3 Safety
        A huge consideration when creating and designing a building is safety. In order
to ensure that a building is safe one must make sure that the building will not collapse.
The number of pounds per square inch that a material can hold before breaking is the
strength of that material. This maximum weight is called the ultimate strength of a
material. Some materials have the same strength when compressed or stretched. In fact,
many metals used in building behave this way. Therefore, for safety reasons, one wants
to load a material to only a percentage of its yield stress, or the point at which the
material changes from elastic to plastic. For example, a safe percentage for steel is 60%.
This is called its allowable stress (Salvadori 63).

       Another safety issue that engineers consider is where certain types of materials
are used. For example, stone and concrete are very strong materials when it comes to
loads that push on them, however, they do not hold up well against loads that pull on
them. So stone beam is never used but it is a very effective substance when used as a
column or an arch (Salvadori 64).
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6.4.3.1   Safety Factors
       Safety is measured in factors of safety. To calculate these take the inverse of the
allowable stress. Since in steel the allowable stress is 60% or 60/100, the factor of safety
is 100/60 = 1.6. In concrete, the number is closer to 2.5. Concrete, limestone, or marble
can reach 12,000 feet in height before it will collapse under its own weight. However,
some of the highest structures made from stone, the pyramids, are only 500 feet in height.
This makes their factor of safety close to 24 (Salvadori 63).

7     BEAMS AND COLUMNS
        To understand how beams and columns work, one must first understand they have
to be balanced and free of any kind of movement to function properly.

7.1   NEWTON’S LAWS
        Isaac Newton created three basic laws that deal with gravity and gravitational
motion. Newton’s Laws explain how objects interact with one another. When dealing
with structures and architecture, these laws and the ideas behind elasticity solve most
structural dilemmas (Salvadori 72).

        The first law “states that a body at rest will not move unless a new, and
unbalanced force is applied to it (Salvadori 73).” The second law, which is more of an
equation, says that the total force is equal to the acceleration of the object multiplied by
the mass of the object, or F=ma. Finally, the third law states that “ when a body is at rest,
for each force applied to it there corresponds an equal and opposite balancing reaction,
also applied to it” (Salvadori 73). Since buildings are stationary objects Newton’s first
and third laws are very important to engineers.

7.1.1 Equilibrium
      A building is at equilibrium when all the forces acting on it are balanced. In other
words when the building is stationary and not overstressed in any direction (Salvadori
73).

7.2   TRANSLATIONAL EQUILIBRIUM
        A building is in translational equilibrium if it is not moving in any of the three
directions. It cannot move up or down, back or forth, or side to side (Salvadori 74).

7.3    ROTATIONAL EQUILIBRIUM
        To understand rotational equilibrium one can think of a seesaw. In order to have
each side balanced in the air, parallel to the ground, the weight on either end has to do
one of two things. It can be the same with the same distance away from the center of the
board. Alternatively, the weights can be different but the heavier weight has to be
proportionally closer to the center. For example, if one weight was 2 times as heavy as
the other then that weight would have to be twice as close to the center for it to be at
rotational equilibrium (Salvadori 75).
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7.4    BEAM ACTION
        Whenever a beam, or other straight element, bends so that the upper and lower
fibers are in tension and compression it has beam action. There are different forms of
this, however, it they all lead to the same result (Salvadori 81).

        When a weight of a building is not enough to keep it standing under a wind load
the columns of the structure must be "anchored into the foundation deep in the ground."
By doing this, although the building will have wind drift, it will not topple over. There is
tension and compression happening on the columns because wind drift can create a
lateral displacement of several feet, while the building is not tipping. However, this
bending is not observable to the eye. In fact, on a 1000 foot skyscraper the columns only
increase and decrease in length by 0.1 inches. Yet, because the floors in the buildings
connect rigidly at 90-degree angles, they will tip to stay at those angles when under a
wind load (Salvadori 77). Therefore, a skyscraper will act like a giant vertical beam, like
a diving board or a cantilever (Salvadori 78).

        A cantilever has a beam held in place at one end and not at the other. When a
force is applied to the unfixed part of the beam it bends. There is stress on all of the
fibers in the beam. The fibers on the extreme upper and lower parts of the beam are
stressed the most and the closer to the centerline of the beam you get the less stressed the
fibers are. The middle line that runs down the center of the beam is called the neutral
axis (Salvadori 78). Furthermore, a beam held in place at both ends has its upper fibers
in compression and lower fibers in tension if a force is applied to the middle of a beam
(Salvadori 79). This situation leads itself to cracking on the underside of a beam
(Salvadori 80).

        To alleviate these problems of the bending and stressing of beams they make
them in the shape of an I, or I-beams. The top and bottom parts are called the flanges and
the vertical central strip is called the web. These beams allow the force exerted on it to
travel down the neutral axis to the ends of the beam so that eventually it cal be channeled
to ground (Salvadori 81).

7.4.1 Moment if Inertia
      The stiffness of a beam is the quantity given by the moment of inertia. All beam
manuals contain these measurements (Salvadori 81).

7.5   SHEAR
       In order to keep elements in equilibrium there must be equal and opposite forces
acting on it. If a beam or column has a downward force acting on it, there must be an
upward force of the same magnitude acting on it as well. This response force is called
shear (Salvadori 83).

        The shear reaction is what happens to the element when both of these forces are
applied. Since the load force and the shear force do not usually act at the exact same
point along the element, there is a length of the element between them. These parts of the
element experiences shear reaction because it wants to rotate. Therefor, the resulting
                                                                                       13


stress on the element has tension acting downward at a 45-degree angle and compression
acting upward at a 45-degree angle (Salvadori 84).

         Shear reaction happens mostly in concrete beam and not in steal beams because of
steal's resistance to tension (Salvadori 85).

7.6    BUCKLING
         When a straight element curves under compression, it is called buckling. A bent
ruler is a good demonstration of is. If one pushes on both ends towards the center of the
ruler hard enough, it begins to bend. At this point, it becomes unstable and the load at
which this happens is called the critical value (Salvadori 86). The longer and thinner the
column the more likely it will buckle. Furthermore, this is more likely to happen with
steal columns than cement ones. So in order to prevent buckling columns, I shaped
columns are used (Salvadori 87).

8     DOMES AND DISHES
8.1   STRUCTURE OF DOME
        A dome is a type of roof and it has been around for over 2000 years. Like all
roofs, they must support it's own weight and all of the lives loads that may act on it. In
order to understand this think of a half sphere. Like a globe of the earth, the dome has
parallels and meridians comprised of materials such as wood, stone, concrete, or steal.
These parallels and meridians are the elements that channel the forces down to the ground
(Salvadori 226). The thickness of a dome can be a small as 1/300 of its radius if it is
spherical and 1/30 if it is another shape such as an oval (Salvadori 227).

8.2    MODERN DOMES
        Computers and model analysis make modern domes possible. Without these two
tools, many of today’s stadiums and public arenas would not be possible. The price tag
associated with the trial and error process as compared with the modeling process is
exorbitant (Salvadori 242). I am not going to go into the ideas behind all of the modern
domes since they come in many different styles ranging in shape from triangles to
ellipses. All have different concepts and physics behind them.

8.3   HANGING DISH
        The hanging dish is an inverted dome. However, instead of having parallels and
meridians, it has only the meridians, called radial cables. These cables connect at the
center of the roof by a tension ring. The radial cables support the reinforced concrete
slabs between them. These slabs are what keep the tension in the cables and the tension
ring (Salvadori 280).

       Hanging dish roofs are usually light. Therefore, methods had to change in order
to keep the roof stable under wind loads and other forces. Putting weights on in between
the normal process of putting on the slabs and then putting cement mortar on the cables
was the innovation. This stretched the cables before the cementing and sealing took place
making the roof stiffer and able to withstand more force. Removing the additional
                                                                                         14


weights makes the roof want to move upward; however, the cement grout holds it in
place. In other words, it is prestressed (Salvadori 282).

        Another problem with this kind of roof is drainage. Unlike conventional roofs,
where the rainwater slides from the highest point in the center of the roof, the hanging
dish roof has water sliding from the outer edges into the center. This soon creates a
trapped pool of water. Pipes running from the center of the roof to the outside make for a
visually unpleasant sight. So pumps are used to remove the water, with backup gasoline
pumps incase of power failure (Salvadori 283).

9     FORM-RESISTANT STRUCTURES
        Form resistant structures owe their resistance solely to their shape (Salvadori
186).

9.1   GRIDS AND FLAT SLABS
        Flat roofs became possible only with the invention of steel and reinforced
concrete. The reason behind this is that a curved roof, or other element, is stronger than a
flat one. You can see this is a curved piece of paper. If held along the short end the
paper will wilt, however, if you hold it the same way except curve the paper upward
along the edges, it will stiffen and support a small amount of weight. This holds true for
all other materials as well (Salvadori 187). When manipulated correctly, steel and
reinforced concrete are rigid and strong enough to be able to create a flat roof.

        By arranging the steel beams into a grid of either square or diamond shaped
patterns gives it enough strength to create a flat roof. By doing this the beams want to
twist if a load acts on a part of the grid. Yet, because of firmly attached beams, the
twisting cannot take place. This actually strengthens the grid. Therefore, if a load acts on
one part of the grid, the whole grid will support it by beam action and the twisting of all
of the beams (Salvadori 180).

        Slabs of reinforce concrete are placed on top of the grids. Yet, the tendency of
any flat surface with it’s end supported is to curve downward in the center. Placing wire
mesh layers or curved ribs inside the reinforced concrete strengthens and stiffens it so
that this stretching does not occur (Salvadori 185).

9.2    STRENGTH THROUGH FORM
        With structural elements, thickness is an aspect of their strength. If they are too
thin then they become too flexible. Another aspect of strength and stiffness is the shape
of the element. Like the paper, curved roofs are stronger (Salvadori 186).

9.3   CURVED SURFACES
       There are three different types of curves, cylinder-like, dome-like, saddle-like.
Many people know the first two. To understand the third however, just picture a horse
saddle or a piece of paper with two opposite corners curving upward and the other two
curving downward. Roofs can only have these three basic designs (Salvadori 189).
                                                                                         15



9.4   BARREL ROOFS AND FOLDED PLATES
       Barrel roofs are in the shape of half cylinders and are usually made of reinforced
concrete. Supported on either side by the walls, a barrel roof acts like a series of arches.
These roofs experience beam action down the center of the roof and arch action, which is
the push of the arch outward from its base, perpendicular to the beam action. Support
from arches underneath or end walls in necessary to avoid collapse (Salvadori 191).

       Folded plate roofs consist of a series of slabs that zigzag across the top of the
building. This roof looks like an accordion and has beam action along the creases in the
roof as well as perpendicular to it. These roofs can support up to 400 times it’s own
weight (Salvadori 193).

9.5   SADDLE ROOFS
        Although usually very thin, saddle roofs are very strong as well. One of the types
of saddle roofs, called the hyperbolic paraboloid or hypar, is one of the finest examples of
a saddle roof. These roof comprised of a square or rectangular shaped “slab” that is
curved downward at two corners and upward at the other two. This roof acquires the
same tension and compression all over when loaded. This makes for a very strong roof;
however, the cost involved in the framework for this roof is expensive compared to the
alternative roofing styles (Salvadori 197).

9.6   COMPLEX ROOFS
        There are many combinations of these three basic roof types. The hypar and the
barrel roof combined create the groin vault. This roof is centuries old and can be seen in
gothic cathedrals. This roof consists of two barrel roofs that cross each other at 90-
degree angles. This gives it a similar look to four hypars connected together at an upper
corner. There are many roof designs throughout the world but they all come from the
three basic curved surfaces (Salvadori 198).

10 SKYSCRAPERS
10.1 HIGH-RISE
       The high-rise, or skyscraper, is a modern convention. The first skyscraper, the
Woolworth Building, reaches a height of 791 feet with 55 stories. From then on, the
world has been striving to outdo the last with taller and more exotic buildings. The
skyscrapers it contains, and how many there are, now define a noteworthy city. Though
they usually contain offices they also many have stores, hotels, and apartments (Salvadori
107).

10.2 STRUCTURE OF A SKYSCRAPER
        The steel framework, reinforced concrete and the high-speed elevator made the
skyscraper possible. Wood, stone, and brick do not have the immense strength needed
for the first floor to support the 100th floor of a building. The only metal and reinforced
concrete are strong enough. Furthermore, since these buildings are very tall and contain
people and sometime valuable equipment they cannot sway in the wind too much.
                                                                                            16


Complete rigidity is impossible; it is necessary to have some flexibility. In addition, too
much flexibility may cause damage to items inside and people could experience
airsickness, just as if they were on a rocking boat. Furthermore, the swaying may cause
damage to the elevators since most use gravity to aid their decent (Salvadori 116).

         Carefully placed columns and beams ensure rigidity of these buildings. Closely
space columns and deep beams help to guarantee this. However, with all of this metal the
buildings own weight becomes more and more of an issue. The solution to this is to have
two separate structures. One, the outer framework being lightweight and relatively
flexible by itself, helps reduce the overall dead load of the building. However, the second
structure is at the core of the building and is comprised of wind-bracing materials. Inside
this area are the elevators, pipes, and ducts that fuel the activities of the building. All and
all, this design creates a more rigid building as well as a lighter framework (Salvadori
117).
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11 PROPOSAL
11.1 APPROACH
        I will research and examine damaged/collapsed buildings. I will analyze the
failure due to structural defects at length. Then I will compare my findings to the
engineers who teamed up to investigate and assess it after the damage had been down.

        In order to accomplish this I will begin with the analysis on the buildings.
Criteria needs to be set on the type of building and building failures. Next, I will explore
what went wrong, what cause the failure. I will research building codes of time period
and area, the design process, the myths involved and the math behind it. Furthermore, I
might need to learn more about specific materials strengths and weaknesses.

11.2 TASK LIST
11.2.1 Decide What Buildings to Research
11.2.1.1   Criteria
         In order to start my research on individual buildings; I first need to decide what
my criteria for the buildings are going to be. I will have to narrow down the search from
all buildings to a specific group of buildings such as skyscrapers or warehouses. After
doing this I will have to figure out where I will do my research. If I pick an area too
large, like the whole of the United States, I will spend all of my time looking up building
codes for the different regions instead of studying the actual buildings. I will also have to
decide on a time-period to study. Since building codes change over time, sometimes
yearly, narrowing the timeline down will help me sift through the background work
faster. Most of this will depend on what information I can get my hands on over January.

11.2.1.2   Deciding Building Failure
        After deciding my criteria for the buildings, I am going to look at I need to decide
what kind of building failures I am going to study. There are many types of structural
failures and each one has its own structural elements and design aspects so I will narrow
the spectrum down to two similar buildings.

11.2.1.3   Deciding on the Buildings
        After all of the criteria are set I will choose from the available buildings that meet
the criteria. However, I do know that these building must be similar in type and
construction. If they are not I will not have enough time to complete my thesis. The
building type will also be dependent on what information I can get during January or
soon after.

11.2.2 Research on Individual Buildings
11.2.2.1   Research Codes of Time Period and Area
       In order to understand why the building was designed a specific way, I need to
research the building codes under which it was constructed. Since each area and time
period had its own set of codes, it is necessary for me to be able to obtain this data. The
numbers I receive from this will allow me to build a mathematical diagram of why the
building failed.
                                                                                           18



11.2.2.2   Research Material’s Strengths/Weaknesses
        Each building I will look at will be made of materials that have positive and
negative aspects to it. Any manufacturing flaws or improper use will help me decide
whether the material was to blame. If the material is used appropriately then I will have
to look at the actual structure of the building to see if the techniques used for construction
were appropriate. Most of the material obtained this semester will help me understand
this.

11.2.2.3   Research Design Process
        If the materials used were satisfactory, I will look at the building design. Since
the materials were not at fault, perhaps the design was implemented inappropriately and
caused the structural failure. From concept to the architect’s plans the actual construction
of the building something could have gone askew. This information is available in most
standard write-ups on a history of a building.

11.2.2.4   Successful Use of Architectural Feature/Design
       Once I find the problem then I will check whether a previously built building
featured this design/element and whether that building suffered the same fate. This will
give me insight into the failure.

11.2.2.5   Myths
        Next, I will research the media’s portrayal of the failure. Sometimes the media
hides or misinterprets the truth in order to create a better story or out of ignorance. By
doing this I might be able to see how the public reacted to the incident and what the
effects where on architecture that came after it.

11.2.2.6   Math
        Since all structural failures have physics behind it, I will explain what happened
to the building from a mathematical viewpoint. I will use the information gathered this
semester to aid me with this. Most of my background chapter deals with the ideas behind
the math. An understanding of the concepts is needed before the actual implementation
and calculations can be done. I did not include the equations involved in the process in
the paper because they vary with each type, size, and use of a structural element.
However, I do have many of the equations I will need.

11.2.3 Analyze Findings
11.2.3.1   Expert’s Findings
       Teams of engineers assemble after all building failures. They try to figure out
what went wrong. Their purpose is to analyze the failure and come up with a reason why
it happened. Then creating of new codes insures that it does not happen again. I will
research their findings and interpretations of the building failure.

11.2.3.2   Evaluation of Structural Failure
        I will observe how they analyzed the structural failure and see the steps taken to
achieve a conclusion. I will see whether they have a set process for doing this, whether it
varies from group to group, or situation to situation.
                                                                                       19


11.2.4 Compare my Analysis to Expert’s Findings
11.2.4.1   Differences
        I will then compare my analysis to the engineer’s analysis to see if there are
differences in the approach. If there are, I will try to understand them. I know that they
will have the advantage of years of training in addition to actual on site appraisal.
However, the numbers should be relatively similar.

11.2.5 Presentation
       I will present my findings during my scheduled science colloquium.

11.2.6 Write and Hand in Paper
        After I have finished the research and analyses I will write up my findings in my
thesis and hand it in at the end of the semester.


11.3 GANTT CHART
                                                                                              20



12 APPENDIX I: VOCABULARY

Arch action – the push of an arch outward at it’s base, a “need” to be flat
Allowable Stress – a percentage of the yield stress that is calculated by veteran engineers

Beam action – when a beam, or other straight element, is bent so that it’s upper and
        lower fibers are in tension and compression
Brittle – materials that do not behave plastically; materials that break without warning;
        materials that have elasticity but not plasticity
Buckling – what happens when a straight element bends under compression
Building codes – a set of rules and regulations that deal with the safety and aesthetic
        value of a building

Cantilever – a beam that is held in place at one end and not at the other
Compression – what happens to a building that is being pushed by a load
Critical load - the load at which an element becomes unstable
Curves - there are three types: cylinders, domes, and saddles

Dynamic loads – loads that change suddenly or rapidly

Elasticity – the ability of a material to stretch of contract when a load is applied to it and
       return to normal when the load is lifted
Equilibrium – when all forces acting on a material are balanced by another equal and
       opposite force

Factor of safety – the scale by which safety is measured
Flanges – the top and bottom parts of an I-beam
Form resistant structures – structures that owe their existence solely to their shape

Lamination stress – the slicing of steel into thin layers that happens at high altitudes if
      not treated properly
Law of least work – a load on a building will find the easiest path in a structure to the
      ground, the path that requires the minimum amount of work on the structural
      materials
Linearly elastic – elasticity that behaves linearly; when a load is increased by a factor
      the stretching or bending increases by that factor as well.
Loads – the forces that act on a building; loads either push or pull
Lock-in loads – hidden loads, loads that are invisible to the eye such as thermal and
      settlement loads

Moment of inertia – a quantity of stiffness of a beam

Natural period of oscillation – time it takes a building to complete one oscillation or
      swing back and forth once
                                                                                           21


Neutral axis – the invisible middle line that runs down the center of the beam
Newton’s Laws – three basic laws that explain gravity and gravitational motion

Plastically – the behavior of a material that carries a load so great that it causes
       permanent deformation when unloaded
Plumb – equilibrium

Resonance – wind load that happens gradually over time and pushes against a building in
       time with it’s natural period of oscillation
Richter scale – scale on which earthquakes was measured

Shear – the response force that acts on a loaded element in order to keep it at equilibrium
Static loads – permanent or semi-permanent loads
Strain – the change in length of a material under stress divided by the original length
Stress – what loads do to a structure
Structure - the skeleton of a building; the framework that supports all of the loads that
        act on a building; channels loads on the building to the ground

Tension – what happens to a building that is being pulled by a load

Ultimate strength – the maximum number of pounds per square inch that an element can
      hold before breaking

Yielding strength – the weight at which something starts to weaken under a load
Yield stress – the weight at which the material changes from elastic to plastic behavior

Web – the central strip of an I-beam
Wind drift – the lateral displacement of the top of the building from equilibrium
                                                                                        22



13 BIBLIOGRAPHY

Levy, Matthys, Mario Salvadori. Why Buildings Fall Down. New York: Norton, 1992.

Salvadori, Mario. Why Buildings Stand Up. New York: Norton, 1980.

Anonymous. “Glass Curtain Wall Covers 11 Stories in South Korea Office Tower.”
American Society of Civil Engineers Jan 2000, Vol. 70. Proquest. Online. 5 Oct. 2001.

Senders, C. “Shock Steady: Smart Buildings Guard Against Bad Vibrations.” Omni
May 1992, Vol. 14. EBSCOhost. Online. 4 Oct. 2001.

Lacayo, Richard. “What Will Our Skyline Look Like?” Time 21 Feb. 2000, Vol.155.
EBSCOhost. Online. 4 Oct. 2001.

Herbert, Wray. “Wright’s Fallingwater is Slowly Falling Down.” U.S. News & World
Report 3 May 1999, Vol. 126. EBSCOhost. Online. 4 Oct. 2001.

Anonymous. “Repeat Performance.” HD: Hospital Development Apr 2000, Vol. 31.
EBSCOhost. Online. 4 Oct. 2001.

Watson, Robert. “Radar: High Tech.” Architecture Australia May/Jun 2001, Vol.90.
EBSCOhost. Online. 4 Oct. 2001.

Bartelink, Dirk. “Alternative Device and Process Architectures.” Solid State Technology
Mar 1996, Vol. 39. EBSCOhost. Online. 4 Oct. 2001.

Glanz, James. “Towers Believed to Be Safe Proved Vulnerable to an Intense Jet Fuel
Fire, Experts Say.” New York Times 12 Sept 2001, late ed. Proquest. Online. 5 Oct.
2001.

Anonymous. “The Skyscrapers, the Subways, the Sewers.” New York Times 5 Dec
1999, late ed. Proquest. Online. 5 Oct. 2001

				
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