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Contents

Cover

Title Page

Copyright

Preface

Chapter 1: Architects, Engineers, and Design

Chapter 2: Stability and Strength

Chapter 3: Loads

3.1 Gravity Loads

3.2 Lateral Loads

3.3 Dynamic Loads

3.4 Impact Loads

3.5 Load Paths

Chapter 4: States of Stress

4.1 Tension

4.2 Compression

4.3 Shear

4.4 Torsion

4.5 Bending

Chapter 5: Forces, Movement, Levers, and Moment

5.1 Applied and Reactive Forces

5.2 Translational Movement

5.3 Rotational Movement

5.4 Levers

5.5 Moment

Chapter 6: Stability and Equilibrium

6.1 Introduction

6.2 Translational Equilibrium

6.3 Rotational Equilibrium

6.4 Sign Conventions

6.5 The Equilibrium Equations

6.6 Free-Body Diagrams and Familiar Examples of Equilibrium

6.7 Introduction to Bending in Beams

Chapter 7: Working with Forces

7.1 Forces, Vectors, and Lines of Action

7.2 Combining and Resolving Concurrent Forces

7.3 Familiar Examples of Concurrent Forces

Chapter 8: Supports, Reactions, and Restraint of Movement

8.1 Roller and Frictionless-Surface Supports

8.2 Pinned Supports

8.3 Fixed Supports

8.4 Hanger Supports

8.5 Familiar Examples of Support Conditions

8.6 Stable or Unstable?

Chapter 9: Load Distribution

9.1 Point Loads

9.2 Distributed Loads

9.3 Equivalent Point Loads

9.4 Uniformly Distributed Loads

9.5 Non-Uniformly Distributed Loads

Chapter 10: Introduction to Beams

10.1 Beam Types

10.2 Predicting Deformation, Deflection, and Beam Behavior

10.3 Statically Determinate and Statically Indeterminate Beams

10.4 Other Considerations for Beams

Chapter 11: Framing Systems and Load Tributary Areas

11.1 One-Way Systems

11.2 Two-Way Slab and Beam Systems

11.3 Two-Way Slab/Two-Way Joist Systems

Chapter 12: Shear and Moment Diagrams for Beams

12.1 Sign Conventions

12.2 Typical Shear and Moment Diagrams

12.3 Creating Shear and Moment Diagrams

12.4 Comparing V and M for Uniformly Distributed Versus Concentrated Loading

12.5 Summary of Deformation, Shear, and Moment Relationships

Chapter 13: Stress, Strain, and Properties of Materials

13.1 Stress

13.2 Strain

13.3 Stress versus Strain

13.4 Properties of Materials

13.5 Stress Distribution Diagrams

Chapter 14: Introduction to Columns

14.1 Columns, Compression, and Bending

14.2 Column Loading

14.3 Column Compression

14.4 Column Bending

14.5 Leonhard Euler and Column Buckling

Chapter 15: Frames, Rigidity, and Lateral Resistance Systems

15.1 Triangular Frames

15.2 Rectangular Frames

15.3 Making Rectangular Frames Rigid

15.4 Lateral Resistance Systems

Chapter 16: Introduction to Trusses

16.1 Introduction

16.2 Trusses as Beams

16.3 Types of Trusses

16.4 Design Considerations

16.5 Truss Joints

16.6 Truss Loading

16.7 Truss Analysis

Chapter 17: Structural Walls

17.1 Loads and Deformational Stresses

17.2 Stresses and Wall Construction

17.3 Retaining Walls

Chapter 18: Soils and Rock

18.1 The Earth's Interior

18.2 The Earth's Crust

18.3 Natural Soils

18.4 Groundwater

18.5 Engineered Fill

18.6 Foundation Settlement

18.7 Soil Bearing Capacity and Subsurface Conditions

Chapter 19: Foundations

19.1 Shallow Foundations

19.2 Deep Foundations

Chapter 20: Summing Up

Creation of Stress

States of Stress

Resistance to Stress

Appendix 1: Structural Forms

Appendix 2: Structural Materials—Steel

A2.1 Composition And Manufacture

A2.2 Characteristics and Properties

A2.3 The American Institute of Steel Construction

A2.4 Grades of Structural Steel

A2.5 Shapes and Forms

A2.6 Joining Steel

A2.7 Decking

A2.8 The Design/Fabrication/Erection Process

A2.9 Related Terms

Appendix 3: Structural Materials—Reinforced Concrete

A3.1 Composition and Manufacture

A3.2 Curing

A3.3 Characteristics and Properties

A3.4 Related Terms

Appendix 4: Structural Materials— Wood

A4.1 Source and Manufacture

A4.2 Products

A4.3 Characteristics and Properties

A4.4 Structural Considerations

A4.5 Related Terms

Appendix 5: Properties of Sections

A5.1 Center of Gravity and Centroids

A5.2 Moment of Inertia

A5.3 Section Modulus

A5.4 Radius of Gyration

Appendix 6: Basic Trigonometry

A6.1 Basic Trigonometric Functions of a Right Triangle

A6.2 Basic Trigonometric Values of Frequently Used Angles

A6.3 Proportions of Special Right Triangles

A6.4 The Pythagorean Theorem

Index

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Library of Congress Cataloging-in-Publication Data:

Dabby, Ramsey.
Structure for architects : a primer / Ramsey Dabby and Ashwani Bedi.
p. cm.
Includes index.
ISBN 978-0-470-63376-2 (hardback); ISBN 978-0-470-90294-8(ebk);
ISBN 978-0-470-90246-2 (ebk); ISBN 978-0-470-90249-3(ebk);
ISBN 978-0-470-95096-8(ebk); ISBN 978-0-470-95113-2(ebk)
1. Architecture. 2. Structural engineering. 3. Thought and thinking. I. Bedi, Ashwani. II. Title.
TH845.D33 2011
624.1'7–dc22

2010054173

Preface

The concept for this preliminary textbook arose a few years ago when we jointly taught a Structures course to architectural students in the Architectural Technology Department at The New York City College of Technology. Noting the lack of an appropriate introductory text covering the intended topics, we decided to draw upon our professional and classroom experiences and began work on a structures textbook primarily aimed at the architectural student. Thus began a journey that has spanned over several years and continues to evolve.

Architects tend to think visually, in concepts, while engineers tend to think mathematically, in details. The disparity between the way architects and engineers perceive and process information is not addressed by most structural engineering textbooks, which focus heavily on technical aspects and often intimidate the architectural student. Actually, structures is the most intuitive of engineering disciplines, its principles easily perceived and visible in countless everyday situations. Our intent in this work is to de-mystify structural principles and present them in an intuitive, easy-to-read, and graphically friendly format.

We wish to thank Tim Maldonado, former Dean of the School of Technology at The NYC College of Technology, for his encouragement and guidance especially during the early stages of development. We also wish to thank Stella Deporis, R. Elias Dabby, and Latif Dabby for their advice and inspiration, as well as Andrzej Flakowicz, and Rodrigo da Silva (our former student and now graduate architect) for their much-valued early assistance on the illustrations.

While we collaborated with and also thank our many other academic and professional colleagues, we would not have imagined this work to be complete without the thoughts and reviews from two very talented engineers—our dear friends, Tom Michon and Sunil Saigal. Tom is simply one of the most brilliant practicing structural engineers with whom we've ever had the pleasure of knowing and working. Sunil, Dean of The Newark College of Engineering at NJIT and Distinguished Professor of Structures, has always placed his students before anything else. With an avid passion for structures and academics, Tom and Sunil's primary desire was to help develop quality technical material for students, while keeping it easy-to-understand.

We would like to express our appreciation to Wiley Acquisitions Editor Paul Drougas and Senior Production Manager Kerstin Nasdeo for their confidence, patience, and publishing guidance.

Finally, we wish to thank our families who wondered about, and put up with, our discussions lasting hours on end. Barbara and Kiran, we could not have accomplished this without your support and understanding—we lovingly dedicate this to you.

We welcome and appreciate any comments, suggestions, or corrections by the reader.

Ramsey Dabby, RA
Ashwani K. Bedi, PE
StructureForArchitects@gmail.com

CHAPTER 1

Architects, Engineers, and Design

To the general public the distinction between architects and engineers, and their relationship to design, is blurred. What exactly is the difference between an architect and an engineer? Between architecture and engineering? Don't architects, after all, study engineering? What do engineers have to do with design? Isn't design what architects do? And if architects and engineers are so highly trained in design and construction, why is a third group—contractors—needed to construct buildings? The confusion is understandable.

For centuries, there was little, if any, distinction among architects, engineers, and builders. With the advent of the Industrial Revolution, the world became increasingly complex. The guild and trades system, in which skills and techniques were handed down from generation to generation, began to break down. By the mid-1800s, architecture in the United States evolved into a profession distinct from engineering and construction.

There are many ways to define architecture, but perhaps the most expressive definition was the one provided by Marcus Vitruvius Pollio, a first-century AD Roman writer, architect, and engineer. Vitruvius wrote De architectura, a Latin treatise on architecture, in which he asserted that a structure (architecture) must exhibit the three qualities of firmitas, utilitas, and venustas, loosely translated as strength, having soundness of construction; usefulness, having practical value or purpose; and beauty, giving pleasure and delight to those who experience it.

Determining strength and usefulness is relatively easy. Determining beauty is more difficult, since each of us is free to decide what gives us visual pleasure and delight. With all due respect to Vitruvius, perhaps another way to define architecture is to simply call it the art and science of constructing.

In modern practice, the knowledge and information needed to design and construct a large building requires many areas of expertise, too much for any one profession to know. The entire process of determining a building's appearance, the materials and systems to be used, and their configurations and sizes is broadly called design. Design falls mainly on the shoulders of architects and engineers. Architects have primary responsibility for determining the building's size and shape, along with the myriad architectural materials, finishes, and details. Engineers have primary responsibility for determining the mechanical, electrical, and structural systems, along with the many engineering calculations and details.

Contemporary architects, as the leaders and orchestrators of most building projects, are trained as generalists and humanists conversant with aesthetics, planning, sociology, and economics, as well as engineering. By contrast, the training of contemporary engineers is highly technical and focused on a specific engineering discipline. Early engineering had only two disciplines, military and civil. As technology advanced, new branches of engineering such as mechanical, electrical, and chemical engineering emerged from civil engineering as individual disciplines. Structural engineering, however, the branch of engineering concerned with designing buildings and other types of structures to stand up and resist loads, has always been considered a part of civil engineering and remains so today.

Structural engineering is the engineering discipline most closely intertwined with architectural form. The best architecture exhibits a strong understanding of how forces move through a structure. Toward that end, the primary intent of this book is to increase the structural vocabulary of future architects. It is our hope that by doing so, the architect's dialogue with the structural engineer will be enriched, thereby affording architecture the opportunity to reach its fullest potential.

CHAPTER 2

Stability and Strength

In a broad sense, all structural engineering can be reduced to satisfying two basic conditions: stability and strength.

Through stability, the various forces that act on a structure are kept in balance, preventing the structure from toppling, sliding, bending, or twisting.

Through strength, the size and physical makeup of the structural materials are made sufficient to withstand the various forces acting on them.

Let's use an example of a weightlifter, Andre, holding a barbell over his head in order to illustrate the concepts of stability and strength. Suppose that the barbell has a 100 lb weight on each end and that Andre is well trained and intuitively keeps his hands evenly spaced. Since the barbell is balanced by the spacing of his hands, and since Andre has the strength to support the 200 total lbs, Andre stands upright, in firm control of the barbell and weights (Figure 2.1).

Now suppose that Andre's hands are not evenly spaced. The barbell would tend to tilt and eventually topple. Although he would be strong enough to support the 200 total lbs, he would be unable to control the load due to a failure of stability (Figure 2.2).

Now suppose that Andre's hands are evenly spaced but that the weight on each end is increased from 100 lbs to 200 lbs. His arms and legs would tend to bow and eventually would buckle beneath the increased weight. Although he would be sufficiently well balanced to control the 400 total lbs, he would be unable to support the load due to a failure of strength (Figure 2.3).

Without stability, the strongest of buildings will fail, and without strength, the most stable of buildings will fail. Not only must the building as a whole satisfy these two conditions, but every one of its components must do so as well.

CHAPTER 3

Loads

Structures are subject to numerous and sometimes complex forces, called loads, that exert pressure vertically, horizontally, or at some angle in between. Loads can be predictable, such as fixed mechanical equipment on a roof, or unpredictable, such as wind on a façade; they can be concentrated, such as a column supported by a beam, or distributed over a wide area, such as snow falling on a roof. Loads can be static and subject to little or no change over time, or dynamic and subject to rapid change. With respect to the engineering analysis of structures, however, all loads are ultimately analyzed as acting statically in either a vertical or a horizontal direction. For this reason, perhaps the best way to categorize loads is by grouping them into vertical gravity loads and horizontal lateral loads.

3.1 Gravity Loads

Gravity loads act downward, pulling all objects toward the center of the Earth. They may be classified as dead loads or live loads.

Dead loads are those that are built into a structure, such as the weight of permanent floors, roofs, walls, and fixed mechanical equipment. Dead loads are finite and can be accurately determined.

Live loads are variable, unpredictable, and mobile, such as people, furniture, snow, rain, and ice. These loads can vary at any given moment, so building codes specify minimum live loads to be used for the design of floors and roofs. Live loads are expressed in pounds per square foot (psf), such as 40 psf for office floors or 150 psf for warehouse storage floors (Figure 3.1).

3.2 Lateral Loads

Lateral loads are caused by wind and seismic movement (earthquake) and, in general, are considered to act horizontally. Although wind and seismic loads are unpredictable, codes account for their complexity by prescribing equivalent static lateral loads based upon geographic zones.

Wind loads are dependent upon many factors such as velocity and the shape and height of the building, as well as the geometry and proximity of adjacent buildings. Wind loads exert pressure on the sides of a building, causing it to sway (Figure 3.2a).

Seismic loads are created by random, variable, and erratic motions of the ground during an earthquake. Seismic loads also cause a building to sway (Figure 3.2b).

Although the behavior of a building under wind and seismic loads is different, the net effect is similar in that both types of lateral loads create conditions of (a) bending and (b) base shear on the building (Figures 3.3 and 3.4).

Wind loads create positive pressure by pushing inward against the building's exterior surfaces on the windward side, and negative pressure (suction) by pulling outward on the building's exterior surfaces on the leeward side (Figure 3.5). For very tall or irregularly shaped structures, wind tunnel tests are often used to supplement information provided in codes and to predict actual aerodynamic forces more precisely.

Wind and seismic loads also tend to twist a structure, creating torsion, a complex behavior in a building (Figure 3.6).

Wind and seismic loads can also create uplift forces at the base of a structure, tending to overturn it. Communications towers, which are relatively lightweight, are particularly susceptible to uplift and overturning (Figure 3.7).

Structural systems that resist lateral loads will be examined more closely in Chapter 15.

3.3 Dynamic Loads

Loads that change rapidly, that are applied suddenly, or that are the result of an amplified rhythmic movement are called dynamic loads. Examples of dynamic loads include heavy vibrating machinery, an elevator starting and stopping in its shaft, a vehicle starting or stopping in a garage, and soldiers marching in rhythm on a bridge (Figure 3.8). The net effect of a dynamic load is that it increases its actual static load. Since the analysis of dynamic loads is complex, codes typically account for them by substituting additional equivalent static loads.

3.4 Impact Loads

Loads that result from a sudden collision or an explosion are called impact loads. For example, columns in a garage are normally designed to withstand a moderate impact force from an automobile. Blast-resistant design must consider the impact force of the explosion as well as the impact force from projectiles being hurtled about. Codes typically account for impact loads by prescribing additional factors of safety on the static loads.

3.5 Load Paths

All loads applied to a structure, whether gravity or lateral, eventually make their way down through the structure's components to the ground. Let's take the simple example of a man sitting on a four-legged stool. The man's weight is transferred from the seat of the stool to the legs, and from the legs to the ground. If the man weighs 200 lbs, the seat will transmit 50 lbs to each leg, and each leg will transmit 50 lbs to the floor. The flow of loads through a structure, in this case the stool, is called the load path (Figure 3.9).

The most efficient load path is a direct line to the ground (Figure 3.10).

In framed buildings, loads applied to the roof, floors, and vertical supports make their way down through the structure to the foundations and ultimately to the ground. The ground, in turn, exerts resisting forces against the foundations, continuing through the structure and opposing the downward flow of loads—in a sense, a reverse load path (Figure 3.11).

In a cable suspension bridge (Figure 3.12), the vehicle loads from the roadway are supported by vertical suspension cables (in tension) extending up to the main cable (in tension), down through the towers (in compression) to the foundations, and ultimately to the ground. The main cable is held in tension by attachments in the anchorage abutments. The concepts of tension and compression will be explored more fully in Chapter 4.

For any structure to be stable and not move, all of the forces acting on it and all of its components must be in equilibrium (i.e., in balance).

We'll examine equilibrium and how this balance of forces is analyzed in Chapter 6.

CHAPTER 4

States of Stress

While loads are external forces applied to a body, stress is the internal resistance of the body to those forces. There are three basic types of stress: tension, compression, and shear. All stress consists of these three basic types or some combination thereof.

4.1 Tension

Tension is the tendency of a body to be pulled apart. The rope in Figure 4.1a has direct tensile stress acting on it (the two men pulling on each end) in a direction perpendicular to its cross section (Figure 4.1b).

4.2 Compression

Compression is the tendency of a body to be crushed. The post in Figure 4.2a has direct compressive stress acting on it (the downward force and the upward resistance of the ground) in a direction perpendicular to its cross section (Figure 4.2b).

4.3 Shear

Shear is the tendency of a body to be sliced. The bolt in Figure 4.3a has direct shear stress acting on it (the two bars pulling in opposition to each other) in a direction parallel to its cross section (Figure 4.3b).

4.4 Torsion

Torsion is a type of shear in which a body tends to be twisted, resulting in shear stresses (Figures 4.4 and 4.5).

4.5 Bending

Bending is the tendency of a body, such as a beam, to bow, thereby creating stress in the body. When bowed, the body compresses along one edge and stretches along the other. The bending of a simply supported beam under load produces tension along the bottom of the beam and compression along the top (Figure 4.6). Moving away from the tension and compression edges toward the centerline of the beam, the tensile and compressive stresses gradually diminish until they reach zero. The imaginary plane passing through the centerline of a beam along its length, at which no tension or compression occurs, is called the neutral plane or neutral axis. Although bending is of paramount importance in beams, it may occur in any structural member, including columns. Bending is also referred to as flexure.

In addition to producing tensile and compressive stresses from bending, a beam under load will produce shear stress, both perpendicular (i.e., vertical) and parallel (i.e., horizontal) to the length of the beam (Figures 4.7 and 4.8).

With a load placed at the center of a span, the maximum bending stresses in a beam occur at the center of the span (Figure 4.9), with the maximum compressive stress at the top edge and the maximum tensile stress at the bottom edge (4.10).

Since tensile, compressive, and shear stresses vary for any point along the length of a beam, their computation in beams is more complex than in members under direct stress. Beam analysis, as well as the analysis of members under direct stress, will be examined more closely in subsequent chapters.