Structure: Form Vs Function
STRUCTURE: FORM VS FUNCTION
By Danielle Cove
Senior Thesis
5/10/02
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 5
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 8
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 10
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 11
7.4.1 Moment if Inertia 12
7.5 SHEAR 12
7.6 BUCKLING 13
8 TRUSSES 13
9 DOMES AND DISHES 13
9.1 STRUCTURE OF DOME 13
9.2 MODERN DOMES 13
9.3 HANGING DISH 13
0 FORM-RESISTANT STRUCTURES 14
0.1 GRIDS AND FLAT SLABS 14
0.2 STRENGTH THROUGH FORM 14
0.3 CURVED SURFACES 14
0.4 BARREL ROOFS AND FOLDED PLATES 15
0.5 SADDLE ROOFS 15
0.6 COMPLEX ROOFS 15
1 SKYSCRAPERS 15
1.1 HIGH-RISE 15
1.2 STRUCTURE OF A SKYSCRAPER 15
2 APPROACH 16
2.1 DECIDING THE BUILDINGS 16
2.1.1 Criteria 16
2.1.2 location 16
2.1.3 time period 16
2.1.4 Building type 16
2.1.5 Buildings 17
3 KEMPER ARENA ROOF: KANSAS CITY, MISSOURI 17
3.1 HISTORY 17
3.2 DIMENSIONS AND STRUCTURE 17
3.2.1 Scenario 18
3.3 EXPLANATION 19
3.3.1 Media coverage 19
3.3.2 Why it collapsed 20
3.3.3 Calculations 20
4 HYATT REGENCY: KANSAS CITY, MISSOURI 21
4.1 HISTORY 21
4.2 DIMENSIONS AND STRUCTURE 22
4.2.1 Scenario 22
4.3 EXPLANATIONS 22
4.3.1 Media Coverage 23
4.3.2 Why it collapsed 23
4.3.3 Calculations 23
5 APPENDIX I: VOCABULARY 25
6 BIBLIOGRAPHY 27
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 paper, 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, trusses, domes, dishes, form resistant structures, and skyscrapers all have sections dedicated to them.
I then evaluated two modern buildings that have failed, the Kemper Memorial Arena and the Hyatt Regency Hotel. I investigated these structures and explained what happened mathematically. I examined the concepts behind the failure, the process used to evaluate it, and the work that went into creating a building.
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, gained a better understanding of what work goes into creating a building. By examining failed structures I understood what happened. Doing helped me have 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, 8, 9, and 10 takes a general look at some other structural elements. Chapter 11 looks at some ideas behind the skyscraper. I discuss my approach in chapter 12. Finally, in chapter 13 and 14 I look at the Kemper Memorial Arena and Hyatt Regency Hotel respectively.
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.
.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).
.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).
.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. Engineers base 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).
.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 forces can be the most destructive and the hardest to guard against (Salvadori 45).
.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).
.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).
.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).
.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 1/2 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 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).
.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).
.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).
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).
.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).
2 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
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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).
.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).
2 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
2.1 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).
2.2 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).
2.3 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).
2.4 FORCES ON MATERIALS
2.4.1 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).
2.4.1.1 Yield Stress
The weight at which a material changes from elastic to plastic behavior is called the yield stress (Salvadori 63).
2.4.1.2 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).
2.4.2 ELASTICITY AND PLASTICITY
2.4.2.1 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 point; however, with large loads the materials sometimes deform permanently (Salvadori 61).
2.4.2.2 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).
2.4.2.3 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).
2.4.2.3.1 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).
2.4.2.3.2 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).
2.4.3 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).
2.4.3.1 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).
3 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.
3.1 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 "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.
3.1.1 EQUILIBRIUM
A building is at equilibrium when all the forces acting on it are balanced. When the building is stationary and not overstressed in any direction it is in equilibrium (Salvadori 73).
3.2 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).
3.3 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).
3.4 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).
3.4.1 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).
3.5 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. Therefore, the resulting 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).
3.6 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).
4 TRUSSES
A truss is a structural element developed to absorb tension or compression and stay rigid without bending. One can see trusses in many modern structures, from roofs to bridges. By combining compression struts and tension bars into triangular patterns one gets a very stable structure. There are many different variations on the truss. Two of the most common are the Warren truss and the Pratt truss. (Levi 229)
5 DOMES AND DISHES
5.1 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 their own weight and all of the lives loads that may act on it. 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).
5.2 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.
5.3 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 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).
6 FORM-RESISTANT STRUCTURES
Form resistant structures owe their resistance solely to their shape (Salvadori 186).
6.1 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).
6.2 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).
6.3 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).
6.4 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).
6.5 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).
6.6 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).
7 SKYSCRAPERS
7.1 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).
7.2 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. 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).
8 APPROACH
8.1 DECIDING THE BUILDINGS
8.1.1 CRITERIA
In order to start my research on individual buildings; I needed to decide what my criteria for the buildings are going to be. I narrowed down the search from all buildings to a specific group of buildings. I looked at three main criteria: location, time period, and building type.
8.1.2 LOCATION
I decided that I needed to conduct my search on buildings that were in the same area of the United States. 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. The area that I chose was the South East section of the U.S. By choosing this section, I made sure that I considered no Building Codes associated with winter. It was also the closest of these regions to me. So, if need be, I would be able to obtain the data for these buildings faster and more efficiently.
8.1.3 TIME PERIOD
I also had 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. The farther back I go the harder it is to obtain information on the building because information on many older buildings is not readily available. Therefore, I decided that I would only look at buildings built after 1970.
8.1.4 BUILDING TYPE
Since I narrowed down the time frame and the proximity to one another I started to look at individual buildings that fit into those categories. However, I found that many different building types arose. To narrow my search even further I discarded all skyscrapers and private buildings since their architecture is either very complicated or fairly simple. My focus was large public buildings used for recreation.
8.1.5 BUILDINGS
I ran into some problems during this step. I found several buildings that fit the above criteria; but many did not have enough information on them. Another problem dealt with finding two buildings that matched the same criteria. I considered looking at the Hartford Connecticut Arena but did not fit the criteria because it was Northern and the roof collapsed due to snow. In addition, the data on that building also turned out to be minimal.
I found, by chance mostly, that two buildings in the same city had suffered from structural damage. The Hyatt Regency and the Kemper Arena, both situated in Kansas City, Missouri, were built after the cut off date of 1970.
9 KEMPER ARENA ROOF: KANSAS CITY, MISSOURI
9.1 HISTORY
From its beginning in 1859, Kansas City, Missouri has been a growing city complete with museums, schools, and sports teams. In 1973, the Kemper Arena was built for the Kansas City Kings, basketball team. It sat 17,000 people and was built on the site of the old Royals baseball stadium. Named after R. Crosby Kemper, one of the city's founding fathers, people hailed the stadium as a work of art and an engineering feat. However, shortly after the stadium finished construction the Kings moved to Sacramento so the stadium was multipurpose. It held rodeos ice shows, conferences, soccer, and collegiate basketball games (Levy 57).
Many people, including the city, revered the Kemper Arena because it was groundbreaking and exotic. The American Institute of Architects credited the arena with an award in 1976 and "confirmed its importance as a monument by holding in it its 1979 national conference (Levy 57)." This would prove to be an ironic coincidence.
9.2 DIMENSIONS AND STRUCTURE
Helmuth John, from C. F. Murphy, designed the Kemper Memorial Arena. The arena sat on four acres of land on the border of the city and cost $23.3 million to build. The arena is 306 ft long, 324 ft wide and 81 ft high. It is considered of interest and a tourist attraction because of the engineering, creative design, and practicality (Levy 58).
The Kemper Arena's structure was innovative for the period. Steel trusses that hung from three huge portals supported the reinforced concrete roof. These portals supported the reinforced roof, the upper part of the walls and all other loads that acted on them They were spaced 153 ft (north to south) apart from one another and were 81 ft high and 360 ft long (east to west) (Levy 60). The actual portals had "beams" that ran length wise along the building and "consisted of a space frame of steel tubes with an equilateral triangular cross section (Levy 61)." The equilateral triangles are 54 ft in length per side. In addition, two reinforced concrete conical footings that were 54 ft apart grounded the portals (Levy 61).
The reinforced concrete roof attached to a corrugated steel deck, which a light steel open web joists supported. An open web joist consists of "light trusses with angles chords and bent rod diagonals, 54ft long and spaces 9 ft apart in the north-south direction (Levy 61)." This system then rests on another set of trusses called drop trusses. These were 99 ft long and in turn supported three more trusses at each end called cantilever trusses. This whole configuration hung from the three portals using 42 hanger assemblies. A square grid, seven across and six long, arranged these hanger assemblies. These 42 hangers were the primary support for the entire roof structure below it. (Refer to Figures A and B.)
The structure of the hanger assemblies is very import in understanding the actual failure of the Kemper Arena roof since their design is the primary cause of the collapse.
The hanger assemblies had to be very strong since the roof itself weighed 26 pounds per square foot (psf), or about 1,500 tons of dead load, and had to carry 25 psf, or another 1,500 tons of live load. So in effect, the 42 hangers had to support 140,000 lbs in tension over an area measuring 129,000 square ft. In addition to this the roof had to withstand a wind load had a tendency to swing the roof back and forth like a pendulum. Six hangers had hinges at both the top and half way down the shaft while the other 36 had hinges at the top only. This insured rigidity as well as flexibility (Levy 62).
Four vertical stiffeners, a base plate, and plastic composite plate, called Micarta, and four high strength bolts that held the truss and the hanger together connected the hangers and the trusses. The Micarta added to the roof while the rest of the assembly ensured rigidity. The engineers "estimated that during the six years preceding the failure these connections were subjected to at least 24,000 oscillations, which in turn introduced oscillating variations in the initial tension of the bolts (Levy 63)." These oscillations caused the metal to fatigue and therefore fail at lower load values than initially designed for. In addition, the steel used for the bolts, specifically A490, is not resilient under variable loads. This particular aspect was overlooked by the design team because the "coefficient of safety of the bolts under design loads appeared to be sufficiently high (Levy 64)." (Refer to Figure C.)
9.2.1 SCENARIO
On June 4th, 1979 at 6:45pm, a downpour of rain with 70 mph hit Kansas City. Arther LaMuster, worker and only person in the arena at the time, heard odd noises 25 minutes later. He inspected the area and barely had time to get out as the center of the roof collapsed. It was determined later that approximately one acre, or 200 x 215 ft of roof collapsed. The air pressure, increased by the rapidly falling roof caused some of the walls to blow out. However, the portals remained undamaged. Ironically, thousands of architects there for the American Institute of Architects Convention had been sitting in the arena only 24 hours before (Levy 59).
9.3 EXPLANATION
The arena collapse shocked the engineering world. For six years, it had withstood harder winds and downpours than that night (Levy 59). However, once inspected, people began to understand what went wrong.
Kansas City was growing and the sewer systems could not keep up with the waste and water dumped into it. Therefore, the Kemper Arena roof design had the feature of using the roof as a "temporary reservoir" in big downpours. The city drainage system would benefit from the limiting of the rate of water that drained from the roof. However, the roof of the arena had only eight drains that were 5 inches in diameter and placed 2 inches above the base of the roof. This prevented no more than 1/10 of a cubic foot per second. The maximum downpour codes for Kansas City required 55 of these drains even though these downpours only happened every 10 years (Levy 64).
The water pooling on the roof, the 70 mph wind, and the suction of the water up onto the northern part of the roof cause by the wind "were not sufficient to produce a dangerous accumulation of water on the southern portion of the roof [were the collapse occurred] (Levy 64)." Therefore, a ponding effect was the main cause of the collapse. Ponding happens when water covers stiff horizontal surfaces. As the water accumulates, the middle of the roof begins to sag or deflect. This causes more water to accumulate and thus more of a deflection, continuing until the roof becomes unstable. To tell whether a roof is unstable the critical g is calculated. If this number is greater than one (the unit weight of water), then the roof is stable, however, if this value is less than one then the roof is unstable. Therefore, the formulas used to calculate ponding in this case determined a g of 0.627. This means that the water level at the drains on the roof was 9 inches deep (Levy 65).
As a result, the bolts on hanger 1 failed due to fatigue. Then, this caused the surrounding hangers, 2, 3, and 4 to fail because they were unable to carry the extra weight of the roof. This inevitably caused a domino effect across all of the hangers on the south end of the roof.
9.3.1 MEDIA COVERAGE
The press took the Kemper Arena collapse seriously. However, they also glorified and simplified the disaster. One headline read "Single Bolt Collapses Arena!" (Levy 67). The day after the collapse the Washington Post read "Arena Roof Collapses" and goes on to state "authorities believe the collapse may have been relates to the storm." On that same day, the New York Times stated, "thunderstorms cause roof of Kemper Arena, Kansas City, MO, to collapse." In fact, it was not until August 9, 1979 that the New York Times considers the "collapse of the Kemper Arena...inevitable." Therefore, during the two-month period between this brief statement and the actual collapse the media seemed to display it as a momentary thing. Something that only one night created instead of a building of stresses and strains up to that point. The idea of a momentary collapse is a scary one, somewhat uncontrollable. However, this rarely happens and engineers know that. Therefore, it seems that the media's goal in the case was to instill a sense of fear and distrust in their readers. Even though a sense of scrutiny and skepticism is common and justified in these cases, the press played off that and exaggerated the failure.
9.3.2 WHY IT COLLAPSED
Two major oversights sum up this collapse despite the many factors that played into it.
The first mistake in designing the roof of the arena deals with the type of bolt used. The bolt used on the Kemper Memorial roof was the A490. They are a high strength fastener used only for tensile strength. However, these bolts had dynamic loading on them from the gusting wind. This weakened the bolts by placing repeated stress on them. It was reported that the "A490 high strength steel bolts lack ductility and only maintain tensile strength for static conditions. Their installation in the Crosby Kemper Memorial Arena [caused the] roof to collapse (Fasteners 1)." Engineers concluded this after the bolts were tested under dynamic stresses. The test showed that the bolts failed at only one third of their capacity after tightening and loosening, simulating dynamic stress, five times (Fasteners 1).
The other major oversight involves the number of assembly hangers involved. The 42 hangers had to support 3,000 tons of weight and a wind displacement. By looking at the numbers below one can tell that if they used more hangers there would not have been such stresses placed on the bolts or the hangers (Levy 67).
9.3.3 CALCULATIONS
Weight of live load = Wll = 1,500 tons
Area of roof = ar = 129,000 ft2
Depth of water at sides = 2 in
Depth of water at center = 9 in
) Break up volume of water into the area of a pyramid and a rectangular box.
Pyramid:
Volume of a pyramid = Vp = 1/3arhp
Height = hp = 7 in
7 in (1 ft/12 in) = 0.583 ft
Vp = 1/3 (129,000 ft2) (0.583) = 25,100 ft3
Rectangular box:
Volume of box = Vb = arhb
Height = hb = 2 in
2 in (1 ft/12 in) = 0.167 ft
Vb = (.167 ft) (129,000 ft2) = 21500 ft3
Total volume:
Vt = Vp + Vb = 25,100 ft3 + 21,500 ft3 = 46,600 ft3
2) Find the weight of the water.
g water = 1 cm3 water
00cm = 3.28ft
46,600 ft3 (100 cm/ 3.28 ft)3 = 1.32 109 cm3
(1 g/1 cm3) (1.32 109 m3) = 1.32 109 g = 1.32 106 kg
.32 106 kg (9.8 m/s2) = 1.29 107 N
3) Find live load that was meant to carry.
ton = 2000 lbs
N = 0.225 lbs
500 tons (2000 lbs/ 1 ton) = 3.00 106 lbs
3.00 106 lbs (1 N/ 0.225 lbs) = 6.75 105 N
4) Find difference between actual load and designed load.
.29 107 N - 6.75 105 N = 1.22 107 N
Conclusion:
Since there is a significant difference between the actual load and the live load to roof was unable to hold the load. The design is not strong enough.
0 HYATT REGENCY: KANSAS CITY, MISSOURI
0.1 HISTORY
The Hyatt Regency underwent two years of design and another two years of actual construction. The Hyatt was a glamorous hotel filled with 750 room and suites as well as several restaurants (Levy 221). The entire hotel consisted of three separate buildings. The north building of the complex was a tower that contained all of the guest accommodations and the south building was a four-story "function block" that housed the dining areas, kitchens, meeting room and other service areas. Reinforced concrete was the material used to construct the tower and the function block. The atrium glass was between these two areas. Three separate pedestrian bridges, or walkways, connected the north and south buildings. The fourth and second floor walkways hung one above the other and the third floor walkway hung offset to one side. These walkways all connected to steel trusses that hung from the atrium ceiling (Levy 222). Designers place a bar under the second and fourth floor walkways and a dance area covered the main floor.
The hotel opened in July of 1980, only one year after the Kemper Arena collapse. The shock of that failure was still fresh in the mind of the city. What happened here would shatter them.
0.2 DIMENSIONS AND STRUCTURE
Designers used four 30 ft long spans on each side of the walkways. These consisted of 2 wide-flange steel beams that were 16 inches deep and four 30 ft beams that "were connected by steel angles bolted to the upper flanges at the beams' ends (Levy 225)." In addition to this, each walkway was welded to floor plates on the South end (entering the function block) and was supported by sliding bearings on the north side (entering the tower). The sliding bearings allowed the beams to "expand or contract wit the temperature changes without giving rise to thermal stresses (Levy, 225)."
In addition to this, supports placed at 30 ft intervals helped carry the load of the walkways. However, the original design called for a box beam, created by welding together two eight in deep C-beams, with a "single [hole] at both ends of the flanges, through each of which was threaded a single 1 1/4 in steel rod that served as hanger for both the second- and fourth-floor walkways (Levy 227)." To keep the walkways at their given heights, nuts were to screw onto all of the poles at both the fourth hand second floor heights (Levy 227). (Refer to Figure D.)
However, this was not the design eventually implemented. Instead the design called for two holes though both flanges, one at 2 in and the other at 6 in from the end. So instead of each box beam holding only the dead and live weight of it's own walkway, the fourth floor walkway supported the second floor loads as well as its own (Levy 227). (Refer to Figure E.)
0.2.1 SCENARIO
On July 17, 1981, the atrium filled with upwards of 1600 people for a taped dance contest. People filled the walkways on all of the floors to watch the dancing below. At 7:05pm, with people stomping to the rhythm of the music, one of the steel rods in the east center of the fourth floor walkway ripped out of the box beam. This created a domino effect and within seconds the other rods had failed. The fourth floor walkway came crashing down on the second floor walkway, which all came down on the people surrounding the bar. As a result, chaos ensued.
0.3 EXPLANATIONS
On the day of the collapse, a video tape was made of the competition. It showed 63 people on the walkway right before it collapsed. Kansas City Building Codes require a live load of 100 lbs/square foot, or 72,000 lbs for one walkway. Since the actual live load was far below the capacity of the walkways engineers tested both new and old box beams as well as the hanging rods. The conclusion drawn from the testing states that each of the six hangers that held the walkway up supported 24,000 lbs. This was twice the designed load therefore; the hangers could not support the actual load. As soon as one hanger failed, the others followed (Levy 228).
The National Bureau of Standards reported, "The ultimate capacity actually available using the original connection detail would have been approximately 60% of that expected of a connection designed in accordance with the specifications of the Kansas City Code (Levy 230)." Therefore, the original design was unsafe as well.
0.3.1 MEDIA COVERAGE
Since Kansas City had just gotten over the Kemper Arena collapse, the newspapers jumped on this disaster and rumors about the cause of the collapse flew. One headline on June 20th from the New York Times read, "Before Hotel Disaster, Walkway Swayed to the Rhythm of Dancers." At first people speculated that the foot stomping of the people on the walkways was in resonance with the steel in the walkways. This would have made the walkways bounce and sway like the Tacoma Narrows Bridge in Washington. However, this was not the case. The newspapers then started interviewing the survivors and looking for someone to place the blame on.
0.3.2 WHY IT COLLAPSED
The walkways collapsed because of a change in design during the construction process. The original design had both walkways supporting just their weight and live load on them. The second design had the fourth floor walkway holding both its own weight and the weight of the second floor. Since no other reinforcement was added to the design, the fourth floor box beams were unable to handle the immense weight. Therefore, if the designers used more box beams and hangers then the weight of the apparatus would have been dispersed more, giving each individual hanger less weight to carry. Another adaptation is stronger box beams and hangers. This would ensure that the unit could hold it own weight. The final possibility is to return to the more expensive original design and have it modified as well so that it is up to Code standards.
0.3.3 CALCULATIONS
Density of concrete = dc = 150 lb/ft3
Details for stringers = W16 x 26 steel = 16 in deep and 26 lb/ft
Details for box beams = MC8 x 8.5 = 8 in deep and 8.5 lb/ft
Concrete thickness = t = 3.25 in
Length of walkway = l = 120 ft
Width of walkway = w = 18 ft
Number of stringers = 2
Number of box beams = 3
) Find weight of concrete:
Area of walkways = aw = (120 ft) (18 ft) = 2,160 ft2
3.25 in (1ft/ 12 in) = 0.271 ft
Volume of concrete = vc = (2,160 ft2) (0.271 ft) = 585 ft3
Weight of concrete = Wc = (585 ft3) (150 lb/ft3) = 87,800 lb
(87,800 lb) (1 N/ 0.225 lbs) = 390,000 N
2) Find weight of box beams.
Weight of box beams = Wb = (18 ft) (8.5 ft/lb) (3) = 4,590 lbs
(4,590 lbs) (1 N/ 0.225 lbs) = 20,400 N
3) Find weight of stringers.
Weight of stringers = Ws = (120 ft) (26 lb/ft) (2) = 6240 lbs
(6,240 lbs) (1 N/ 0.225 lbs) = 27,700 N
4) Find total weight of walkway.
Weight of one walkway = Ww = Wc + Wb + Ws = 390,000 N + 20,400 N + 27,700 N = 438,000 N
5) Find total weight of live load.
Number of people on walkways = 63
Average weight of person = 150 lbs = 667 N
Total live load = Wl = (63) (667 N) = 42,000 N
6) Find total weight on fourth floor walkway.
Total Weight = WT = (438,000 N) (2) + (42,000 N) = 918,000 N
7) Find the factor of safety of the walkway.
Capacity of box beams = Cb = 115,000 lbs = 511,000 N
Factor of safety designed = Sd = Cb/WT
Factor of safety code = Sc = 1.67
Sd = (511,000 N)/ (918,000 N) = 0.557
Conclusion:
Since the Sd is substantially lower than the Sc the walkway is unsafe and unstable.
1 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
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
Truss - a structural element developed to absorb tension or compression and stay rigid without bending
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
2 APPENDEX II: DIAGRAMS
Figure A: Diagram of Kemper Arena Portal (Levy 61)
Figure B: Diagram of Kemper Arena Roof Structure (Levy 60)
Figure C: Diagram of Kemper Arena Hanger Assembly (Levy 62)
Figure D: Diagram of Hyatt Regency 4th Floor Walkway Assembly (initial) (Levy 226)
Figure E: Diagram of Hyatt Regency 4th Floor Walkway Assembly (actual) (Levy 226)
3 BIBLIOGRAPHY
Books:
Beer, Ferdinand P., Johnston, E. Russell. Mechanics of Materials. New York: McGraw-Hill, 1992
Domel, August W. Basic Engineering Calculations for Contractors. New York: McGraw-Hill, 1997.
Hutchings, Jonathan F. National Building Codes Handbook. New York: McGraw-Hill, 1998.
Levy, Matthys, Mario Salvadori. Why Buildings Fall Down. New York: Norton, 1992.
Patterson, Terry L. Illustrated 2000 Building Code Handbook. New York: McGraw-Hill, 2001.
Salvadori, Mario. Why Buildings Stand Up. New York: Norton, 1980.
Schwartz, Max. Basic Engineering for Builders. Carlsbad, CA: Craftsman Book Company, 1993.
Articles, Periodicals, and Online Sources:
<http://www.engineeringdiagnostics.com/failure_inverstigations.htm> (30 March 2002).
"20 years Ago: 46 killed in Hyatt collapse as tea dance turns to terror." July 18, 1981. <http://www.kcstar/projects/hyatt/> (1 April 2002).
"Ethics Case Study." 2001. <http://www.acsu.buffalo.edu/`jjensen/ethics_2001.htm> (30 March 2002).
"Engineering Ethics." Negligence And The Professional "Debate" Over Responsibility For Design. Date unknown. <http://ethics.tamu.edu/ethics/hyatt/hyatt1.htm> (30 March 2002).
"Fasteners." Potential Hazards. 1999. <www.safety-training.net/topics/fasteners.doc> (20 March 2002).
"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.
"Kansas City Hyatt Regency Walkway Collapse Packet." <http://www.mech.utah.edu/ergo/educate/safety_modules/kc/> (1 April 2002).
"Repeat Performance." HD: Hospital Development Apr 2000, Vol. 31. EBSCOhost. Online. 4 Oct. 2001.
"The Skyscrapers, the Subways, the Sewers." New York Times 5 Dec 1999, late ed. Proquest. Online. 5 Oct. 2001
"Victims of the Kansas City Regency Walkway Collapse - 1981." October 24, 1999. <http://www.eos.uoguelph.ca/webfiles/james/homepage/Teaching/210/WebShare/WWWROOT/Home/Disaster_Page/disaster_page.htm> (1 April 2002).
Bartelink, Dirk. "Alternative Device and Process Architectures." Solid State Technology Mar 1996, Vol. 39. EBSCOhost. Online. 4 Oct. 2001.
Foote, Donna, McGrath, Peter. "Design failure lessons." What Happened at the Hyatt?. August 3, 1981. <http://www.me.utexas.edu/`me179/topics/lessons/case2articles/case2artical2.html> (30 March 2002).
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.
Herbert, Wray. "Wright's Fallingwater is Slowly Falling Down." U.S. News & World Report 3 May 1999, Vol. 126. EBSCOhost. Online. 4 Oct. 2001.
Kasper, Shirl. "In the '70s, we knew the world was watching." September 19, 1998. <http://www.kcstar.com/millennium/part15/stories/70s.htm> (1 April 2002).
Knickerbocker, Laura, Fitzpatrick, James C. "20 Years Ago: Walkway began to buckle; people just disappears." July 18, 1981. <http://www.kcstar/projects/hyatt/> (1 April 2002).
Knott, Dr. Albert W. "Hyatt Regency Failure Example." Date unknown. <http://carbon.cudenver.edu/`krens/forensic/akhyatte.doc> (1 April 2002).
Lacayo, Richard. "What Will Our Skyline Look Like?" Time 21 Feb. 2000, Vol.155. EBSCOhost. Online. 4 Oct. 2001.
Lank, Steve, Robinson, Matt, Sevigny, Steve, Steger, Matt,Tsai, James. "Failure in Design." Smash and Crash: The Kansas City Hyatt Regency Walkway Collapse. November 18, 1997. <http://www.people.virginia.edu/`jtt3e/hyatt/paper.htm> (1 April 2002).
Montgomery. "Next: The '80s - From extreme to extreme." July 15, 2001. <http://www.kcstar.com/millennium/part15/stories/80s.htm> (1 April 2002).
Nicastro, David H. "Failure Investigations." A Love Ito the Art and Science of Forensic Engineering.
Senders, C. "Shock Steady: Smart Buildings Guard Against Bad Vibrations." Omni May 1992, Vol. 14. EBSCOhost. Online. 4 Oct. 2001.
Watson, Robert. "Radar: High Tech." Architecture Australia May/Jun 2001, Vol.90. EBSCOhost. Online. 4 Oct. 2001.
Woodward, Steve, Pessek, RobertJ. "20 Years Ago: The Hyatt Horror: 111 dead, 188 hurt and a city in shock" July 19, 1981. <http://www.kcstar/projects/hyatt/> (1 April 2002).