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G G Schierle Architectural Structures

G G Schierle

Architectural Structures

Excerpts

ISBN 0-18-195009-x

Copyright © G Schierle 1990-2006. All rights reserved

Portions of this document reproduce sections from the 2003 International Building Code, International Code Council, Falls Church, Virginia. All rights reserved.

AISC data, copyright © American Institute of Steel Construction, Inc. Reprinted with permission. All rights reserved

USGS data copyright © United States Geological Survey, courtesy USGS

University of Southern California Custom Publishing

C/O Chauncey Jemes

Los Angeles, CA 90089-2540 e-mail:jemes@usc.edu

Tel. 213-740-8946

Fax: 213-740-7686

Preface

To foster informed intuition for structures, this book has many illustrations visualizing structural behavior and to complement and clarify mathematical concepts. While the book is primarily targeted for students of architecture, it also serves as reference book for students of civil engineering, and professional architects, engineers, and contractors. The book is organized in six parts. Part I starts with an introduction of key developments in the historic evolution of structures and proceeds to introduce loads on buildings and basic systems to resist them. Part II introduces fundamentals: statics and strength of material, as well as analysis and design of basic elements, such as beams and columns. Part III introduces design methods: ASD and LRFD; design of masonry (ASD) and concrete (strength method); design for wind and seismic forces; as well as conceptual design, explored on case studies. Part IV introduces structure systems for horizontal spans, categorized by bending, axial, form, and tensile resistance. All systems are introduced with conceptual diagrams, describing their structural behavior and alternate options. Case studies describe their use in real projects. Part V introduces vertical structures in similar fashion. Part VI introduces material properties and details for wood, steel, masonry, concrete, and membrane structures. Appendices include math derivation, graphs and tables. Text and graphics are correlated on the same page for easy reading and comprehension. Prerequisites for the book are algebra, trigonometry, and Newtonian physics. The book can be used in courses of statics and strength of material, structure systems and structural materials. Math derivations visualized help understanding and to introduce concepts also to readers with more artistic or visual modes of learning. The book includes many graphs to streamline complex tasks. The graphs, which feature US and SI units to facilitate correlation, include:

Design graphs for span limits and span/depth ratios

Column design graphs

Seismic design graphs

Wind design graphs

Acknowledgements

I am grateful to many students and others for various contributions to this book, ranging from suggestions to illustrations; most notably drawings by Bronne Dytog and June Yip; but also Xiaojun Cheng. Lucia Ho, Maki Kawaguchi, Ping Kuo, Jennifer Lin, Sassu Mitra, Rick Patratara, Shina Rau, Srinivas Rau, Madhu Thangavelu, and Sharmilla Thanka. Students that provided data and comments include Laura Mae Bryan, Sabina Cheng, Samy Chong, Claudia Chiu, Kristin Donour, Miriam Figueroa, Ping Han, Nick Ketpura, Samuel Kuo, Jason Mazin, Neha Sivaprasad, Timothy Petrash, Musette Profant, Katie Rahill, Reed Suzuki, Bogdan Tomalevski, Carole Wong, Nasim Yalpani. Others that provided comments or material: include: Andrea Cohen Gehring, Jeff Guh, Robert Harris, Theo Heizmann, Helge Wang, Will Shepphird, Robert Timme, Matt Warren, and Walter Winkle. Architects and engineers that provided drawings include: Norman Foster, Von Gerkan Marg, Arata Isozaki, David Lawrence Gray, Paul M. Kaufmann, Pierre Koenig, Panos Koulermos, Edward Niles, Jörg Schlaich, James Tyler, Widom Wein Cohen, and Dimitry Vergun.

To my family

Units

SI * units (metric)

 

 

Conversion

 

 

US units

 

 

 

Remark

 

factor **

 

 

 

Remark

 

 

 

 

Length

 

 

 

Millimeter

mm

 

25.4

Inch

in

 

Centimeter

cm

10 mm

30.48

Foot

ft

12 in

Meter

m

1000 mm

0.9144

Yard

yd

3 ft

Kilometer

km

1000 m

1.609

Mile

mi

5280 ft

 

 

 

 

Area

 

 

 

Square millimeter

mm2

 

645.16

Square in

in2

 

Sq. centimeter

cm2

100 mm2

929

Square foot

ft2

144 in2

Square meter

m2

1 Mil

0.835

Sq. yard

yd2

9 ft2

Hectar

ha

10000 m2

2.472

Acre

Acre =

4840 yd2

 

 

 

 

Volume

 

 

 

Cubic millimeter

mm3

 

16387

Cubic inch

in3

 

Cubic centimeter

cm3

1 k mm3

28317

Cubic foot

ft3

 

Cubic meter

m3

1 Mil cm3

0.7646

Cubic yard

yd3

 

Liter

l

0.001 m3

0.264

Gallon

US gal =

3.785 liter

 

 

 

 

Mass

 

 

 

Gram

g

 

28.35

Ounce

oz

 

Kilogram

kg

1000 g

0.4536

Pound

Lb, #

16 oz

Tonn

t

1000 kg

0.4536

Kip

k

1000 #

 

 

 

Force / load

 

 

 

Newton

N

 

4.448

Pound

Lb, #

 

Kilo Newton

kN

1000 N

4.448

Kip

k

1000 #

Newton/ meter

N/m

 

14.59

Pound/ ft

plf

 

Kilo Newton/ m

kN/m

 

14.59

Kip/ ft

klf

1000 plf

 

 

 

 

Stress

 

 

 

Pascal= N/m2

Pa

 

6895

 

Pound/ in2

psi

 

Kilo Pascal

kPa

1000 Pa

6895

 

Kip / in2

ksi

1000

 

 

 

Fabric stress

 

 

 

Kilo Newton / m

kN/m

 

175

Pound/ in

Lb/in

Fabric

 

 

Load / soil pressure

 

 

Kilo Pascal

kPa

1000 Pa

47.88

 

Pound/ ft2

psf

 

 

 

 

 

Moment

 

 

 

 

Newton-meter

N-m

 

1.356

 

Pound-foot

Lb-ft, #’

 

Kilo Newton-m

kN-m

1000 N-

1.356

 

Kip-foot

k-ft, k’

1000#’

 

 

 

Temperature

 

 

 

Celcius

°C

 

 

.55(F-32)

 

Fahrenheit

°F

 

Water freezing

 

0°C

=

 

32°F

 

 

Water boiling

 

100°C

=

 

212°F

 

 

Prefixes

Prefix

Factor

Micro-

0.000001

MIli-, m

0.00001

Centi-

0.01

Deci-

0.1

Semi-, hemi-, demi-

0.5

Uni-

1

Bi-, di-

2

Tri-, ter-

3

Tetra-, tetr-, quadr-

4

Pent-, penta-, quintu-

5

Sex-, sexi-, hexi-, hexa-,

6

Hep-, septi-,

7

Oct-, oct-, octa-, octo-

8

Non-, nona-

9

Dec-, deca-, deci, deka-

10

Hect-, hector-

100

Kilo-, k

1,000

Mega-, M

1,000,000

Giga-, G

1,000,000,000

Tera-

1,000,000,000,000

*SI = System International (French - designation for metric system)

**Multiplying US units with conversion factor = SI units Dividing SI units by conversion factor = US units

Contents

PART I: BACKGROUND

1

Historic Evolution

1-2

Walls

1-6

Post-and-beam

1-10

Arch, Vault, Dome

1-21

Suspended

1-24

Truss

1-26

Skyscraper

2

Loads

2-2

Introduction

2-2

Dead load

2-4

Live load

2-5

Seismic load

2-6

Wind load

2-8

Tributary load and load path

3

Basic Concepts

3-2

Synergy, Strength, Stiffness, Stability

3-3

Rupture length

3-4

Horizontal structures

 

Slab, plate, deck (one & two-way)

 

Beam, arch and cable

 

Truss

3-9

Vertical/lateral structures

 

Wall

 

Cantilever

 

Moment frame

 

Braced frame

PART II: MECHANICS

4

Statics

4-2

Force and moment

4-3

Static equilibrium

4-4

Supports

4-5

Reactions

4-10

Static determinacy

4-13

Vector analysis

4-15

Truss analysis

4-17

Funicular

4-21

Vector reactions

5

Strength Stiffness Stability

5-2

Force types

5-3

Force vs. stress

5-4

Allowable stress

5-5

Axial stress

5-6

Shear stress

5-8

Torsion

5-9

Principal stress

5-10

Strain

5-10

Hook’s law

5-11

Elastic Modulus

5-14

Thermal strain

5-14

Thermal stress

5-17

Stability

6

Bending

6-4

Bending and shear

6-8

Equilibrium method

6-10

Area method

6-13

Indeterminate beams

6-14

Flexure formula

6-15

Section modulus

6-16

Moment of inertia

6-18

Shear stress

6-22

Deflection

7

Buckling

7-3

Euler formula

7-3

Slenderness ratio

7-4

Combined stress

7-5

Kern

7-6

Arch and vault

7-7

Wood buckling

7-12

Steel buckling

PART III: DESIGN METHODS

8 ASD, LRFD, Masonry and Concrete Design

8-2 ASD (Allowable Stress Design)

8-3 LRFD (Load Resistance Factor Design)

8-4 Masonry design (ASD)

8-10 Concrete strength design (LRFD)

9

Lateral Force Design

13

Form-Resistant

9-2

Design for wind

13-2

Funicular concepts

9-8

Seismic design

13-4

Arch

9-13

SD-graphs

13-10

Vault

9-15

Analysis steps

13-17

Dome

9-18

Vertical distribution

13-23

Grid shell

9-19

Horizontal diaphragms

13-29

HP shell

9-22

Eccentricity

13-37

Freeform shell

9-23

Hazard configurations

14

Tensile Resistant

9-24

Stability issues

9-27

Seismic safety items

14-1

Tension members

10

Conceptual Design

14-2

Prestress

14-3

Stayed structures

10-1

System selection

14-8

Propped structures

10-3

Global moment and shear

14-10

Suspended structures

10-4

Radial pressure

14-17

Cable truss

10-5

Examples

14-21

Anticlastic structures

10-7

Case studies

14-42

Pneumatic structures

10-15

Portal method

PART V: VERTICAL SYSTEMS

10-17

Moment frame

10-19

Braced frame

15

General Background

10-21

Test models

10-23

Sample projects

15-2

Tall structures

10-29

Computer aided design

15-3

Gravity load

PART IV: HORIZONTAL SYSTEMS

15-4

Lateral load

15-7

Structure systems

11

Bending Resistant

15-11

Floor framing

15-12

Beam-column interaction

11-1

Bending concepts

 

 

11-3

Beam optimization

16

Shear Resistant

11-5

Joist, beam, girder

16-2

Classic walls

11-11

Vierendeel

16-3

Seismic failures

11-17

Folded plate

16-4

Shear walls

11-22

Cylindrical shell

16-6

Shear wall stability

12

Axial Resistant

16-7

Wood shear walls

16-10

Shear wall reinforcing

12-2

Truss

 

 

 

Truss configurations

17

Bending Resistant

 

Prismatic truss

17-2

Cantilever

 

Folded truss

17-6

Moment frame

12-13

Space truss

17-13

Framed tube

12-22

Tree structures

17-16

Bundled tube

18

Axial Resistant

24

Fabric and cables

18-2

Braced frame

24-1

Material

18-8

Belt truss and outrigger

24-2

Fabric

18-12

Braced tube

24-4

Cables

18-16

Eccentric braced frame

24-10

Projects

19

Suspended high-rise

Appendix A: Beam Formulas

19-2

Suspension rational

A-2

Beam formulas

19-3

Design options

A-3

Bending coefficients

19-3

Limits

Appendix B: Geometric Properties

19-4

Case studies

PART VI: MATERIAL

B-2

Centroid

B-4

Moment of Inertia

20

Wood

B-6

Parallel Axis Theorem

B-7

Radius of Gyration

20-1

Material

B-8

Geometric properties

20-5

Heavy timber

Appendix C: Lateral Design Data

20-13

Grid structures

 

Balloon framing

C-2

Wind design data

 

Platform framing

C-7

Seismic design data

20-29

Projects

Appendix D: Material and Buckling Data

21

Steel

D-2

Wood

21-1

Material

D-8

Steel

21-7

Heavy steel

Appendix E: Design Tables

21-29

Light gauge steel

21-33

Projects

E-2

Span Ranges for Structure Elements

22

Masonry

E-3

Span Ranges for Structure Systems

 

 

22-1

Material

 

 

22-7

Brick masonry

 

 

22-18

Concrete masonry

 

 

22-22

Stone masonry

 

 

22-23

Projects

 

 

23

Concrete

 

 

23-1

Material

 

 

23-4

Reinforced concrete

 

 

23-17

Prestressed concrete

 

 

23-20

Precast concrete

 

 

23-24

Tilt-up concrete

 

 

23-26

Projects

 

 

3

Basic Concepts

This chapter on basic concept introduces:

Structural design for:

Strength

Stiffness

Stability

Synergy

Rupture length (material properties, i.e., structural efficiency)

Basic structure systems

Horizontal structures

Vertical / lateral structures for:

o Gravity load o Lateral load

3-1 BACKGROUND Basic Concepts

Strength, Stiffness, Stability, Synergy

Structures must be designed to satisfy three Ss and should satisfy all four Ss of structural design – as demonstrated on the following examples, illustrated at left.

1Strength to prevent breaking

2Stiffness to prevent excessive deformation

3Stability to prevent collapse

4Synergy to reinforce architectural design, described on two examples:

Pragmatic example: Beam composed of wooden boards

Philosophical example: Auditorium design

Comparing beams of wooden boards, b = 12” wide and d = 1”deep, each. Stiffness is defined by the Moment of Inertia, I = b d3/12

1 board, I = 12x13/12

I = 1

10 boards I = 10 (12x13/12)

I = 10

10 boards glued, I = 12x103/12

I = 1000

Strength is defined by the Section modulus, S = I/(d/2)

 

1 board, S = 1/o.5

S = 2

10 boards, S = 10/0.5

S = 20

10 boards, glued, S =1000/5

S = 200

Note:

The same amount of material is 100 times stiffer and 10 times stronger when glued together to transfer shear and thereby engage top and bottom fibers in compression and tension (a system, greater than the sum of its parts). On a philosophical level, structures can strengthen architectural design as shown on the example of an auditorium:

Architecturally, columns define the circulation

Structurally, column location reduces bending in roof beams over 500% !

3-2 BACKGROUND Basic Concepts

Rupture length

Rupture length is the maximum length a bar of constant cross section area can be suspended without rupture under its weight in tension (compression for concrete & masonry).

Rapture length defines material efficiency as strength / weight ratio:

R = F / λ

R = rupture length

F = breaking strength

λ = specific gravity (self weight)

Rupture length, is of particular importance for long-span structures. The depth of horizontal span members increases with span. Consequently the weight also increases with span. Therefore the capacity of material to span depends on both its strength and weight. This is why lightweight material, such as glass fiber fabrics are good for longspan structures. For some material, a thin line extends the rupture length to account for different material grades.

The graph data is partly based on a study of the Light weight Structures Institute, University Stuttgart, Germany

3-3 BACKGROUND Basic Concepts

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