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structural system-for-architects
1. Draft
LECTURE NOTES
AREN4525
STUCTURAL CONCEPTS AND SYSTEMS
FOR ARCHITECTS
VICTOR E. SAOUMA
SPRING 1997
Dept. of Civil Environmental and Architectural Engineering
University of Colorado, Boulder, CO 80309-0428
April 30, 1997
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0{2
In order to invent a structure and to give it ex-
act proportions, one must follow both the intu-
itive and the mathematical paths.
-Pier Luigi Nervi
Victor Saouma Structural Concepts and Systems for Architects
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0{2 LIST OF TABLES
Victor Saouma Structural Concepts and Systems for Architects
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Chapter 1
INTRODUCTION
1.1 Science and Technology
1 There is a fundamental dierence between science and and technology. Engineering or technology is
the making of things that did not previously exist, whereas science is the discovering of things that have
long existed. Technological results are forms that exist only because people want to make them, whereas
scienti
21. c results are informations of what exists independently of human intentions. Technology deals
with the arti
22. cial, science with the natural. (Billington 1985)
1.2 Structural Engineering
2 Structural engineers are responsible for the detailed analysis and design of:
Architectural structures: Buildings, houses, factories. They must work in close cooperation with an
architect who will ultimately be responsible for the design.
Civil Infrastructures: Bridges, dams, pipelines, oshore structures. They work with transportation,
hydraulic, nuclear and other engineers. For those structures they play the leading role.
Aerospace, Mechanical, Naval structures: aeroplanes, spacecrafts, cars, ships, submarines to en-
sure the structural safety of those important structures.
1.3 Structures and their Surroundings
3 Structural design is aected by various environmental constraints:
1. Major movements: For example, elevator shafts are usually shear walls good at resisting lateral
load (wind, earthquake).
2. Sound and structure interact:
A dome roof will concentrate the sound
A dish roof will diuse the sound
3. Natural light:
A
at roof in a building may not provide adequate light.
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1{2 INTRODUCTION
A Folded plate will provide adequate lighting (analysis more complex).
A bearing and shear wall building may not have enough openings for daylight.
A Frame design will allow more light in (analysis more complex).
4. Conduits for cables (electric, telephone, computer), HVAC ducts, may dictate type of
oor system.
5. Net clearance between columns (unobstructed surface) will dictate type of framing.
1.4 Architecture Engineering
4 Architecture must be the product of a creative collaboration of architects and engineers.
5 Architect stress the overall, rather than elemental approach to design. In the design process, they
conceptualize a space-form scheme as a total system. They are generalists.
6 The engineer, partly due to his/her education think in reverse, starting with details and without
sucient regards for the overall picture. (S)he is a pragmatist who knows everything about nothing.
7 Thus there is a conceptual gap between architects and engineers at all levels of design.
8 Engineer's education is more specialized and in depth than the architect's. However, engineer must
be kept aware of overall architectural objective.
9 In the last resort, it is the architect who is the leader of the construction team, and the engineers are
his/her servant.
10 A possible compromise might be an Architectural Engineer.
1.5 Architectural Design Process
11 Architectural design is hierarchical:
Schematic: conceptual overall space-form feasibility of basic schematic options. Collaboration is mostly
between the owner and the architect.
Preliminary: Establish basic physical properties of major subsystems and key components to prove
design feasibility. Some collaboration with engineers is necessary.
Final design:
25. nements of all subsystems and components and preparation of
working documents (blue-prints). Engineers play a leading role.
1.6 Architectural Design
12 Architectural design must respect various constraints:
Functionality: In
uence of the adopted structure on the purposes for which the structure was erected.
Aesthetics: The architect often imposes his aesthetic concerns on the engineer. This in turn can place
severe limitations on the structural system.
Economy: It should be kept in mind that the two largest components of a structure are labors and
materials. Design cost is comparatively negligible.
Victor Saouma Structural Concepts and Systems for Architects
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1.7 Structural Analysis 1{3
13 Buildings may have dierent functions:
Residential: housing, which includes low-rise (up tp 2-3
oors), mid-rise (up to 6-8
oors) and high
rise buildings.
Commercial: Oces, retail stores, shopping centers, hotels, restaurants.
Industrial: warehouses, manufacturing.
Institutional: Schools, hospitals, prisons, chruch, government buildings.
Special: Towers, stadium, parking, airport, etc.
1.7 Structural Analysis
14 Given an existing structure subjected to a certain load determine internal forces (axial, shear,
ex-
ural, torsional; or stresses), de
ections, and verify that no unstable failure can occur.
15 Thus the basic structural requirements are:
Strength: stresses should not exceed critical values: f
Stiness: de
ections should be controlled: max
Stability: buckling or cracking should also be prevented
1.8 Structural Design
16 Given a set of forces, dimension the structural element.
Steel/wood Structures Select appropriate section.
Reinforced Concrete: Determine dimensions of the element and internal reinforcement (number and
sizes of reinforcing bars).
17 For new structures, iterative process between analysis and design. A preliminary design is made
using rules of thumbs (best known to Engineers with design experience) and analyzed. Following
design, we check for
Serviceability: de
ections, crack widths under the applied load. Compare with acceptable values
speci
27. ed in the design code.
Failure (limit state): and compare the failure load with the applied load times the appropriate factors
of safety.
If the design is found not to be acceptable, then it must be modi
29. cation of an old infrastructure, analysis is the most
important component.
19 In summary, analysis is always required.
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1{4 INTRODUCTION
Figure 1.1: Types of Forces in Structural Elements (1D)
1.9 Load Transfer Mechanisms
20 From Strength of Materials, loads can be transferred through various mechanisms, Fig. 1.1
Axial: cables, truss elements, arches, membrane, shells
Flexural: Beams, frames, grids, plates
Torsional: Grids, 3D frames
Shear: Frames, grids, shear walls.
1.10 Structure Types
21 Structures can be classi
31. ed as follows:
Tension Compression Structures: only, no shear,
exure, or torsion. Those are the most e-
cient types of structures.
Cable (tension only): The high strength of steel cables, combined with the eciency of simple
tension, makes cables ideal structural elements to span large distances such as bridges, and
dish roofs, Fig. 1.2. A cable structure develops its load carrying capacity by adjusting its
shape so as to provide maximum resistance (form follows function). Care should be exercised
in minimizing large de
ections and vibrations.
Arches (mostly compression) is a reversed cable structure. In an arch,
exure/shear is mini-
mized and most of the load is transfered through axial forces only. Arches are used for large
span roofs and bridges, Fig. 1.3
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1.10 Structure Types 1{5
Figure 1.2: Basic Aspects of Cable Systems
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1.10 Structure Types 1{7
Trusses have pin connected elements which can transmit axial forces only (tension and com-
pression). Elements are connected by either slotted, screwed, or gusset plate connectors.
However, due to construction details, there may be secondary stresses caused by relatively
rigid connections. Trusses are used for joists, roofs, bridges, electric tower, Fig. 1.4
Figure 1.4: Types of Trusses
Post and Beams: Essentially a support column on which a beam rests, Fig. 1.5, and 1.6.
Beams: Shear,
exure and sometimes axial forces. Recall that = Mc
I is applicable only for shallow
beams, i.e. span/depth at least equal to
35. ve.
Whereas r/c beams are mostly rectangular or T shaped, steel beams are usually I shaped (if the
top
anges are not properly stiened, they may buckle, thus we must have stieners).
Frames: Load is co-planar with the structure. Axial, shear,
exure (with respect to one axis in 2D
structures and with respect to two axis in 3D structures), torsion (only in 3D). The frame is
composed of at least one horizontalmember (beam) rigidly connected to vertical ones1. The vertical
1
The precursor of the frame structures were the Post and Lintel where the post is vertical member on which the lintel
is simply posed.
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1.10 Structure Types 1{9
OVERLAPPING SINGLE-STRUT
CABLE-SUPPORTED BEAM
CABLE-STAYED BEAM
BRACED BEAM
VIERENDEEL TRUSS TREE-SUPPORTED TRUSS
CABLE-SUPPORTED
MULTI-STRUT
BEAM OR TRUSS
CABLE-SUPPORTED PORTAL FRAME
CABLE-SUPPORTED ARCHED FRAME
SUSPENDED CABLE
SUPPORTED BEAM
CABLE-SUPPORTED
STRUTED ARCH OR
CABLE BEAM/TRUSS
GABLED TRUSS
BOWSTRING TRUSS
Figure 1.6: Dierent Beam Types
Victor Saouma Structural Concepts and Systems for Architects
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1{10 INTRODUCTION
members can have dierent boundary conditions (which are usually governed by soil conditions).
Frames are extensively used for houses and buildings, Fig. 1.7.
Figure 1.7: Basic Forms of Frames
Grids and Plates: Load is orthogonal to the plane of the structure. Flexure, shear, torsion.
In a grid, beams are at right angles resulting in a two-way dispersal of loads. Because of the rigid
connections between the beams, additional stiness is introduced by the torsional resistance of
members.
Grids can also be skewed to achieve greater eciency if the aspect ratio is not close to one.
Plates are
at, rigid, two dimensional structures which transmit vertical load to their supports.
Used mostly for
oor slabs.
Folded plates is a combination of transverse and longitudinal beam action. Used for long span
roofs. Note that the plate may be folded circularly rather than longitudinally. Folded plates are
used mostly as long span roofs. However, they can also be used as vertical walls to support both
vertical and horizontal loads.
Membranes: 3D structures composed of a
exible 2D surface resisting tension only. They are usually
cable-supported and are used for tents and long span roofs Fig. 1.8.
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1.10 Structure Types 1{11
Figure 1.8: Examples of Air Supported Structures
Victor Saouma Structural Concepts and Systems for Architects
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1{12 INTRODUCTION
Shells: 3D structures composed of a curved 2D surface, they are usually shaped to transmit compressive
axial stresses only, Fig. 1.9.
Figure 1.9: Basic Forms of Shells
Shells are classi
42. ed in terms of their curvature.
1.11 Structural Engineering Courses
22 Structural engineering education can be approached from either one of two points of views, depending
on the audience, ??.
Architects Engineers
Approach Global Elemental
Emphasis Structure Component
Analysis Approximate, rules of thumbs Exact, detailled
preliminary Final
Structures Most Trusses, Frames
Design Approximate Per code
Table 1.1: Structural Engineering Coverage for Architects and Engineers
Table 1.2: tab:secae
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1.12 References 1{13
Architects: Start from overall design, and move toward detailed analysis. Emphasis on good under-
standing of overall structural behavior. Develop a good understanding of load transfer mechanism
for most types of structures, cables, arches, beams, frames, shells, plates. Approximate analysis
for most of them.
Engineers: Emphasis is on the individual structural elements and not always on the total system.
Focus on beams, frames (mostly 2D) and trusses. Very seldom are arches covered. Plates and
shells are not even mentioned.
1.12 References
23 Following are some useful references for structural engineering, those marked by y were consulted,
and borrowed from in preparing the Lecture Notes or are particularly recommended.
Structures for Architect
1. Ambrose, J., Building Structures, second Ed. Wiley, 1993.
2. Billington, D.P. Rober Maillart's Bridges; The Art of Engineering, Princeton University Pres,
1979.
3. yBillington, D.P., The Tower and the Bridge; The new art of structural engineering, Princeton
University Pres,, 1983.
4. yBillington, D.P., Structures and the Urban Environment, Lectures Notes CE 262, Department
of Civil Engineering, Princeton University, 1978
5. French, S., Determinate Structures; Statics, Strength, Analysis, Design, Delmar, 1996.
6. Gordon, J.E., Structures, or Why Things Do'nt Fall Down, Da Capo paperback, New York,
1978.
7. Gordon, J.E., The Science of Structures and Materials, Scienti
44. c American Library, 1988.
8. Hawkes, N., Structures, the way things are built, MacMillan, 1990.
9. Levy, M. and Salvadori, M., Why Buildings Fall Down, W.W.Norton, 1992.
10. yLin, T.Y. and Stotesbury, S.D., Structural Concepts and Systems for Architects and Engi-
neers, John Wiley, 1981.
11. yMainstone, R., Developments in Structural Form, Allen Lane Publishers, 1975.
12. Petroski, H., To Enginer is Human, Vintage Books, 1992.
13. ySalvadori, M. and Heller, R., Structure in Architecture; The Building of Buildings, Prentice
Hall, Third Edition, 1986.
14. Salvadori, M. and Levy, M., Structural Design in Architecture, Prentice hall, Second Edition,
1981.
15. Salvadori, M., Why Buildings Stand Up; The Strength of Architecture, Norton Paperack, 1990.
16. ySandaker, B.N. and Eggen, A.P., The Structural Basis of Architecture, Whitney Library of
Design, 1992.
17. ySchueller, W., The design of Building Structures, Prentice Hall, 1996.
Structures for Engineers
1. y Arbadi, F. Structural Analysis and Behavior, McGraw-Hill, Inc., 1991.
2. Biggs, J.M., Introduction to Structural Engineering; Analysis and Design, Prentice Hall, 1986.
Victor Saouma Structural Concepts and Systems for Architects
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1{14 INTRODUCTION
3. Hsieh, Y.Y., Elementary Theory of Structures, Third Edition, Prentice Hall, 1988.
4. Ghali, A., and Neville, A.M., Structural Analysis, Third Edition, Chapman and Hall, 1989
5. White, R. Gergely, P. and Sexmith, R., Structural Engineering; Combined Edition, John
Wiley, 1976.
6. y Nilson, A., and Winter, G. Design of Concrete Structures, Eleventh Edition, McGraw Hill,
1991.
7. Galambos, T., Lin, F.J., and Johnston, B.G., Basic Steel Design with LRFD, Prentice Hall,
1996.
8. y Salmon C. and Johnson, J. Steel Structures, Third Edition, Harper Collins Publisher, 1990.
9. y Gaylord, E.H., Gaylord, C.N. and Stallmeyer, J.E., Design of Steel Structures, Third Edi-
tion, McGraw Hill, 1992.
10. Vitruvius, The Ten Books on Architecture, Dover Publications, 1960.
11. Palladio, A., The Four Books of Architecture, Dover Publication.
Codes
1. ACI-318-89, Building Code Requirements for Reinforced Concrete, American Concrete Insti-
tute
2. Load Resistance Factor Design, Manual of Steel Construction, American Institute of Steel
Construction.
3. Uniform Building Code, International Conference of Building Ocials, 5360 South Workman
Road; Whittier, CA 90601
4. Minimum Design Loads in Buildings and Other Structures, ANSI A58.1, American National
Standards Institute, Inc., New York, 1972.
Victor Saouma Structural Concepts and Systems for Architects
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Chapter 2
LOADS
2.1 Introduction
1 The main purpose of a structure is to transfer load from one point to another: bridge deck to pier;
slab to beam; beam to girder; girder to column; column to foundation; foundation to soil.
2 There can also be secondary loads such as thermal (in restrained structures), dierential settlement
of foundations, P-Delta eects (additional moment caused by the product of the vertical force and the
lateral displacement caused by lateral load in a high rise building).
3 Loads are generally subdivided into two categories
Vertical Loads or gravity load
1. dead load (DL)
2. live load (LL)
also included are snow loads.
Lateral Loads which act horizontally on the structure
1. Wind load (WL)
2. Earthquake load (EL)
this also includes hydrostatic and earth loads.
4 This distinction is helpful not only to compute a structure's load, but also to assign dierent factor of
safety to each one.
5 For a detailed coverage of loads, refer to the Universal Building Code (UBC), (UBC 1995).
2.2 Vertical Loads
6 For closely spaced identical loads (such as joist loads), it is customary to treat them as a uniformly
distributed load rather than as discrete loads, Fig. 2.1
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2{2 LOADS
P P P P P P P
1 2 3 4 5 6 7
TYPICAL SYSTEM OF JOISTS
SUPPORT BEAM
REPETITIVE JOIST LOADS
ACTUAL DISCRETE LOADS ON SUPPORT BEAM
ASSUMED EQUIVALENT UNIFORM LOAD
w LB/FT = TOTAL LOAD / SPAN
SPAN
Figure 2.1: Approximation of a Series of Closely Spaced Loads
2.2.1 Dead Load
7 Dead loads (DL) consist of the weight of the structure itself, and other permanent
48. xtures (such as
walls, slabs, machinery).
8 For analysis purposes, dead loads can easily be determined from the structure's dimensions and density,
Table 2.1
Material lb=ft3 kN=m3
Aluminum 173 27.2
Brick 120 18.9
Concrete 145 33.8
Steel 490 77.0
Wood (pine) 40 6.3
Table 2.1: Unit Weight of Materials
9 For steel structures, the weight per unit length of rolled sections is given in the AISC Manual of Steel
Construction.
10 For design purposes, dead loads must be estimated and veri
49. ed at the end of the design cycle. This
makes the design process iterative.
11 Weights for building materials is given in Table 2.2
12 For preliminary design purposes the average dead loads of Table 2.3 can be used:
2.2.2 Live Loads
13 Contrarily to dead loads which are
50. xed and vertical, live loads (LL) are movable or moving and may
be horizontal.
14 Occupancy load may be due to people, furniture, equipment. The loads are essentially variable point
loads which can be placed anywhere.
Victor Saouma Structural Concepts and Systems for Architects
52. ber tile 1
Floors
Steel deck 2-10
Concrete-plain 1 in. 12
Linoleum 1/4 in. 1
Hardwood 4
Roofs
Copper or tin 1-5
5 ply felt and gravel 6
Shingles asphalt 3
Clay tiles 9-14
Sheathing wood 3
Insulation 1 in. poured in place 2
Partitions
Clay tile 3 in. 17
Clay tile 10 in. 40
Gypsum Block 5 in. 14
Wood studs 2x4 (12-16 in. o.c.) 2
Plaster 1 in. cement 10
Plaster 1 in. gypsum 5
Walls
Bricks 4 in. 40
Bricks 12 in. 120
Hollow concrete block (heavy aggregate)
4 in. 30
8 in. 55
12 in. 80
Hollow concrete block (light aggregate)
4 in. 21
8 in. 38
12 in. 55
Table 2.2: Weights of Building Materials
Material lb=ft2
Timber 40-50
Steel 50-80
Reinforced concrete 100-150
Table 2.3: Average Gross Dead Load in Buildings
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2{4 LOADS
15 In analysis load placement should be such that their eect (shear/moment) are maximized.
16 A statistical approach is used to determine a uniformly distributed static load which is equivalent to
the weight of the maximum concentration of occupants. These loads are de
54. ned in codes such as the
Uniform Building Code or the ANSI Code, Table 2.4.
Use or Occupancy lb=ft2
Assembly areas 50
Cornices, marquees, residential balconies 60
Corridors, stairs 100
Garage 50
Oce buildings 50
Residential 40
Storage 125-250
Table 2.4: Minimum Uniformly Distributed Live Loads, (UBC 1995)
17 For small areas (30 to 50 sq ft) the eect of concentrated load should be considered separately.
18 Since there is a small probability that the whole
oor in a building be fully loaded, the UBC code
speci
55. es that the occupancy load for members supporting an area A larger than 150 ft2 (i.e. a column
with a total tributary area, including
oors above it, larger than 150 ft2) may be reduced by R where
R = r(A ;150) 23:1
1 + DL
LL
(2.1)
where r = :08 for
oors, A is the supported area ( ft
2) DL and LL are the dead and live loads per unit
area supported by the member. R can not exceed 40% for horizontal members and 60% for vertical ones.
Example 2-1: Live Load Reduction
In a 10 story oce building with a column spacing of 16 ft in both directions, the total dead load
is 60 psf, snow load 20 psf and live load 80 psf. what is the total live load and total load for which a
column must be designed on the ground
oor
Solution:
1. The tributary area is 1616 = 256ft2 150
p
2. The reduction R for the roof is is R = :08(1616;150) = 8:48%
3. Maximum allowable reduction Rmax = 23:1
;
1 + 60
80
= 40:4% which is less than 60%
p
4. The reduced cumulative load for the column of each
oor is
Floor Roof 10 9 8 7 6 5 4 3 2
A 256 512 768 1024 1280 1536 1792 2048 2304 2560
A;150 106 362 618 874 1130 1386 1642 1898 2154 2410
R0 8.48 28.96 49.44 69.92 90.40 110.88 131.36 151.84 172.32 192.8
R % 8.48 28.96 40.4 40.4 40.4 40.4 40.4 40.4 40.4 40.4
LL 20 80 80 80 80 80 80 80 80 80
(100 ;R) LL=100 18.3 56.83 47.68 47.68 47.68 47.68 47.68 47.68 47.68 47.68
Victor Saouma Structural Concepts and Systems for Architects
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2.3 Lateral Loads 2{5
The resulting design live load for the bottom column has been reduced from
LLBefore = (20) psf(256) ft
2
| {z }
Roof
+(9)(80) psf(256) ft
2
| {z }
9
oors
= 189,440 lbs (2.2)
to
LLReduced = (18:3) psf(256) ft
2
| {z }
Roof
+(9)(47:68) psf(256) ft
2
| {z }
9
oors
= 114,540 lbs (2.3)
5. The total dead load is DL = (10)(60) psf(256) ft
2 k
(1;000) lbs
= 153:6 Kips, thus the total reduction
in load is from 153:6+189:4 = 343 k to 153:6+114:5 = 268:1 k a reduction of 343;268
343 100= 22% .
2.2.3 Snow
19 Roof snow load vary greatly depending on geographic location and elevation. They range from
20 to 45 psf, Fig. 2.2.
Figure 2.2: Snow Map of the United States, ubc
20 Snow loads are always given on the projected length or area on a slope, Fig. 2.3.
21 The steeper the roof, the lower the snow retention. For snow loads greater than 20 psf and roof pitches
more than 20 the snow load p may be reduced by
R = ( ;20)
p
40 ;0:5
(psf) (2.4)
2.3 Lateral Loads
2.3.1 Wind
22 Wind load depend on: velocity of the wind, shape of the building, height, geographical
location, texture of the building surface and stiness of the structure.
Victor Saouma Structural Concepts and Systems for Architects
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2{6 LOADS
LIVE LOAD
DEAD LOAD
L
E
N
G
T
H
RISE
RUN
WIND
LOAD
Figure 2.3: Loads on Projected Dimensions
23 Wind loads are particularly signi
58. cant on tall buildings1.
24 When a steady streamline air
ow of velocity V is completely stopped by a rigid body, the stagnation
pressure (or velocity pressure) qs was derived by Bernouilli (1700-1782)
qs = 1
2V 2 (2.5)
where the air mass density is the air weight divided by the accleration of gravity g = 32:2 ft/sec2. At
sea level and a temperature of 15oC (59oF), the ai weighs 0.0765 lb/ft3 this would yield a pressure of
qs = 1
2
(0:0765)lb/ft3
(32:2)ft/sec2
(5280)ft/mile
(3600)sec/hr V
2
(2.6)
or
qs = 0:00256V2 (2.7)
where V is the maximum wind velocity (in miles per hour) and qs is in psf. V can be obtained from
wind maps (in the United States 70 V 110), Fig. 2.4.
25 During storms, wind velocities may reach values up to or greater than 150 miles per hour, which
corresponds to a dynamic pressure qs of about 60 psf (as high as the average vertical occupancy load in
buildings).
1
The primary design consideration for very high rise buildings is the excessive drift caused by lateral load (wind and
possibly earthquakes).
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2.3 Lateral Loads 2{7
Figure 2.4: Wind Map of the United States, (UBC 1995)
26 Wind pressure increases with height, Table 2.5.
Height Zone Wind-Velocity Map Area
(in feet) 20 25 30 35 40 45 50
30 15 20 25 25 30 35 40
30 to 49 20 25 30 35 40 45 50
50 to 99 25 30 40 45 50 55 60
100 to 499 30 40 45 55 60 70 75
500 to 1199 35 45 55 60 70 80 90
1,200 40 50 60 70 80 90 100
Table 2.5: Wind Velocity Variation above Ground
27 Wind load will cause suction on the leeward sides, Fig. 2.6
28 This magnitude must be modi
60. ed to account for the shape and surroundings of the building. Thus,
the design base pressure (at 33.3 ft from the ground) p (psf) is given by
p = CeCqIqs (2.8)
The pressure is assumed to be normal to all walls and roofs and
Ce Velocity Pressure Coecient accounts for height, exposure and gust factor. It accounts for the
fact that wind velocity increases with height and that dynamic character of the air
ow (i.e the
wind pressure is not steady), Table 2.6. l
Cq Pressure Coecient is a shape factor which is given in Table 2.7 for gabled frames.
I Importance Factor as given by Table 2.8. where
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2{8 LOADS
Figure 2.5: Eect of Wind Load on Structures(Schueller 1996)
Ce Exposure
1.39-2.34 D Open,
at terrain facing large bodies of water
1.06-2.19 C Flat open terrain, extending one-half mile or open from the site in
any full quadrant
0.62-1.80 B Terrain with buildings, forest, or surface irregularities 20 ft or more
in height
Table 2.6: Ce Coecients for Wind Load, (UBC 1995)
Windward Side Leeward Side
Gabled Frames (V:H)
Roof Slope 9:12 ;0:7 ;0:7
9:12 to 12:12 0:4 ;0:7
12:12 0:7 ;0:7
Walls 0:8 ;0:5
Buildings (height 200 ft)
Vertical Projections height 40 ft 1:3 ;1:3
height 40 ft 1:4 ;1:4
Horizontal Projections ;0:7 ;0:7
Table 2.7: Wind Pressure Coecients Cq, (UBC 1995)
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2.3 Lateral Loads 2{9
Imprtance Factor I
Occupancy Category Earthquake Wind
I Essential facilities 1.25 1.15
II Hazardous facilities 1.25 1.15
III Special occupancy structures 1.00 1.00
IV Standard occupancy structures 1.00 1.00
Table 2.8: Importance Factors for Wind and Earthquake Load, (UBC 1995)
I Essential Facilities: Hospitals; Fire and police stations; Tanks; Emergency vehicle shelters,
standby power-generating equipment; Structures and equipment in government. communica-
tion centers.
II Hazardous Facilities: Structures housing, supporting or containing sucient quantities of
toxic or explosive substances to be dangerous to the safety of the general public if released.
III Special occupancy structure: Covered structures whose primary occupancy is public as-
sembly, capacity 300 persons.
Buildings for schools through secondary or day-care centers, capacity 250 persons.
Buildings for colleges or adult education schools, capacity 500 persons.
Medical facilities with 50 or more resident incapacitated patients, but not included above
Jails and detention facilities
All structures with occupancy 5,000 persons.
Structures and equipment in power generating stations and other public utilitiy facilities not
included above, and required for continued operation.
IV Standard occupancy structure: All structures having occupancies or functions not listed
above.
29 For the preliminary design of ordinary buildings Ce = 1:0 and Cq = 1:3 may be assumed, yielding
p = (1:3):020256V2 = :00333V2 (2.9)
which corresponds to a pressure of 21 psf for a wind speed of 80 mph, Fig. 2.6, Table 2.9.
Example 2-2: Wind Load
Determine the wind forces on the building shown on below which is built in St Louis and is surrouded
by trees.
Solution:
1. From Fig. 2.4 the maximum wind velocity is St. Louis is 70 mph, since the building is protected
we can take Ce = 0:7, I = 1:. The base wind pressure is qs = 0:00256(70)2 = 12:54 psf.
Victor Saouma Structural Concepts and Systems for Architects
64. Draft
2.3 Lateral Loads 2{11
2. The slope of the roof is 8:15=6.4:12 which gives Cq = ;0:7 for both the windward and leeward
sides. The vertical walls have Cq = 0:8 for the winward side and Cq = ;0:5 for the leeward one.
3. Thus the applied pressure on the roof is p = 0:7 (;0:7) 12:54 = -6.14 psf that is the roof is
subjected to uplift.
4. The winward wall, the pressure is 0:7 0:8 12:54 = 7.02 psf , and for the leeward wall 0:7
(;0:5)12:54 = -4.39 psf (suction) ,
5. The direction of the wind can change and hence each structural component must be designed to
resist all possible load combinations.
6. For large structures which may be subjected to large wind loads, testing in a wind tunnel of the
structure itself and its surroundings is often accomplished.
2.3.2 Earthquakes
30 Buildings should be able to resist
Minor earthquakes without damage
Moderate earthquakes without structural damage but possibly with some nonstructural damages
Major earthquakes without collapse but possibly with some structural damage as well as nonstruc-
tural damage
This is achieved through an appropriate dynamic analysis.
31 For preliminary designs or for small structures an equivalent horizontal static load can be deter-
mined.
32 Actual loads depend on the following
1. Intensity of the ground acceleration (including soil/rock properties).
2. Dynamic properties of the building, such as its mode shapes and periods of vibration and its
damping characteristics.
3. Mass of the building.
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2{12 LOADS
33 A critical factor in the dynamic response of a structure is the fundamental period of the structure's
vibration (or
66. rst mode of vibration). This is the time required for one full cycle of motion, Fig. 2.7. If
the earthquake excitation has a frequency close to the one of the building, then resonance may occur.
This should be avoided.
Figure 2.7: Vibrations of a Building
34 Earthquake load manifests itself as a horizontal force due to the (primarily) horizontal inertia force
(F = ma).
35 The horizontal force at each level is calculated as a portion of the base shear force V
V = ZIC
RW
W (2.10)
where:
Z: Zone Factor: to be determined from Fig. 2.8 and Table 2.10.
Seismic Zone 0 1 2A 2B 3 4
Z 0 0.075 0.15 0.2 0.3 0.4
Table 2.10: Z Factors for Dierent Seismic Zones, ubc
I: Importance Factor: which was given by Table 2.8.
C: Design Response Spectrum given by
C = 1:25S
T2=3 2:75 (2.11)
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2.3 Lateral Loads 2{13
Figure 2.8: Seismic Zones of the United States, (UBC 1995)
T is the fundamental period of vibration of the building in seconds. This can be determined from
either the free vibration analysis of the building, or estimated from the following empirical formula
T = Ct(hn)3=4 (2.12)
where:
hn is the building height above base in ft.
and
Ct 0.035 steel moment resisting frames
Ct 0.030 reinforced concrete moment resisting frames and eccentrically braced frames
Ct 0.020 all other buildings
S: Site Coecient given by Table 2.11 Note that most of the damages in the 1990? earthquake
Type Description S Factor
S1 A soil pro
68. le with either rock-like material or sti/dense soil less
than 200 ft.
1.0
S2 Dense or sti soil exceeding 200 ft 1.2
S3 70 ft or more soil containing more than 20 ft of soft to medium sti
clay but not more than 40 ft. of soft clay.
1.5
S4 Soil containing more than 40 ft of soft clay 2.0
Table 2.11: S Site Coecients for Earthquake Loading, (UBC 1995)
in San Francisco occurred in the marina where many houses were built on soft soil.
and
C
RW
0:075 (2.13)
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2{14 LOADS
RW is given by Table 2.12.
W Load total structure load.
36 The horizontal force V is distributed over the height of the building in two parts. The
70. rst (applied
only if T 0:7 sec.) is a concentrated force F1 equal to
Ft = 0:07TV 0:25V (2.14)
is applied at the top of the building due to whiplash. The balance of the force V ;Ft is distributed as
a triangular load diminishing to zero at the base.
37 Assuming a
oor weight constant for every
oor level, then the force acting on each one is given by
Fx = (V ;Ft)hx
h1 + h2 + + hn
= (V ;Ft)hx
n
i=1hi
(2.15)
where hi and hx are the height in ft above the base to level i, or x respectively. Note that it is assumed
that all
oors have also same width.
Example 2-3: Earthquake Load on a Frame
Determine the approximate earthquake forces for the ductile hospital frame structure shown below.
The DL for each
oor is 200 lb/ft and the LL is 400 lb/ft. The structure is built on soft soil. Use DL
plus 50%LL as the weight of each
oor. The building is in zone 3.
Solution:
1. The fundamental period of vibration is
T = Ct(hn)3=4 = (0:030)(24)3=4 = 0:32 sec. (2.16)
2. The C coecient is
C = 1:25S
T2=3 = (1:25)(2:0)
(0:32)2=3 = 5:344 2:75 (2.17)
use C = 2:75.
3. The other coecients are: Z =0.3; I=1.25; RW=12
Victor Saouma Structural Concepts and Systems for Architects
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2.3 Lateral Loads 2{15
Structural System RW H (ft)
Bearing wall system
Light-framed walls with shear panels
Plywood walls for structures three stories or less 8 65
All other light-framed walls 6 65
Shear walls
Concrete 8 240
Masonry 8 160
Building frame system using trussing or shear walls)
Steel eccentrically braced ductile frame 10 240
Light-framed walls with shear panels
Plywood walls for structures three stories or less 9 65
All other light-framed walls 7 65
Shear walls
Concrete 8 240
Masonry 8 160
Concentrically braced frames
Steel 8 160
Concrete (only for zones I and 2) 8 -
Heavy timber 8 65
Moment-resisting frame system
Special moment-resisting frames (SMRF)
Steel 12 N.L.
Concrete 12 N.L.
Concrete intermediate moment-resisting frames (IMRF)only for zones 1 and 2 8 -
Ordinary moment-resisting frames (OMRF)
Steel 6 160
Concrete (only for zone 1) 5 -
Dual systems (selected cases are for ductile rigid frames only)
Shear walls
Concrete with SMRF 12 N.L.
Masonry with SMRF 8 160
Steel eccentrically braced ductile frame 6-12 160-N.L.
Concentrically braced frame 12 N. L.
Steel with steel SMRF 10 N.L.
Steel with steel OMRF 6 160
Concrete with concrete SMRF (only for zones 1 and 2) 9 -
Table 2.12: Partial List of RW for Various Structure Systems, (UBC 1995)
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2{16 LOADS
4. Check
C
RW
= 2:75
12 = 0:23 0:075
p (2.18)
5. The total vertical load is
W = 2((200 + 0:5(400))(20) = 16000 lbs (2.19)
6. The total seismic base shear is
V = ZIC
RW
= (0:3)(1:25)(2:75)
12 = 0:086W (2.20-a)
= (0:086)(16000) = 1375 lbs (2.20-b)
7. Since T 0:7 sec. there is no whiplash.
8. The load on each
oor is thus given by
F2 = (1375)(24)
12+ 24 = 916.7 lbs (2.21-a)
F1 = (1375)(12)
12+ 24 = 458.3 lbs (2.21-b)
Example 2-4: Earthquake Load on a Tall Building, (Schueller 1996)
Determine the approximate critical lateral loading for a 25 storey, ductile, rigid space frame concrete
structure in the short direction. The rigid frames are spaced 25 ft apart in the cross section and 20
ft in the longitudinal direction. The plan dimension of the building is 175x100 ft, and the structure is
25(12)=300 ft high. This oce building is located in an urban environment with a wind velocity of 70
mph and in seismic zone 4. For this investigation, an average building total dead load of 192 psf is used.
Soil conditions are unknown.
Victor Saouma Structural Concepts and Systems for Architects
73. Draft
2.3 Lateral Loads 2{17
470 k
2638 k
1523 k
2(300)/3=200’
300/2=150’
25(12)=300’
84000 k
3108 k
5(20)=100’
7(25)=175’
Solution:
1. The total building weight is
W = (0:1926) ksf(100175) ft
2 25 storeys = 84;000 k (2.22)
2. the fundamental period of vibration for a rigid frame is
T = Ct(hn)3=4 = 0:030(300)3=4 = 2:16 sec. 0:7 sec.
p (2.23)
3. The C coecient is
C = 1:25S
T2=3 = (1:25)(1:5)
(2:16)2=3 = 1:12 2:75
p (2.24)
4. The other coecients are Z=0.4; I=1, RW=12
5. We check
C
RW
= 1:12
12 = 0:093 0:075
p (2.25)
6. The total seismic base shear along the critical short direction is
V = ZIC
RW
W = (0:4)(1)(1:12)
(12) W = 0:037W (2.26-a)
= (0:037)(84000) = 3108 kip (2.26-b)
7. Since T 0:7 sec., the whiplash eect must be considered
Ft = 0:07TV = (0:07)(2:16)(3108) = 470 k (2.27-a)
le 0:25V = (0:25)(3108) = 777 k (2.27-b)
Victor Saouma Structural Concepts and Systems for Architects
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2{18 LOADS
Hence the total triangular load is
V ;Ft = 3108;470 = 2638 k (2.28)
8. let us check if wind load governs. From Table xx we conservatively assume a uniform wind pressure
of 29 psf resulting in a total lateral force of
PW = (0:029) psf(175300) ft
2 = 1523 k 3108 k (2.29)
The magnitude of the total seismic load is clearly larger than the total wind force.
2.4 Other Loads
2.4.1 Hydrostatic and Earth
38 Structures below ground must resist lateral earth pressure.
q = K
h (2.30)
where
is the soil density, K = 1;sin
1+sin is the pressure coecient, h is the height.
39 For sand and gravel
= 120 lb= ft3, and 30.
40 If the structure is partially submerged, it must also resist hydrostatic pressure of water, Fig. 2.9.
Figure 2.9: Earth and Hydrostatic Loads on Structures
q =
Wh (2.31)
where
W = 62:4 lbs=ft
3.
Example 2-5: Hydrostatic Load
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75. Draft
2.4 Other Loads 2{19
The basement of a building is 12 ft below grade. Ground water is located 9 ft below grade, what
thickness concrete slab is required to exactly balance the hydrostatic uplift?
Solution:
The hydrostatic pressure must be countered by the pressure caused by the weight of concrete. Since p =
hwe equate the two pressures and solve for h the height of the concrete slab (62:4) lbs=ft
3 (12 ;9) ft
| {z }
water
=
(150) lbs=ft
3 h
| {z }
concrete
) h = (62:4) lbs=ft
3
(150) lbs=ft
3 (3) ft(12) in/ft = 14:976 in ' 15.0 inch
2.4.2 Thermal
41 If a member is uniformly heated (or cooled) without restraint, then it will expand (or contract).
This expansion is given by
l = lT (2.32)
where is the coecient of thermal expansion, Table 2.13
(/F)
Steel 6:510;6
Concrete 5:510;6
Table 2.13: Coecients of Thermal Expansion
42 If the member is restrained against expansion, then a compressive stress = ET is developed.
43 To avoid excessive stresses due to thermal loading expansion jointsare used in bridges and buildings.
Example 2-6: Thermal Expansion/Stress (Schueller 1996)
A low-rise building is enclosed along one side by a 100 ft-long clay masonary ( = 3:6 10;6
in./in./oF, E = 2;400;000 psi) bearing wall. The structure was built at a temperature of 60oF and
is located in the northern part of the United States where the temperature range is between -20o and
+120oF.
Solution:
1. Assuming that the wall can move freely with no restraint from cross-walls and foundation, the wall
expansion and contraction (summer and winter) are given by
LSummer = TL = (3:6 10;6) in= in=oF(120;60)oF(100) ft(12) in/ft = 0.26 in
(2.33-a)
LWinter = TL = (3:6 10;6) in= in=oF(;20 ;60)oF(100) ft(12) in/ft = -0.35 in
(2.33-b)
Victor Saouma Structural Concepts and Systems for Architects
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2{20 LOADS
2. We now assume (conservatively) that the free movement cannot occur (L = 0) hence the resulting
stress would be equal to = E = EL
L = ETL
L = ET
Summer = ET = (2;400;000)lbs
in
2 (3:610;6) in= in=oF(120;60)oF = 518 lbs
in
2 Tension
(2.34-a)
Winter = ET = (2;400;000)lbs
in
2 (3:610;6) in= in=oF(;20;60)oF = -691 lbs
in
2 Compression
(2.34-b)
(2.34-c)
Note that the tensile stresses being beyond the masonary capacity, cracking will occur.
2.5 Other Important Considerations
2.5.1 Load Combinations
44 Live loads speci
77. ed by codes represent the maximum possible loads.
45 The likelihood of all these loads occurring simultaneously is remote. Hence, building codes allow
certain reduction when certain loads are combined together.
46 Furthermore, structures should be designed to resist a combination of loads.
47 Denoting D= dead; L= live; Lr= roof live; W= wind; E= earthquake; S= snow; T= temperature;
H= soil:
48 For the load and resistance factor design (LRFD) method of concrete structures, the American Con-
crete Institute (ACI) Building design code (318) (318 n.d.) requires that the following load combinations
be considered:
1. 1.4D+1.7L
2. 0.75(1.4D+1.7L+1.7W)
3. 0.9D+1.3W
4. 1.4D +1.7L+1.7H
5. 0.75(1.4D+1.4T+1.7L)
6. 1.4(D+T)
whereas for steel structures, the American Institute of Steel Construction (AISC) code, (of Steel COn-
struction 1986) requires that the following combinations be veri
78. ed
1. 1.4D
2. 1.2D+1.6L+0.5(Lr or S)
3. 1.2D+0.5L (or 0.8W)+1.6(Lr or S)
4. 1.2D+0.5L+0.5(Lr or S)+1.3W
5. 1.2D+0.5L(or 0.2 S)+1.5E
Victor Saouma Structural Concepts and Systems for Architects
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2.5 Other Important Considerations 2{21
6. 0.9D+1.3W(or 1.5 E)
49 Analysis can be separately performed for each of the basic loads (L, D, W, etc) and then using the
principle of superposition the loads can be linearly combined (unless the elastic limit has been reached).
50 Loads are often characterized as Usual, Unusual and Extreme.
2.5.2 Load Placement
51 Only the dead load is static. The live load on the other hand may or may not be applied on a given
component of a structure. Hence, the load placement arrangement resulting in the highest internal forces
(moment +ve or -ve, shear) at dierent locations must be considered, Fig. 2.10.
Figure 2.10: Load Placement to Maximize Moments
2.5.3 Load Transfer
52 Whereas we will be focusing on the design of a reinforced concrete or steel section, we must keep in
mind the following:
1. The section is part of a beam or girder.
2. The beam or girder is really part of a three dimensional structure in which load is transmitted
from any point in the structure to the foundation through any one of various structural forms.
53 Load transfer in a structure is accomplished through a hierarchy of simple
exural elements which
are then connected to the columns, Fig. 2.11 or by two way slabs as illustrated in Fig. 2.12.
2.5.4 Structural Response
54 Under the action of the various forces and loadings described above, the structure must be able to
respond with proper behavior, Fig. 9.1.
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2{22 LOADS
Figure 2.11: Load Transfer in R/C Buildings
Victor Saouma Structural Concepts and Systems for Architects
81. Draft
2.5 Other Important Considerations 2{23
Figure 2.12: Two Way Actions
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2{24 LOADS
Figure 2.13: Load Life of a Structure, (Lin and Stotesbury 1981)
Victor Saouma Structural Concepts and Systems for Architects
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Chapter 3
STRUCTURAL MATERIALS
1 Proper understanding of structural materials is essential to both structural analysis and to structural
design.
2 Characteristics of the most commonly used structural materials will be highlighted.
3.1 Steel
3.1.1 Structural Steel
3 Steel is an alloy of iron and carbon. Its properties can be greatly varied by altering the carbon content
(always less than 0.5%) or by adding other elements such as silicon, nickle, manganese and copper.
4 Practically all grades of steel have a Young Modulus equal to 29,000 ksi, density of 490 lb/cu ft, and
a coecient of thermal expansion equal to 0:6510;5 /deg F.
5 The yield stress of steel can vary from 40 ksi to 250 ksi. Most commonly used structural steel are A36
(yld = 36 ksi) and A572 (yld = 50 ksi), Fig. 3.1
6 Structural steel can be rolled into a wide variety of shapes and sizes. Usually the most desirable
members are those which have a large section moduli (S) in proportion to their area (A), Fig. 3.2.
7 Steel can be bolted, riveted or welded.
8 Sections are designated by the shape of their cross section, their depth and their weight. For example
W 27 114 is a W section, 27 in. deep weighing 114 lb/ft.
9 Common sections are:
S sections were the
86. rst ones rolled in America and have a slope on their inside
ange surfaces of 1 to
6.
W or wide
ange sections have a much smaller inner slope which facilitates connections and rivetting.
W sections constitute about 50% of the tonnage of rolled structural steel.
C are channel sections
MC Miscellaneous channel which can not be classi
87. ed as a C shape by dimensions.
HP is a bearing pile section.
88. Draft
3{2 STRUCTURAL MATERIALS
Figure 3.1: Stress Strain Curves of Concrete and Steel
Figure 3.2: Standard Rolled Sections
Victor Saouma Structural Concepts and Systems for Architects
89. Draft
3.1 Steel 3{3
M is a miscellaneous section.
L are angle sections which may have equal or unequal sides.
WT is a T section cut from a W section in two.
10 The section modulus Sx of a W section can be roughly approximated by the following formula
Sx wd=10 or Ix Sx
d
2 wd2=20 (3.1)
and the plastic modulus can be approximated by
Zx wd=9 (3.2)
11 Properties of structural steel are tabulated in Table 3.1.
ASTM
Desig.
Shapes Available Use y (kksi) u (kksi)
A36 Shapes and bars Riveted, bolted, welded;
Buildings and bridges
36 up through 8 in. (32 above
8.)
A500 Cold formed welded and
seamless sections;
General structural pur-
pose Riveted, welded or
bolted;
Grade A: 33; Grade B: 42;
Grade C: 46
A501 Hot formed welded and seam-
less sections;
Bolted and welded 36
A529 Plates and bars 1
2
in and less
thick;
Building frames and
trusses; Bolted and
welded
42
A606 Hot and cold rolled sheets; Atmospheric corrosion
resistant
45-50
A611 Cold rolled sheet in cut
lengths
Cold formed sections Grade C 33; Grade D 40;
Grade E 80
A 709 Structural shapes, plates and
bars
Bridges Grade 36: 36 (to 4 in.); Grade
50: 50; Grade 100: 100 (to
2.5in.) and 90 (over 2.5 to 4
in.)
Table 3.1: Properties of Major Structural Steels
12 Rolled sections, Fig. 3.3 and welded ones, Fig3.4 have residual stresses. Those originate during the
rolling or fabrication of a member. The member is hot just after rolling or welding, it cools unevenly
because of varying exposure. The area that cool
90. rst become stier, resist contraction, and develop
compressive stresses. The remaining regions continue to cool and contract in the plastic condition and
develop tensile stresses.
13 Due to those residual stresses, the stress-strain curve of a rolled section exhibits a non-linear segment
prior to the theoretical yielding, Fig. 3.5. This would have important implications on the
exural and
axial strength of beams and columns.
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91. Draft
3{4 STRUCTURAL MATERIALS
Compression (-)
Tension (+)
(+)
(-)
Maximum compressive
stress, say 12 ksi average
Figure 3.3: Residual Stresses in Rolled Sections
-
+ +
+
_
+
+
-
-
say 12 ksi
20 ksi
Welded H
say 35 ksi
tension
say 20 ksi
say 40 ksi
Welded box
say 20 ksi
compression
Figure 3.4: Residual Stresses in Welded Sections
Victor Saouma Structural Concepts and Systems for Architects
92. Draft
3.1 Steel 3{5
.
.
.
Maximum
residual
compressive
stress
no residual stress
Ideal coupon containing
Members with
residual stress
F
F
y
p
2
1
3
1
2 3
Average copressive strain
Average
stress
P/A
Shaded portion indicates area
which has achieved a stress F
y
Figure 3.5: In
uence of Residual Stress on Average Stress-Strain Curve of a Rolled Section
3.1.2 Reinforcing Steel
14 Steel is also used as reinforcing bars in concrete, Table 3.2. Those bars have a deformation on their
surface to increase the bond with concrete, and usually have a yield stress of 60 ksi1.
Bar Designation Diameter Area Perimeter Weight
(in.) ( in
2) in lb/ft
No. 2 2/8=0.250 0.05 0.79 0.167
No. 3 3/8=0.375 0.11 1.18 0.376
No. 4 4/8=0.500 0.20 1.57 0.668
No. 5 5/8=0.625 0.31 1.96 1.043
No. 6 6/8=0.750 0.44 2.36 1.5202
No. 7 7/8=0.875 0.60 2.75 2.044
No. 8 8/8=1.000 0.79 3.14 2.670
No. 9 9/8=1.128 1.00 3.54 3.400
No. 10 10/8=1.270 1.27 3.99 4.303
No. 11 11/8=1.410 1.56 4.43 5.313
No. 14 14/8=1.693 2.25 5.32 7.650
No. 18 18/8=2.257 4.00 7.09 13.60
Table 3.2: Properties of Reinforcing Bars
15 Steel loses its strength rapidly above 700 deg. F (and thus must be properly protected from
93. re), and
becomes brittle at ;30 deg. F
16 Steel is also used as wire strands and ropes for suspended roofs, cable-stayed bridges, fabric roofs and
other structural applications. A strand is a helical arrangement of wires around a central wire. A rope
consists of multiple strands helically wound around a central plastic core, and a modulus of elasticity of
20,000 ksi, and an ultimate strength of 220 ksi.
17 Prestressing Steel cables have an ultimate strength up to 270 ksi.
1
Stirrups which are used as vertical reinforcement to resist shear usually have a yield stress of only 40 ksi.
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3{6 STRUCTURAL MATERIALS
3.2 Aluminum
18 Aluminum is used whenever light weight combined with strength is an important factor. Those
properties, along with its resistance to corrosion have made it the material of choice for airplane
structures, light roof framing.
19 Aluminum members can be connected by riveting, bolting and to a lesser extent by welding.
20 Aluminum has a modulus of elasticity equal to 10,000 ksi (about three times lower than steel),
a coecient of thermal expansion of 2:410;5 and a density of 173 lbs=ft
3.
21 The ultimate strength of pure aluminum is low (13,000 psi) but with the addition of alloys it can go
up.
22 When aluminum is in contact with other metals in the presence of an electrolyte, galvanic corrosion
may cause damage. Thus, steel and aluminum in a structure must be carefully separated by means of
painting or a nonconductive material.
3.3 Concrete
23 Concrete is a mixture of Portland cement2, water, and aggregates (usually sand and crushed stone).
An ideal mixture is one in which:
1. A minimum amount of cement-water paste is used to
95. ll the interstices between the particles of
aggregates.
2. A minimum amount of water is provided to complete the chemical reaction with cement.
In such a mixture, about 3/4 of the volume is constituted by the aggregates, and the remaining 1/4
being the cement paste.
24 Smaller particles up to 1/4 in. in size are called
96. ne aggregates, and the larger ones being coarse
aggregates.
25 Contrarily to steel to modulus of elasticity of concrete depends on the strength and is given by
E = 57;000
p
f0
c (3.3)
or
E = 33
1:5p
f0
c (3.4)
where both f0
c and E are in psi and
is in lbs=ft
3.
26 Typical concrete (compressive) strengths range from 3,000 to 6,000 psi; However high strength
concrete can go up to 14,000 psi.
27 All concrete fail at an ultimate strain of 0.003, Fig. 3.1.
28 Pre-peak nonlinearity is caused by micro-cracking Fig. 3.6.
29 The tensile strength of concrete f0
t is about 10% of the compressive strength.
30 Density of normal weight concrete is 145 lbs=ft
3 and 100 lbs=ft
3 for lightweight concrete.
2
Portland cement is a mixture of calcareous and argillaceous materials which are calcined in a kiln and then pulverized.
When mixed with water, cement hardens through a process called hydration.
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3.4 Masonry 3{7
ε
u
f’
c
.5f’
c
linear
non-linear
Figure 3.6: Concrete microcracking
31 Coecient of thermal expansion is 0:6510;5 /deg F for normal weight concrete.
32 When concrete is poured (or rather placed), the free water not needed for the hydration process
evaporates over a period of time and the concrete will shrink. This shrinkage is about 0.05% after one
year (strain). Thus if the concrete is restrained, then cracking will occur3.
33 Concrete will also deform with time due to the applied load, this is called creep. This should be taken
into consideration when computing the de
ections (which can be up to three times the instantaneous
elastic de
ection).
3.4 Masonry
34 Masonry consists of either natural materials, such as stones, or of manufactured products such as
bricks and concrete blocks4, stacked and bonded together with mortar.
35 As for concrete, all modern structural masonry blocks are essentially compression members with low
tensile resistance.
36 The mortar used is a mixture of sand, masonry cement, and either Portland cement or hydrated lime.
3.5 Timber
37 Timber is one of the earliest construction materials, and one of the few natural materials with good
tensile properties.
38 The properties of timber vary greatly, and the strength is time dependent.
39 Timber is a good shock absorber (many wood structures in Japan have resisted repeated earthquakes).
40 The most commonly used species of timber in construction are Douglas
98. r, southern pine, hemlock
and larch.
41 Members can be laminated together under good quality control, and
exural strengths as high as
2,500 psi can be achieved.
3
For this reason a minimum amount of reinforcement is always necessary in concrete, and a 2% reinforcement, can
reduce the shrinkage by 75%.
4
Mud bricks were used by the Babylonians, stones by the Egyptians, and ice blocks by the Eskimos...
Victor Saouma Structural Concepts and Systems for Architects
99. Draft
3{8 STRUCTURAL MATERIALS
3.6 Steel Section Properties
42 Dimensions and properties of rolled sections are tabulated in the following pages, Fig. 3.7.
Figure 3.7: W and C sections
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Victor Saouma Structural Concepts and Systems for Architects