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).
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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

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