Table Of ContentStructural Elements for
Architects and Builders
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Structural Elements for
Architects and Builders
Design of Columns, Beams and
Tension Elements in Wood, Steel and
Reinforced Concrete
Jonathan Ochshorn
Department of Architecture,
Cornell University
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Contents
Preface ....................................................................................................................... v ii
List of examples. .........................................................................................................ix
List of appendices ...................................................................................................... x i
CHAPTER 1 Statics ............................................................................................... 1
Tributary areas ................................................................................... 2
Equilibrium ........................................................................................ 7
Reactions .......................................................................................... 1 0
Internal forces and moments ........................................................... 1 7
Indeterminate structures .................................................................. 3 1
Strength of materials ........................................................................ 3 3
CHAPTER 2 Loads ............................................................................................... 39
Dead loads ........................................................................................ 3 9
Live loads ......................................................................................... 4 1
Environmental loads. ........................................................................ 46
CHAPTER 3 Material properties ...................................................................... 6 1
Wood ................................................................................................ 63
Steel .................................................................................................. 6 8
Reinforced concrete ........................................................................ 7 0
CHAPTER 4 Sectional properties .................................................................... 73
Wood ................................................................................................ 73
Steel .................................................................................................. 7 4
Reinforced concrete ........................................................................ 7 5
CHAPTER 5 Design approaches ...................................................................... 79
Allowable stress design .................................................................... 7 9
Strength design ................................................................................ 8 0
CHAPTER 6 Tension elements ......................................................................... 87
Wood ................................................................................................ 89
Steel .................................................................................................. 9 6
Reinforced concrete ...................................................................... 1 04
CHAPTER 7 Columns ........................................................................................ 1 07
Wood .............................................................................................. 109
Steel ................................................................................................ 1 15
Reinforced concrete ...................................................................... 1 20
v
vi Contents
CHAPTER 8 Beams ........................................................................................... 129
Defl ection ....................................................................................... 129
Bending stress ................................................................................ 1 30
Shear stress .....................................................................................136
Wood .............................................................................................. 139
Steel ................................................................................................ 1 50
Reinforced concrete ...................................................................... 1 64
CHAPTER 9 Connections ................................................................................. 1 93
Wood .............................................................................................. 194
Steel ................................................................................................ 2 26
Reinforced concrete ...................................................................... 2 38
Appendix 1: Tables for Chapter 1 (statics) ......................................................... 2 49
Appendix 2: Tables for Chapter 2 (loads) ............................................................ 2 51
Appendix 3: Tables for Chapter 3 (material properties) ...................................... 2 65
Appendix 4: Tables for Chapter 4 (sectional properties). .................................... 287
Appendix 5: Tables for Chapter 5 (design approaches) ...................................... 3 09
Appendix 6: Tables for Chapter 6 (tension elements) ......................................... 3 11
Appendix 7: Tables for Chapter 7 (columns) ....................................................... 3 15
Appendix 8: Tables for Chapter 8 (beams) .......................................................... 3 29
Appendix 9: Tables for Chapter 9 (connections) ................................................. 3 45
Appendix 10: Unit abbreviations and conversion .................................................. 3 73
References ............................................................................................................... 3 75
Glossary ................................................................................................................... 3 77
Index ....................................................................................................................... 3 83
Preface
As is well known, architects and builders rarely design the structural elements and
systems within their buildings, instead engaging the services of (and, it is to be
hoped, collaborating with) structural engineers, or relying upon standard practices
sanctioned by building codes. Where architects or builders wish to be adventurous
with their structures, some knowledge of structural behavior and the potential of
structural materials is certainly useful. On the other hand, where they are content
to employ generic structural systems— platform framing in wood, simple skeletal
frames in steel or reinforced concrete— one can get by with little actual knowledge
of structural design, relying instead on the expertise of structural consultants and
the knowledge of common spans, heights, and cross-sectional dimensions around
which many ordinary buildings can be planned.
The heroic stage of modernism, in which architects often sought to reconcile
structural behavior and overall building form— some fi nding inspiration in the struc-
tural frame or the load-bearing wall— was also the heroic stage of structural educa-
tion for architects: it was hardly necessary, in that context, to explain why architects
needed to learn about structures. Some of the same excitement about the potential
of structure in architecture still remains, but it is also true that a “ mannerist ” ten-
dency has emerged, interested not necessarily in renouncing the role of structure in
architecture, but rather reveling in its potential to distort, twist, fragment, and other-
wise subvert modernist conventions and the architectural forms they support.
Yet all structures, whether hidden from view or boldly expressed, follow the
same laws of equilibrium, are exposed to the same types of forces, and are con-
strained by the same material properties and manufacturing practices. It is, there-
fore, appropriate for architects and builders to study structures in such a way that
the basic principles underlying all structural form become clear. This can be accom-
plished in three phases: (1) by studying the concepts of statics and strength of
materials, (2) by learning how these concepts are applied to the design of common
structural elements fabricated from real materials, and (3) by gaining insight into the
design of structural systems comprised of structural elements interconnected in a
coherent pattern.
Much of the material presented in this text can be found elsewhere; the basic
conditions of equilibrium, historical insights into structural behavior that form the
basis for structural design, and recommendations for design procedures incorpo-
rated into building codes are all widely disseminated through industry-published
manuals, government-sanctioned codes, and academic texts. Many excellent struc-
tures texts have been written specifi cally for architects and builders. Thus, the ques-
tion naturally arises: Why write another one?
The primary motivation for writing this text is to organize the material in a man-
ner consistent with the structures curriculum developed within the Department
viii Preface
of Architecture at Cornell University, based on the three sequential “ phases ” just
described — structural concepts, elements, and systems. While this text does contain
a concise introduction to structural concepts (statics), it is primarily concerned with
the design and analysis of structural elements: columns, beams, and tension mem-
bers, and their connections. This material is organized into a single volume that is
concise, comprehensive, and self-suffi cient, including all necessary data for the pre-
liminary design and analysis of these structural elements in wood, steel, and rein-
forced concrete.
A second motivation for writing this text is to present material in a manner con-
sistent with my own priorities and sensibilities. Every chapter contains insight, spec-
ulation, or forms of presentation developed by the author and generally not found
elsewhere. Additionally, the Appendices included at the end of the text contain
numerous tables and graphs, based on material contained in industry publications, but
reorganized and formatted especially for this text to improve clarity and simplicity—
without sacrifi cing comprehensiveness.
Methods for designing structures and modeling loads are constantly being
refi ned. Within the past several years, important changes have occurred in the
design of wood, steel, and reinforced concrete structures, as well as in the model-
ing of loads. These changes include revised procedures for beam and column design
in wood; the replacement of the standard specifi cation for 36-ksi steel with a new
standard based on 50-ksi steel for wide-fl ange sections; a major modifi cation in the
load factors used in reinforced concrete design, aligning them with those recom-
mended by SEI/ASCE 7 and already used in the design of wood and steel structures;
and numerous refi nements in the modeling of environmental loads. These changes
have all been incorporated into this text.
Finally , a disclaimer: This text is intended to be used only for the preliminary
(schematic) design and understanding of structural elements. For the design of an
actual structure, a competent professional should be consulted.
List of examples
1 .1 Find reactions for simply supported beam
1 .2 Find reactions for three-hinged arch
1 .3 Find reactions for a cable
1 .4 Find internal shear and bending moment for simply supported beam with
“ point ” loads
1 .5 Find internal shear and bending moments for a simply supported cantilever
beam with distributed loads
1 .6 Find internal axial forces in a truss (section method)
1 .7 Find internal axial forces in a three-hinged arch
1 .8 Find internal axial forces in a cable
2 .1 Calculate dead loads
2 .2 Calculate live loads
2 .3 Calculate snow loads
2 .4 Calculate wind loads
2 .5 Calculate seismic loads
5 .1 Load combinations (Part I)
5 .2 Load combinations (Part II)
5 .3 Load combinations (Part III)
6 .1 Find elongation in tension element
6 .2 Analyze wood tension element
6 .3 Design wood tension element
6 .4 Analyze steel tension element
6 .5 Design steel tension element
7 .1 Analyze wood column
7 .2 Design wood column
7 .3 Analyze steel column
7 .4 Design steel column
7 .5 Analyze axially loaded reinforced concrete column
7 .6 Design axially loaded reinforced concrete column with cross-sectional dimen-
sions assumed
7 .7 Design axially loaded reinforced concrete column with reinforcement ratio assumed
8 .1 Analyze wood beam, dimension lumber
8 .2 Analyze wood beam, timbers
8 .3 Design wood beam, glulam
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