of the national building
TRANSCRIPT
COMMENTARIES ON PART 4
OF THE NATIONAL BUILDING CODE OF CANADA 1977
SUPPLEMENT No.4 TO THE NATIONAL BUILDING
CODE OF CANADA
ARCHIVES Issued by the
Associate Committee on the National Building Code National Research Council of Canada
Ottawa
Price $2.50 NRCC No. 15558
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ASSOCIATE COMMITIEE ON THE NATIONAL BUILDING CODE
A. G. Wilson (Chairman) H. B. Dickens (Deputy Chairman) S. D. C. Chutter D. E. Cornish S. Cumming R. F. DeGrace M.G. Dixon J. T. Gregg W. B. Guihan R. V. Hebert J. S. Hicks M. S. Hurst (ex officio) H. T. Jones P. M. Keenleyside J. Longworth J. A. McCambly C. J. McConnell R. C. McMillan
Retired·
D. O. Monsen (ex officio) A. T. Muir** F.-X. Perreault A. R. Pitt G. B. Pope H. R. Stenson R. A. W. Switzer A. D. Thompson J. E. Turnbull C. J. Ward
D. W. Boyd (Research AdvisorMeteorology)
R. S. Ferguson (Research Advisor) R. H. Dunn (Secretary)
C. D. Carruthers (Chairman until November, 1975)
STANDING COMMITTEE ON STRUcrURAL DESIGN
J. Longworth (Chairman) N. N.Aylon R. L. Booth L. H. Bush J. F. Cutler A. G. Davenport V. C. Fenton P. J. Harris D. J. Kathol D. E. Kennedy D. J. L. Kennedy H. Krentz N. C. Lind
Retired·
G. W. Elkington O. Safir
C. Marsh W. McCarthy V. Milligan W. Paul B. G. W. Peter A. G. Stermac E. Y. Uzumeri H. P. Vokey
W. R. Schriever (Research Advisor) R. H. Dunn (Secretary)
CSA/NBC JOINT LIAISON COMMITTEE ON LIMIT STATES DESIGN
D. J. L. Kennedy (Chairman) L. H. Bush A. G. Davenport J. L. deStein V.c. Fenton P. J. Harris
N. C. Lind J. Longworth C. Marsh V. Milligan C. R. Wilson
D. E. Allen (Research Advisor and Secretary)
*Committee term completed during preparation of 1977 Code. **Deceased September 16, 1976.
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COMMENTARIES ON PART 4
OF THE NATIONAL BUILDING CODE OF CANADA 1977
SUPPLEMENT No.4 TO THE NATIONAL BUILDING
CODE OF CANADA
Issued by the
Associate Committee on the National Building Code National Research Council of Canada
Ottawa
NRCC No. 15558 Cop
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First Edition 1970 Second Edition 1975 Third Edition 1977
© National Research Council of Canada 1977 World Rights Reserved
Printed in Canada
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v
TABLE OF CONTENTS Page
Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. vii
Commentary A
Commentary B
Commentary C
Commentary D
Commentary E
Commentary F
Commentary G
Commentary H
Commentary I
Commentary J
Commentary K
Commentary L
Serviceability Criteria for Deflections and Vibrations 1
Wind Loads ............................... 7
Progressive Collapse and Structural Integrity. . . . . . . . . . . . . . . . . . . . . . .. 37
Effects of Deformations in Building Components ..... . . . . . . . . . . . . . . . .. 45
Load Combinations for Structural Design. . . . . . . .. 51
Limit States Design ......................... 55
Tributary Area . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 63
Snow Loads ............................... 69
Rain Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 85
Effects of Earthquakes ....................... 89
Dynamic Analysis for the Seismic Response of Buildings 109
Foundations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 125
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vii
PREFACE
The purpose of these commentaries is to make available to the designer detailed design information which will assist him in his use of the National Building Code. The commentaries are provided as background information and, in some cases, as suggested approaches to certain design questions, but not as mandatory requirements.
This edition contains an important new Commentary on foundations (Commentary L), which has been prepared to provide background material in support of Section 4.2 (Foundations) of the NBC.
Because the information provided in these commentaries cannot cover all conditions or types of structures that occur in practice, and also because new information may become available in the future, the designer should try to obtain the latest and most appropriate design information available. For unusual types of structures it may be necessary to resort to specialized information such as theoretical studies, model tests or wind tunnel experiments to provide adequate design values.
CSA Standard S304-1976, "Masonry Design and Construction for Buildings" now replaces the design requirements for plain and reinforced masonry, formerly included as Part I of the 1975 edition of this Supplement. This Standard is now referenced in Section 4.4 of the 1977 NBC. It was produced under the auspices of a Joint CSA/NBC Committee and is essentially an updated version of Part I.
The reference to CSA S304-1976 in Part 4 of the Code is a continuation of the policy established in 1975 by which the design Standards for Timber, Concrete, Steel and Aluminum were removed from this document and simply referenced in Part 4. This action was necessary to avoid the need for major revisions to the Supplement whenever new revisions to these Standards were released.
To assist the user of the Supplement who intends to work in metric, a pamphlet has been prepared which gives the appropriate metric values for the imperial units of measure contained herein. The pamphlet, which is distributed with each copy of the Supplement, is intended to provide a basis for working in metric terms pending completion of a fully metric document in a subsequent edition.
These commentaries were prepared with the assistance of the following: D. E. Allen D. J. L. Kennedy J. H. Rainer W. A. Dalgliesh D. A. Lutes W. R. Schriever A. G. Davenport W. G. Plewes D. A. Taylor
Commentary L (Foundations) was prepared with the assistance of a Task Group appointed by the Standing Committee on Structural Design and consisted of the following members: V. Milligan (Chairman), L. Brzezinski, D. Klajnerman, W. E. Lardner and E. Y. Uzumeri.
Comments and inquiries on aspects of these commentaries pertaining to the interpretation and use of the National Building Code should be addressed to the Secretary, Associate Committee on the National Building Code, National Research Council of Canada, Ottawa, Ontario KIA OR6. Requests for technical information of a non-Code nature are also welcome and should be directed to the staff of the Division of Building Research, who provide supporting services to the Code Committees.
Le Code national du batiment, ses supplements et les documents qui s'y rattachent sont disponibles en fran~ais. On peut se les procurer en s'adressant au Secn!taire, Comite associe du Code national du batiment, Conseil national de recherches du Canada, Ottawa, Ontario KIA OR6.
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COMMENTARY A
SERVICEABILITY CRITERIA FOR
DEFLECTIONS AND VIBRATIONS
TABLE OF CONTENTS
1
Page
Deflections .••................•........••.•..........•...... 3 Vibrations . . . . • • . . . . . . . . . . . . . . . . • • . . . . . . . . . . . . . . . . . . . • . . . . .. 3 References ...•..•.......... ~ . . . . . . . . . . . . . . . . . . . • • • . . . . . . . .. 5
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3
COMMENTARY A
Serviceability Criteria for Deflections and Vibrations
I. The advent of stronger materials, lighter more rigid cladding, smaller damping and more accurate strength calculations taking account of interaction of components means that excessive deflections and vibrations now have a greater influence in structural design than before. Excessive deflections and vibrations are usually controlled in codes by limiting the member deflection under specified load to some ratio of the span (L), for example, L/360 (for cantilevers, L may be taken as twice the length of the cantilever). Table A-I summarizes deflection criteria in this form in various standards pertinent to the National Building Code of Canada 1977. These deflection criteria depend on the types of construction and materials and on the conditions of use. As an aid to the designer, the problems associated with excessive deflection and excessive vibration are briefly discussed and references are given.
DEFLECTIONS
2. Excessive structural deflections can create a variety of problems: cracks or crushing in non-structural components such as partitions, lack of fit for doors, walls out of plumb or eccentricity of loading caused by rotation, unsightly droopiness and ponding. Cracks, besides being unsightly, may transmit unwanted sound through partitions, or water and cold air through exterior surfaces, and thus promote corrosion. Control of cracking in structural concrete is separately covered in CSA A23.3-1973, "Code for the Design of Concrete Structures for Buildings."
3. There are usually a number of alternative design solutions to problems caused by excessive deflection. Partition cracking, for example, can be avoided either by making the supporting structure stiff enough or by providing flexible joints in the partitions. Similarly, to avoid cracking, plastered ceilings should be hung from the floor beams, not rigidly attached to them.
4. The deflection criteria in Table A-I apply to conventional forms of construction under conventional conditions of use. The most severe deflection requirement, 1/480, for members supporting plastered ceilings or partitions,(1) may not be sufficient for cracking of plaster or rigid partitions.(3) As an aid to the designer for new or unusual cases, more detailed deflection criteria are suggested in Reference (2); case histories of damage due to excessive deflections (including also differential settlement and temperature movements) are given in References (4) to (7).
VIBRATIONS
5. Two types of vibration problems arise in building construction: continuous vibrations and transient vibrations. Continuous vibrations arise due to the periodic forces of machinery or certain human activities such as dancing; these vibrations can be considerably amplified when the periodic forces are synchronized with a building frequency-a condition called resonance. Transient vibrations are caused by footsteps or other impact and decay at a rate which depends on the available damping.
6. The undesirable effects of continuous vibrations caused by machines can be minimized by special design provisions,(8),(9) such as locating machinery away from sensitive occupancies, vibration isolation or alteration of the frequency of the structure. Human beings can create periodic forces in the frequency range of approximately 1-4 Hz, and floor frequencies less than about 5 Hz should be avoided for light residential floors, schools, auditoria, gymnasia and similar occupancies. For very repetitive activities such as dancing, it is possible to get some resonance when the beat is on every second cycle of floor vibration, and it is therefore recommended that the frequency of such floors be 10 Hz or more, unless there is a large amount of damping.
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Tab
le A
-I
SU
MM
AR
Y O
F M
AX
IMU
M D
EF
LE
CT
ION
/SP
AN
RA
TIO
S I
N N
BC
197
7 A
ND
PE
RT
INE
NT
CS
A S
TA
ND
AR
DS(
/)
CS
A 0
86-1
976,
C
SA
A23
.3-1
973,
C
SA
SI6
-196
9;
CS
A S
I57-
1969
, N
BC
197
7-P
art 9
, W
ood
Con
cret
e S
I6.1
-197
4,
Str
uctu
ral
Alu
min
um
Res
iden
tial
Sta
ndar
ds
Str
uctu
ral
Stee
l
Ro
of o
r fl
oor
mem
bers
I
1 (3
) 1
(3)
I I
I su
ppor
ting
pla
ster
ed
360
480
or
240
360
360
360
ceil
ings
, par
titi
ons,
etc
.
Flo
or m
embe
rs n
ot
1(2)
(4
) I
(5)
I 1(
7)
I su
ppor
ting
pla
ster
ed
180
320
200
240
or
360
ceil
ings
, par
titi
ons,
etc
. -
Ro
of
mem
bers
not
1
(2)
I I
(6)
I (6
) 1
I (8
) 1
supp
orti
ng p
last
ered
18
0 18
0 18
0 or
240
18
0 18
0 or
240
ce
ilin
gs,
etc.
Wal
l m
embe
rs
1 (2
) 1
180
-18
0 -
Col
umn
1 2
3 4
5 6
Not
es t
o T
able
A-I
: (I
) D
efle
ctio
n un
der
live
load
onl
y un
less
oth
erw
ise
note
d.
(2)
Mod
ulus
use
d fo
r ca
lcul
atio
n ba
sed
on s
hort
ter
m t
est b
ut t
here
is a
war
ning
cla
use
on c
reep
def
lect
ion.
(3
) D
efle
ctio
n w
hich
occ
urs
afte
r at
tach
men
t o
f no
n-st
ruct
ural
ele
men
ts,
incl
udin
g cr
eep
defl
ecti
on d
ue t
o su
stai
ned
load
plu
s im
med
iate
def
lect
ion
due
to a
ddit
iona
l liv
e lo
ad. T
he lo
wer
fig
ure
appl
ies
whe
n no
n-st
ruct
ural
ele
men
ts a
re n
ot li
kely
to
be d
amag
ed b
y la
rge
defl
ecti
ons.
(4
) Im
med
iate
live
-loa
d de
flec
tion
. The
re is
a w
arni
ng o
n po
ndin
g fo
r ro
of m
embe
rs.
(5)
The
re is
a w
arni
ng c
laus
e on
vib
rati
ons.
(6
) 1/
180
appl
ies
to s
heet
met
al o
r el
asti
c m
embr
ane
roof
cov
er a
nd
112
40 t
o as
phal
tic
buil
t-up
roo
fs.
The
re is
a w
arni
ng c
laus
e on
pon
ding
. (7
) F
or b
edro
oms
only
. (8
) If
ther
e is
no c
eilin
g.
.&;.
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5
7. Transient vibrations in floor systems due to foot impact may cause discomfort or annoyance to the occupants as a result of, for instance, china rattling. In Table A-I the deflection criteria of 11360 for wood floors(J) and 1/320 for steel floors which do not support brittle materials attempt to control such vibration effects. These criteria apply only to conventional floors with spans less than approximately 20 ft and frequencies greater than about 10 Hz. They do not apply to long span floors, especially for those without partitions, or for floors for special purposes; Reference (10) contains further information and criteria on these cases. References (I) and (II) contain further information for light residential floors with wood decks.
REFERENCES (1) Russell, W. A. Deflection Characteristics of Residential Wood-Joist Floor Systems. Housing
and Home Finance Agency, Housing Research Paper 30, Washington, D.C., April 1954.
(2) Allowable Deflections. Subcommittee I, ACI Committee 435. Journal, Am. Concrete Inst., VoL 65, No.6, June 1968, p. 433.
(3) Plewes, W. G. and Garden, G. K. Deflections of Horizontal Structural Members. National Research Council of Canada, Division of Building Research, Canadian Building Digest No. 54, Ottawa, June 1964.
(4) Mayer, H. and Riisch, H. Bauschaden als Folge der Durchbiegung von Stahlbeton-Bauteilen (Building Damage Caused by Deflection of Reinforced Concrete Building Components). Deutscher Ausschuss fUr Stahlbeton, Heft 193, Berlin 1967. National Research Council of Canada Technical Translation TT1412, 1970.
(5) Pfeffermann, O. Les Fissures dans les Constructions Consequences de Phenomenes Physiques Naturels. Annales de l'Institut Technique du Batiment et des Travaux Publics, No. 250, October 1968.
(6) Skempton, A. W. and MacDonald, D. H. The Allowable Settlements of Buildings. Proc., Institution of Civil Engineers, VoL 5, Part III, 1956, p. 727.
(7) Khan, F. R. and Fintel, M. Effects of Column Exposure in Tall Structures-Design Considerations and Field Observations of Buildings. Journal, Am. Concrete Inst. VoL 65, No.2, February 1968, p. 99.
(8) Thomson, W. T. Vibration Theory and Applications. Prentice-Hall. (9) Steffens, R. J. Some Aspects of Structural Vibration. Building Research Current Paper Engi
neering Series 37, Building Research Station, Ministry of Technology, Great Britain. (10) CSA Standard CSA SI6.l-1974. Steel Structures for Buildings-Limit States Design. Appen
dix Guide on Floor Vibrations. (II) Onysko, D. M. Performance of Wood·Joist Floor Systems. Forest Products Laboratory
Information Report OP-X-24, Canadian Forestry Service, Department of the Environment, January 1970, Ottawa.
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7
COMMENTARY B
WIND LOADS
TABLE OF CONTENTS Page
Reference Wind Speed, v, and Pressure, q .........•............... 7 Exposure Factor, Ce ••••••••••••••••••••••••••••••••••••••••• 10 Gust Effect Factor, Cg ••••••••••••••••••••••• '.' • • • • • • • • • • • • • • • 11 Vortex Shedding . . . . • . • • . . . . . . . . • . . . . . . . . . . . • . • . . . . . . . . . . . . . 14 Pressure Coefficients . . . . . . . . . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . .. 15 Lateral Deflection of Tall Buildings Under Wind Loading. . . . . . • . . . . . . 16 Construction Stages ..........•..•..........•........••...... 19 References ..........•......•..•.•.....•....•...•........•• 20
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COMMENTARY B
Wind Loads I. Three different approaches to the problem of determining design wind loads on buildings
are mentioned in Subsection 4.1.8., "Effects of Wind" of the 1977 edition of the National Building Code.(lj
2. The first approach, called "simple procedure," is similar to that in the 1960 and 1965 editions of the NBC. It is supplied along with numerical values for all the factors involved, except for climatic data (given in Reference 2) and pressure coefficients (given in this Commentary). This simple procedure gives approximately the same wind pressures and suctions as the earlier editions, and is intended for the majority of buildings for which wind loading does not have a major effect on the structural design.
3. The 2 other approaches to wind load analysis are referred to in Article 4.1.8.2. of the 1977 NBC, where the designer is required to use either (a) special wind tunnel tests or other experimental methods, or (b) a dynamic approach to the action of wind gusts to be called "detailed procedure," whenever the building is likely to be susceptible to wind-induced vibration. This may be true, for example, of tall and slender structures or doubly cantilevered canopies for which wind loading plays a major role in the structural design. Background information on the need for, and development of, new and more accurate methods of predicting wind loading effects on structures can be found in References (3), (4) and (5).
4. Special wind tunnel tests in which the relevant properties of the building plus immediate surroundings and of the oncoming flow must be adequately represented are recommended whenever the cost, the unusual nature of the building or site or other such considerations can justify the expense involved. For many cases for which the simple procedure is inadequate, however, there is still no clear indication of the need for a special wind tunnel test.
5. The third approach, the "detailed procedure," was devised(6) specifically for this intermediate category of wind loading problems, although it can be used in other situations if its scope and limitations are recognized. The detailed procedure consists of a series of calculations involving (i) the intensity of wind turbulence for the site as a function of height and of the surface roughness of the surrounding terrain, and (ii) properties of the building such as height, width, natural frequency of vibration and damping. The end-product of the calculations is the gust effect factor Cg, which is multiplied by the reference wind pressure, q, the exposure factor, Ce, and the pressure coefficient Cp' to give that static design pressure which is expected to produce the same peak load effect as the actual turbulent wind for the appropriate probability leveL The format of the simple procedure in the NBC has been arranged to permit an easy transition to this more detailed consideration of wind effects.
REFERENCE WIND SPEED, V, AND PRESSURE, q
6. The reference wind speed, Y, is determined by extreme value analysis of meteorological observations of hourly mean wind speeds, taken at sites (usually airports) chosen in most cases to be representative of a height of 30 ft in an open exposure. The reference wind pressure, q, is determined from Y by the following equation:
q(in pst) = C \f2 (1)
7. The factor C depends on the atmospheric pressure and the air temperature. The atmospheric pressure in turn is influenced mainly by elevation above sea level, but also varies somewhat in accordance with changes in the weather.
8. The following value of C is chosen to represent Canadian conditions:
ifY is in miles per hour, C=0.OO27 ifY is in feet per second, C=0.OOI25
I
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9. The NBC Supplement No. I, "Climatic Information for Building Design in Canada 1977" contains a description of the procedures followed in obtaining the reference wind pressures, q, for 3 different levels of probability of being exceeded per year (1/10, 1130 and 1/100), that is, the values commonly referred to as having return periods of 10, 30 and 100 years, respectively. These values of q are tabulated in Supplement No.1 for many Canadian locations along with other climatic design data. A reference giving more detail on the choice of the conversion factor, C, from wind speed to pressure and a table for converting from pressure in pounds per square foot to speed in feet per second are also supplied in Supplement No. I to the NBC.
EXPOSURE FACTOR, Ce
Simple Procedure 10. In the simple procedure of the 1977 Code(1) the exposure factor, Ce• is exactly the same as
the old height factor, Ch, in the earlier editions of the Code. The name has been changed to describe better the function of this factor when applied in the detailed analytical procedure where it reflects not only changes in wind speed with height, but also the effects of variations in the surrounding terrain. For the simple procedure, Ce' is based on the lis power law which is appropriate for wind gust pressures in open terrain (Ilio power law for wind gust speeds). The wind gust referred to is thought to last about 3 to 5 sec. and to represent a "parcel" of wind which is assumed effective over the whole of most ordinary buildings.
Detailed Procedure II. For the detailed procedure the exposure factor, Ce, is based on the mean wind speed
profile, which varies considerably depending on the general roughness of the terrain over which the wind has been blowing before it reaches the building. This dependence on terrain is much more significant than is the case for the gust speed profile, i.e. variation of gust speed with height, and hence 3 categories have been established as follows:
Exposure A (open or standard exposure): open level terrain with only scattered buildings, trees or other obstructions, open water or shorelines thereof. This is the exposure on which the reference wind speeds are based.
(2)
Exposure B: suburban and urban areas, wooded terrain or centres of large towns.
( Z )0.50
Ce = 0.6 ,Ce >0.5 60 -
(3)
Exposure C: centres of large cities with heavy concentrations of tall buildings. At least 50 per cent of the buildings should exceed 4 storeys.
( Z )0.72
Ce = 0.4 100 ,Ce~O.4 (4)
In Equations (2) to (4), Z is the height above ground in feet.
12. Exposure B or C should not be used unless the appropriate terrain roughness persists in the upwind direction for at least I mile, and the exposure factor should be varied according to the terrain if the roughness differs from one direction to another. Abrupt changes in ground slope near the building site may result in significantly higher wind speeds than over level ground, and thus exposure A may have to be applied in such situations even though the surface roughness may seem appropriate for B or C.
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Use of Exposure Factors 13. Exposure factors can be calculated from Equations (2) to (4) or obtained directly from
the graphs in Figure B-1. They should be applied to the wind pressure rather than to speed; where it is necessary to determine the hourly mean wind speed at height, h, use the square root of C •.
14. The exposure factor is needed in 3 different capacities in the detailed procedure. First, the square root of C. is needed to determine the hourly mean wind speed at the top of the structure being designed, V H:
(5)
15. The reference wind speed, V, can be obtained from the reference wind pressure and the conversion table in Supplement No. lor by applying Equation (I).
16. Secondly, C. appears in Equation (7) used for calculating the gust effect factor, Cg• Here again, Co is calculated using the height H of the structure.
17. Thirdly, Co is used in the calculation of pressure coefficients for the windward and leeward faces of tall, slender buildings. For the windward face, Co varies continuously with the height, Z, to the elevation in question; for the leeward face, Co is evaluated once at 'h the height, H, of the building.
GUST EFFECT FACTOR, Cg
Simple Procedure IS. The implied gust effect factor of the earlier editions of the Code varied from 2.04 at 60
mph design gust wind speed to I.S4 at 120 mph design gusi wind speed, and was the same whether the whole structure was being designed, or some part of it such as a window or a wall panel. In the 1977 NBC(i) the gust effect factor for the simple procedure is 2.0 for the structure as a whole, and 2.5 for cladding or windows. On the other hand, the consequences of wind damage to cladding are less serious than structural damage, and the risk may be considered acceptably small if a probability of 1/10 is used for cladding design wind pressures rather than the 1130 or 1/100 specified for design of the structure. The net result is that, although smaller, more severe gusts can be expected over small areas (and hence a larger gust effect factor of 2.5 is specified) the use of a more probable (and hence lower) reference wind pressure gives approximately the same design pressure for a panel or window as for the structure.
Detailed Procedure 19. The calculation procedure for the gust effect factor, Cg, is given in detail below, including
a sample calculation of Cg worked out in complete detail. In the detailed procedure the gust effect factor is the ratio of the expected peak loading effect to the mean loading effect. Cg therefore makes allowances for the variable effectiveness of different sizes of gusts and the load magnification effect caused by gusts in resonance with the structure vibrating as a single-degree-of-freedom cantilever. Cg is defined as follows:
(6)
where a standard deviation of total loading effect, Ii mean value of total loading effect, g peak factor of total loading effect.
The standard deviation divided by the mean, a/Ii, is the "coefficient of variation" for the total loading effect
(7)
I
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where K
s =
F
p =
a factor related to the surface roughness coefficient of the terrain 0.08 for Exposure A 0.10 for Exposure B 0.14 for Exposure C, exposure factor, previously defined, obtained from Figure B-1, background turbulence factor, obtained from Figure B-2 as a function of height, H, and width, W, of the windward face of the structure, size reduction factor, obtained from Figure B-3 as a function of the ratio of width, W, to height, H, of the windward face of the structure and the reduced frequency, gust energy ratio at the natural frequency of the structure, obtained from Figure B-4 as a function of the wave number (natural frequency (cycles/sec.) divided by mean wind speed (fUsec.) at height, H, of structure), critical damping ratio.
20. Suggested values for buildings are 0.01 for steel frames and 0.02 for reinforced concrete frames. On the other hand, the critical damping ratio for welded steel stacks may go as low as 0.001 for moderate amplitudes of displacement. Prestressed concrete structures having no microcracks due to tension may also have very low values for structural damping.
21. The peak factor, g, in Equation (6) gives the number of standard deviations by which the peak load effect is expected to exceed the mean load effect, and is given in Figure B-5 as a function of the average fluctuation rate. The average fluctuation rate, v, can be estimated as follows:
where
v = no V __ sF __ sF + PB
no = natural frequency of vibration, cycles/sec. s, F, p, B as defined for Equation (7).
Explanatory Notes Regarding (Jlp. and g
(8)
22. The response of a tall, slender building to a randomly fluctuating force can be evaluated rather simply by treating it as a rigid, spring-mounted cantilever whose dynamical properties are specified by a single natural frequency and an appropriate damping value. The variance of the output quantity or loading effect is the area under the spectrum of the input quantity (the forcing function) after it has been multiplied by the transfer function. The transfer function is the square of the well-known dynamic load magnification factor for a one-degree-of-freedom oscillating mechanical system.
23. In the case of wind as the random input, the spectrum of the wind speed must first be multiplied by another transfer function called the "aerodynamic admittance function," which in effect describes how the turbulence in the wind is modified by its encounter with the building, at least insofar as its ability to produce a loading effect on the structure is concerned.
24. For the purposes of calculating (J/p., the spectrum of the wind speed is represented by an algebraic expression based on observations of real wind. The aerodynamic admittance function is also an algebraic expression, computed on the basis of somewhat simplified assumptions but appearing to be in reasonable agreement with the limited experimental evidence at present available. The spectrum of wind speed is a function of frequency having the shape of a rather broad hump (Figure B-4). The effect of the aerodynamic admittance is to reduce the ordinates of the curve to the right of the hump more and more as the frequency increases. This is partly a reflection of the reduced effectiveness of small gusts in loading a large area. The effect of the dynamic load magnification factor or mechanical admittance is to create a new peak or hump centred at the natural frequency of the structure, usually well to the right of the broad peak, which represents the maximum density of input power of the wind.
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25. The area under the loading effect spectrum, the square root of which is the coefficient of variation olp., is taken as the sum of 2 components: the area under the broad hump, which must be integrated numerically for each structure, and the area under the resonance peak, for which a single analytic expression is available. These components are represented in Equation (7) by Band sFI{3, respectively. The factor K/C. can be thought of as scaling the result for the appropriate input turbulence level. If resonance effects are small, then sF 1 {3 will be small compared to the background turbulence B and vice versa. Note that although C. is normally a function of height, in Equation (7) it is evaluated at a particular height (usually H, the height of the building), and is treated as a single-valued parameter for calculating Cg•
26. If this method for calculating Cg is used for buildings or parts of buildings that are not well represented by the simple model of a rigid cantilever oscillating about a spring-mounted base, additional sources of error will be introduced, although these are perhaps not very important when resonance effects are small. In the absence of a more precise analysis, the present method can serve as a guide to the peak gust loading on buildings that are not tall and slender, or even for windows or wall panels located on the windward sides of buildings. In considering a portion of the windward face, use the dimensions of the element for D and H in Equations (7) and (8), the natural frequency of the element itself for no and velocity V z (where Z is the height of the element above ground) rather than V H' the velocity at the top of the structure. Similarly, Co should in this case be evaluated at height Z for Equation (7).
27. The peak factor, g, depends on the average number of times the mean value of the loading effect is crossed during the averaging time of I hr (3,600 sec.). The functional relationship in Figure B-5 was shown by Davenport(7) to hold when the probability distribution of the mean loading effect was normal (Gaussian).
28. As stated in Article 4.1.8.3. of the 1977 Code, structures must be able to withstand partial or unbalanced loading as well as the full design load. All structures, particularly those susceptible to unbalanced loading due to wind, such as double overhang girders and canopies, members subject to stress reversal and structures with broad frontal area, should be capable of withstanding the effects of a reduced dynamic factor equal to 0.75 Cg, acting over any portion of the structure.
Sample Calculation of Cg
29. To illustrate the calculation of a gust effect factor the following sample problem will be worked in detail: Required: To obtain the gust effect factor for a building with the following properties:
Height -600 ft Width -100 ft Depth -100 ft Fundamental natural frequency ---4>.2 Hz Critical damping ratio ---4>.015 Terrain for site -Exposure B Reference wind speed at 30 ft open terrain 90 ft/sec.
Step I: Calculate required parameters Mean wind speed at top of building V 600' from Equation (5)
=90x V 1.90= 123 ftlsec. (Figure B-1) Aspect ratio W/H= 100/600=0.17 Wave number for calculation of F: no/V 600 = 0.00163 Reduced frequency for calculation of s:
noH/V 600=0.975
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Step 2: Calculate alll, from Equation (7) (I) K=O.IO for Exposure B (2) Ce = 1.90 (from Figure B-1) (3) B = 0.62 (from Figure B-2) (4) s = 0.11 (from Figure B-3) (5) F=0.28 (from Figure B-4) (6) ,B=O.oJ5 (given)
YO.IO (7)alll = -
1.90 (
0.11 x 0.28 ) 0.62 + = 0.375
0.015
Step 3: Calculate v, from Equation (8) (I) no = 0.2 Hz (given)
Y 0.11 x 0.28 (2)v = 0.2 = 0.175/sec.
0.11 X 0.28 + 0.015 X 0.62
Step 4: Obtain peak factor g: (I) g=3.75 (from Figure B-5)
Step 5: Cg (from Equation (6»= 1 +3.75xO.375=2.41
VORTEX SHEDDING
30. Slender exposed structural elements and tall slender cylindrical structures such as chimney stacks, observation towers and in some cases, high-rise buildings, should be designed to resist the dynamic effects of vortex shedding. When the wind blows across a slender prismatic or cylindrical body, vortices are shed alternately from one side and then the other giving rise to a fluctuating force acting at right angles to the wind direction along the length of the body. A structure may be considered slender in this context if the ratio of height to diameter exceeds 5. The frequency, n. of the vortex shedding and of the force fluctuations is given by
where n the frequency, Hz, S the Strouhal number given below, V H= the mean wind speed at the top of the structure as defined in Equation (5), ftlsec., o = the diameter, ft.
For circular cylinders S = 0.18 for Re <2X 105, S 0.25 for Re>2x 105,
VHO where. Reynolds' number Re = X 105•
16
For bodies with angular sections such as a rectangular, rolled-steel shape, S=0.15.
(9)
31. If the structure is free to oscillate in the plane normal to the wind, large oscillations will develop when the vortex shedding frequency is resonant with the natural frequency of the structure. The dynamic influence will be approximately equivalent to the influence of a static force per unit height, FL , acting in the direction of oscillations
0.5 FL -CLOqcr (10)
,B
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the critical damping ratio as defined for Equation (7), 0.2 for circular cylinders, velocity pressure for the mean wind speed which produces resonance.
15
32. For tapered stacks there is some reduction in the effective length over which the vortex shedding forces act. If the diameter of a section of the stack at height Z is Dz, then the velocity at which vortices are shed from this section resonant with the structure is given by the Equation (9), where n is set equal to the resonance frequency of the stack. The height over which these resonant eddy shedding forces then act is determined by the height of stack over which the diameter only changes by ± 5 per cent from the value Dz. Thus, on tapered stacks the vortex excitation can take place over a range of wind velocities corresponding to the variation in diameter of the stack. For each velocity the fluctuation force only acts over a limited section of the stack.
PRESSURE COEFFICIENTS
33. Pressure coefficients are the non-dimensional ratios of wind-induced pressures on a building to the dynamic pressure (velocity pressure) of the wind speed that would be measured (usually) at the top of the building in the undisturbed air stream. Pressures on the surfaces of structures vary considerably with the shape, wind direction and the profile of the wind velocity. Pressure coefficients are usually determined from wind tunnel experiments on small-scale building models, although in a few recent instances measurements on full-scale buildings have been used directly. It is essential in most cases that these pressures be measured in a wind tunnel in which the correct velocity profile is simulated; experiments in uniform flow can be highly misleading.(8).(9)
34. The pressure coefficients given in Figures B-6 to B-20 are all time-averaged values, that is, they refer to the mean value of the pressure on a surface. In addition, all pressure coefficients except the local pressure coefficients, Cp *, usually represent a spatially averaged pressure. The local maximum and minimum pressures acting over a small area are designated by Cp * and are appropriate for cladding design.
35. The internal pressure coefficients, Cpi, define the effect of wind on the air pressure inside the building and are necessary for the design of cladding and secondary supporting members for wall and roof systems. Like the external pressure coefficients, the Cpi are time-averaged values, but unless there are large openings joining the interior to regions of extreme wind speed, pressure or suction (windward and side walls), the maximum instantaneous internal pressures will not be appreciably different from the time-averages. On the other hand, if the permeability of the building is gradually increased, the gustiness in the wind will have an increasing effect in causing peaks and lulls in the internal pressure. At present it must be left to the designer to decide in doubtful cases whether or not the gust effect factor, C.I.' should be applied to internal pressure coefficients (formula (b) in Sentence 4.1.8.1.(2) of the NBc).
36. Values of pressure coefficients sufficient for general purposes for 2 classes of structures are given in Figures B-6 to B-8. The pressure coefficients, unless otherwise noted, are based on the velocity pressures at the top of the building. Pressure coefficients for various other structures that have been tested in turbulent shear flows may be obtained from Reference 8.
37. Figures B-9 to B-20 are based on wind tunnel experiments in which the correct velocity profile and wind turbulence were not simulated, and should therefore be regarded with a certain measure of caution. These figures are the same as in Tables 20 to 31 in the 1961 and 1965 editions of Supplement No.3 for use with the 1960 and 1965 National Building Codes, respectively, except for some deletions and a few corrections. They are based on the Swiss Association of Engineers and Architects Standards, S.I.A., No. 160, published in 1956.(10)
Rounded Structures 38. For rounded structures (in contrast to sharp-edged structures) the pressures vary with the
wind velocity, depending on the Reynolds' number, ~. (defined following Equation (9». In Fig-
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ures B-ll, B-12, B-15 and B-20, which have been translated and reproduced from the Swiss tables(IO), the Reynolds' number is expressed by dVq where d is the diameter of the sphere or cylinder in feet and q is the velocity pressure in pounds per square foot. To convert to Re, multiply dVq by 1.8 X lOS.
39. The roughness of rounded structures may be of considerable importance. Common welllaid brickwork without parging can be considered as having a "moderately smooth" surface (Figure B-II). Surfaces with ribs projecting more than 2 per cent of the diameter are considered as "very rough." In case of doubt, it is recommended to use those Cn values which result in the greater forces. For cylindrical and spherical objects with substantial stiffening ribs, supports and attached structural members, the pressure coefficients depend on the type, location and relative magnitude of these roughnesses.
Icing 40. In locations where the strongest winds and icing may occur simultaneously, structural
members, cables and ropes must be calculated assuming an ice covering based on climatic and local experience. For the iced condition, values of Cn given in Table B-15 for thick wire cables for a "rough" surface should be used.
Structural Members 41. In Figures B-16, B-17, B-19 and B-20 pressure coefficients with the subscript 00 are used
to indicate that they apply to structural members of infinite lengths and this is multiplied by a reduction factor, k, for finite lengths of members. If a member projects from a large plate or wall, the reduction factor, k, should be calculated for a slenderness based on twice the actual length. If a member terminates with both ends in large plates or walls, the reduction factors for infinite length should be used.
Shielding 42. For members that are located behind each other in the direction of the wind, the shield
ing effect may be taken into account. The windward member and those parts of the leeward member that are not shielded should be designed with the full pressure, q, whereas the shielded parts of the leeward member should be designed with the reduced pressure, q" according to Figure B-18.
43. For constructions made from circular sections with dVq<2.5 and Ai A~O.3, the shielding factors can be taken by approximation from Figure B-18. IfdVq>2.5, the shielding effect is small and for a solidity ratio A/ A~0.3, it can be taken into account by a constant shielding factor k, =0.95.
LATERAL DEFLECTION OF TALL BUILDINGS UNDER WIND LOADING
44. Lateral deflection of tall buildings under wind loading may require consideration from the standpoints of serviceability or comfort criteria. There is a general trend toward more flexible structures, partly because adequate strength can now be achieved by using higher strength materials that may not provide a corresponding increase in stiffness.
45. One symptom of unserviceability may be the cracking of masonry and interior finishes. Unless precautions are taken to permit movement of interior partitions without damage, a maximum lateral deflection limitation of 11250 to 1/1000 of the building height should be specified. According to Sentence 4.1.1.5.(4) of the 1977 NBC, 1/500 should be used unless a detailed analysis is made.
Wind-Induced Building Motion 46. While it is generally found that the maximum lateral wind-loading and deflection are in
the direction parallel with the wind (along-wind direction), the maximum acceleration of a building leading to possible human perception of motion or even discomfort may occur in the direction perpendicular to the wind (across-wind direction). Across-wind accelerations are likely to exceed
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along-wind accelerations if the building is slender about both axes, that is if YWD/H is less than Y), where Wand 0 are the across-wind and along-wind plan dimensions and H is the height of the building.
47. Although treatment of this subject is somewhat tentative, the following guidelines may be of assistance. On the basis of a wide range of turbulent boundary layer wind tunnel studies, it has been found that the peak acceleration in the across-wind direction at the top of the building can be found from the following:
(II)
48. In less slender structures or for lower wind speeds, the maximum acceleration may be in the along-wind direction and can be found from the expression
2 2 '" f"i<s"F ( .l ) aD = 477 nD g V -=--::---Cef3D Cg
(12)
where
W, 0 across-wind and along-wind building dimensions, ft. aW,a D peak acceleration in across-wind and along-wind directions, ftlsec2 ,
a, = .0005 [Vu/(nw YWD)V3, Y B = average density of the building, Ib/ft3, f3w,f3D = fraction of critical damping in across-wind and along-wind directions, nw, nD fundamental natural frequencies in across-wind and along-wind directions, Hz, .l maximum wind-induced lateral deflection at the top of the building in along-wind
direction, ft, g, K, s, F, Ce, C9-, as defined previously in connection with Equation (7). Note that f30 = p and no = no in terms of previous definitions.
49. Although many additional factors such as visual cues, body position and orientation and state-of-mind are known to influence human perception of motion, it appears that when the amplitude of acceleration is in the range of 0.5 per cent to 1.5 per cent of the acceleration due to gravity, movement of the building becomes perceptible to most people.(ll) to (13)
50. Based on this and other information, a tentative acceleration limitation of I to 3 per cent of gravity once every 10 years is recommended; for use in conjunction with Equations (II) and (2) the lower value might be considered appropriate for apartment buildings, the higher value for office buildings. The application of Formulas (II) and (12) tend to give conservative results insofar as they assume that the wind always comes from the most sensitive direction, and this factor has also been considered in setting the above limitation. If the designer has available more detailed information he can make suitable allowances.
51. Owing to the relative sensitivity of the two expressions (II) and (2) to the natural frequency of vibration, and in (12) to the corresponding building stiffness, it is recommended that these be determined using fairly rigorous methods, and that approximate formulas be used with caution. For example, the adoption of a natural frequency of WIN where N is the number of storeys may not be consistent with the assumption that the displacement under wind loading is as large as H/500.
52. If a more rigorous analysis is not available, the maximum deflection resulting from the equivalent static wind loading can be related to the fundamental building frequency using modal representation of the building motion. The following assumptions may be acceptable:
(I) Use first mode only, assumed linear </>(Z) = rlZ (13)
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(2) Uniform distribution of building mass
WDYB m(Z) =--
go
As a consequence of modal representation
H f cp(Z)m(Z)cp(Z)dZ = I o
u(Z) r 2CP(Z)
H W P(Z) 4w2ni> = f CP(Z) -- CP(Z) dZ
o u(Z)
where CP(Z) = fundamental eigenvector, r l , r2 = constants, m(Z) = distribution of building mass, with height Z, 0 < Z < H, slugs/ft, go acceleration due to gravity 32.2 ftlsec.2
,
u(Z) = displacement at height Z, 0 < Z < H, ft, P(Z) = distribution of equivalent static wind pressure with height Z, 0 < Z <
H,psf. Other symbols are as defined earlier.
From Equations (13), (14) and (I 5)
$(Z) = CV w~: H' )Z
From Equations (16), (17) and (I 8)
Substituting Equation (19) into Equation (16), the deflection at height H becomes
H 3go f Z P(Z)dZ
~ = 0 4w2ni> D YB H2
(14)
(15)
(16)
(17)
(I8)
(19)
(20)
One possible expression for P(Z) assumes a power law variation of a maximum at the top of qCeCgCp
(21)
where Cp 0.8 (-.5) = 1.3 and a is the appropriate exponent from Equations (2), (3) and (4).
Substituting Equations (20) and (21) into (12)
aD/go g V KsF (~)( Ceq) (22) C.flD 2 + a DYB C
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53. Sample Calculation of aw and aD- A detailed calculation for aw and ao using Equations (II) and (12) will be made for the sample problem worked earlier to illustrate the calculation of a gust effect factor:
assume that nw = no 0.2 Hz f3w = f30 = 0.015
Illb/ft3 'YB
Step 1: Calculate ar :
ar = .0005 (123/ (0.2 X 100W 3
.201
Step 2: :alculate aw ( 0.201 ) aw -0.2 x 0.2 x 3.75 x 100 ,~
= 2.24 ft/sec. 2 11 v.015 awl&:> = 6.9 per cent
Step 3: Calculate q q = 0.00126 X 90 X 90
= 10.2 psf
Step 4: Calculate aD/&:>
V 0.10 X 0.11 X 0.28 ( 3.9 ) (1.90 X 10.2) ao/&:> = 3.75 -
1.90 X 0.015 2.50 100 X 11 = 3.4 per cent
54. In this example clearly the across-wind accelerations overshadow the along-wind accelerations. Table B-1 gives the results of calculations for 5 sample buildings (generally for wind along both axes) for 3 different reference wind pressures and the 3 different terrains. Case 5 is in fact the building treated in the above example, and the reference wind pressures are appropriate for cities like Montreal, Toronto and Vancouver, respectively.
Pressure Differences Across Interior Walls and Partitions 55. Considerable pressure differences can result across interior walls and partitions in high
rise buildings and in low-rise buildings in exposed locations if windows are broken during a storm. In certain locations this could result in almost the full pressure difference between the windward and leeward sides of the building being applied across the interior wall or partition. This could happen for example if a large window on the windward side were broken by flying debris and the full positive pressure were to act on the walls of a small room located at this broken window. Similar conditions could prevail in an apartment building with operable windows or doors. This pressure difference could be aggravated by stack effects in a tall building in the winter time. On the other hand, general experience does not indicate many failures of interior walls due to this cause, and thus it is not always considered necessary to design interior walls and partitions for the maximum possible pressure difference. A design pressure difference of the order of 10 psf may be appropriate.
CONSTRUCTION STAGES
56. It should be noted that the shape of a structure may change during erection. The wind loads, therefore. may be temporarily higher during erection than after completion of the structure.(l3) These increased wind loads should be taken into account using the appropriate coefficients from Figures B-6 to B-20.
REFERENCES
(I) National Building Code of Canada 1977. National Research Council of Canada. Associate Committee on the National Building Code, Ottawa, NRCC No. 15555.
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(2) Climatic Information for Building Design in Canada. Supplement No. I to the National Building Code of Canada 1977. National Research Council of Canada. Associate Committee on the National Building Code, Ottawa, NRCC No. 15556.
(3) Dalgliesh, W. A. and Schriever, W. R. Recent Research on Wind Forces on Tall Buildings. Proc., Canadian Structural Engineering Conference, Toronto, 19/20 February 1968, University of Toronto Press.
(4) Davenport, A. G. New Approaches to the Design of Structures Against Wind Action. Proc., Canadian Structural Engineering Conference, Toronto, 19/20 February 1968, University of Toronto Press.
(5) Proceedings, International Research Seminar on Wind Effects on Buildings and Structures. Ottawa, 1967-published September 1968 by University of Toronto Press.
(6) Davenport, A. G. Gust Loading Factors. Journal Structural Division, Proc., Am. Soc. Civ. Engrs., Vol. 93, June 1967, pp. 12-34.
(7) Davenport, A. G. Note on the Distribution of the Largest Value of a Random Function with Application to Gust Loading. Proc., Institution Civil Engineers, Vol. 28, June 19~4, pp. 187-196. London.
(8) Jensen, M. and Franck, N. Model Scale Tests in Turbulent Wind, Part II. Danish Technical Press, Copenhagen, 1965.
(9) Leutheusser, H. J. and Baines, W. D. Similitude Problems in Building Aerodynamics. Journal of Hydraulics Division, Proc., Am. Soc. Civ. Engrs., Vol. 93, May 1967, pp. 35-49.
(to) Normen fur die Belastungsannehmen, die Inbetriebnahme und die Uberwachung der Bauten. (Standards for Load Assumptions, Acceptance and Inspection of Structures). Schweizerischer Ingenieur und Architekten Verein (Swiss Association of Engineers and Architects), No. 160, Zurich, Switzerland, 1956.
(II) Chen, P. W. and Robertson, L. E. Human Perception Thresholds of Horizontal Motion. Journal of Structural Division, Proc., Am. Soc. Civ: Engrs., Vol. 98, August 1972, pp.1681-1695.
(12) Chang, F. K. Human Response to Motions in Tall Buildings. Journal of Structural Division, Proc., Am. Soc. Civ. Engrs., Vol. 99, June 1973, pp. 1259-1272.
(13) Hansen, R. J., Reed, J. W. and Van Marcke, E. H. Human Response to Wind-Induced Motion of Buildings. Journal of Structural Division, Proc., Am. Soc. Civ. Engrs., Vol. 99, July 1973, pp. 1587-1605.
(14) Walshe, D. E. Measurements of Wind Force on a Model of a Power Station Boiler House at Various Stages of Erection. National Physical Laboratory, NPL Aero Report 1165, September 1965, Teddington, England.
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Table B·I
WIND INDUCED BUILDING MOTIONS: EXAMPLES OF CALCULATED PEAK ACCELERATIONS
(a) IN ALONG·WIND (D) AND ACROSS·WIND (W) DIRECTIONS AT TOP OF BUILDING (H)
Expo- q = 6.6 psf (1/ I 0 basis) q = 8.1 psf (I / 10 basis) q = 9.3 psf (1/10 basis)
Zone sure
Factor V(H) aD aw V (H) V(H) aw Ce in fps in %g in%g in fps in g in g in fps in g in %g
Case I: 400 x 175 x 100 ft building(l)
OPEN 2.07 104 1.26 3.19 115 1.71 4.47 124 2.11 5.62 SUBR 1.55 90 0.95 1.98 100 1.30 2.78 108 1.61 3.49 CITY 1.09 76 0.72 1.10 84 0.98 1.55 90 1.22 1.94
Case 2: 400 x 100 x 175 ft building(1l
OPEN 2.07 104 2.72 1.98 115 3.70 2.77 124 4.55 3.48 SUBR 1.55 90 2.06 1.23 100 2.82 1.72 108 3.48 2.17 CITY 1.09 76 1.55 0.68 84 2.13 0.96 90 2.63 1.21
i
Case 3: 500 x 175 x 100 ft building!!;
OPEN 2.20 108 1.90 3.18 119 2.56 4.46 128 3.13 5.60 SUBR 1.73 95 1.53 2.15 106 2.07 3.01 113 2.54 3.77 CITY 1.27 82 1.22 1.29 91 1.66 1.81 97 2.05 2.27
Case 4: 500 x 100 x 175 ft buildinglll
OPEN 2.20 108 2.41 3.75 119 3.29 5.25 128 4.05 3.60 SUBR 1.73 95 1.92 2.53 106 2.63 3.55 113 3.25 4.45 CITY 1.27 82 1.52 1.52 91 2.08 2.14 97 2.58 2.68
Case 5: 600 x 100 x 100 ft building(1)
OPEN 2.31 110 2.15 4.89 122 2.92 6.85 130 3.57 8.61 SUBR 1.90 100 1.80 3.52 III 2.44 4.94 119 3.00 6.21 CITY 1.45 87 1.49 2.27 97 2.03 3.18 104 2.50 3.99
Case 6: 600 x 100 x 150 ft building\li
OPEN 2.31 110 1.62 2.66 122 2.21 3.72 130 2.72 4.68 SUBR 1.90 100 1.35 1.91 III 1.84 2.68 119 2.27 3.37 CITY 1.45 87 1.11 1.23 97 1.52 1.73 104 1.88 2.17
Case 7: 800 x 250 x 125 ft building(')
OPEN 2.51 115 0.93 3.01 127 1.26 4.22 136 1.54 5.30 SUBR 2.19 107 0.83 2.41 119 1.13 3.38 128 1.38 4.24 CITY 1.79 97 0.74 1.72 107 1.00 2.42 liS 1.23 3.03
Case 8: 800 x 125 x 250 ft buildingm
OPEN 2.51 lIS 2.12 1.97 127 2.88 2.76 136 3.52 3.47 SUBR 2.19 107 1.89 1.57 119 2.57 2.21 128 3.15 2.77 CITY 1.79 97 1.68 1.12 107 2.28 1.58 liS 2.81 1.98
Col. I 2 3 4 5 6 7 8 9 10 II
Note to Table B-1: (I 'Full dimensions and properties of Cases I to 8 are given in the Table at the top of p. 22.
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Note to Table 8-1 (Cont'd)
Height H. Density. in D Direction in W Direction Case
ft Ib/cu ft Dimen. Frequency Damping Dimen. Frequency Damping
I 400 9.0 175 0.250 0.015 100 0.200 0.010 2 400 9.0 100 0.200 0.010 175 0.250 0.015 3 500 10.0 175 0.175 0.010 100 0.200 0.010 4 500 \0.0 100 0.200 0.010 175 0.175 0.010 5 600 I \.0 100 0.200 0.015 100 0.200 0.015 6 600 11.0 100 0.200 0.020 150 0.200 0.020 7 800 12.0 250 0.150 0.015 125 0.125 0.010 8 800 12.0 125 0.125 0.010 250 0.150 0.015
Column I 2 3 4 5 6 7 8 9
II L~~ -.l ~
L 111 Imt / I'-tt, ,
" L I I I
L I I I II .
1000
800
600 500
L lL 1 V Il I
400
1.1 / v / 1 I
~v / I J
EXPOSURE c,V sV AI I I
t I'f' V ~ I
I 1 I I f-
I I I f-i
I I I I f-J I LL f-
, 1/ I f-I f-
I f-I i 1. I f-I f-
I L
300 I-L..L..
0 200 z :::> 0 0::: <.:)
I.l..i 100 > 0
80 a:l <C
I- 60 I <.:) 50 w...J
I 40 , I I
I I 30
, 1 1 I I 20 I
I
10 ! I
. 1 . 2 .3.4.5.6.81 2 3 4 6 8 10
EXPOSURE FACTOR. Ce
Figure 8-1 Exposure factor as a function of terrain roughness and heigh t above ground
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.,....
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1000
800
600
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400
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, " " " " " " ~
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23
'" '" 3000/H " " " f - -, I' '" '" B = 4/3 1 _1_ x _
" " " .. [I' I;~O J [I' 4'O~] ~I ,,2)4/3] d'_ ~ '" '" '" I\. '" -"- "- "- "- 0
r\ 1\.'\ '" I'-'\. '\. I\. I\. " '\. ~I\. ~'- '- r\.
I\. \ '\. '\. I" r'\. " " " i\. ~" ~' ~ ~ 1'\ ~ r\. '" " r'\.' 1\.' " ~/H "- '" 1\ Jr\.' " ~ '" ~ ~ ~ ~ "- ~.I
1\ 1\ ~ r\ ~ ~ ~ ~ \ r-l0 1\ ~ 1\,3.0 ~.5
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'\. " ~' ~ , ~ ~\ ~ 1. '~ '\ \ \.\ \' 1\\ ~\ U
"\ \. \ \ l\' 1\\ ~\ ~' '\ \ [\ ~ ~ ~ ~ ~
0.6 0.8 1.0 1.2 1.4 1.6 1.8
BACKGROUND TURBULENCE FACTOR, B
Figure 8-2 Background turbulence factor as a function of width and height of structure
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Fig
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B-3
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as a
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f wid
th, h
eigh
t an
d re
duce
d fr
eque
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of s
truc
ture
t
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B-4
G
ust
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atio
as
a fu
ncti
on o
f wav
e nu
mbe
r ~
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, 6.
0
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g
= j2
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Fig
ure
B-5
P
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fact
or a
s a
func
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of a
vera
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luct
uati
on r
ate
""---~-~-"----------_
__
__
__
_ ~c. _
__
_ _
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-
Notes to Figure B-6:
Cp = +0.7
10.8
+0.4
- 0.4 Cl.
U - O. 8
- 1. 2
- 1. 6
O. 5
ELEVATION OF BUILDING
p varies depending on surroundings - roof should be checked for the range of pressures and suctions indicated by the shaded area
GRAPH OF Cp FOR WI~VVARD ROOF SURFACE,
WIND NORMAL TO RIDGE
Figure B-6 Pitched roof buildings of height less than twice the width
III Wind parallel to use D as width and proceed as in the case of a flat roof (tan a = 0).
27
121 Wind normal to the width is B (not shown on the figure, see Figure B-8) and values ofCp for windward roof surface must read from the graph below the figure.
(31 Wind at an angle to the ridge: normally does not give the most !>erious loading of building as a whole, but does produce severe local suctions along.the edges of the roof surface. For local suction maxima on roofs, use the Cp * given in Figure B-8. These local maximum coefficients Cp *. should be considered for the design of roofing attachment but need not be added to the Cp for determining over-all loads.
(41 End walls: (those walls to the wind direction), Cp are given in Figure B-8. (5) Interior pressure: C pi' are given in Figure B-8. (61 Eaves: positive pressure on the windward wall also causes an upward force on roof overhangs which should
be considered in addition to suction from above. (71 Exposure factor: for calculating Ce exposure factor use height H.
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-1. 0
D
ELEVATION OF BUILDING
Figure 8-7
Flat roof buildings of height greater than twice the width
Notes to Figure 8-7: (1) Wind perpendicular to one wall: for width use the dimension perpendicular to the wind direction. (2) Wind at an angle to the wall: this condition produces high local suctions at the leading edge of the wall which
is at a slight angle to the wind. The coefficient Cp• applies over the shaded area on the figure for the design of cladding, but need not be considered in conjunction with the Cp for over-all loading. The coefficient Cp• for the roof are given in Figure 8-8.
(3) End walls: pressure coefficients for end walls (parallel to wind direction) are given in Figure B-8. (4) Interior pressure: coefficients Cp• for interior pressures are given in Figure B-8. ()) Exposure factor: for the calculation of exposure factor C e, use 1/2 the height H for the leeward wall. the height
H for the roof and the actual height Z to the level under consideration for the windward walL 16) Height HI: the height to which Ce is constant is 30 ft for the simplified method and exposure A. 40 ft for expo
sure 8 and 100 ft for exposure C. (7) Windward Wall Cp: the pressure coefficient is 0.8 for the entire height. The variation shown in pressure is due
to variation in exposure factor Ceo
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-~ ...... ----- -~. ~--- -~-- ---.---... -~---
~--------------------------------------------.-.. --
1.
2.
3.
4.
CpO. 7
Cp -3.0~
~~7zLZ;iLll== Cp 2. O~ ~iC~io. 20 1
;,-: I O. 10 ;,-: 0.20 I
I~ O. 10
o .1 PLAN VIEW OF BUILDING
INTERIOR PRESSURES
Openings mai n Iy in windward wa II.
Openings mai n Iy in leeward wa II.
Openings mainly in walls parallel to wind direction.
Openings uniformly distributed in all 4 walls.
Figure B-8
W
- O. 7
Cpi
+0. 7
-0.5
- O. 7
- O. 3
"" "I'" ,
29
End wall pressure coefficients, local suction maxima on the roof and interior pressures for use with Figures B-6 and B-7
Notes to Figure B-8: (II Local maximum suctions: the coefficients Cp" for the roof surface occur for wind at an angle to one comer.
and are used in the design of the roofing itself and its anchorage to the structure. Cp• are not to be added to the Cp for determining total uplift on the roof.
121 End walls: the end walls are the ones parallel to the wind direction and have a uniform pressure distribution over the whole building height. except for local maximum suction as indicated in Figure 8-7.
m Exposure factor: for the calculation of the exposure factor Ce for end walls, use the total height H of the building.
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C • pi
EXTERNAL PRESSURE COEFFICIENTS
INTERNAL PRESSURE COEFFICIENTS
OPENINGS
-0. 5
on side "A" +0.7
on side "B" '-1.1
Pr ('dominating on side "C" -1. 3
Figure B·9 Closed passage between large walls
!eND IV"'LLS
\ff/~ ~ 10 T h ~r-I _l..;..l_h_"_IO_-,
I ~f'~ c::::::: ===;::::=:=
¢4~ lj" c t"ORCE cou,~} FOi,
11
WALLS 0:\ TIlt: GH.OU:\I)
j 1
Figure B·I0 Free standing plates, walls and billboards
1
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TOTAL FORCE F"" Cn
q . A where A ad. h
Figure B-ll Cylinders, chimneys and tanks
TOTAL FORCE F = Cn
q'Cg
Ce
A; A z
fur d.f4 > 1'2 dlld ~;uuoth sLlriace
C FORCE: COEFFICIE:;:T
PI for closf>d
-C ·C g
EXTER"AL PRESSURE COEFF. for d {q > I'Z and moderatel y
Figure B-12 Spheres
180·
31
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L
C pe EXTER:-';AL PRESSURE COEFFICIENTS
111.0. r= o/",b h,b l= 1'1712 ¢ IA BlclOIEIFIG H J I
K
~b 0°1 + o. 71 -O. 2 1- O. 3 1- O. 3 i ·0 I 1- 0 5 - O. 8 -0.8 -0.41 -0. I
L \. ~ GIHJ_.r:y. 30°1 +0. 6i -0.31 +0.21-0.41-0. I 1-0.41-0.7 -0.9 -0.7 i -0.4
h A-~'B' ¢ I A I B I C I 0 L I MI N 0 P I Q
y.o\~:~») 90'1-0.31-0 3l+0.9l-o:31-0.8-071-0 5 -0. 3 -0. II -0. I 30°1 SectlOn C pe '" = -1.8 with Cpe·mro. = -2. 5
~mJ pl' INT ERNAL PRESSURE COEFFICIENTS
if AN' B OPENINGS ¢ =0'1 ¢ =30' ¢ =90
O· L Uniformly Ulstributed :'0.2 1:'0.2 +
P . -0.2
Q- ....I. Winuow Y <)p~~r no ~!d{' HAl< + O. 4 1+0 7 -I 0
0 All doors opt'n .", "dl 'C' - 0 1 '+0 6 + O. 8 51-1AO£lJ AREA ,'"0 SCALE... O,lly door X )Pt.'J'; on 51dt' "e" 1-1.51+0.7 + O. 4
Figure B-13 Hangar, curved roof with moderately smooth surface
h: d: r 1: t: r·'!)
-n-- 0·1 d
Fn~ ,Tr!7l ~~
Figure B-14
Total forcE' on roof
working pressure in psf
A
. q . c g
C external pressure pe coefficient • -1.0
Roof load on smooth closed tank
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Ljd > 100 FORCE COEFFICIENTS
d..[(f < 2.5 >2,5
1 Z 0, 5 A
• 1.3 1.1
Figure B-15 Poles, rods and wires
L Length '11 I, .\'1n,),"r
I \ h L .\ I'Cd
For wind normal to F =k C q'C C 'A nco g e
f lr c, Ctoo·q·C g C A
e
cl,d C i,jr ,\:1 i,li~lnt('h l'l1t'tnlH'r 00 too
+F\I 'Wi;? h + Ft h {t+ Ft tty +Ft ¥ +F,4:>-1'?'] + Fn o.-~ ~o oll-t;t .~Fn I~ +Fn O".h- =t> 0°_ !~ O'-h t::l> o~; ~ I~ ~L I, ~!~ rfOlh id ~ +F~ ~,045h
h --..l-C2 43 h
ex: C C C Ictc><> !CIlOO
C C C C:"OO c C Ic n 00 too Il_ loo noo , to<> too nDO too
° + I. 9 ,0. 9'1 + 1 M I.H "I. 7' 1'0. I + I. b I ° 1+ 0 ° 1+ OS! ° i' + l. H +0, H 1+ I 1+ H ·0. HS .0. H- +1. 1-0 1 'I to.9 'I.H~l +0.6
90' ,2. ° +1. ? I-I 9 i·1 ° - 0, ) + 1. 7- -0 9')1+0 7 1-1,6 I .. L 1 0 r +0 6
135 0 -I. H-O 1 -Z.O +0. 3 ·0, 7 =>:-1-0,7" -0.5+1.05 .) I +2.4 -1. 6 I +0,4
I KO' -2.0 +0, 1 I-I. 4 -1. 4 -I. 7 5! -0, 1 1-1 5 j 0 1-1. 7 .22. 1 -I 8 I 0
h ~ +Ft h if+Ft h 1f+Ft h If+F t h 4f+Ft h if+ Ft
o\T]I+Fn 0olI~ ~:E+Fn O·1-I~ °1f]:t .+Fn ~ ,h ~ 0- - =e> 0- c 9>
~ ci!46'h J.-h-J -00114- O~5~' IJW 0/ o·lh
ex: Cnoo jC
t <>0 Ic!)c><> C C C Icn .,., ICt 00 C noo let IX)
~ too nco tt;;)ll';)
o· +1. 4 0 1+2 )' 0 + I. 6 0 +2.0 0 +2.1 0
45 • + 1. 2. 1+ 1.6 + 1. 9' '0.6 +J.,)+1.5 + 1. 8 1+0 I + l. 4 • 0.7
90' 0 +2,2. ~O, +0,9 0 : ~ l. 9 0 -+0.1 I 0 0.75 0 +2. 0
For slenderness, F k' Reduction factor for members of finite
"oc " <0 ", ""d ~ slenderness (in general use full length res not panel length)
DO~\* rOM" 35 50 100 100 L ~ / ~
I--~& h k ,50 75 0.85 O. gO O. 1.0 ex;
Figure B·16 Structural members, single and assembled sections
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L
As = SectIon area
For wlnd nornial to surfacl' A
h t
Solidit\" r,"lti, J
1c§2J~ ~[§2J1 ~~t
l-- -----c'-- - --~ C Fore!' ClIl..'j! for d_l) II1Jltlltl'h
!loa < (.. 1 ()I1;"": t r II ~ s, ():::: ~ _ ::::: I
Re(iu( llOil factor fur trusses of
fiTlltt' length anc] slenderness
~ 0, L'i 0, 'i 0,9 O,9S I. 0
o,qtJ o,q O,~70, 77 O,bO
Figure B-17 Plane trusses made from sharp-edged sections
k SHIELDING FACTOR x
I'L,\:\".OI- f' 1 . .-\'.1-. ()F ~ II, I n . .!. I l 0, 4 0, e 10,,' 0, H 1,0
l\11Cl\lIlER I ~lEl\\l\U, II 0, 'i (),(. ; U. --;; (). I
3M 0 I
"1 0 I" f---- --- f---- ---
~rt-~~ ~q 0, ':'i 0, HI o. tJ ~ O. 4H 0, 3L 0, I- 0, hO, IS
h. ,x L 1. 00 0, HI U, "i3 0, 'iY 0, 44 0, 300, 300, 30 t - ~ ~
r---4 1. 00 p, gO 0, 7 R 0, 6') 0, 'iL 0, 4C 0, 400, 40
qx 1,00 p, G 3 0, H 3 0, 7.'.0, b I 0, SO 0, SO 0, SO
Figure B-18 Shielding factors
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CASE I WITHOUT VEHICLES
Figure B-19
lB = Length bridge
k. Cnoo
As kx from Figs. B-17 I\. B-1 8
Pedestrian
Truss and plate girder bridges
A = d . l or h . l L = true length of member
A s
C n 1. 5
I. l
1.0
(3 angle formed by wind d,rection and the normal to aXIS
k x a function of and x/b TOTAL LOAD IN WIND DIRECTION F '[ F m
Figure B-20
F FORCE ON MEMBER m
F k . 111
(Shielded F
c g
in =
Three-dimensional trusses
Acos ~
Acos P )
0.9<;
'm&anl
35
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COMMENTARYC
PROGRESSIVE COLLAPSE
AND STRUCTURAL INTEGRITY
TABLE OF CONTENTS
37
Page
Introduction .......•......•...•...•••••..........•..•.. 39 General Design Considerations for Reducing the Probability of
Progressive Collapse .....•......•.•..........•••••....... 40 References ...........•...•.......••................••••. 42
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COMMENTARY C
Progressive Collapse and Structural Integrity
INTRODUCTION 1. Progressive collapse is the spread of an initial local failure from element to element eventu
ally resulting in structural collapse disproportionate to the initial cause or to the initial local damage.
2. The present Article in Section 4.1 of the Code dealing with progressive collapse is:
4.1.1.8. Structural systems for buildings shall be designed to minimize the probability that an initial local failure of a structural element, caused by an abnormal event or severe overload, will spread to other structural members and precipitate the collapse of a disproportionately large portion of the structure.
3. Clearly it is not possible to design structures for absolute safety, nor is it economical to design for abnormal events unless they have a reasonable chance of occurrence. However, when they do, Article 4.1.1.8. requires that the designer consider rational means of limiting the spread of local failure that could result in progressive collapse. Frequently, this can be achieved by providing continuous ductile load-resisting elements and connections with inherent ductility as well as strength.
4. It is desirable to make a distinction between general and progressive collapse with regard to the consequences of the initial "local" damage. The failure of a major element leading to a general collapse is beyond the scope of the present provisions guarding against progressive collapse. For example, the failure of a column in a 1-, 2-, 3- or possibly even 4-column structure could be expected to precipitate general collapse because the local ruptured element is such a significant part of the total support of the structure at that level.
Abnonnal Events 5. Some examples of abnormal events are explosions due to gas, boiler failures or ignition of
some industrial liquids; vehicle impact; falling or swinging objects, usually during construction or demolition; adjacent excavation or flooding causing severe local foundation failure; very high winds such as tornadoes; and sonic booms.
6. Most of the foregoing events would not ordinarily be considered in design; however, events such as fires, earthquakes and corrosion, which the Code requires to be taken into account during the ordinary design process, should also not cause progressive collapse at the load levels specified in the Code.
7. On the other hand, although a building should have resistance to progressive collapse due to "accidental" abnormal events, it is accepted that well placed explosives could bring down any structure. It is not fair to the designer, therefore, to expect that his building have specific resistance to a sabotage bomb or explosive placed to cause its destruction.
8. Major disaster can result from an incident where final damage in a structure without adequate integrity may be totally disproportionate to the initial local damage. A prominent case which focussed world attention on this problem was that of a 22-storey apartment block of large, precast concrete, loadbearing panels called Ronan Point(l) in Canning Town, England in 1968, where a domestic gas explosion in an 18th storey apartment blew out the livingroom wall. The explosion led to the collapse of the whole corner of the building, when the apartments above, suddenly losing support from below, and being insufficiently tied and reinforced, collapsed one after the other. The falling debris ruptured successive floors and walls below the 18th storey and the failure progressed rapidly to ground level.
J
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9. After this collapse a Commission of Inquiry investigated the incident and made a number of controversial recommendations.(I) Subsequently, further guidelines and discussions(2) were published to clarify the design problems and resolve doubts about the economic effects of the Commission's recommendations. In addition, a great deal of research on the behaviour of building systems and on the effects of gas explosions was initiated.(3) to (7)
10. Since 1968 research into progressive collapse and abnormal loading has been in progress in many countries. Some references to this work are included.(8) to (30) Various sectors of the building industry in Canada are studying the problem and are presently attempting to synthesize simple design approaches.
II. It is recognized that in some traditional construction systems there is inherent structural integrity, a tying together of elements and an ability to redistribute overloads which is frequently overlooked. As a result, when new systems, particularly prefabricated systems, are proposed, they are often designed only to resist the primary gravity and lateral forces. Hence, some of the beneficial characteristics of the traditional systems may be lost. It is recommended that when new systems are developed and utilized by designers, their resistance to progressive collapse be thoroughly evaluated. If resistance to progressive collapse is not inherent in the new system, it should be provided by other means.
GENERAL DESIGN CONSIDERATIONS FOR REDUCING THE PROBABILITY OF PROGRESSIVE COLLAPSE
Limitation of Collapse 12. Although it is difficult and perhaps open to argument to suggest limits to the collapse
resulting from an abnormal event, it has been suggested that collapse should probably be limited (a) where the progression might be vertical to the storey where the abnormal event occurred
and the storey immediately above and below, and (b) where the progression might be horizontal,
(i) to the truss, beam or precast strip floor or roof panel initially damaged and perhaps to I on either side, or
(ii) to I bay of a full bay-sized floor or roof slab, except that where the principal support at one end of a slab is removed, 2 bay-sized slabs may hang together as a catenary.
13. There are 4 general considerations that can be used in designing to avoid progressive collapse: (I) reduction of the probability of occurrence of an abnormal event, (2) design using ductile connections, (3) design to resist abnormal loads and (4) design for alternative paths. The latter 2 are alternatives that can usefully be combined in some buildings.
14. A procedure based on the alternative path method, which is tending to become favoured because it is easier to apply and administer, is the provision of continuous ductile longitudinal and transverse ties and ties around or very near the periphery of the floors or roof and around the periphery of significant openings in them and in addition, where necessary, continuous ductile vertical ties in loadbearing walls. The tie forces are obtained by envisaging typical damage caused by abnormal events and finding alternative paths around the damaged areas.
15. The horizontal forces induced in the tie system should be resisted by frame action, walls or the undamaged parts of the structure, so that the tie forces do not in themselves cause the failure to spread.
(1) Reduction of the Probability of Occurrence of An Abnormal Event 16. In some cases the risk due to a particular abnormal event such as an explosion or vehicle
impact on walls and columns can be reduced by preventing the use or storage of explosive materials on the one hand, and by providing fenders on the other. Even when this is done, however, the structure should still be resistant to progressive collapse resulting from other causes.
..,
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17. Because a great many general failures and about 50 per cent of progressive collapses occur during construction,(12) the construction sequence should be carefully planned and monitored to ensure that at every stage the structure has sufficient strength, ductility and lateral stability to be resistant to progressive collapse if a construction accident causes the collapse of a panel or important structural element.
(2) Design Using Ductile Connections 18. Generally, connections between structural components should be ductile and capable of
considerable deformations and energy absorption under the effect of abnormal conditions. This requires that connections consist of ductile materials and be detailed in such a manner that full ductility is realized. Joints relying on friction due to gravity only, for example, are brittle in nature and their ultimate behaviour is unpredictable, hence they are generally not adequate.
(3) Design to Resist the Abnormal Events 19. If the removal of a structural member by an abnormal event will initiate progressive col
lapse, the member should be designed to remain functional when the abnormal event occurs. The major difficulty with choosing design option (3) rather than (4) is that all the abnormal events have to be anticipated and assessed.
(4) Design for Alternative Paths by Which tbe Load May Be Supported 20. One method of coping with progressive collapse is to design a structure in such a way that
it can bridge the gap left when a structural component is removed. Following are a number of ways to achieve the required integrity to carry the loads around missing walls, trusses, beams, columns and floors.(IO)
(a) Good Floor Plan. The use of a good floor plan with the proper layout of walls and columns is probably the most important single step in achieving structural integrity. In bearing-wall buildings there should be an arrangement of longitudinal spine walls to support and redu".; the span of long sections of cross-walls and to enhance the stability of the cross-wall and of the building as a whole. In the case of an explosion or vehicle impact, this will also decrease the length of wall likely to be affected.
(b) Return on Walls. The use of returns on internal and external walls will enhance their stability.
(c) Strong Points. In some designs, certain elements may be strengthened to carry the abnormal load in order to complete an "alternate path:t. Sometimes a wall return may be used to advantage as a strong point when it is adequately reinforced.
(d) Changing Direction of Span of Floor or Roof Slab. The use of a floor or roof slab reinforced in order that with a load factor just greater than 1.0 it can span in another direction if a loadbearing wall is removed will prevent the collapse of the slab and, in addition, debris loading of other parts of the structure will be minimized. Sometimes shrinkage, temperature and distribution steel will be enough to enable the slab to span in a new direction.
(e) Non-Loadbearing Walls. Internal and external non-Ioadbearing walls may be designed to support portions of the slab when an abnormal event removes a major slab support.
(1) Tensile Action of Floor Slab. Where the slab cannot change span direction, the span will increase substantially if an intermediate support is removed. In this case, if the reinforcement is securely anchored and a shear failure does not occur, the sagging of the slab will stretch the reinforcement until sufficient tension and curvature is built up to support the load as a membrane. This tension structure acts as a ductile steel net which can accommodate very heavy and variable loads by changing shape and depth and can absorb large amounts of energy through its ability to move and cushion an impact.
(g) Beam Action of Walls. Walls can be used to span over an opening if sufficient tying steel at the top and bottom of the walls allows them to act as beams with the slabs above and below possibly acting as flanges.
(h) Bracing of Trusses in Groups. In some cases the bracing or diaphragm connection of trusses into groups may be possible and may be used with lines of weakness between groups to limit the collapse to one "group" when a single truss collapses.
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Loading 21. In the application of the provisions of Article 4.1.1.8., severe deformation is acceptable in
the vicinity of the local failure at the ultimate conditions caused by the abnormal event. A load combination of dead load plus one-third of the specified live load and wind load should be used in evaluating the ultimate stability and ultimate strength of the damaged structure after the abnormal event.
REFERENCES (1) Griffiths, H., Pugsley, A. and Saunders, O. Report of Inquiry into the Collapse of Flats at
Ronan Point, Canning Town. Ministry of Housing and Local Government, H.M.S.O., London, 1968.
(2) Comments of the Institution of Structural Engineers to the Ministry of Housing and Local Government on the Proposed (Fifth) Amandments to the Building Regulations. The Structural Engineer, Vol. 47, No.9, September 1969, p. 376.
(3) Institution of Structural Engineers Report on Stability of Modem Buildings. London, September 1971.
(4) Institution of Structural Engineers Stability of Modem Buildings - introduced by L.R. Creasy in the Structural Engineer, Vol. 50, No.1, January 1972, pp. 3-6 and major discussion in Vol. 50, No.7, July 1972, pp. 275-288.
(5) Graff, S. Structural Joints in Precast Concrete Industrialized Buildings. Industrialized Forum, Vol. 2, No.4, July 1971, pp. 25-32.
(6) Rasbash, D.J. and Stretch, K.L. Explosions in Domestic Structures. The Structural Engineer, Vol. 27, No. 10, October 1969, p. 403.
(7) Alexander, S.J. and Hambly, E.C. The Design of Structures to Withstand Gaseous Explosions. Concrete, February 1970, pp. 62 and 107.
(8) Ligtenberg, F.K. Structural Safety and Catastrophic Events, from Symposium on Concepts of Safety of Structures and Methods of Design. International Association for Bridge and Structural Engineering, Final Report, Vol. 4, London 1969.
(9) Morton, J., Davies, S.R., and Hendry, A.W. The Stability of Loadbearing Brickwork Structures Following Accidental Damage to a Major Bearing Wall or Pier. Edited by H.W.H. West, Pap. No. 45, Proc. 2nd Int. Brick Masonry Conf., Stoke-on-Trent, England, published by Br. Ceram. Res. Assoc., 1970.
(10) Ferahian, R.H. Design Against Progressive Collapse. Publication NRCC No. 11769 of the Division of Building Research, National Research Council of Canada, Ottawa, April 1971.
(11) Ferahian, R.H. Buildings: Design for Prevention of Progressive Collapse. Civil EngineeringASCE, February 1972, p. 66.
(12) Allen, D.E. and Schriever, W.R. Progressive Collapse, Abnormal Loads and Building Codes. Proceedings of the ASCE National Meeting on Structural Engineering held in Cleveland, Ohio, April 1972, pp. 21-47. Also Research Paper No. 578, publication NRCC No. 13658 of the Division of Building Research, National Research Council of Canada, Ottawa.
(13) Granstrom, S.A. The Scandinavian Approach to Structural Safety. Paper No.7 of Buildings and the Hazard of Explosion. Proc. of a symposium at the British Research Establishment, Garston, U.K., 18 October 1972, edited by R.J. Mainstone.
(14) Burnett, E.F.P., Somes, N.F. and Leyendecker, E.V. Residential Buildings and Gas-Related Explosions. National Bureau of Standards, Centre for Building Technology, Washington, D.C., Report NBSIR 73-208, 1973.
(15) Steele, W.A., Bowser, D. and Chapman, R.E. The Incidence of Hazardous Material Accidents During Transportation and Storage. National Bureau of Standards, Washington, D.C., Report NBSIR 73-412, November 1973.
(16) Leyendecker, E.V. and Fattal, S.G. Investigation of Skyline Plaza Collapse in Fairfax County, Virginia. National Bureau of Standards, Washington, D.C., Report NBSIR 73-222, 1973.
(17) Dragosavic, M. Structural Measures Against Natural Gas Explosions in High-Rise Blocks of Flats. Heron, Vol. 19, No.4, 1973.
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(18) Somes, N.F. Abnormal Loading on Buildings and Progressive Collapse. National Bureau of Standards, Centre for Building Technology, Washington, D.C., Report NBSIR 73-221, 1973.
(19) Taylor, N. and Alexander, SJ. Structural Damage in Buildings Caused by Gaseous Explosions and Other Accidental Loadings. Current Paper 45174, Building Research Establishment. Watford, England, 1974.
(20) Lewicki, B., and Olesen, S.O. Limiting the Possibility of Progressive Collapse. Build. Res. Pract., Vol. 2, No.1, 1974, pp. 10-13.
(21) Granstrom, S. and Carlsson, M. Byggforskningen T3: Byggnaders Beteende Vid Overpaverkningar (The Behaviour of Buildings at Excessive Loadings). Swed. Inst. Building. Res., Stockholm, 1974.
(22) Leyendecker, E.V., Breen, J.E., Somes, N.F. and Swatta, M. Abnormal Loading on Buildings and Progressive Collapse, An Annotated Bibliography. Bldg. Sci. Series 67, NBS (376 References), May 1975.
(23) Burnett, E.F.P. Abnormal Loading and Building Safety. Industrialization in Concrete Building Construction, SPA8, ACI, Detroit, 1975.
(24) Regan, P.E. Catenary Action in Damaged Concrete Structures. Industrialization in Concrete Building Construction, SP-48, ACI, Detroit, 1975.
(25) Burnett, E.F.P. Building Safety, Abnormal Loads and the Avoidance of Progressive Collapse: Regulatory Approaches to the Problem. National Bureau of Standards, Centre for Building Technology, Washington, D.C., Report NB-GRC 75-48, October 1975.
(26) Taylor, D.A. Progressive Collapse. Canadian Journal of Civil Engineering, Vol. 2, No.4, December 1975, pp. 517-529.
(27) Taylor, D.A. and Schriever, W.R. Notes on a One-day Colloquium on Progressive CoIlapse. Proceedings No. I of the Division of Building Research, publication NRCC No. 15377, National Research Council, Ottawa, June 1976.
(28) Agarwal, R.K. and Gardner, N.J. Form and Shore Requirements for Multistorey Flat Slab Type Buildings. Journal of the American Concrete Institute, Proc. Vol. 71, No. II, November 1974, pp. 559-569.
(29) Feld, J. Reshoring of Multistorey Concrete Buildings, Concrete Construction, May 1974, pp. 243-248.
(30) Fintel, M., Schultz, D.M. A Philosophy for Structural Integrity of Large Panel Buildings. Journal of the Prestressed Concrete Institute, Vol. 21, No.3, May/June 1976, pp. 46-69.
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F
COMMENTARY D
Effects of Deformations
in Building Components
TABLE OF CONTENTS
45
Page
Structural Effects ................•.....•..••.....•..•....... 47 Effects on Cladding . . . . . . . . • . . . . . • . . . . . . . . . • . . . . . . . . . . • . . . . .. 48 Bibliography of Temperature Effects
on Structures .......••.•..............•..•.•.•..•..•..... 49
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COMMENTARYD
Effects of Deformations in Building Components
Structural Effects 1. When building materials expand and contract due to temperature changes, considerable
forces may be produced in restrained structural elements, i.e. in those elements that are not free to expand and contract with the changes in temperature. Often these forces are compounded with those produced by shrinkage, by creep and by moisture content changes and are, therefore, difficult to analyse or predict. In many situations, however, it is very important for the structural designer to consider the probable structural effects of the forces produced by temperature changes along with all other forces; indeed the designer is required to do so by Sentence 4.1.2.1.(1) of the National Building Code 1977.
2. In addition to expansion and contraction, temperature changes may produce differential deformation or warping of materials as a result of a gradient in temperature through the thickness of materials or assemblies. Again this may tend to complicate the assessment of deformations or stresses, but a rational judgement must be made in design if building elements are to perform in a satisfactory manner.
3. If these forces are not properly considered, the stresses resulting from such forces can lead to serious failures (usually cracking) in materials and structural members. Failures occur when clearances are insufficient, when fasteners do not allow movement or deformations, or, in the case of restrained elements, when the elements are not strong enough to withstand the stresses induced. An elementary review of the phenomenon of thermal and moisture deformations in building materials is given in Reference (l), from which Table D-I has been adapted, to give an indication of the order of magnitude of movement to which various materials are liable.
4. The daily temperature changes that should be considered will depend on the climate of the locality and may often be as much as 80 FO in materials exposed to outside weather conditions. The seasonal temperature changes are considerably larger and, as explainedpl may be as much as 230 fO for dark-coloured materials backed by insulation. For Iight.coloured and thicker materials the range of temperature change will not be as large. The rate and duration of extreme temperatures have a bearing on the temperature effect. Thus, although temperature ranges of 80 fO and 230 fO have been used in Table D-I, these figures should be considered as examples only, and each situation should be considered separately.
5. An example of the importance of considering temperature variations is the case of multistorey apartment and office buildings with exterior columns partially, and in some cases fully, exposed to the weather. Exposed columns, when subjected to seasonal temperature variations, change their length relative to interior columns, which remain unchanged in a controlled environ· ment. Although in low buildings, this causes insignificant structural problems, in tall buildings temperature stresses become significant and must be investigated thoroughly.
6. Dimensional changes occur not only as the result of temperature changes, but also from shrinkage, moisture content changes, chemical processes and creep deformation in the component materials of a building. If the building or component is not free to contract or expand, tensile or compressive stresses result. These stresses can be relieved or reduced to tolerable limits by con· traction and expansion joints. Such joints are particularly important to allow contraction to take place along certain preselected lines rather than to produce cracks along accidental lines of least resistance.
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48
Table D·l
lYPICAL TEMPERATURE AND MOISTURE DEFORMATIONS FOR SOME COMMON BUILDING MATERIALS
Deformation Due to Moisture
Coefficient Temperature Change Deformation Failing of on Wetting from Modulus
Stress, Thermal Dry to Saturated of
Compo (C) or Expansion,
of80 fO of230 fO (or Vice Versa) Elasticity Tension (T), per of Per In.l Per Iln.l Per In.l
E,psi I psi
Cent 10ft Cent 110ft Cent 10ft
Normal ,
2,500-5,OOO(C) dense 6xlO 6 0.05 0.06 .0.14 0.17 0.01-0.035 0.01-0.04 2.5-4.lxlQ6 concrete I 250-500(T)
2,500(C) or over Brick 3xlO 6 0.024 0.03 0.07 0.08 0.007 0.008 3x 1()6
500(T) or over
Marble 2,600-28,000(C) and dense 3x 1O~6 0.024 0.03 0.07 0.08 <.001 ~ IOxl()6 limestone 600(T) or over
Sandstone I 0.05610.07 5,OOO-20,000(C)
7xlO 6 0.16 0.19 0.07 0.08 3.3x106
I
400(T)
Rein-forced IOxlO~6 0.08 0.10 0.23 0.28 <.001 0.3-2.0x I Q6 10,OOO-50,OOO(T) polyester
Steel 6.3xlo-o 0.05 0.06 0.14 0.17 none ~ 29x )()6 (yield strength)
Copper IOxlO 6 0.08 0.10 0.23 0.28 none 17x)()6 28,OOO-50,OOO(T)
Alumi-14xlO 6 0.11 0.13 0.32 0.38 1O.3xl()6 20,OOO-40,OOO(T) none ~
num
Col.I 2 3 4 5 6 7 8 9 lO
Effects on Cladding 7. In the design of all buildings, but particularly very long and very high buildings, the effects
of movements of the structural members on the cladding elements should be considered. Shortening and lengthening of columns due to temperature and shrinkage effects and creep can crack, buckle or otherwise overstress cladding materials and their fastenings. Deflections and linear movements of beams and spandrels and building sidesway can have similar effects. Failure to consider these differential movements in design has caused many cases of cladding damage. For example, shortening of concrete frames has been known to cause spalling and loosening of brick and stone c1addings. The phenomenon is not, however, limited to concrete frames, nor are the effects limited to stone and brick cladding. References (3) and (12) to (17) discuss these effects in greater detail.
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BIBLIOGRAPHY OF TEMPERATURE EFFECTS ON STRUcruRES (1) Baker, M. C. Thermal and Moisture Deformations in Building Materials. Division of Build
ing Research, Canadian Building Digest 56, National Research Council of Canada, August 1964.
(2) Stephenson, D. G. Extreme Temperatures at the Outer Surface of Buildings. Division of Building Research, Canadian Building Digest 47, National Research Council of Canada, November 1963.
(3) Khan, F. R. and Fintel, M. Effects of Column Exposure in Tall Structures. Paper in three parts. (a) Temperature Variations and Their Effects, (b) Analysis of Length Changes in Exposed Columns, and (c) Design Considerations and Field Observations of Buildings. Jour. American Concrete Inst., Vol. 63, No.8, August 1966 and Vol. 65, No.2, February 1968.
(4) Weidlinger, P. Temperature Stresses in Tall Reinforced Concrete Buildings. Civil Engineering, New York, Vol. 34, No.8, August 1964.
(5) Jones, K. Restraint of Structures Attached to Mass Concrete. Jour. Structural Division, Am. Soc. Civ. Engrs., Vol. 87, No. ST8, December 1961.
(6) Marshal, W. T. Shrinkage and Temperature Stresses in Reinforced Concrete. Civil Engineering, London, Vol. 56, No. 665, December 1961.
(7) Fischer, P. Differential Temperature Movements in Rigid Frame. Jour. American Concrete Inst., Vol. 59, No.6, June 1962.
(8) Allen, D. W. The Calculation of Temperature Stresses. Concrete & Constructional Engineering, Vol. LVII, No.9, September 1962.
(9) England, G. L. and Ross, A. D. Reinforced Concrete under Thermal Gradients. Magazine of Concrete Research, Vol. 14, No. 40, March 1962.
(10) Principles of Modern Buildings, Vol. 1, British Building Research Station, HMSO, London, 1959.
(11) Slack, J. H. and Walker, M. 1. Movement Joints in Concrete. Concrete Society Limited, Grosvenor Gardens, London, S.W.I, Technical Paper, 1967.
(12) Deflections of Reinforced Concrete Flexural Members. Report of ACI Committee 435, ACI Manual of Concrete Practice 1970, Part 2.
(13) Mayer, H. and Rusch, H. Building Damage Caused by Deflection of Reinforced Concrete Building Components. Deutscher Ausschuss fur Stahlbeton, Heft 193, Berlin 1967, National Research Council Technical Translation TT1412.
(14) Plewes, W. G. Cladding Problems Due to Frame Movements. Division of Building Research, Canadian Building Digest CBD 125, National Research Council of Canada, Ottawa, May 1970.
(15) Copeland, R. E. Flexible Anchorage of Masonry Walls. Concrete Products, Vol. 71, No.7, 1968, p. 54.
(16) Finte], M. and Khan, F. R. Effects of Column Creep and Shrinkage in Tall Structures-Prediction of Inelastic Column Shortening. Jour. of ACI, December 1969, Proc. V66, No. 12, p. 957.
(17) Foster, D. Some Observations on the Design of Brickwork Cladding to Multi-storey RIC Framed Structures. BDA Tech. Note, Vol. 1, No.4, September 1971, The Brick Development Association, 3-5 Bedford Row, London WC1 4BU.
I
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COMMENTARY E
LOAD COMBINATIONS
FOR STRUCTURAL DESIGN
TABLE OF CONTENTS
51
Page
Introduction ..............................................• 53 Simultaneous wads ....••....•...•.....••................... 53 Stress Reversal (NBC 4.1.3.3. and 4.1.4.2.(3» ...•••..••....••..•..• 53 Overturning, Uplift and Sliding (NBC 4.1.3.4. and 4.1.4.2.(1» • . . . . • • . .. 54 References ..........•......•.••..........•......•.....•... 54
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F
COMMENTARY E
Load Combinations for Structural Design INTRODUCTION
53
I. Subsection 4.1.3. and Article 4.1.4.2. of the National Building Code of Canada 1977 are intended to provide an acceptable and relatively uniform degree of safety in the design of structural members under different load combinations. The rules pertain to the ultimate limit states (allowable stresses, required structural resistance) and not, in general, to serviceability considerations such as deflection. The rules take into consideration the probability of simultaneous occurrence of the design loads stipulated in NBC Subsections 4.1.5. to 4.1.10. They are not intended to take into account the change in material strengths with changes in duration ofloading.
SIMULTANEOUS LOADS
2. As dead load is nearly constant throughout the life of a structure, a combination of dead load with any other load constitutes a basic combination in which the basic safety or load factors are applicable. When dead load is combined with 2 or more other loads, the simultaneous occurrence of the full design values of each of the load effects is less likely to occur than the basic combination above. Sentences 4.1.3.2.(1) and 4.1.4.2.(4) of the NBC take this into consideration by allowing reductions in the total effect due to combinations of the dead load effect with 2 or more other load effects.
3. Because of the very short duration of some design loads, the probability of their simultaneous occurrence is extremely small. Thus, according to NBC Sentence 4.1.2.1.(1), earthquake load does not need to be considered simultaneously with wind load. When L includes horizontal loads caused by crane operations, the load combination factor of .75 is intended to be applied when a single crane only is in operation. For industrial buildings with multiple crane operations, the same load combination factor for horizontal crane loads should be applied on the basis that the largest crane only is operating at maximum capacity in the most critical location. The load combination factor for the combined effect of wind or earthquake forces acting simultaneously with the horizontal forces from multiple crane operations should be assessed by the designer on a rational basis in consultation with the building user.
STRESS REVERSAL (NBC 4.1.3.3. AND 4.1.4.2.(3» "-
4. Stress reversal may occur at a critical section of a member when the dead load effect is counteracted by a load effect of opposite sign, such as in a truss member which is in tension under dead load, but undergoes compression due to wind load or non-uniformly distributed snow loads, or a support which is in compression under dead load but undergoes tension due to wind load. Unsafe designs may result(l) if, as in working stress design, the usual safety factor is applied to a small difference between 2 independent load effects. An example is the collapse of cooling towers at Ferrybridge, England.(2)
5. This kind of error is avoided in limit states design by considering that the safety factor is made up of 2 factors: one a load factor to take account of overloads or underloads, the other a performance factor to take into account deviations of structural resistance from that based on specified material properties and dimensions. In the example of stress reversal due to wind load, a safe design results if an overload factor is applied to the wind effect (Q) and an underload factor to the dead load effect (0). In accordance with NBC Article 4. t .4.2., this is achieved by the following requirement:
cpR 2 1.5Q-O.850 (1)
where R is the resistance and cp the performance factor.
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6. Since this approach to the safety factor is not at present used in working stress design in NBC Subsection 4.1.3., empirical rules are given in CSA A23.3-l973, "Code for the Design of Concrete Structures for Buildings" and in CSA SI6-1969, "Steel Structures for Buildings." These rules may not be satisfactory for structures such as towers that are subject primarily to wind load and dead load only; Equation (I) is recommended for such cases.
OVERTURNING, UPLIFT AND SLIDING (NBC 4.1.3.4. AND 4.1.4.2.(1»
7. In the case of overturning, uplift and sliding, the stabilizing effect of the dead load is overcome by the counteracting effect of a load such as wind, earthquake, earth pressure or eccentric live load. In this sense, overturning and sliding are similar to stress reversal, and the reasoning given above regarding the safety provisions for stress reversal also applies to overturning, uplift and sliding. For working stress design, NBC Sentence 4.1.3.4. requires a safety factor of not less than 2.0 on the loads tending to cause overturning or sliding. For limit states design Equation (I) applies.
8. With regard to overturning, it is assumed that the designer considers that: (I) unless the foundation material has a high strength the point of overturning is not at the toe of the building, and (2) for flexible structures the dead load acts through the centre of gravity of the deflected structure.
References (I) Allen, D. E. Safety Factors for Stress Reversal. Publications, International Association for
Bridge and Structural Engineering, Vol. 29/II. (2) Report of the Committee of Inquiry into Collapse of Cooling Towers at Ferrybridge, Monday,
I November 1965. Central Electricity Generating Board, London .
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COMMENTARY F
LIMIT STATES DESIGN
TABLE OF CONTENTS
Limit States Safety and Serviceability Criteria .............................. . Definition of Specified Loads and Resistances ..................... . Partial Factors ............................................ . Performance Factors ........................................ . References ......•.......... " ............................. .
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57 57 59 59 60 61
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COMMENTARY F
Limit States Design
1. Limit states design was introduced by Subsection 4.1.4., a new Subsection of the National Building Code 1975 as an alternative to existing procedures for design calculations of building structures. This Commentary describes what is meant by limit states design and the reasons for introducing it into the National Building Code and associated CSA Structural Standards. In addition, a background explanation is given of the safety and serviceability criteria contained in NBC Subsection 4.1.4. The criteria are the result of meetings of a CSA/NBC Joint Liaison Committee on Limit States Design, a Committee which represents all structural and foundation standards used by the National Building Code of Canada.
LIMIT STATES
2. All building structures have the same basic functional requirements, namely that they should be safe from collapse during construction and that they should be safe from collapse and be serviceable during the useful life of the building. The onset of various types of collapse and unserviceability are called limit states. Those concerning safety are called ultimate limit states and include the attainment of load-carrying capacity, fracture, overturning, sliding and large deformation. Those concerning serviceability are called serviceability limit states, and include excessive deflection. permanent deformation, cracking and vibration.
3. The primary aim of limit states design is to prevent the attainment oflimit states, that is to prevent various kinds of failure. This should be clearly understood by the designer when reading and interpreting structural standards, since any detailed requirement is aimed at preventing the attainment of a particular limit state.
4. Limit states design is not new, it is basically a clarification of previously well-known principles. There is, however, a change of emphasis.
5. Existing design methods-allowable stress design, plastic design, ultimate strength design-put the mam emphasis on a particular structural theory such as elastic or plastic theory. No particular theory, however, is universally applicable to all limit states and all types of construction. Elastic theory is generally applicable for serviceability limit states and fatigue, plastic theory for ultimate limit states in some cases, a stability analysis for overturning. The appropriate theory will either be indicated in the structural material standard or chosen by the designer.
6. Furthermore, existing design methods emphasize only one limit state, usually associated with a limiting stress or member strength. Due to changes to lighter composite-acting construction with less in the way of stiffening and damping from curtain walls and partitions. serviceability requirements such as deflection and vibration are becoming more critical in structural design, and deserve the same consideration as strength requirements. In contrast to existing design methods, limit states design applies to all kinds of failure such as collapse, overturning and vibration, and to all materials and types of construction.
7. In summary, limit states design provides a unified rational basis for design calculations of building structures of all materials. This is the main reason that it is being adopted for international standardization.(l)
SAFETY AND SERVICEABILITY CRITERIA
8. As already stated, the aim of limit states design calculations is to prevent failure, that is the attainment of a limit state, Unpredictable factors such as loads and workmanship enter into the calculations, however, and so there is the further qualification "that the probability of failure be sufficiently small." The more serious the consequences of failure, the smaller should be the proba-
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bility of failure. Satisfactory failure probabilities are achieved through the use of reliable materials, through competent structural engineering, manufacture and erection and by the use of safety and serviceability criteria in the design calculations. The safety and serviceability criteria should provide adequate human safety and serviceability on the one hand, and economy on the other hand, i.e. provide optimum or smaller failure probabilities.m This is achieved in limit states design through the statistical definition of specified loads and material properties and the use of partial factors.
9. The general form of safety and serviceability criteria contailled in NBC Subsection 4.1.4. can be expressed as follows:
where
¢R;::::effect of[a[)D+ y 1/; (aLL+ aQQ+aT T)] (I)
D, L, Q and T are the specified loads (dead, live, wind or earthquake, temperature, etc.) defined in NBC Sentence 4.1.2.1 (I).
a = a load factor applied to one of the specified loads which takes into account variability of the load and load patterns and, to some extent, inaccuracy in the structural analysis.
1/; a load combination factor applied to loads other than dead load to take into account reduced probability of simultaneous occurrence of loads from different sources,
y an importance factor applied to the loads other than dead load which takes into account the consequences of collapse as related to the use and occupancy of the building, i.e. the danger to human safety, the economic loss.
R the calculated resistance of member. connection or structure based on the specified material properties.
<p a performance factor applied to the resistance or specified material property which takes into account variability of material properties and dimensions, workmanship, type of failure (for instance brittle versus ductile) and uncertainty in the prediction of resistance.
10. When the specified loads and resistances are multiplied by the appropriate partial factors. the products are called the factored loads and factored resistances. The load factors, load combination factor and importance factor in the right side of Equation (l) are given in NBC Subsection 4.1.4., the same for all building structures. The resistance and performance factors in the left side of Equation (1) are contained in the appropriate structural standard, different for different materials. type of structural element and type of behaviour.
11. In the case of the ultimate limit states, Equation (I) states that the factored resistance must be greater than or equal to the effect of factored loads. A special situation arises in cases of overturning. uplift and stress reversal, where the load effects tending to cause failure are counteracted by the dead load effect. For such cases positive anchorage is required if the factored load effects tending to cause failure are greater than the stabilizing effect of the dead load multiplied b~ a dead load factor of 0.85.
12. With regard to overturning, it is assumed that the designer considers that: (1) unless the foundation material has a high strength the point of overturning is not at the toe of the building. and (2) for flexible structures the dead load acts through the centre of gravity of the deflected structure.
13. Pattern loading considerations are required in accordance with NBC Sentence 4.1.6.3.( 1 ) for floor live load and NBC Sentence 4.1.7.2.(2) for snow load. Such pattern loading requirements should be considered in conjunction with the dead load multiplied either by 1.25 on all spans or 0.85 on all spans, whichever produces the most unfavourable effect. .
14. For the serviceability limit states, instead of a factored resistance. cpR represents a criterion such as an allowable deflection, acceleration or crack width. Equation (l) therefore results in serviceability requirements of the same type as contained in the past. It is important, however. to understand which limit state a particular criterion is attempting to prevent.
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DEFINITION OF SPECIFIED LOADS AND RESISTANCES
15. For limit states design. specified loads and specified material properties used to calculate resistance are defined on the basis of probability of occurrence. Values so defined are called characteristic values. Material properties are controlled by statistical sampling and the characteristic value corresponds to a limiting probability of unfavourable test values. Climatic loads are based on measurements taken at weather stations, and the characteristic value corresponds to a return period. Characteristic values for material properties and loads used in the National Building Code are given in Table F-1. Where statistical information is lacking, e.g. for live loads, the specified values correspond to the existing nominal values.
16. For new materials or new control methods, it is recommended that material resistance be defined on the basis of the 5 per cent probability level and material stiffness on the basis of the 50 per cent probability level; where statistical sampling is used a 75 per cent confidence level is recommended.
17. Since the characteristic values in Table F-I refer to standard tests or measurements (for example the standard cylinder test for concrete, hourly wind speed at an airport). the probability levels cannot be directly applied to what happens in the structure without further considerations.
Table F-l
CHARACTERISTIC VALUES FOR LOADS AND MATERIAL PROPERTIES IN THE NATIONAL BUILDING CODE
Materials Probability Level Concrete (cylinder test) to per cent Wood (tests on small clear specimens) 5 per cent Steel-(yield in tension) Not defined C- I to 2 per cent) Masonry (for prism tests) to per cent
Loads Return Period Dead Not defined Floor Not defined Snow 30 years Wind-ultimate limit states 30 years
--serviceability limit states 10 years Earthquake-ultimate limit states 100 years
Column I 2
PARTIAL FACTORS
18. To provide sufficiently small failure probabilities for the limit state under consideration, limit states design makes use of partial factors in contrast to the total safety factor used by existing design methods. The use of partial factors gives more consistent safety for different load combinations as well as for different combinations of materials, with a consequent economy of materials. It also provides a better basis for development of new types of construction or for unusual situations, since all partial factors, including performance factors for the well-known basic structural materials, will either be known or can be established on a rational basis.
19. The partial factors contained in NBC Subsection 4.1.4. were determined by the CSAINBC Joint Liaison Committee on Limit States Design on the following basis:
For buildings of normal human occupancy the importance factor was taken equal to 1.0 for practical purposes, since this classification corresponds to most buildings.
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Load factors were first chosen on the basis of variability of the loads and load patterns only, excluding approximations in structural analysis. Based on the probabilistic assumptions given in Reference (3) for a 30-year life, the following load factors were obtained, corresponding to a probability level 3 standard deviations above the mean: 1.2 for dead load and 1.4 for live load and wind load.
To take into account approximations in structural analysis these load factors were increased to 1.25 for dead load and 1.5 for live load and wind or earthquake. The load factor for imposed strains (temperature, shrinkage, differential settlement) was taken as 1.25, the same as for dead load. As a general rule, however, inaccuracy in structural analysis should be taken care of by means of conservative assumptions in the analysis. Inaccuracies in member resistance are taken into account in the factored resistance.
The load combination factor, 1/;, was determined on the basis of a probabilistic study for the combination of dead, live and wind loads for office or residential buildings.(3) These studies indicate that 1/;=0.7 gives a safety consistent with that for the basic combination of dead load plus live load. The same studies also indicate that for overturning, uplift and stress reversal, safety consistent with that for dead load plus live load is obtained when lXD=0.85.
The importance factor is equal to 1.0 for buildings of normal human occupancy. For post disaster buildings, importance factors greater than 1.0 are applied to wind load in NBC Subsection 4.1.8. (by means of increased return period) and earthquake load in NBC Subsection 4.1.9. The reason for retaining this approach is that the importance factor should be applied only to those loads which can cause a disaster. For buildings of low human occupancy, such as farm or storage sheds, an importance factor less than 1.0 applied to loads other than dead load is justified on the basis of reduced hazard to humans. The factor 0.8 along with the reduction in dead load factor from 1.5 to 1.25 closely corresponds to the 25 per cent increase in allowable stress contained for some years in the ACNBC Canadian Farm Building Code.
For the serviceability limit states, in accordance with NBC Article 4.1.4.3., the partial factors are generally taken as 1.0; an exception is the reduction for load combinations. Two reasons for continuing this traditional approach are: the consequences of serviceability failure are considerably less serious than for collapse, and therefore the partial factors are closer to 1.0; since the criteria for serviceability failures cannot be accurately defined, only simple empirical rules which absorb safety factors are justified.
20. The load factors in NBC Subsection 4.1.4. for materials other than concrete are less than those presently in use for concrete ultimate strength design in CSA A23.3-1973, "Code for the Design of Concrete Structures for Buildings." In accordance with NBC Sentence 4.1.4.2.(6), the load factors and rules for load combinations and pattern loading in CSA A23.3-1973 should be used for concrete structures.
21. During construction all permanent and temporary structural members should have sufficient factored resistance to carry the effect of factored construction loads. Adequate load factors not less than 1.25 (greater if the construction load is more uncertain than the dead load), with importance factor equal to 1.0, are recommended.
PERFORMANCE FACTORS
22. The performance factors will be determined by each structural materials standard as it develops limit states design. In accordance with the definition, the performance factor takes into account variability of material properties and dimensions, including the effects of workmanship, uncertainty in the prediction of resistance and also the type of failure, whether it gives warning or not. Also systematic effects relating material properties from the standard test to those in the structure, e.g. rate effect, test location, curing and casting conditions and moisture content, should be taken into account either separately or by adjustments in the performance factors.
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23. In accordance with the basic requirements of safety, the partial factors are chosen to give sufficiently low consistent failure probabilities, depending on the consequences of failure and independent of type of material or construction. With all other partial factors fixed in NBC Subsection 4.1.4., this leaves the performance factors to be chosen to satisfy this requirement. This can be achieved in 2 ways. One is by calibration(4) to existing rules, that is performance factors which give the same structural dimensions as existing rules for certain practical cases, such as yielding of steel or crushing of concrete, which experience has shown to be adequately safe. The other is by direct probability studies such as those carried out in References (2) to (4). In general, a combination of both approaches is needed.
REFERENCES (I) General Principles for the Verification of Safety of Structures. International Standard ISO
2394. First Edition-1973-02-15. (2) Ravindra, M. K. and Lind, N. C. Theory of Structural Code Optimization. ASCE Journal of
the Structural Division, Vol. 99, ST7, July 1973, p. 1541. (3) Allen, D. E. Limit States Design-A Probabilistic Study. Canadian Journal of Civil Engineer
ing, Vol. 2, No.1, March 1975, p. 36. (4) Siu, W., Parimi, S. R. and Lind, N. C. Practical Approach to Code Calibration. ASCE Journal
of the Structural Division, Vol. 101, ST7, July 1975, p. 1469.
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COMMENTARYG
TRIBUTARY AREA
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COMMENTARYG
Tributary Area 1. Since live loads are generally given as uniformly distributed loads over a floor area, and
because dead loads can usually be considered as uniform loads, either over an area or along the length of a flexural member, design engineers have for years used the concept of tributary area to determine the loads that beams, girders and columns carry. Once the concept is applied to any floor, it is easily extended for multiwstorey columns to any number of floors.
2. Earlier design standards recognized that the probability that all the floors of a multi-storey building would be loaded to the full live load simultaneously was very remote. Therefore, to design the columns for the full live load of a number of floors was unduly restrictive, and thus reductions in the live load were devised as a function of the number of floors supported by the columns.
3. In the 1960 edition of the National Building Code, with the recognition that the average live load was a function of the area supported, the rationalization was carried one step further and a reduction of 15 per cent was allowed for beams, girders and trusses supporting areas of greater than 200 sq ft.
4. In the 1965, 1970 and 1975 editions and again in the 1977 edition, provisions have been included for live load reduction based on tributary areas with 2 different expressions, one for office and apartment buildings and the other for storage or similar areas.
5. Therefore, for determining the total dead load to be supported by a given member, and to determine what live load reduction factor should be applied, a clear definition of tributary area, about which some confusion appears to have existed, is needed.
6. In simple construction, where the ends of symmetrically loaded flexural members are connected for shear only, a point of zero shear exists at the mid length of the member.
7. The reaction at the end of the member, when uniformly loaded, is equal to all the load on the member from its end to its mid length. Therefore, for the purpose of determining the reaction, all the load on the Ih length of the beam can be used, and the Ih length of the beam can be considered to be the tributary length.
8. By extending this concept to girders and then to columns, the tributary areas for other members can be determined.
9. For continuous construction, unless the end moments on a beam are equal, the point of zero shear will not be at mid length, and therefore tributary areas as determined above will involve some approximation, although for the whole structure all the area will be taken into account.
10. The tributary area for primary floor elements (those that carry floor loads directly such as flat slabs or 2-way slabs but excluding decks, precast units and I-way slabs) is the area bounded by column lines or by a combination of column lines and lines of supporting members such as joists, beams and girders, whichever is the lesser. No live-load reduction factors should be applied to a deck, precast units or I-way slabs because of the uncertainty of the degree of lateral distribution ofloads.
11. The tributary area for a member supporting a portion of a floor is the area enclosing the member and bounded, assuming simple construction and uniformly distributed loads, by assumed lines of zero shear in the elements supported by the member.
12. The tributary area of a column, per floor, is t;2 the sum of the tributary areas of the floor members framing into it.
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13. Examples of tributary areas are given in Figures G-\ to G-5 with the tributary areas designated by the following:
PR IMARY ELEMENT IE:~:::I
JOIST, BEAM OR GIRDER
COLUMN
1"""" ......
w:01 r· .. · '. :'-1 ....... ...... .. '" . '" ..
111111111"
'--
Figure G-l Tributary areas for flat slabs without beams and girders
I
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~I t ~ I Vl
Figure G-2 Tributary areas for I-way slab with girders
JOIST GIRDER
BEAM
Figure G-3 Tributary areas for a I-way deck or slab with joists, beams and girders
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Figure G-4 Tributary areas for a 2-way slab with beams
Figure G-S Tributary areas for a 2-way slab with joists, beams and girders
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COMMENTARY H
SNOW LOADS
TABLE OF CONTENTS Page
Variations of Snow Loads on the Ground and on Roofs ......••.....•. 71 Design Roof Loads in the National Building Code ••• . . . . . . . • . . . . . . . . 74 Determination of Design Snow Loads on Roofs . . . . . . . . . . • . . . . . . . . .. 75 Detailed Explanations of Figures H-l to H-8 . . . . . . . . . . . . . . . . . . . . . .. 77 References ...•.•.•.•..•.....•..••.•...•.........•.•...•••. 78
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COMMENTARYH
Snow Loads
VARIATIONS OF SNOW LOADS ON THE GROUND AND ON ROOFS
1. Snow loads on roofs vary according to geographical location (climate), site exposure, shape and type of roof, and of course from one winter to another.
2. Before the roof snow loads can be discussed, however, the ground loads must be considered, since they are the basis for the determination of the roof loads. Ground snow loads, forming part of the basic climatic information needed for building design in Canada, are dealt with in NBC Supplement No.1, "Climatic Information for Building Design in Canada 1977."(1) There, the snow loads on the ground are given both in the form of a chart (Chart 9) and in the form of a table, "Design Data for Selected Locations in Canada."
Variations with Climate 3. The wide climatic variations existing in Canada produce wide variations in snow load con
ditions across the country. Coastal regions (both Atlantic and Pacific), because of frequent thaws during the winter, are usually characterized by snow loads of short duration, often caused by a single storm. The mountainous regions of British Columbia and Alberta experience the heaviest snow loads in the country, lasting the entire winter and varying considerably with elevation. Prairie and northern regions have very cold winters, with small annual snowfalls; owing to frequent strong winds there is considerable drifting of snow both on roofs and on the ground. Finally, the central region, including Ontario and Quebec, is marked by varying winds and snowfalls, and sufficiently low temperatures in many places to allow snow accumulation all winter. In this area high uniform loads as well as high drift loads occur.
Local Variations-Mountain Areas 4. It should be noted that charts on such a small 'icale as those in Supplement No. I cannot
show local differences in the weather elements even where these are known to exist. Practically all observations used in preparing Chart 9 were, of necessity, taken at centres of population, and hence the Chart applies essentially to the areas where the observations were made. This should be noted by designers particularly for mountainous areas because ground snow loads are known to increase with elevation. In mountain areas therefore, the snow loads of Chart 9 and the Table apply only to the areas listed in the Table of Design Data for Selected Locations in Canada in Supplement No. 1.<1) For some mountain areas water equivalent data, collected for hydrological purposes, are available from which the relationship between elevation and ground snow load can sometimes be determined for a given climatic zone, but in any case local experience should be taken into account.
5. Since 1967 observations have been made by the Geotechnical Section of the Division of Building Research of ground snow loads at several elevations on each of several mountains in B.C.(2) These indicate increases in ground snow load offrom 3 to 9 psfper 100 ft increase in elevation, depending on the local area.
Specific Gravity of Snow on the Ground 6. Snowflakes of falling snow consist of ice crystals with their well-known complex pattern.
Owing to their large surface area to weight ratio they fall to the ground relatively slowly.
7. Freshly fallen snow is very loose and fluffy, with a specific gravity of about 0.05 to 0.1 (Ihoth to 1/lOth of water). Immediately after falling, however, the snow crystals start to change, the thin, lacey, needle-like projections begin to sublime and the crystals gradually become more like
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small irregularly shaped grains. This results in settlement of the snow, and after a few days or weeks the specific gravity will usually have increased to about 0.2 or higher, even at below freezing temperatures. The specific gravity of old snow generally ranges from 0.2 to 0.4. Since maximum snow loads nearly always occur immediately after an unusually heavy snowfall, and hence a large proportion of the snow has a low density, a mean specific gravity of about 0.2 was used to calculate the weight of the whole snow cover in Supplement No. l. The actual value used was 0.192, since it was found convenient to assume that 1 in. of snow cover corresponds to a load of 1 psf.o) To this was added the weight of the maximum I-day rainfall in the period of the year when snow depths are greatest. However, the weight added never exceeded the weight of snow.
Speci6c Gravity of Snow on Roofs 8. The specific gravity of snow on roofs taken from measurements at a number of stations
across Canada varies from about 0.1 to 0.45 (unit weight of 6 to 28 pcf). A reasonably average unit weight for use in design in lieu of better local data is about y= 15 pcf(specific gravity 0.24), assuming that the maximum roof load probably occurs just after a snowstorm deposits relatively light fresh snow on top of old snow. In other cases, however, where the maximum roof load is reached only after an accumulation from many snowstorms, a higher figure, such as y=20 to 25 pcf, may be more appropriate.
Effect of Wind on Snow Accumulation on Roofs 9. In perfectly calm weather falling snow would cover roofs and the ground with a uniform
blanket of snow. If this calm continued, the snow cover would remain undisturbed and the prediction of roof loads would be relatively simple; the design snow load could be considered as a uniformly distributed load and equal to a suitable statistical maximum of the ground snow load.
10. Truly uniform loading conditions, however, are rare and have been observed only in certain areas of the British Columbia mountains and occasionally in other areas on roofs that are well sheltered on all sides by high trees. In most regions snowfalls are accompanied or followed by winds. Snowflakes, having a large surface area for their weight, are easily transported horizontally by the wind. Consequently, since many roofs are well exposed to the wind little snow will accumulate on them.
II. Over certain parts of roofs the wind speed will be slowed down sufficiently to let the snow "drop out" and accumulate in drifts.(4).(5) This can be visualized by reference to the action of snow fences which cause the snow to "settle out." These areas on roofs could be called "areas of aerodynamic shade," and occur mostly behind vertical projections on the roof. An example of this is the area behind a penthouse on a flat roof where drifts often accumulate. Naturally, since the wind direction is not always the same, drifts on all sides of a penthouse would generally have to be considered.
12. Roofs situated below adjacent higher roofs are particularly susceptible to heavy drift loads because the upper roofs can provide a large supply of snow. Canopies, balconies and porches are also susceptible to this kind of loading. The drift loads that accumulate on such roofs often reach a multiple of the ground load, and depend mainly on the difference of elevation of the 2 roofs and on the size of the upper roof. The distribution of load depends on the shape of these drifts, which varies from a triangular cross-section (with the greatest depth nearest to the higher roof) to a more or less uniform depth.
13. Flat roofs with projections such as penthouses or parapet walls often experience triangular snow accumulations that reach the top of the projections on the buildings, but usually the magnitude of the load is less than on roofs situated below adjacent higher roofs.
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14. Peaked and curved roofs subjected to winds at approximately right angles to the ridge provide aerodynamic shade over the leeward slope. This sometimes leads to heavy unbalanced loads, since most of the snow is blown from the windward slope to the leeward slope, producing loads that exceed the ground load on occasions.
Solar Radiadon and Heat Loss 15. Various other factors besides wind modify snow loads, although some of these factors are
effective only under special conditions. It has been found, for example, that solar radiation has little effect in reducing loads in cold weather. Similarly, in cold weather, heat loss from the roof is not very effective in melting the snow, particularly with the present trend to better insulated and ventilated roofs. These 2 factors cannot, therefore, be relied upon to reduce the snow load significantly during the colder periods. During thaws and toward the end of the winter, however, when the air temperature rises nearer to the freezing point, solar radiation and heat loss do contribute to the melting of snow.
16. In special cases roofs have been designed with reduced design loads for areas of the country with large snow loads by incorporating into the roofs snow melting systems which throughout the winter periodically clear them of snow. However, a decision to use such a system should be considered carefully, because with possible future energy shortages, adequate energy may not be available for melting snow.
Redistribudon of wad from Melting Snow 17. Redistribution of snow loads can occur not only as a result of wind action but also as a
result of melting in one area and refreezing in another.
18. On sloped roofs, melt water from slightly warmer roof areas can refreeze on colder parts of the roof or on the eaves and cause high ice loads and also water back-up under shingles by ice damming. This can partly be alleviated by taking steps to decrease the heat loss from the upper parts of the roof. Furthermore, if a roof slopes towards and drains onto a lower roof, melt water sometimes accumulates by refreezing on the lower roof or is retained in the snow.
19. Flat roofs do not generally provide as free drainage under the snow cover as sloped roofs. Melt water, slush and ice may therefore remain on flat roofs longer than on sloped roofs. Also on the flat roofs of industrial and commercial buildings, snow accumulations sometimes occur near projections such as machinery and air ducts which can act as snow fences. When this snow melts, either as a result of heat loss through the roof or solar radiation or the effects of warm air exhausts, the melt water may trickle into the lower areas such as the centre of bays (i.e. areas of maximum deflection), especially if the drains are located at columns (high points). This redistribution of load may cause further deflection and lead to an instability situation similar to that produced by rain ponding (see Commentary I).
20. On very large roofs with only a slight slope, drainage of melt water may not occur because the snow absorbs any melt water or because the water refreezes before it can run off the roof. This phenomenon has apparently been the cause of some roof failures in areas where the ground loads are relatively low.
Unusual Roofs 21. In some cases, particularly roofs of unusual shape or configuration, exceptionally large
roofs and roofs over which the air flow is significantly affected by other buildings or topographic features, the prediction of probable snow loads is difficult. In such cases the designer should calculate and plot to scale the snow depths using '1-15 to 20 pef to judge if the distribution looks reasonable. In some circumstances it may be advisable to consider wind tunnel or water flume tests to assist the designer in his evaluation.
Snow Removal 22. Although it is fairly common practice in some areas to remove snow from roofs after
heavy snowfalls, the National Building Code does not allow a reduction of the design snow load to account for this for the following reasons:
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(a) Snow removal cannot be relied upon. Experience in several countries has shown that during and after extreme snow storms traffic is at a standstill and snow removal crews cannot be obtained,
(b) Snow cannot be effectively removed from the centre oflarge roofs, and (c) Unbalanced loading can occur as a result of certain patterns of snow removal.
Minimum Roof Load
23. For roofs with a slope of 30 deg. or less, Article 4.1.7.1. of the National Building Code provides for a minimum roof load of 20 psf where the calculated snow load is less than this amount.
DESIGN ROOF LOADS IN THE NATIONAL BUILDING CODE
Historical Notes 24. In the past, more particularly in the 1953 National Building Code of Canada,(6) design
snow loads were often considered to be equal to the ground snow load with reductions allowed for sloped roofs only. Such design load values were admittedly rough and have resulted in overdesign in some roofs while allowing underdesign in others, particularly in areas subject to high drift load. Information on which to base a more refined assessment of the loads was, however, not available until a countrywide survey of actual snow loads on roofs was undertaken by the Division of Building Research with the help of many volunteer observersY). This survey provided evidence on the relationship between ground and roof loads and enabled the committees responsible for the 1960 revision of the National Building Code(8) to make some changes in the roof loads compared with the ground load. The roof load was set at 80 per cent of the ground load, the ground load being based on a return period of 30 years and adjusted to allow for the increase in the load caused by rainwater absorbed by the snow.(3).(9)
25. With the introduction of the 1965 Code and Commentary some further changes made by the Revision Committee on Structural Loads and Procedures led to a more rational approach to snow loads for the design of roofs. All roof loads were directly related to the snow load on the ground and consequently the column for the roof snow load in the table of Design Data for Selected Locations in Canada in Supplement No. I was omitted. The basic roof load was again 80 per cent of the ground load, except that for roofs exposed to the wind a roof load of 60 per cent of the ground load could be used under certain conditions described further below. This reduction of roof load for exposed roofs to 60 per cent of the ground load was only made because at the same time allowance was made for a variety of influences causing accumulations of snow loads on roofs. This was done by means of "snow load coefficients" or shape factors which are shown in the form of diagrams and simple formulas similar to Figures H-I to H-7. In addition, the slope reduction formula was changed from the step function used in 1960 to a linear function
(a-30°
f3 = 1 - for 30° < a < 70°. 40°
26. In the 1970 Code and Commentary there were minor changes to the provisions for gable or hip roofs (Figure H-2) and arch roofs (Figure H-3) and more severe "full and partial loading provisions"-"full and zero loading" rather than "full and half loading."
27. In the 1975 Code and Commentary few changes were made, except that the requirement for full and partial loading was considered too severe at "full and zero" and was changed back to "full and half' loading.
28. In the 1977 Commentary the provisions for loads on arches have been changed and a number of rationalizations made as an aid to better understanding of snow loads on roofs.
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DETERMINATION OF DESIGN SNOW LOADS ON ROOFS
Basic Snow Load Coefficients and Modifications to the Coefficients 29. The minimum design snow load on a roof area or any other area above ground which is
subject to snow accumulation is obtained by multiplying the snow load on the ground, g, specified for the municipality or area considered by the snow load coefficient, Cs, applicable to the particular roof area considered
where s g Cs
C.g
design snow load in psf, ground snow load in psf, snow load coefficient.
30. The basic snow load coefficient is 0.8, except that for roofs exposed to the wind, under certain conditions to be described, this value may be reduced to 0.6. These coefficients are to be further modified (increased or decreased) to account for the influences provided for in Article 4.1.-7.3. of the NBC and discussed earlier in this commentary. Such modified snow load coefficients Cs
are given in Figures H-I to H-7 for various fairly common roof shapes. For other roof shapes, other coefficients may have to be used if considered by the designer and the authority having jurisdiction to be more appropriate for the particular roof being designed, and if based on applicable field observations or on model tests.iIO),(lI).(l2) In an effort to provide guidance to designers, the Division of Building Research has published 2 collections of case histories of interesting nonuniform snow loads.(4).(5)
31. Figures H-I to H-3 are for the basic roof shapes. They include the simple flat and shed roofs, the simple gable and hip roofs and thirdly the simple arch and curved roofs. These roofs can be loosely classified as single span roofs. More complex roof shapes can then often be considered as combinations of these 3 roof shapes. The basic roof shapes can be either combined with equal eave heights producing a valley. or unequal eave heights resulting in a multi-level roof.
32. Valleys in 2-span and multi-span roofs lead to increased loads in the troughs from the influence of the wind and, with steeper slopes, from sliding, creeping or melting snow. Coefficients for valley areas are presented in Figure H-4.
33. On multi-level roofs the areas on the lower roofs that are adjacent to the higher roofs are subjected to heavier snow loads due to drifting. The coefficients for the increased load on the lower level of multi-level roofs are provided in Figure H-5.
34. Where the upper roof is sloped towards the lower roof so that snow may slide or melt onto the lower roof, the lower roof should be designed for increased loads. This is specified in ure H-6.
35. Finally, the snow load distribution is influenced by vertical projections. The coefficients for this condition are provided in Figure H-7.
Reduction of Snow Loads for Exposed Roofs 36. Observations in many areas of Canada have shown that where a roof or part of a roof is
fully exposed to wind, a considerable portion of the snow is blown off under certain conditions, and the average snow load consequently reduced.
37. In a few areas of Canada, however, winter winds may not be strong or frequent enough to produce a significant reduction of roof loads. This is the case in winter-calm valleys, mainly in the mountains of British Columbia and Alberta, where often layer after layer of snow accumulates on roofs without any appreciable removal by wind.
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38. In Atlantic and Pacific coastal areas where it is known from local climatic data that the maximum snow load may be the result of one or more snowstorms occurring over a short period of time, occasionally without appreciable winds, a reduction of the basic snow load coefficient below 0.8 should not be used.
39. For roofs fully exposed to the wind, the coefficients may be reduced 25 per cent. Thus the basic snow load coefficient may be reduced from 0.8 to 0.6 provided the designer has demonstrated to the satisfaction of the authority having jurisdiction that (a) the building is located in an exposed location such as open level terrain containing only scattered buildings. trees or other such obstructions, so that the roof is exposed to the winds on all sides and is not likely to become shielded in the future by obstructions higher than the roof within a distance from the building equal to IO times the height of the obstruction above the roof level; and (b) the roof does not have any significant projections such as parapet walls which exceed a height of g125 ft (where g is the ground snow load in pounds per square foot) which may prevent the snow from being blown off.
40. The value g125 is obtained by assuming that the snow will drift to the top of the parapet. Then hdnft = hp.r.pel = 0.6gl'( on the exposed roof, and using '( = 15 pcf, hparapel = 0.6g1 15 = g125.
41. In practice it is sometimes difficult to make a clear distinction between those roofs that will be fully exposed to the winds and those that will not. The designer should, in consultation with the owner, weigh the probability of the roof becoming sheltered in the future by an addition to the building or by adjacent higher buildings or trees. Such future changes could cause either drift loads or higher average loads. With regard to the former, which are the more serious, it may be prudent for the designer to consider a distance of at least 15 ft from another (existing or future) building or from the property line as being the minimum distance to justify disregarding drift loads. This corresponds to the distance used in NBC Article 4.1.7.3. for multi-level roofs. With regard to the latter, that is higher average loads that could result from future more sheltered conditions, it is important to use the basic snow load coefficient of 0.8 instead of 0.6 for any roof area whose exposure may become generally more sheltered in the future.
42. Where a roof has projections or obstructions of a height greater than g125, the reduction of 25 per cent should be applied only to roof areas that are relatively well exposed, i.e. those areas that lie outside a strip IO times the difference between the height of the vertical projection and g125 in width.
43. It should be remembered at this point that it is the designer's responsibility to choose the best possible design snow load assumption.
Full and Partial wading 44. It should be noted that all roof areas, including those to be designed for increased or
decreased loads according to Figures H-l to H-7, must be designed for full load over the entire area or full load distributed on any I portion of the area and half load on the remainder of the area, whichever produces the greatest effects on the members concerned. Where appropriate, even more severe load imbalances such as those resulting from snow removal, melting of snow due to roof fans or uninsulated roof areas in heated buildings, should be taken into consideration.
45. The reason for these overriding requirements is that snow very seldom accumulates evenly. Consequently, since certain structural members (such as diagonals of trusses) are subject to stress reversals or are otherwise sensitive to changes in load distribution, non-uniform loading must always be considered by the designer in addition to uniform loading.
46. Curved and peaked roofs are often used over arenas and are important examples of structures which are generally very sensitive to unbalanced loading, and which if they collapse, often do so catastrophically without much warning. Hence a check on the overall stability of these structures in accordance with NBC Article 4. l.l. 7. is essen tial.
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DETAILED EXPLANATIONS OF FIGURES H-I TO H-8
(I) Flat and Shed Roofs - Slope Reduction (Figure H·I) 47. Since under most conditions steeper roofs tend to accumulate less snow than flat and
moderately sloped roofs, because of sliding, better drainage and saltation, the coefficients are reduced for slopes exceeding 30 deg. as shown in Figure H-I, and for slopes exceeding 70 deg., snow load need not be considered.
48. For multi-level roofs and for roofs with vertical projections, Figures H-5, H-6 and H-7 should be referred to.
(2) Gable or Hip Roofs (Figure H·2) 49. For gable or hip roofs both uniform loads and unbalanced loads should be considered. A
load 25 per cent greater than the uniform load on one side and no load on the other is recommended to account for the snow blown from the windward side over to the leeward side. An unbalanced load is also justified on this type of roof because of the possibility of snow being removed by sliding from one side only.
50. The same reductions as in Figure H-I are permissible in the coefficients for slopes exceeding 30deg.
51. When gable or hip roofs are adjacent to higher roofs or have projections, reference must also be made to Figures H-5 to H-7.
(3) Arch Roofs (Figure H-3) 52. For arch roofs both uniform and unbalanced load distributions are given. Suggested
coefficients for these loads are given in Figure H-3.
53. Where there are adjacent higher roofs or projections, reference must also be made to Figures H-5 to H-7 for additional coefficients, and the effects of snow sliding and drifting that could cause accumulations at the base of the arch must be considered.
(4) Valley Areas of Two-Span and Multi-Span Curved or Sloped Roofs (Figure H-4) 54. For valley areas of 2-span and multi-span roofs, a uniform load with appropriate slope
reductions is used, as well as accumulations of snow in valleys as a result of drifting and sliding snow. Slope reductions do not apply to Cases II and III, since melting or sliding snow will tend to accumulate in the valleys.
55. Should there be adjacent higher roofs or projections, reference must also be made to Figures H-5 to H-7.
(5) Multi-Level Roofs, Obstructions and Parapets 56. Multi-level roofs, obstructions and parapets are all "bluff objects" creating turbulent
wakes in their lee where snow may accumulate as drifts. Such roofs and obstructions can be considered as geometrical variations of a rectangular object of varying dimensions, situated on or adjacent to a lower flat roof. Depending on the dimensions and location of such bluff objects, the distribution of snow will vary from case to case.
57. If the object is narrow and of a height less than the design depth of uniformly distributed snow on the roof it is, for the purposes of this commentary. a "non-obstructing" parapet; if it is higher, it is an obstruction. if it is higher than a "non-obstructing" parapet and wide enough to provide a significant source of snow on its upper surface, it becomes an "upper level" roof.
58. Lower Roofs of Multi-Level Roofs (Figure H-5). The design load for roofs adjacent to higher roofs is recommended to be taken as a triangular load with a maximum load at the apex of the triangle expressed in pounds per square foot equal to 15 times the difference in roof elevation (in feet) reduced to the normal snow load at a distance from the higher roof of twice the difference
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in elevation. This load is based on the assumption of a triangular snow drift extending to the top of the higher roof. Such drift loads occur not only when the upper roof is part of the same building, but also when it is on an adjacent building not more than 15 ft away.
59. An upper limit of3 times the basic ground snow load has been suggested in Figure H-5. It should be noted, however, that higher loads have been observed where an upper roof was very long (measured perpendicularly to the step between the upper and lower roofs). On the other hand, for relatively short upper roofs (say less than 50 ft), a reduction below the value calculated from Figure H-5 may be judged adequate by the designer.
60. The reduction of 25 per cent for exposed roofs should be considered applicable only to the areas of the roof further than \0 times the difference of roof height from the upper roof.
61. Areas Adjacent To Roof Obstructions (Figure H-6). Consideration should also be given to triangular drift loads adjacent to vertical obstructions, such as elevator, air conditioning and fan housings, small penthouses and wide chimneys on roofs, that can produce significant accumulations of snow. The maximum coefficient adjacent to the obstruction may be assumed to be (2/3 yh)/g where h is the obstruction height in feet and y the unit weight in pounds per cubic foot decreasing to the applicable design roof load at a distance of 2h from the obstruction. This coefficient need not in general be larger than 2. nor is it necessary to consider the drift load if the length or width of the obstruction is less than 2.5g/y.
(6) Lower of Multi-Level Roofs with the Upper Roof Sloped Toward the Lower Roof (Figure H-7)
62. Where snow is likely to slide onto a lower roof from an upper roof, the lower roof should be designed for the load as provided for in Figure H-5 plus an additional load produced by the snow that may slide from the upper roof. It is not possible at the moment to provide coefficients for this situation, but the following guide is recommended. Because of the remote probability that both upper and lower roofs will have their full load over the full areas simultaneously when sliding occurs, it may be assumed that the lower roof would be carrying its full load according to Figure H-5 and that sliding of 50 per cent of the total weight of the applicable uniformly distributed snow load from the upper roof would occur. The distribution should be made depending on the relative sizes, slopes and positions of the 2 roofs. If, because of a relatively small lower roof, all the sliding snow cannot be retained on it, appropriate reductions may be made. The density of sliding snow may be rather high.
(7) Example Sheet 1 (Figure H-8) 63. Example sheet No. I shows the design snow loads in pounds per square foot for various
differences in roof elevation for multi-level roofs according to Figure H-5 for 3 typical ground snow loads. It will be noted that 25 per cent reduction for exposed roofs according to Article 4.1.-7.4. should be considered applicable only to areas of the roof that are unprotected, i.e. some distance estimated at 10 times the difference in elevation away from the upper roof.
REFERENCES (I) Climatic Information for Building Design in Canada 1977. Supplement No. I to the National
Building Code of Canada, issued by the Associate Committee on the NBC, National Research Council, Ottawa, Canada, (NRCC No. 15556).
(2) Schaerer, P. A. Variation of Ground Snow Loads in British Columbia. Division of Building Research, National Research Council of Canada, Ottawa, 1970, (NRCC No. 11910).
(3) Boyd, D. W. Maximum Snow Depths and Snow Loads on Roofs in Canada. Proc. 29th Annual Meeting, Western Snow Conference, April 1961 (NRC No. 6312).
(4) Schriever, W. R., Faucher, Y. and Lutes, D. A. Snow Accumulations in Canada: Case Histories: I. National Research Council of Canada, Division of Building Research, January 1967 (NRC No. 9287).
(5) Lutes, D. A. and Schriever, W. R. Snow Accumulations in Canada: Case Histories: II. March 1971. DBR Technical Paper 339 (NRCC No. 11915).
(6) National Building Code of Canada, 1953, issued by the Associate Committee on the NBC, National Research Council, Ottawa, Canada (NRC No. 3188).
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(7) Peter, B. G. W., Dalgliesh, W. A. and Schriever, W. R. Variations of Snow Loads on Roofs. Trans Engineering Inst. of Canada, Vol. 6, No. A-I, April 1963 (NRC No. 7418).
(8) National Building Code of Canada, 1960, issued by the Associate Committee on the NBC, National Research Council, Ottawa, Canada (NRC No. 5800).
(9) Lutes. D. A. Snow Loads for the Design of Roofs in Canada. Reprinted from Proceedings of the Western Snow Conference, Victoria, B.c. 21-23 April 1970, pp. 61-67. DBR Technical Paper No. 338, April 1971 (NRCC No. 11911).
(10) Isyumov, N. An Approach to the Prediction of Snow Loads. Ph.D. Thesis Research Report BLWT-9-71, Faculty of Engineering Science, University of Western Ontario, London, 1971.
(II) Isyumov, N. and Davenport, A. G. A Probabilistic Approach to the Prediction of Snow Loads. Canadian Journal of Civil Engineering, Vol. I, No. I, September 1974, pp. 28-49.
(12) Schriever, W. R. and Otstavnov, V. A. Snow Loads-Preparation of Standards for Snow Loads on Roofs in Various Countries, with Particular Reference to USSR and Canada. Reprint from CIB Report No.9, 1967, pp. 13-33. DBR Research Paper No. 366, May 1968 (NRC No. 10154).
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SImple flat and I shed roofs I I
I I
I I
I : ) ) f! II ! : i ~ I cs*
= 0.8' (3
Typical values
C ci shelt expd
o to 30° 0.8 0.0 40° 0.6 0.4<;
50° 0.4 0.3 60° O. l 0.15
70° to 90c 0 0
Figure H-l
Flat and shed roofs
Notes:
ROOF SHAPES
gable and I h'l) rouf s
I
I
I CASE I I I
Ii: : ; i : i i ! I ; ; i Ics *
CASE II
I I I r:::-::Tlc IWUU 5
for d:S 15° use Case I only
for d.> J 5° I1S., Case I and II
Case I
Case II
15'tolO' lO' to 30' 30' to 70·
~ o lO + ce/l5 1.0
.(0.8·{3l
Figure H-2
Gable or hip roofs
l(,nJ_
,,,o.~x T 7' . :v
r- + 1 ~ .:..: I II
SUllple dr< h dJtd
I; urv('d roofs I
l'inJ"ard Side C
s
Leeward Side
c =
when > usc C
then r s ('. {3
for
for
~ < 1. -
h > ! I 10
use Case J only
Cases I & II
Figure H-3
Arch roofs
"'For roofs exposed to wind according to Article 4.1.7.4.,<') all values of Cs marked with an asterisk ("') may be reduced by 25 per cent. All load distributions shown in these Figures are also to be applied as full and partial loading according to Sentence 4.1. 7.2.(2). The slope reduction relationship in Figures H-I, H-2 and H-3 is:
f3 = 1.0 where 0 s: a s: 30°
a-30° f3 = 1.0---where300<a<70°
40°
f3 = 0.0 where 70°S:aS:90°.
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ROOF SHAPES
Valley areas of two-span and multi-span sloped or curved
roofs
Lower level cf multi-level roofs (when upper roof 15 part of the same building or on an buildmg not more than i5
SNOW LOAD -DISTRIBUTIONS AND COEFFICIENTS. LlMlTATlONS
CASE I It:!! 1 i:::: : i::; i I CS* * C s 0.8'{3
CASE II
-.l
~ ... ' ,I . ,. 05
&: 1 -pJ.,J1-j '2 2.
CASE III
For both Q( I and 0<'2 ~ lOe use Case 1 only.
otherw i se use Case 1. II and 1I I
Figure H-4
Valley areas of 2-span and multi-span curved or sloped roofs
Notes:
Vi
when r l!. < 0.8· C g 0.8'" g
when r ..b... > 3.0 !2
when h < 5 ft Vi : 10
h > 15 ft Vi 30
h ~ difference of roof heights in ft
g = ground snow load in psf
W = width of drift from higher budding in ft
distance between buildings < 15 ft
For load on uppe r roof use Figures H-I to H - 4
Figure H-5
Lower roofs of multi-level roofs
81
·For roofs exposed to wind according to Article 4.1.7.4., all values of C, marked with an asterisk (.) may be reduced by 25 per cent. All load distributions shown in these Figures are also to be applied as full and partial loading according to Sentence 4.1.7.2.(2). The slope reduction relationship in Figure H-4 is:
p = 1.0 where 0::;0:::;30°
0: - 30° P 1.0---where300<0:<70°
40°
p = 0.0 where 70° <0: <90°.
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Notes:
ROOF SHAPES
Roof areas adjacent to projections and obstructions
on roofs
Lower of multi-level roofs with upper roof slofJed towards lower
roof
SNOW LOAD DISTRIBUTIONS AND COEFFICIENTS. LIMITATIONS
W
c 'r y!.!. y "
- ) g' pcf
"hen y!:. <: (] use C = s 0.8'
when y!:. :> 2. (] g
use Cs 2.0
when t <: ~ y use C s
; U.8*
2 b.
when b. < 5
when > 15 it it
use use
W = 10
W = 30
h heIght of projection in it
ground snow load in psf
W width of snow drift in ft
;. length of projection In it
Figure H-6
Areas adjacent to roof projections
LOADFROM~ SLIDING SNOW ,
DRIFT LOAD : . I I : 'OB
I
=-~~----------for loads
H 5 plus a portion of the snow from the upper roof according to text.
H 4
Figure H-7
Lower of multi-level roofs with the upper roof sloped toward the lower roof
*For roofs exposed to wind according to Article 4.1.7.4 .. all values of Cs marked with an asterisk (*) may be reduced by 25 per cent. All load distributions shown in these Figures are also to be applied as alternating full and partial loading according to Sentence 4.1.7.2.(2).
1 I
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es
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COMMENT ARY I
RAIN LOADS
TABLE OF CONTENTS Page
Ponding Instability ................•......................... 87 References ................................................ 88
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87
COMMENTARY I
Rain Loads
l. In accordance with National Building Code Sentence 4.1.7.5.(1), any roof which can accumulate water must be designed for the load that results from a 24-hr rainfall on the horizontal projected area of the roof. This requirement applies whether or not the surface is provided with drainage such as rainwater leaders. The distribution of rain load should be determined by the designer, who should take into account the shape of the roof, including camber, with or without creep deflection due to dead load, and also deflection due to rain.
2. Notwithstanding the above requirement, it is considered good practice to take into account in the location of roof drains not only the roof slope but also deflection of the roof due to creep, snow and rain.
Ponding Instability
3. If a flat roof is too flexible, rainwater will not accumulate evenly over the roof but will flow to form ponds in a few local areas. This may lead to an instability condition similar to buckling which can result in failure of the roof due to local overloading. In the case of I-way roof beams or decking simply supported on rigid supports, ponding instability will occur when the beam stiffness is less than EIelit given by
where E I L S Y
modulus of elasticity, moment of inertia of the beam, span, beam spacing, unit weight of water, pcf.
(1)
4. In the case of a 2-way system of roof joists on girders, the critical stiffness can be approxi-mated by EI
__ J_ +
EIJeri'
(2)
where El j ertt and efit are given by Equation (l) for joists and girders, respectively.
5. Even if the roof system is stiffer than the critical values determined by Equations (I) and (2), calculated moments and deflections may be amplified due to ponding effect. A practical criterion is to require roof stiffness to be at least twice the critical stiffness. In the case of a I-way system on rigid supports, in terms of existing deflection requirements, this can be expressed as follows:
w > 98L (~) allowable (3)
where w is the design load in pounds per square foot specified for deflection calculation and
( ~ ) allo"~ble is the allowable deflection to span ratio (see Table A-I, Commentary A, "Service
ability Criteria for Deflections and Vibrations"). If for a I-way system the design load w is less than the critical value given in Table I-I, the effects of ponding should be considered. This applies particularly to large flat roofs in areas of heavy rainfalL Further information is given in References (I) to (7).
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Table I-I
CRITICAL VALVES OF w FOR PONDING, PSF (ONE-WAY SYSTEM-EQVATION(3»
CRITICAL V ALVES OF w FOR PONDING, PSF I (ONE-WAY SYSTEM-EQVATION(3» '--- -Deflection/Span
Requirement L=20 ft L=40 ft L=60ft L= 100 ft
I 180 II 22 33 55
1 8 16 24 41 240
Column I 2 3 4 5
REFERENCES (1) Sawyer, D. A. Ponding of Rainwater on Flexible Roof Systems. Proc. Am. Soc. Civ. Engrs.,
Journal of Structural Division, VoL 93, STI, February 1967, p. 127. (2) Haussler. R. W. Roof Deflection Caused by Rainwater Pools. Civil Engineering, Vol. 32.
October 1962, p. 58. (3) Marino F. J. Ponding of Two-Way Roof Systems. Engineering Journal of Amer. Inst. of Steel
Construction, Vol. 3, No.3, July 1966, p. 93. (4) Commentary on the Specification for the Design, Fabrication and Erection of Structural Steel
for Buildings. Amer. Inst. of Steel Construction, New York, 12 February 1969. (5) Salama, A. E. and Moody, M. L. Analysis of Beams and Plates for Ponding Loads. Proc., Am.
Soc. eiv. Engrs., Journal of Structural Division, Vol. 93, STI, February 1967, p. 109. (6) Chinn, J .. Mansouri, A. H. and Adams, S. F. Ponding of Liquids on Flat Roofs. Proc., Am.
Soc. Civ. Engrs., Journal of Structural Division, Vol. 95, ST5, May 1969, p. 797. (7) Sawyer, D. A. Roof-Structural Roof-Drainage Interactions. Proc. Am. Soc. Civ. Jour-
nal of Structural Division, Vol. 94, STI, January 1969, p. 175.
I
•
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COMMENTARY J
EFFECTS OF EARTHQUAKES
TABLE OF CONTENTS Page
Objectives of Earthquake-Resistant Design. . . . . . . . . . . . . . . . . . . . . . .. 91 Seismic Regionalization ....••.......•........................ 91 Direction of Earthquake Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . • • . . .. 93 Structural Response to Ground Motion . . • . . . . . . . . . . . • . . . . . . . . • • • . 93 Minimum Earthquake Forces •..........•..........•....•...... 94 Vertical Accelerations . . . . . • . . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . .. 98 Distribution of the Base Shear . . . . . . . . • . . . . . . • . • • . . . . . . . . . . • . . .. 98 Overturning Moments •.....................•...........•..•• 99 Torsional Moments. . . . . . . . • . . . . . . . . . • . . . . . • . . . . . . . . . . . . . . . .. 99 Setbacks • . . . . . . . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . • . . . . . 101 Drift and Separation of Buildings .....•......•.•..............• 104 Design Considerations ............•.............•...... "..... 104 Machinery, Equipment and Components of Buildings ............... 105 Special Provisions. . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 Dynamic Analysis. . . . . . . . . . . • . • . . • . . . . . . . . . . . . . . . . . . . . . . . • . 106 Acknowledgement. . • . . • . . . . . . • . . . . . . . . . . . . . . . . . . • . . • . . . . . . . 106 References .......•...•.................•................. 107
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COMMENTARY J
Effects of Earthquakes OBJEcrIVES OF EARTHQUAKE-RESISTANT DESIGN
1. The earthquake-resistant design requirements of the National Building Code of Canada 1977 provide minimum standards which assure an acceptable level of public safety by designing to prevent major failure and loss of life. Structures designed in conformance with its provisions should be able to resist moderate earthquakes without significant damage, and resist major earthquakes without collapse. For the purpose of this section, collapse is defined as that state which exists when exit of the occupants from the building has become impossible because of failure of the primary structure.
2. Structures could be designed to resist major earthquakes without damage; this, however, would in most cases be considered uneconomical and unwarranted because of the small probability of the occurrence of such events in Canada. Instead, the objective of the NBC provisions is to reduce the probability of fatalities to an appropriately small value and to accept some structural damage in major earthquakes. Damage caused by landslides such as have occurred in Anchorage, Alaska,(I) or damage due to earth consolidation or liquefaction as in Niigata, Japan,(2) will not be prevented by conforming to the seismic requirements of the NBC. The intent of the NBC regulations is to provide buildings with resistance to earthquake ground motions but not to slides, subsidence or active faulting in the immediate vicinity of the structure. These may result from earthquakes and require special study.
3. To design an earthquake-resistant structure one needs to know the characteristics and probability of occurrence of the "design" earthquake, the characteristics of the structure and the foundation, the allowable stresses in the materials of construction, including the foundation soils, and the amount of damage that is tolerable. The design must provide not only sufficient structural strength to resist the ground motion, but also the proper stiffness to limit the lateral deflection or drift. Damage to nonstructural elements may be minimized by proper limitation of distortions and by attention to the details of their connection to the primary structure. The minimum requirements given in the NBC incorporate the above considerations. It is the purpose of this commentary to elaborate on the quantitative and qualitative bases for the NBC requirements, and in some cases to present recommended procedures.
4. It is beyond the scope of the NBC to cover the entire range of problems involved in the aseismic design of all structures. Unusual structures, highly irregular buildings and special-purpose industrial structures such as nuclear reactors, power plants and stacks should be treated as special problems with special design criteria in each instance, including possibly a dynamic analysis. The advice of an experienced structural engineer should be sought to arrive at suitable design criteria for such special structures.
SEISMIC REGIONALIZATION
5. Earthquake-resistant designs should be considered for structures built in areas where major earthquakes have occurred, such as along the West Coast, the S1. Lawrence River Valley and certain parts of the Artic, and also in areas adjacent to these centres of major seismic activityP) Detailed information on earthquakes which have occurred in Canada is contained in the publications of the Earth Physics Branch, Energy, Mines and Resources.(4).(5).(6) From these studies the present seismic Zoning map for Canada(7).(8) has emerged.
6. The seismic zoning map is based on a statistical analysis of the earthquakes which have been experienced in Canada since 1899, as well as from earlier historical records. The data were analyzed by extreme value methods of statistics in the same manner that extremes of floods or
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snow loads can be estimated, and the seismic zoning map derived from the distribution of peak horizontal ground accelerations that have a probability of exceedance of 0.01 in I year; this represents the basis for the minimum design requirements given in the NBC. The range of the ratio of horizontal ground acceleration to the acceleration due to gravity and the acceleration ratios associated with each zone are given in Table J-2. Table J-I includes representative values of acceleration for several other levels of probability of exceedance for a number of Canadian cities. If other probabilities of exceedances are required for any site in Canada, they can be obtained at cost by writing to the Seismology Division, Earth Physics Branch, Department of Energy, Mines & Resources, Ottawa, Ontario KIA OE4.
Table J-I
ESTIMATED INTENSITIES AND RATIOS OF PEAK HORIZONTAL GROUND ACCELERATIONS TO THE ACCELERATION DUE TO GRAVITY, (A)(I)
Probability of Annual Exceedance
Locality 0.1 0.033 0.01 0.005
I A I A I A I A
Fort McPherson IV 0.006 VI 0.025 VIII 0.111 IX 0.264 Prince Rupert IV 0.007 VI 0.027 VIII 0.113 IX 0.260 Victoria V 0.01 VI 0.031 VIII 0.111 IX 0.234 Vancouver IV 0.007 VI 0.022 VII 0.080 VIII 0.169 Calgary II 0.001 II 0.002 III 0.004 IV 0.005 Toronto IV 0.005 V 0.011 VI 0.027 VI 0.045 Ottawa IV 0.009 V 0.02 VII 0.048 VII 0.079 Montreal IV 0.008 V 0.016 VI 0.036 VII 0.056 Quebec City V 0.012 VI 0.027 VII 0.071 VIII 0.124 La Malbaie VI 0.032 VII 0.116 IX 0.495 XI 1.140 Saint John IV 0.007 V 0.017 VI 0.047 VII 0.085 Halifax III 0.004 IV I 0.008 V 0.021 VI 0.037
Column I 2 3 4 5 6 7 8 9
Note to Table J-I: I (I) Intensities are obtained from iog lO A = 3.5 and roun'ded to the nearest unit of intensity.
3
TableJ-2
DEFINITION OF SEISMIC ZONES
Seismic Range of Ratio of Horizontal
I Acceleration Ratio, Zone
Ground Acceleration to the A
Acceleration Due to Gravity i
0 Less than 0.01 0 I Equal to or greater than 0.01
to less than 0.03 0.02 2 Equal to or greater than 0.03
to less than 0.06 0.04 3 Equal to or greater than 0.06 0.08
Column 1 2 3
1 I
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7. The acceleration amplitude which has the 0.01 probability of being exceeded in I year is also called the "I OO-year" acceleration generated by the earthquakes in the region. It can be shown(9) that this" I OO-year" acceleration level gives approximately the same likelihood of structural collapse for cities in Zone 3 as the "30-year" wind speed that is employed elsewhere in the NBC.
8. Acceleration amplitudes which are used in computing the seismic probability map or which are supplied in answer to requests for information at specific sites are the peak horizontal amplitudes on firm ground. In deriving the probable acceleration amplitudes, certain fundamental assumptions had to be made about the data set of earthquakes. Some of these assumptions are: that earthquakes are generated by the tectonic forces currently at work in Canada; that the attenuation of acceleration amplitude with distance from the earthquake epicentre is known; that the catalogue of earthquake epicentres is reasonably complete; and that the earthquakes occur in a random manner with respect to location and time. Given this information, the resulting probability map represents the best current estimate of earthquake risk in Canada.
DIREcrION OF EARTHQUAKE FORCES
9. In general, ground motion in an earthquake is multidirectional. This complex motion is imparted to the supports of a structure; the structure then responds according to its stiffness and inertial properties. At any instant during the earthquake the state of stress in the structure is a function of the inertial forces acting on the structure. In the most general case, seismic analysis would involve the simultaneous translation along the 2 horizontal axes, rocking plus vertical and torsional motions. For normal buildings, however, independent design about each of the horizontal axes together with the associated torsional forces is considered to provide adequate resistance against earthquake motions applied in any direction. This simplification forms the basis for the earthquake requirements in the NBC. Particular attention should be paid, however, to the effect of the combined stresses at the external and re-entrant corners, which are especially vulnerable to the effect of concurrent translational and torsional motions (see Reference (I».
STRUCTURAL RESPONSE TO GROUND MOTION
10. The elastic response of a single-degree-of-freedom system to ground motion depends on the fundamental frequency and the damping characteristics of the system, and on the frequency content and amplitude of the ground motion. The base shear, V, which can be used as a measure of this response is expressed as
where W Sa
(I)
the weight of the system, a function of the natural period T and damping of the system, and depends on the characteristics of the ground motion. This function is known as the acceleration response spectrum of the ground motion in units of gravitational acceleration; details of its derivation can be found in Reference (10).
II. Similar base shear force relations apply with reasonable accuracy to multi-storey buildings having many modes of vibration. For usual buildings oflow and moderate heights, the principal earthquake response is that due to the fundamental mode of vibration. For taller structures some allowance for contributions of the higher modes is made in the base shear calculations in most building codes{1l) including the NBC.
12. Formula (I) is strictly applicable only to the linear range of structural behavior. With the onset of plastic material behaviour the base shear induced by earthquakes is reduced as compared to that of perfectly elastic behaviour. Such a reduction in base shear is implicit in the provisions of most building codes, including the NBC. The lower base shears, however, are justified only if a structure possesses ductility, i.e. the capacity to deform beyond the yield point without major structural failure,c12).(13),(14)
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MINIMUM EARTHQUAKE FORCES
13. The NBC specifies that a structure should be designed for a minimum earthquake force given by
V ASKIFW (2) This is essentially Equation (I) modified to take into account the most important factors involved in the response of buildings to earthquakes. Each of these factors will now be discussed.
Acceleration Ratio, A
14. The factor A is the acceleration ratio. The value of A as well as the relevant seismic zone are given in the Table of Climatic Data in Part 2 of the NBC. For many sites in Canada the seismic zones are listed in the Table of Design Data for Selected Locations in NBC Supplement No.1, "Climatic Information for Building Design in Canada 1977."
15. Values of A that were chosen to correspond with the various seismic zones and zone boundaries are given in Table 1-2. The zone number and hence the appropriate value of A for that site may be obtained from the seismic probability map Figure 1-1. The acceleration amplitude is assumed to be constant within each zone.
Seismic Coefficient S 16. The coefficient S is given by the formula
0.5 S= (3)
which reflects the dependence of seismic acceleration on the fundamental period of the structure, as well as the contributions of the higher modes for tall buildings. In lieu of more accurate estimates, the following empirical formulas can be used for the determination of the fundamental period T for buildings:
or
0.05 hn T=--
v'D (4)
T = O.IN (5) for moment resistant space frames only. The symbols are defined in Sentence 4.1.9.1.(2) of the NBC.
17. Equation (4) is based on approximately 1,600 vibration observations made in 430 buildings, 150 observations on 42 elevated tanks and 250 special observations.oS) In modern multi-storey buildings this period calculation gives values that for the most part are in reasonable agreement with measured values. However, variations in the order of ± 50 per cent have been observed when Equation (5) is applied to framed structures, and similar variations when Equation (4) is applied to mixed shear wall frames and coupled shear wall structures. For pure shear wall structures the natural period is generally overestimated, sometimes by as much as 100 per cent. If the designer wishes, he may determine the period T for a structure by more refined methods of calculation and submit the relevant technical data.
18. One such method is to use the following expression which represents the Rayleigh approximation for determining the natural period of the fundamental mode:
(6)
where 8j (i= 1, ... n) are the elastic deflections in storeys i, due to the forces F t and F j (i= I, ... n) as prescribed in Subsection 4.1.9. of the NBC; g is the acceleration due to gravity; and Wi is as defined in 4.1.9.1.(2). The units need to be consistent. Another method for determining T is outlined in Commentary K, "Dynamic Analysis for the Seismic Response of Buildings."
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Coefficient K 19. The coefficient K assigned to different types of structural systems reflects design and con
struction experience, as well as the evaluation of the performance of structures in major and moderate earthquakes. It endeavours to account for the energy-absorption capacity of the structural system by damping and inelastic action, and the response characteristics of certain types of structures in earthquakes. Types of construction that are recognized to have performed well in earthquakes are assigned lower values of K. The K values of Table 4.1.9.A. of the NBC specifically recognize the following:
(1) The capability of a structure to absorb energy, within acceptable deformations and without failure, is a very desirable characteristic of any earthquake-resistant design.
(2) The existence of alternate load paths or redundancy of a structural system is a desirable characteristic. This increases the locations where energy can be dissipated and reduces the risk of collapse when individual members should fail or become severely damaged. Some mixed wallframe systems are therefore given a lower K value than shear wall structures.
(3) Some stiff structural systems have been shown to attract larger base shear forces in the higher modes than those with more frame action. Consequently, shear wall structures are given a higher K value than some mixed wall-frame systems.
(4) The K values assigned to buildings are lower than those assigned to other structures, because buildings are normally endowed with a multiplicity of nonstrucural elements and resisting elements not considered in the analysis. Furthermore, buildings generally have higher damping values during large amplitude vibrations than mere skeleton strucures.
20. Buildings incorporating inadequately designed shear walls, unreinforced or inadequately reinforced masonry, precast concrete with nominal connections or structural steel with nonductile connections, lack adequate ductility for effective seismic performance and the K values are correspondingly increased.
21. The following should be noted when choosing the K values for the structure:
Cases 1 and 2. Complete moment-resisting ductile space frames with or without ductile flexural walls that qualify for K = 0.7 need to be analyzed so that realistic load distributions among the various members can be ascertained. This requires a frame analysis for space frames and an interactive analysis for a combination wall-frame system. Detailing requirements as specified in CSA A23.3-1973, "Code for the Design of Concrete Structures for Buildings," including Chapter 19 for concrete, and CSA SI6-1969, "Steel Structures for Buildings" for steel, are considered to provide adequate member ductilities. The system ductility factor for these types of structures is approximately 3 to 4 for some visible structural damage and greater for major structural damage.
Case 3. In order to qualify for K = 0.8, the structure must have a complete ductile moment-resisting space frame and shear walls designed so that the total required lateral force is resisted in accordance with the relative rigidities of the walls and the space frame. In addition, the following must be satisfied:
(a) The complete ductile moment-resisting space frame shall be designed to carry as a system separate from the shear walls the total vertical loads and at least 25 per cent of the total required lateral force, i.e. 25 per cent of V = ASKIFW.
(b) The shear walls when acting alone (i.e. independent of the ductile moment-resisting space frame), must be capable of carrying the total lateral force. Concrete shear walls have to be provided at their edges either with encased structural steel elements conforming to CSA G40.21-1976, "Structural Quality Steel" or with built-in concrete columns specially detailed for ductility. While detailing requirements for this Case are not fully covered in CSA A23.3-1973, "Code for the Design of Concrete Structures for Buildings," the recommendations given in the Appendix of ACI 318-71, "Building Code Requirements for Reinforced Concrete" on the seismic design of shear walls provides an adequate design for these elements. For the purpose of the NBC earthquake provisions, tension-diagonal steel bracing systems are also classed as shear walls.
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Case 4. K = 1.0 is required for buildings that consist entirely or mainly of concrete flexural walls designed in a ductile manner according to CSA A23.3-l973, "Code for the Design of Concrete Structures for Buildings," Chapter 19, and all other ductile framing systems that do not qualify for K=0.7 or K=O.S. This includes wood structures with framing and lateral load resistant elements made of wood, and possessing adequate connections and joint details. Frames with structural steel "K" bracing or with tension-compression diagonal bracing are also considered to form a ductile structural system requiring K = 1.0.
Case 5. K= 1.3 for frame buildings where I or more bays have infills or reinforced masonry so as to form a wall cantilevering up from the foundations. While the inclusion of isolated infill panels need not affect the K value for the buildings, K = 1.3 would be required if more than 50 per cent of the building height contains masonry infill panels.
It should be noted that K is to be increased to 2.0 for buildings of Case 6, located in Zone 3 and over 200 ft in height, as described in Sentence 4.1.9.3.(1).
Case 6. K will be taken as 1.3 for structures without special provisions for ductility in the loadcarrying structural system. This includes structures having nominal ductility such as those of continuously reinforced concrete, reinforced masonry shear wall buildings, steel structures which may exhibit a degrading stiffness characteristic, such as frames relying solely on a tension-diagonallateral bracing system and post and beam wood construction where the earthquake loads are resisted primarily by tension-diagonal steel cross bracing. Continuously reinforced concrete refers to reinforced concrete conforming to CSA A23.3 Chapters I to IS. Precast concrete construction may be used in Case 6 provided the reinforcing is made continuous by means of lapped or welded splices in accordance with CSA A23.3-l973. The splices are to be encased with cast-in-place concrete.
Case 7. K = 2.0 for buildings which exhibit little ductility and damping. This includes unreinforced masonry buildings and unreinforced masonry components. K = 2.0 also for structures other than buildings that consist of only I or a few component parts.
Case 8. Cross-braced towers supporting elevated water tanks require K = 3.0. This high value is considered appropriate because of the poor performance of such structures in past earthquakes and the special importance of maintaining their integrity in case of fire following an earthquake.
Foundation Factor, F 22. The soil conditions at a site have been shown to exert a major influence on the character
istics of earthquake motions and the response spectra computed for them. As the motions propagate from bedrock to the surface, the soil may amplify the motions in selected frequency ranges around the natural frequencies of the surficial layer. In addition, a structure founded on the surficiallayer and some of whose natural frequencies are close to those of the layer may experience even more intense shaking due to the development of a state of quasi-resonance between structure and foundation soil. Direct calculation of these effects by suitable mathematical models such as lumped mass, wave propagation and by 2-dimensional finite element models using realistic soil properties is possible with the assumption that the earthquake motions are shear waves propagated vertically from bedrock. This simplified model of wave transmission ignores the source mechanism of the earthquake, the geology of the travel path and the effect of surface waves. Because of the uncertainties and complexities in the realistic estimation of site effects on the seismic response of structures and ground, only a rough allowance can be made at this time.
23. The seismic provisions of the NBC incorporates site effects by categorizing the wide variety of possible soil conditions into 3 types and assigning values to a foundation factor, F, as per sentence 4.1.9.1.(9), depending on soil type and depth. The factor F reflects experience with these soil conditions in the field, and in an approximate way integrates the effect of soil amplification and soil-structure resonance into the estimation of the seismic design forces for buildings having no unusual structural characteristics.
24. When the surficial layer consists of a number of soil layers, an F value appropriate to some average conditions may be used. However, when substantial layers of soft clay are present, F should be taken as 1.5.
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25. The seismic design procedures outlined in the NBC are based on the assumption that the structures are founded on a rigid base moving with the ground surface motion. Real foundations possess both flexibility and damping capacity which alter structural response. The flexibility of the foundation increases the fundamental period of a structure, and the damping capacity allows dissipation of energy by radiation away from the structure and through hysteretic damping in the foundation, thus increasing the effective damping of the structure. These effects are described as soil structure interaction and are not considered explicitly in the NBC. For most buildings considered by the NBC, neglecting soil-structure interaction results in conservative design.
26. It should be emphasized that the influence of the site conditions incorporated in the foundation factor, F, are related to levels of structure shaking only, and assume that the foundation soils maintain their integrity. The designer should consider the possibility of ground failure beneath the structure due to excessive settlements in loose sands, liquefaction of saturated sands, fault displacements and loss of strength of sensitive clays. The advice of an experienced geotechnical engineer should be sought for the evaluation of the suitability of the site and its possible behaviour under seismic motions.
Importance Factor I 27. Some structures are designed for essential public services, and it is imperative that these
structures be operative after an earthquake. These include buildings that house electrical generating and distribution systems, fire and police stations, hospitals, radio stations and radio towers, telephone exchanges, water and sewage pumping stations, fuel supplies, civil defence buildings and schools. Such structures are assigned an I factor of 1.3. This factor is not intended to cover the design considerations associated with special purpose structures whose failure could endanger the lives of a large number of people or affect the environment well beyond the confines of the building. These would include facilities for the manufacture or storage of toxic materials, nuclear power stations, etc.
VERTICAL ACCELERATIONS
28. Ground motion during an earthquake is multi-directional, and may contain a substantial vertical component. Outside the epicentral zone the vertical accelerations are generally 30 to 60 per cent of the horizontal accelerations, while in the immediate vicinity of the epicentre the vertical accelerations could be higher.
29. Under abnormally high vertical accelerations, columns at the upper floors, especially at the roof level, could be adversely affected. However, there is usually sufficient reserve strength in vertical load-carrying members that vertical accelerations can be safely neglected. Certain special structures have been noted(25) where these accelerations may have led to instability or unusual reductions in the factors of safety. When this becomes a governing design consideration, dynamic analysis should be employed.
DISTRIBUTION OF THE BASE SHEAR
30. The base shear is the algebraic sum 01- .he inertial forces acting on the masses of the structure caused by the seismic motion of the base. The motion of the structure is complex, involving the superposition of a number of modes of vibration about several axes. For translational vibrations, the addition of the spectral modal responses results in a lateral inertial force distribution that is approximately triangular in shape with the apex at the base. As the inertia forces Fx induced at any level x are proportional to the weight Wx at that level, the distribution of seismic forces is approximated by
(7)
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For a lumped mass system the use of this equation is reasonable for stubby structures, i.e. those with height-to-width ratios less than 3, or those with fundamental periods less than about I sec. For more slender buildings, higher forces are induced at the top of the structure(12).(26) due to increasing contributions to top storey amplitudes by all the contributing modes. This re-distribution of forces is accounted for by applying part of the base shear as a concentrated force, F t , to the top of the structure.
31. It should be noted that Vn, the shear force for the top storey, and Vx, the shear force transmitted to the supporting structure just below the level i = x, are given by
(8)
Vx = F t + f F, (9) i=~
32. The dimension Ds should be the plan dimension of the lateral force-resisting system that contributes substantially to resisting the lateral loads.
OVERTURNING MOMENTS
33. The lateral forces that are induced in a structure by earthquakes give rise to moments which are the product of the induced lateral forces times the distance to the storey level under consideration. There they have to be resisted by axial forces and moments in the verticalload-carrying members. While the base shear contributions of modes higher than the fundamental can be significant, the corresponding modal overturning moments for the higher modes are small. As the equivalent static lateral base shear in the NBC also includes the contributions from higher modes for moderately tall and tall structures, a reduction in the overturning moments computed from these lateral forces appears justified. This is achieved by means of the multiplier, J, as given in NBC Sentence 4.1.9.1.(14) and shown in Figure J-2. If, however, a structure did respond exclusively in its fundamental mode, the overturning moment at the base would be the sum of the moments corresponding to the forces Fx about the base without any J-factor reductions. A more refined method of accounting for the maximum overturning moments is through the methods of dynamic analysis.
34. The overturning moment reduction factor, J, in many building codes has recently been adjusted upwards, as it was realized on the basis of theoretical investigations and recent earthquake experience that small values of J were not justified. Examples of this trend are seen in the California SEAOC, the New Zealand Codes as well as the NBC as shown in Figure J-2.
TORSIONAL MOMENTS
35. The inertial forces induced in the structure by earthquake ground motions act through the centre of gravity of the masses, e.g. basically at each floor level. If the centre of mass and the centre of rigidity do not coincide because of asymmetrical arrangement of structural elements or uneven mass distributions, torsional moments will arise. The designer should endeavour to make the structural system as symmetrical as possible and should consider the effect of torsion on the behaviour of the structural elements.
36. A realistic approach to aseismic torsional design should consider the effect of the dynamic magnification(27).(28) of the torsional moments, the effect of simultaneous action of the 2 horizontal components of the ground disturbance, and accidental torsion. Accidental torsional moments are intended to account for the possible additional torsion arising from variations in the estimates of the relative rigidities, uncertain estimates of dead and live loads at the floor levels, addition of wall panels and partitions after completion of the building, variation of the stiffness with time, and inelastic or plastic action. The effects of possible torsional motion of the ground should also be considered. For most practical situations, however, these concepts and effects can only be accounted for by the use of adjustment factors.
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37. The torsional provisions of the NBC deal with the complex nature of torsion and the effect of the simultaneous action of the 2 horizontal ground motion components by increasing or decreasing the computed torsion by 50 per cent, whichever produces the worst effect in a member. The part played by accidental torsion is recognized by specifying an additional torsion due to an eccentricity of 0.05 times the plan dimension in the direction of the computed eccentricity. The NBC also specifies that when the total torsional eccentricity exceeds 25 per cent of the appropriate plan dimension, a dynamic analysis shall be mandatory or the effects of torsion in the static analysis shall be doubled. This accounts for the complexity and importance of the torsional effects under these conditions.
38. For structural elements to resist torsional moments most effectively, they should preferably be located near the periphery of the building, i.e. some distance from the centre of rigidity. Wall elements that are intended for resisting torsional forces should be oriented so that their inplane forces are associated with as large a moment arm as possible about the centre of rigidity. In buildings with complete diaphragms such as complete reinforced concrete floor slabs, all elements interconnected by such members can be counted on to resist torsional forces.
39. In core-type buildings where all stiffening elements are located in a central core away from the periphery, accidental torsion and torsional ground motion are particularly significant. In odd- and irregularly-shaped buildings, such as the L-shaped building, and in buildings with the core located at one side or comer, large torsional oscillations are induced by horizontal ground motion. These are some examples of torsion situations that should be avoided in building layouts. Torsional effects should also be evaluated for parts of structures relative to the whole. For example, it is important that the torsional effects of projecting wings on buildings be considered in relation to the motion of the building as a whole.
40. When the torsional frequency of a structure is close to one of the translational frequencies of the structure, large torsional amplifications can occur,(29).(30) even in symmetrical buildings. Such cases should be analyzed dynamically. It is, however, not yet feasible to identify such situations simply, without actually performing a detailed modal analysis.
SETBACKS
41. A setback is considered to be a sudden change in plan dimension or a sudden change in stiffness along the height of a building. Only the case of sudden changes in plan dimensions will be treated here. The effects of major changes in stiffness are best investigated by dynamic methods.
42. The following guidelines are extracted from the 1967 Edition of the SEAOC Code Commentary.ol) These are considered most suitable for the majority of cases encountered in practice.
43. The problem of seismic design for buildings with setbacks is rather complex because of the many factors and variables involved. Setbacks in practice can be symmetrical or asymmetrical about the base portion in one or both axes. Towers and bases can vary in types of construction, the amount of the setback and the height of the tower as compared to that of the base. Also, the relative masses of the tower and base portions will influence the dynamic behaviour of the entire structure.
44. In consideration of the many variables involved in this problem, mathematical, experimental and judgment-type factors have all been employed in arriving at the following recommended procedure. While many setbacks are 3-dimensional in geometry, it is considered satisfactory that the 2 dimensions in the plane under consideration be used.
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Tenninology 45. The following definitions and symbols are employed in this Subsection of the Commen
tary as well as in the associated diagram, Figure J-3:
Setback = a change in either or both plan dimensions of a building from one storey to
Base another, the portion of a building below a setback level, the portion of a building above a setback level, Tower
b t H
the width in feet of the base parallel to the direction under consideration. the width in feet of the tower parallel to the direction under consideration, the height in feet of the entire building (base plus tower), the height in feet of the tower only on the face parallel to the direction under consideration.
Seismic Forces for Setbacks 46. The seismic design forces as set forth in Subsection 4.1.9. of the NBC must be adjusted
for setbacks as shown in Table J-3.
TableJ-3
SPECIAL SEISMIC FORCE REQUIREMENTS FOR SETBACKS
Ratio of t/b Ratio ofH/H Procedure *
1.00 to 0.80 Any A
Less than 0.80 to 0.60 1.00 to 0.65 C Less than 0.80 to 0.60 Less than 0.65 to 0.35 D Less than 0.80 to 0.60 Less than 0.35 B
Less than 0.60 to 0.40 1.00 to 0.75 C Less than 0.60 to 0.40 Less than 0.75 to 0.25 D Less than 0.60 to 0.40 Less than 0.25 B
Less than 0.40 1.00 to 0.80 C Less than 0.40 Less than 0.80 to 0.40 D Less than 0.40 Less than 0.40 B
Column I 2 3
*Procedures referred to in Table J-3: A. Consider as one building of full height, H, use weighted average width in determining
period and base shear. S. The base shall be considered a separate building of its own height, with the tower weight
and tower base shear applied at the roof level. The tower base shear coefficient shall be 40 per cent greater than that obtained on the assumption that the tower is a separate building situated on the ground. The other tower shears shall be determined pro rata from this tower base shear as for a separate building.
C. Extend the tower through the base to the foundation level and treat as a separate building unit of height H to get seismic coefficients for the tower. The additional weight of the portions of the base not included in the extended tower shall be used with the seismic coefficients for a fictitious building having the height of the base only to determine additional lateral forces at the lower levels. At least 70 per cent of all tower originated forces shan be provided for within the plan limits of the extended tower.
D. Whichever of the following procedures produces lateral forces which govern the design at any location or member must be used: (I) Assume the tower and the base constitute I building offull height H, and of a weighted
average width, b, to determine the seismic coefficients; such coefficients shall then be increased by 20 per cent, or
(2) Treat the base and tower as 2 separate buildings and follow procedure "B" above.
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Multiple Setbacks 47. Where there is more than I setback with a tlb ratio less than 0.80, a condition of multiple
setbacks is considered to exist for the purposes of this guide. This condition is approached with the same general intent as above for single setbacks, but with the portion above and below each setback level considered the "tower" and the "base," respectively. The resulting design for the building as a whole and for each portion thereof must comply with all preceding applicable requirements.
Structural Requirements for Setbacks 48. In addition to the recommended approximate procedure for the seismic loads on the
building, the "notch" effect must be considered in design, particularly where the tower framing does not extend downward through the base. A shear wall type of design for both a tower and base could produce severe stresses at and about the 90 deg. notches.
49. Some setbacks may consist of simple I-storey penthouses, whereas others may constitute substantial portions of the entire building. In view of the dynamic and also the notch effect phenomena that may occur, it is recommended that the lateral load resisting elements should be vertically continuous through the setback portion. If the lateral load resisting elements are not vertically continuous through the setback and all the way to the foundations, it is recommended that a special analysis be carried out to demonstrate that the offsets are fully compatible with the setback conditions.
DRIFT AND SEPARATION OF BUILDINGS
50. Drift refers to the lateral deflection at any point in the structure relative to the ground. Incremental drift or interstorey drift refers to the lateral deflection of a storey relative to the one just below it.
51. The requirement to calculate drift as 3 times the elastic deflection resulting from the design earthquake forces as specified in the NBC includes allowance for some plastic deformation to occur in the structural system. The separation of 2 adjacent structures is required to be 2 times the combined deflection of the structures under the design earthquake loads. This accounts not only for some plastic deformation of the structures, but also for the reduced likelihood that the maximum deflection of both structures is reached simultaneously.
52. The NBC requires that all portions of a structure be designed to act as an integral unit in resisting horizontal forces, unless separated by a distance sufficient to avoid contact under deflection due to seismic action or wind forces. The amount of separation required depends upon the movement to be accommodated and is thus connected with the drift limitations.
53. Drift limitations should be established in consideration of the acceptable damage to the non structural components, e.g. fragile glass panels,(32) plaster walls and other partitions. A recommended interstorey drift limitation is 0.005 times the storey height under the specified earthquake loads. The effect of the drift on the vertical load carrying capacity of the lateral force-resisting system should also be considered.
DESIGN CONSIDERATIONS
54. In choosing the structural system for a building, large dissimilarities in the stiffness and ductility characteristics of framing systems in the orthogonal directions should be avoided. For example, a moment resistant ductile frame in one direction and reinforced masonry walls in the other would be unsuitable, whereas ductile reinforced concrete flexural walls and regular reinforced concrete walls in orthogonal directions would be acceptable. The reason for this recommendation is that the seismic displacements that are induced in flexible framing systems would likely cause failure in the relatively brittle and weak directions of elements that resist the load in the orthogonal direction.
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55. The nonstructural components of the structure should be detailed so as not to transfer to the structural system any forces that are not accounted for in the design. Ifnonstructural members are designed as isolated units, their connections should be detailed to be capable of accommodating the anticipated movement due to drift and temperature changes.(33) If on the other hand, these components are rigidly attached to the structure, then their effect on the behaviour of the structure should be considered and allowed for in the elastic, plastic and fracture stages. An example is the stair that may act as a stiffening element. Failures of some buildings in the Caracas 29 July, 1967, earthquake were caused by the partition tile walls which acted as shear walls, thus changing the relative rigidity of the bents from that assumed in the design.(34)
56. Most failures in structures subjected to seismic loading can be traced to poor detailing, especially at beam and column connections. This becomes the governing factor in good aseismic behaviour of buildings built of precast elements.(I)
57. Floor systems that act as diaphragms should be studied to ensure that they are capable of distributing the loads to the various elements.
58. When the shear wall contains numerous openings, the design should account for its real behaviour under lateral loads, i.e. whether the wall acts as a unit or as a number of units because of the reduced rigidities due to the openings. Overstress at the openings should be examined. This is a common cause of damage to lintels above door openings and to piers between window openings.(1) Suggested design details are also given in Chapter 19 of CSA A23.3-1973, "Code for the Design of Concrete Structures for Buildings."
59. Construction joints should be designed to transfer earthquake forces without transverse or rotational slippage (Reference (1), p. 145).
60. Unreinforced masonry buildings have fared badly when subjected to earthquakes.(1) The presence of reinforcing embedded in mortar or grout increases ductility and reduces the likelihood of brittle failure. Examples and detail sheets for the aseismic design of reinforced masonry can be found in References (33) and (35).
61. Sentence 4.1.9.3.(4) of the NBC requires that masonry in Zones 2 and 3 be reinforced. These elements include exterior loadbearing and non-Ioadbearing walls, parapet walls, interior load bearing walls and non-load bearing partitions that weigh more than 40 psf or are more than 10 ft high. Masonry elements around stair and elevator shafts are required to be reinforced to ensure a safe exit from the structure.
62. The structural configuration should be such that elastic-plastic action in the members or failure of individual elements will not produce instability or initiate progress collapse.
MACHINERY, EQUIPMENT AND COMPONENTS OF BUILDINGS
63. Machinery and electrical and mechanical equipment mounted within buildings should be designed to withstand the forces and displacements that arise from the seismic response of the structure. Elevators and their counterweights are vulnerable to large structural displacement as well as lateral forces. Guide rails should be designed to accommodate these effects and to prevent derailment of the components. The mountings and supports of motors, fans and other machinery and equipment need sufficient strength to resist the seismic forces transmitted through these components. In order to prevent injury to persons and to avoid secondary damage to the structure, stops need to be provided on resilient machinery mounts to keep the component from jumping off the springs during an earthquake. Minimum design forces for components and portions of buildings are given in NBC Sentence 4.1.9.1.(12). Some suggested design considerations and details are presented in Reference (36) (see also Reference (37». The failure of interior partitions, finishes and hung ceilings also pose hazards to occupants.
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SPECIAL PROVISIONS
64. The NBC specifies that, except in seismic Zones 0 and 1, buildings shall have structural systems as described by Cases 1 through 6 in NBC Table 4.1.9.A. For Zone 3, buildings over 200 ft in height having a structural system described by Case 6 shall use K = 2.0. Analyses('2) of buildings of approximately 200 ft in height have shown that if damage is to be minimized in a moderate earthquake, the structure must incorporate ductile features that are associated with these low K values. Alternatively, extra strength is to be provided by using a higher K value. The height limitations associated with the provisions of NBC Article 4.1.9.3. and cases described in Table 4.1.9.A. are summarized in Table 1-4.
Table J-4
SUMMARY OF CASES PERMIITED BY ARTICLE 4.1.9.3.
Height of Building Zone 1 Zone 2 Zone 3
Up to 3 storeys in 1-7
1-7, except unreinforced 1-7, except unrein forced building height masonry masonry
Greater than 3 storeys but not more than 200 ft 1-7 1-6 1-6 in building height
Greater than 200 ft in 1-7 1-6
1-6, except for 6 use building height K=2.0
Column 1 2 3 4
DYNAMIC ANALYSIS
65. The NBC allows the use of dynamic analysis for the evaluation of the seismic design loads provided that the design is based on an acceleration ratio, A, not less than that specified in the NBC. For conventional multi-storey buildings the NBC approach is quite satisfactory, but some tall or unusual buildings may require dynamic analysis to verify the seismic adequacy of their structural systems. Buildings with irregular layouts, large setbacks or unusual taper, or critical industrial structures, should be designed on the basis of dynamic analysis.
66. The seismic static loads given by the NBC may be used as a preliminary estimate for the evaluation of the member sizes of these structures. The judgment of an experienced structural engineer must be relied upon to decide when dynamic analysis is needed. A recommended method of dynamic analysis is presented in Commentary K.
67. It should be noted that the NBC 1977 limits the base shear computed from a dynamic analysis to be not less than 90 per cent of that obtained by the procedure in Subsection 4.1.9. Two major reasons for this limitation are (a) different response spectra, based on different assumptions, can result in greatly varying design forces,(38) and (b) there is some uncertainty in the manner of accounting for the ductility requirements for multi-degree-of-freedom systems in simplified dynamic analyses, including the one presented in Commentary K. Until these aspects can be satisfactorily resolved, it appears prudent to limit the acceptable deviation between the base shear calculated according to Subsection 4.1.9. of the NBC and that obtained from a dynamic analysis.
ACKNOWLEDGEMENT
68. Results of recent research and experience in earthquake engineering in Canada, U.S.A., Japan, Mexico, New Zealand and other countries have been used in the Section of the NBC dealing with loads due to earthquakes.
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REFERENCES (I) The Prince William Sound, Alaska, Earthquake of 1964 and Aftershocks, Vol. II, Research
Studies, Seismology and Marine Geology. U.S. Department of Commerce, U.S. Environmental Science Services Administration, U.S. Coast and Geodetic Survey, U.S. Government Printing Office, Washington, 1967.
(2) The Niigata Earthquake, 16 June 1964, and Resulting Damage to Reinforced Concrete Buildings. International Institute of Seismology and Earthquake Engineering, Tokyo, Japan, February 1965.
(3) Hodgson, J. H. There are Earthquake Risks in Canada. Canadian Consulting Engineer, Vol. 7, No.7, July 1965.
(4) Smith, W. E. T. Earthquakes of Eastern Canada and Adjacent Areas, 1534-1927. Publications of the Dominion Observatory, Ottawa, Vol. 26, No.5, 1962.
(5) Smith, W. E. T. Earthquakes of Eastern Canada and Adjacent Areas 1928-1959. Publications of the Dominion Observatory, Ottawa, Vol. 32, No.3, 1966.
(6) Milne, W. G. and Lucas, K. A. Seismic Activity in Western Canada 1955 to 1959 Inclusive. Publications of the Dominion Observatory, Ottawa, Vol. 26, No. I, 1961.
(7) Davenport, A. G. and Milne, W. G. Distribution of Earthquake Risk in Canada. Fourth World Conference on Earthquake Engineering, Santiago, Chile, January 1969. (Also Bulletin, Seismological Society of America, Vol. 59, No.2, April 1969, pp. 729-754.
(8) Whitham, K., Milne, W. G. and Smith, W. E. T. The New Seismic Zoning Map for Canada. 1970 Edition, Geophysics, Reprinted from The Canadian Underwriter, 15 June 1970.
(9) Ferahian, R. H. Comparison of the Probabilities of Wind and Earthquake Loads in the NBC 1970. National Research Council of Canada, Division of Building Research, Building Research Note 72, Ottawa, 1970.
(10) Housner, A. W. et al. Spectrum Analysis of Strong Motion Earthquakes. Bulletin, Seismological Society of America, Vol. 43, 1953.
(11) Earthquake Resistant Regulations, A World List 1973, compiled by International Association for Earthquake Engineering, Tokyo, Japan.
(12) Clough, R. W. and Benuska, K. L. FHA Study of Seismic Design Criteria for High Rise Buildings. A report prepared for the Technical Studies Program and the Federal Housing Administration, HUD TS-3, August 1966.
(13) Penzien, J. Dynamic Response of Elasto-Plastic Frames. Trans. Am. Soc. Civ. Engrs., Paper 3284, Vol. 127, 1962, Part II.
(14) Blume, J. A. et al. Design of Multistorey Reinforced Concrete Buildings for Earthquake Motions. Portland Cement Association, Skokie, Illinois, 1961.
(15) Anderson, A. et al. Lateral Forces of Earthquake and Wind. Paper No. 2514, Trans. Am. Soc. Civ. Engrs., Vol. 1l7, 1952.
(16) Tezcan, S. S. and Ipek, M. March 28, 1970. Gediz Turkey Earthquake and its Long Distance Effects. Research Center, Robert College, Istanbul, Turkey, 1971.
(17) The Caracas Earthquake of July 29, 1967. Venezuelan Official Seismic Commission, Proceedings, Fourth World Conference on Earthquake Engineering, Santiago, 1969, Session J-2, Volume 3, pp. 75-86.
(18) Seed, H. B. et al. Soil Conditions and Building Damage in 1967 Caracas Earthquake. Journal of the Soil Mechanics and Foundations Div., ASCE, Vol. 98, No. SM8, August 1972, pp. 787-806.
(19) Rosenblueth, E. The Earthquake of 28 July, 1957 in Mexico City. Proc. Second World Conference on Earthquake Engineering, Japan, 1960, Vol. I, pp. 359-379.
(20) Roesset, J. M., Whitman, R. V. and Dobry, R. Modal Analysis for Structures with Foundation Interaction. Journal of the Structural Division, ASCE, Vol. 99, No. ST 3, March 1973, pp. 399-416.
(21) Novak, M. Effect of Soil on Structural Response to Wind and Earthquake. Journal on Earthquake Engineering and Structural Dynamics, Vol. 3, No. I, 1974.
(22) Finn, W. D. L. et al. Sand Liquefaction in Triaxial and Simple Shear Tests. Journal of Soil Mech. and Foundations Div., ASCE, Vol. 97, No. SM4, April 1971, pp. 639-659.
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(23) Seed, H. B. and Idriss, I. M. Simplified Procedure for Evaluating Soil Liquefaction Potential. Journal of the Soil Mechanics and Foundations Div., ASCE, Vol. 97, No. SM9, September 1971, pp. 1249-1273.
(24) Ishihara, K. and Yasuda, S. Sand Liquefaction due to Irregular Excitation. Soils and Foundations, Vol. 12, No.4, December 1972, pp. 65-77.
(25) Jaeger, L. G. and Barr, A. D. S. Parametric Instabilities in Structures Subjected to Prescribed Periodic Support Motion. Proc. Symposium on Design for Earthquake Loadings, McGill University, September 1966.
(26) Blume, J. A. Structural Dynamics of Cantilever Type Buildings. Ref. (61), Session A-3, pp. 1-16, Vol. 1.
(27) Housner, G. W. and Outinen, H. The Effect of Torsional Oscillations on Earthquake Stresses. Bulletin, Seismological Society of America, Vol. 48, No.3, July 1958, pp. 221-229.
(28) Bustamante, J. I. and Rosenblueth, E. Building Code Provisions on Torsional Oscilations. Proc. Second World Conference on Earthquake Engineering, Japan, 1960, Vol. 2, pp. 879-892.
(29) Keintzel, E. On the Seismic Analysis of Unsymmetrical Storied Buildings. Paper No. 10, Session I B, Proceedings, Fifth W orId Conference on Earthquake Engineering, Rome 1973.
(30) Tso, W. K. and Asmis, K. G. Torsional Vibration of Symmetric Structures. Pages 178-186, Proceedings of the First Canadian Conference on Earthquake Engineering, u.B.c., September 1965.
(31) Recommended Lateral Force Requirements and Commentary. Seismology Committee, Structural Engineers Association of California, 1967.
(32) Bouwkamp, J. G. Behaviour of Window Panels Under In-Plane Forces. A report to the Division of Architecture, Dept. of Public Works, State of California, February 1960.
(33) Seismic Design for Buildings. Dept. of Army Technical Manual TM5-809-IO, Washington, D.C., March 1966. Plate 2-16, pp. 2-62.
(34) Sozen, M. A. et al. Engineering Report on the Caracas Earthquake of 29 July, 1967. National Academy of Sciences, Washington, D.C., 1968.
(35) Amrhein, J. E. Reinforced Masonry Engineering Handbook. Masonry Institute of America, Los Angeles, Calif., July 1972, 320 pp.
(36) Ayres, J. M. and Sun, T. Y. Criteria for Building Services and Furnishings. Building Science Series 46, National Bureau of Standards, February 1973, pp. 253-285.
(37) Anonymous. Design Could Mitigate Disaster Results. Engineering News Record, November 15, 1973, p. 13. See also November 29, 1973, p. 64.
(38) Rainer, J. H. Evaluation of the Dynamic Seismic Analysis Recommended for the 1975 National Building Code. NRCC No. 15479, July 1976.
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COMMENTARYK
DYNAMIC ANALYSIS FOR
THE SEISMIC RESPONSE
OF BUILDINGS
TABLE OF CONTENTS
109
Pages
Seismic Design . . • • . . . . . . • • . . . • • . . • . • • . . . . . . • • . . . • • • . . . . • • . 111 Definitions of Terms ••.. • • • . . . . . . . • • . . . . . • . • • . • . • • • . . . • • . . . • 112 Design Criteria . . . . . . . . . . . . . . • . • . • . . . • . . . . • • . . . . . • • • • . . . • . . 112 Alternatives for Appropriate Design Ground Motions .•••.....••..•. 113 Average Design Spectrum • . . . • . . • • . . . • • • . . . . . . . . . . . • . . . . • . . . . 114 Influence of Soil and Foundation . . • • • • • . . • • . . • • • • . • • . . . . . • . . . . . 117 Importance Factor ..•.••..•••.•••..•••....•.••...••••..•••. 117 Structural Analysis •••....•...•••.••...•....••••......•..... 118 Detailing Requirements .•..•.••..•..•.•....•.....•••..•..... 122 References ••....•........•...•••..•.•..••.••....••...•... 122
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III
COMMENTARYK
Dynamic Analysis for the Seismic Response of Buildings I. The purpose of this commentary is to present guidelines for an acceptable dynamic analy
sis that can be used as an alternative to the quasi-static seismic analysis presented in Subsection 4.1.9. of the National Building Code of Canada 1977, as permitted by Article 4.1.9.1. The design forces obtained from the dynamic analysis need to be multiplied by the appropriate load factors given in the NBC and treated in the same manner as loads obtained from NBC Subsection 4.1.9.
2. It is anticipated that the dynamic analysis recommended here will permit a more realistic description of the behaviour of a building subjected to earthquake loadings than the static code provisions. The major use of these recommendations is expected to be in the design of unusual or complex structural configurations for which the static NBC procedures are necessarily crude, inadequate or inapplicable. This may be the case for buildings with major setbacks, large torsional eccentricities, unusual mass or stiffness distributions, unusual foundation conditions and others. For regular buildings, the static NBC requirements and the recommended dynamic procedure should give similar results. References (1) and (2) present some comparison studies.
3. However, in accordance with Sentence 4.1.9.l(I)(b) of the NBC, the base shear from a dynamic analysis shall not be less than 90 per cent of the base shear obtained by the static analysis as prescribed by 4.1.9.1.(l)(a). Where the base shear computed from a dynamic analysis is less than 90 per cent of that of the Code, all the computed storey shears, moments and displacements need to be scaled upwards in the ratio of 0.90 times the Code base shear divided by the dynamic base shear.
4. Whereas the method presented is quite general and may be applicable to structures other than buildings, the application of this recommended procedure to other types of structures should be carried out with due caution. The user of this recommended dynamic procedure should have a working knowledge of structural dynamics.
5. Since it is desirable to present this recommended dynamic procedure as a self-contained package, there will necessarily be some overlapping or duplication with Commentary J on the static seismic provisions of the NBC.
SEISMIC DESIGN
6. The following major steps comprise the procedure employed in the seismic design of struc-tures:
(a) Establishment of general design criteria. (b) Determination of design ground motion. (c) Analysis of a preliminary design to see if it satisfies both the general design criteria and all
applicable NBC requirements. (d) Detailing of members and connections to assure compliance with both the general design
criteria and all applicable NBC requirements. (e) Iterating the process at one or more stages if necessary.
7. These steps will be described subsequently in more detail, with major emphasis placed on the recommended ground motion and on the structural analysis. It is hoped that the broad principles presented here will enable the designer to make the appropriate decisions applicable to a particular problem. The user of this guide should also consult Commentary J on "Effects of Earthquakes" for additional information on specific topics.
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112
DEFINITIONS OF TERMS 8. Critical damping means the minimum value of damping that will allow a displaced oscilla
tor to return to its initial position without oscillation. Damping ratio (fraction of critical) means the ratio of the damping coefficient to the critical
damping coefficient for a single-degree-of-freedom oscillator or a normal mode. Ductility means the ability of a structural member to deform after yielding without failure
under constant or increasing load. Ductility factor means the ratio of total elastic-plastic deformation to the yield deformation. Member ductility factor means the ductility factor applicable to a particular member within a
structure. Natural period means the period of free vibration of a single-degree-of-freedom structure. For
a multi-degree-of-freedom system, the natural periods are the periods of the normal modes of vibrations. The inverse of natural periods are the natural frequencies in cycles per second or Hz (hertz). Both the normal modes and the natural periods can be determined from an eigenvalue formulation for the structure.
Normal mode (natural mode, eigenmode) means the geometric configuration of a structure vibrating at the associated natural frequency.
Response Spectrum means envelope of maximum response of a single-degree-of-freedom oscillator subjected to a particular disturbance, and plotted as a function of the natural period (or frequency) of the oscillator. Different spectrum curves are obtained for different damping ratios.
Response Spectrum AnalySiS means a procedure for computing the response of a structure to a given disturbance for which response spectra have been computed. The total structural response is obtained by combining the contribution of the various modal responses of the structure.
Structure ductility factor (system ductility factor) means the ratio of the total elastic-plastic deformation to the yield deformation of the structure. The yield deformation is an extrapolated point formed by the intersection of the elastic deformation curve and the predominant plastic deformation curve of the structure, and may not necessarily coincid,e with the first yielding of any member in that structure.
Time Series AnalySiS means a step-by-step calculation in the time domain of the response of a structure to a particular disturbance.
DESIGN CRITERIA
9. The establishment of design criteria involves primarily the choice of an acceptable risk level from which the associated design earthquake intensity is derived. The costs of construction need to be balanced against the economic and social consequences of damage or failure of the structure.
10. Design criteria for a building must also consider the functional requirements of the building and the manner in which seismic motions are resisted, so that an appropriate structural system can be chosen.
Seismic Risk II. Since earthquakes cannot as yet be predicted with any degree of certainty as to location,
magnitude and time of occurrence, a statistical approach is used for the establishment of earthquake acceleration amplitude levels. A probability of exceedance of 0.01 per annum (or the H100 year" earthquake) was taken as the standard risk level for the determination of peak ground acceleration for the seismic design of buildings in Canada. This has been shown to be roughly equal to the risk of exceedance for the present wind load requirements,ol The calculation of peak ground accelerations associated with this probability and other probabilities of exceedance have been determined from an evaluation of instrumental and historical data of earthquake activity throughout Canada,<4}.(5).(6) This culminated in the seismic risk map (or zoning map)(7M8) which gives the peak horizontal ground accelerations having a probability of exceedance of 0.01 per annum. For special or important types of structures, peak ground accelerations having probabilities of exceedance less than 0.01 per annum may be appropriate.
i I
II
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Resistance 12. The resistance of a structure to seismic motions is governed mainly by its strength, sti
ffness and ductility of the component members and their connections, and by stability considerations. As the risk of some structural damage is accepted in the minimum design criteria implied by the Code, deformations will exceed the elastic limit, causing I or more members or joints to deform in the plastic range of material behaviour. This plastic deformation will be accompanied by major cracking in concrete, plaster, partitions and brickwork. In addition, the deflections that accompany the plastic deformations may cause severe distress to architectural finishes and to certain services in a building such as elevators, piping, glazing, etc.(9)
13. An important consequence of plastic deformation is that yielding limits the induced forces in a particular member or above an entire storey. This means that lower elastic design forces can be employed, but at the same time it is necessary to provide sufficient ductility in the members so that this plastic deformation can occur without collapse. A corollary to this requirement is that during plastic deformation brittle fracture in members and connections has to be prevented. Ductility in members and connections may be achieved by proper choice of materials and detailing.
Functional Requirements and Acceptable Damage Criteria 14. The damage level that is acceptable is closely related to the seismic risk level and the
associated peak ground acceleration and the ductility required in the structure. Intimately linked also is the question of initial costs versus repair or replacement costs of the structure and its contents, and the possible loss of serviceability of the structure in the event of a major earthquake. Since architectural, mechanical and electrical fixtures are in general quite vulnerable to large building deformations associated with high ductility ratios, and since their cost of replacement or repair is often comparable to or greater than that of the structural frame, the economics of a given situation may dictate lower ductility ratios for the structure than are considered minimal.
ALTERNATIVES FOR APPROPRIATE DESIGN GROUND MOTIONS
15. The choice of an appropriate and realistic ground motion depends on many factors, some of which are not yet well understood or quantifiable. Among these variables are the composition and structure of the earth's crust, the present and past history of the state of stress and strain in the crust, location, depth and type of potential zones of fracture and others.
16. Generally speaking, the following options are available for the definition of an appropriate ground motion at a particular site:
(a) Recorded earthquakes from the same geographical location, taking into consideration possible variations that may occur for future events.
(b) Recorded earthquakes from other locations that can be expected to have similar ground motions as the site under consideration.
(c) Artificially generated earthquake records appropriately shaped and scaled to account for the geologic properties of the ground, distance to epicentre, depth of hypocentre and the type of source mechanism that can be expected.
(d) Average design spectra, the spectra being based on observed and theoretical studies of earthquake motion.
(e) Quasi-static loading requirements specified by many building codes.
17. Although a few small strong-motion earthquakes have recently been recorded in Canada,(IO) they are not yet of sufficient number or magnitude to be useful as general design input motions. They should, however, be consulted as one of the many factors to be considered in arriving at appropriate ground motions for major or critical projects. Under certain circumstances, the Earth Physics Branch, Department of Energy, Mines, and Resources, Ottawa, Ontario, may be able to provide more extensive advice on predicted Fourier amplitude spectra for a design ground acceleration for localities in CanadaYI)
18. The use of recorded or artificially generated earthquake motions in the design of structures should be based on a careful consideration of the applicability of the motions to the problem
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at hand. In particular, more than one possible ground motion should be used in order to reduce the likelihood of incorporating into the design a particular bias that may be inherent in anyone input.
AVERAGE DESIGN SPECTRUM
19. For the purpose of seismic design of buildings, an average response spectrum approach is recommended here. The properties of the average response spectrum were derived so that its general shape matches the spectra of a large number of recorded earthquakes.(I2) Excluded from this evaluation are those earthquake records where identifiable unique site conditions exist, such as in Mexico City. The agreement of the recommended average response spectrum with the response spectra of these recorded earthquakes is particularly good in the short period range, but is not as satisfactory in the long period range. This variation can, in part, be traced to the presence of different amounts of surface wave energy in the earthquakes that were recorded. The recommended average spectrum bound in the long period range is, therefore, chosen conservatively.
20. The recommended average response spectrum is calculated from the peak ground motion bounds. The peak ground motion bounds in turn are linked to the seismic risk level by way of the peak horizontal ground acceleration that can be expected. For a risk level of exceedance of 0.01 per annum, the corresponding peak ground accelerations were arrived at by the methods outlined in Reference (7). For many sites in Canada the seismic Zones are listed in the Table of "Design Data for Selected Locations" in NBC Supplement No. I, '<Climatic Information for Building Design in Canada 1977." Values of A that correspond with the various seismic Zones are given in Figure J-1. Peak ground accelerations for other probabilities of exceedance and for specific geographical locations may be obtained by writing to the Seismology Division, Earth Physics Branch, Department of Energy, Mines and Resources, Ottawa, Ontario KIA OE4. These estimates will, of necessity, be more and more unreliable as lower probabilities are requested.
Definition of Peak Ground Motion Bounds 21. The horizontal peak ground motion bounds are given by the 3 intersecting straight-line
bounds shown on the logarithmic plot in Figure K-I. These straight-line bounds represent a statistical average of peak ground acceleration, peak ground velocity and peak ground displacement, and were derived from an examination of the accelerograms of numerous earthquakes and their peak integrated velocities and displacements.(I2),(I3) The levels of ground velocity and displacement bounds correspond to those observed on rock and firm ground. For medium and soft soil deposits the maximum velocities and displacements corresponding to a given peak ground acceleration are generally larger,(I2) and need to be accounted for as discussed under Influence of Soil and Foundation below.
22. While there exists some variability of the ground motions derived from the various recorded earthquakes,(12),(IJ) for the purposes of this recommended procedure the following peak ground motion bounds have been adopted:
(a) Acceleration bound: peak horizontal ground acceleration corresponding to a given probability of exceedance. *
(b) Velocity bound: a straight line of constant spectral velocity drawn from the intersection of the acceleration bound and T = 0.65 sec.
(c) Displacement bound: a straight line of constant spectral displacement from the intersection of the velocity bound and T = 5 sec.
23. The peak ground motion bounds in Figure K-I are drawn for a peak ground acceleration of 1.0 g. The corresponding velocity bound is 40 in./sec., and the displacement bound 32 in. For other values of peak ground acceleration the bounds in Figure K-l are scaled linearly.
*The 0.01 probability of exceedance at a particular location is the risk level for which the Acceleration Ratio, A, is given in the Table of Climatic Data in Part 2 of the NBC. For many sites in Canada the seismic Zones are listed in the Table of "Design Data for Selected Locations" in NBC Supplement No. I, "Climatic Information for Building Design in Canada 1977." Values of A that correspond with the various seismic Zones are given in Figure 1-\' It should be noted that the assigned values of A are assumed to be constant within each zone. However, particularly in Zone 3, the "100 year acceleration" may greatly exceed the assigned constant value.
I
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Elastic Average Response Spectrum
24. The applicable average elastic response spectrum is obtained by multiplying the peak ground motion bounds by the multipliers given in Table K-1. These represent the average amplification factors for a single-degree-of-freedom oscillator from peak ground motion to peak structural response and were adapted from References (12) and (13).
Table K-l
Damping,{!) Multiplier for Spectral Bounds of:
per cent of critical Acce I Velocity Displacement
0.5 5.8 3.3 3.0 2 4.2 2.5 2.5 3 3.8 2.4 2.4 5 3.0 2.0 2.0
10 2.2 1.7 1.7
Column I 2 3 4
Note to Table K-l: (II For other values of damping. linear interpolation may be used. The resulting average response spectrum
curves for various damping ratios are shown in Figure K-l for a maximum ground acceleration of 1.0 g. The design damping ratios for typical structures that approach the material yield level may be taken as given in Table K-2.
Table K-2
Design Type of structure Damping
Ratio '\, %( I)
Structural steel, welded connections with lightweight exterior and interior wall construction 3
Structural steel, welded or bolted connection with heavy exterior walls, normal interior partitions
Reinforced concrete structures 5 Wood beam and column structures Prestressed concrete
Concrete frame with substantially integral interior or exterior masonry walls
Masonry construction 10 Wood framing with wood shear panels
Column I 2
Note to Table K-2: (I) These damping values were adapted from those given in References (12) and (\3).
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117
INFLUENCE OF SOIL AND FOUNDATION
25. Seismic waves emanating from a hypocentre can be modified significantly by the soil overlying the bedrock. This can result in substantial amplifications of motion in the frequency bands near the natural frequencies of the soil layers. When such a natural frequency coincides with I of the natural frequencies of the structure, a condition commonly called "quasi resonance" occurs, which can result in severe overstress of the structure. Further information may be found in References (14). (15) and (16). Unless a detailed analysis of the influence of soil conditions is carried out, the F factor given in NBC Subsection 4.1.9. shall be applied as a multiplier to the average response spectrum. The possible occurrence of sand liquefaction, settlemen t of loose sands or land slides needs to be investigated separately.(I7) to (21)
IMPORTANCE FACTOR
26. Certain important or critical types of structures are required to be designed for higher earthquake loads than is considered standard. The importance factors given in NBC Subsection 4.1.9. shall be used as minimum multipliers to the average response spectrum.
27. A more detailed procedure of accounting for the importance of a structure would be to consider: (a) an adjustment of the probability of exceedance (or return period) of peak ground acceleration, and (b) modifications of the acceptable degree of plastic deformation, as expressed by the ductility factor p.. For example, a structure that is required to remain fully serviceable after being subjected to a "design" earthquake should be designed for a smaller ductility factor than the standard performance requirement intended for prevention of collapse. Furthermore, highly critical structures should be designed for maximum ground accelerations having a probability of exceedance less than 1/100 per annum.
28. It is conceivable that 2 or more criteria have to be satisfied concurrently. For example, for a particular structure the hypothetical requirements given in Table K-3 might have to be met.
Table K-3(\)
Probability of Exceedance Per Maximum Acceptable Annum of Peak Ground Ground Ductility
Acceleration Acceleration, g Factor
0.005 0.15 4 0.01 0.10 2
Column 1 2 3
Note to Table K-3: (I) Additional information on the above and related topics may be found in References (16) and (22). Reference
(23) introduces another concept of accounting for different risk level requirements.
29. Another aspect associated with damage limitations is interstorey drift control. For flexible structures large relative interstorey displacement as well as the accelerations can induce damage to architectural finishes and furnishings such as partitions, false ceilings, light fixtures, glazing and equipment. Failure of these "nonstructural" components can represent high economic losses as well as endanger occupants inside and outside the building. A maximum recommended total drift limitation is 0.005 times the storey height. The deflection may be computed as outlined in the section dealing with the "Computation of Structural Response."
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118
STRUCfURAL ANALYSIS
Introduction 30. Before the seismic analysis of a structure can be commenced, a preliminary design for the
building is required. This can usually be obtained to sufficient accuracy by sizing the members to satisfy the various loading requirements, including the earthquake loads, specified by the National Building Code.
General Requirements 31. For symmetric structures the influence of seismic disturbances is to be considered along
both principal axes of symmetry. For non-symmetric structures, seismic effects may be considered along two arbitrarily chosen orthogonal axes. For both symmetric and non-symmetric structures, the seismic effects along the 2 orthogonal axes may be considered independent of one another, except that the design forces in comer columns shall consist of the combined loading that results from the seismic effects applied in each of the principal directions, multiplied by I/V2. But in no case shall the resulting column designs be less critical than those required when the seismic loads are applied to the structure in each principal direction independently.
32. The General Provisions and Special Provisions of NBC Subsection 4.1.9. are also applicable to this recommended procedure.
Vertical Forces 33. Where it is deemed necessary to consider the influence of vertical seismic motions, the
average vertical design spectrum may be taken as ¥.! the average horizontal seismic response spectrum.(l2).(I3) It should be noted that the relevant resonance frequencies of the structure and its components in the vertical direction are generally quite different from those in the horizontal direction.
Appendages 34. The seismic design of essential services, building contents and appendages can be
achieved by considering the forces and displacements that are imparted to these components by the motion of the structure. Methods of modifying the response spectrum towards this goal may be found in References (24) and (25). In the absence of such techniques, the requirements for portions of buildings and appendages in Subsection 4.1.9. of the NBC shall apply.
Response Modification Due to Plastic Behaviour 35. For a structure designed to undergo elastic-plastic deformation, the average elastic
response spectrum may be modified as follows:<I3)
(a) Elastic-plastic spectral acceleration. The elastic spectral acceleration Sa for any mode having a period T as computed from
2", S = S .- (I)
a Y T
may be divided by the ductility factor, p., that can be realized in the structure for modal periods falling in the range of the velocity and displacement bounds (i.e. for T greater than about 0.5 sec.), and by ~ for modal periods along the acceleration bound (Le. for T less than about 0.5 sec.).
(b) Elastic-plastic spectral displacement. The total elastic-plastic spectral displacement sg is obtained from the average elastic response spectrum as follows:
T sg = Sy' - for modal periods along the velocity and displacement bounds,
2",
T and sg = Sy . . P. I V 2p.-1 for modal periods along the acceleration bounds.
2",
(2)
(3)
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The elastic portion of the total elastic-plastic displacement is given by the total elastic-plastic displacement Sli divided by the ductility factor. f.L.
36. The maximum structural ductility factors f.L given in Table K-4 must be used. except where tests and calculations demonstrate that higher values are justified.
Table K-4
Structural I
Building Type Ductility Factor
Ductile moment resisting space frame 4
Combined system of 25 per cent ductile moment resisting space frame and ductile flexural walls 3
Ductile reinforced concrete flexural walls 3
Regular reinforced concrete structures. cross-braced frame structures and reinforced masonry 2
Structures having no ductility. plain masonry I
Column I 2
37. For structural ductility factors f.L equal to or greater than 5, this recommended procedure should not be used, but a time series analysis with realistic material behaviour should be performed. It should be noted that in order to achieve a given structural ductility, ductility factors of some individual members, particularly those of girders, may need to be greater than the structural ductility. Methods of verifying member ductility requirements may be found in References (26), (27) and (28).
38. For structures having setbacks, ductility requirements at the re-entrant corners may be higher than in a uniform structure. The design and detailing of members and joints near setbacks should recognize this possibility. While elastic analysis may point to a condition of high ductility demands, a full investigation of this aspect would require an elastic-plastic analysis.(29)
Computation of Structural Response 39. For development of the theory treated here, see References (16), (22) and (30)*
40. The seismic response ofa structure may be computed by summing the contributions of its 2'!t
normal modes. The normal modes <l>j, i = 1, ... n, and the corresponding periods Ti = - are ob-
tained from the eigenvalue formulation for the structure:
([ m] [~ ] [k]) {x} = 0 (Ii
(4)
• Additional studies on frame and shear wall analysis, torsional oscillations, dynamic behaviour of soils and foundations. plastic analysis and related topics are contained in References (31) to (35).
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lUM
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Y
mn
j =
n
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I I
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j =
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j =
1
mk I I I m2
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NA
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ODE
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ES
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REY
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ECO
ND
SHEA
R FO
RCES
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ANSl
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NA
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OD
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i 2
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S
chem
atic
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eism
ic f
orce
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a b
uild
ing
"'"' ~
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121
where [m 1 is the mass rna trix, [k 1 the stiffness matrix and {x} is the generalized displacemen t vector. The generalized displacement vector incorporates translational and rotational components. In the coo:putation of modal response, it is convenient to define the "modal participation factors" y, for the (th mode q,i as
Yi = L 2' j = I, ... n m)q, I)
(5)
where m) mj when the direction of ground motion is parallel to the direction of the coordinate j, otherwise m) = O. For synmmetric buildings m) = m) for all degrees of freedom of the de-coupled system. For a consistent basis of comparison among various structures, the mode shapes q,. are frequently normalized so that either the top storey amplitude or the mean square amplitude in each mode is equal to unity.
41. Forces. For a schematic diagram of forces acting on a structure see Figure K-2.
The lateral storey forces p,.) for any mode, i. and at storey level. j. are computed from
Pl.) q".) . y, . Sal . m) (6)
42. The design member forces, storey shears and associated overturning moments are obtained by treating the forces PI,) from each natural mode. i, as individual loading cases. The combined effects are obtained by taking the square root of the sum of the squares of the effect from each mode.
43. When the structural yield capacities exceed the design yield levels, the foundation must be capable of resisting the increased forces caused by these higher yield levels. This requirement is intended to assure that in a major earthquake, yielding will occur in the structure and not in the foundation.
44. Displacements. The displacements D,.) for any mode, t, and storey level, j. are computed from
(7)
The total displacement Dk at level j = k may be estimated with sufficient accuracy by considering only the deformations in the fundamental mode.o6)
45. Interstorey drift may be computed by taking the square root of the sum of the squares of the interstorey drifts of the contributing modes of vibration.
Torsional Effects 46. Uncoupled analysis. The lateral modes along the 2 principal axes may be assumed to be
de-coupled for structures in which the computed eccentricity, e, between the centre of mass and the centre of resistance is less than 0.05 Dn in all storeys, and in which the fundamental torsional frequency is removed at least ± 20 per cent from the fundamental lateral frequency. Dn is the base dimension of the structure normal to the seismic force. For this case the torsional moment shall be computed at every storey level using a design eccentricity ed where ed is either 1.5e+ 0.05 Dn throughout the structure or ed = 0.5e 0.05 Dn throughout the structure, whichever produces the worst effect in a member. The torsional moments M
J at any floor j are found from
MJ = p)' eJ
and the total torsional moments in storey j k are k
Mk =L MJ J=n
(8)
(9)
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When the lowest torsional period lies within 20 per cent of the fundamental period of I of the lateral modes of vibration, the torsional moments shall be doubled to account for sympathetic resonance effects of torsional mode with the lateral modes.(37).(38)
47. Coupled analysis. Where the centres of mass and stiffness are separated by more than 0.10 On in either orthogonal direction at any floor level of the structure, the torsional modes must be considered coupled with the translational modes. For this case, the eigenvalue formulation has to incorporate both translational and rotational degrees of freedom. The torsional moments obtained from the modal analysis must be either increased throughout the structure or decreased throughout the structure by 25 per cent, whichever produces the worst effect in a member. This procedure is intended to take account of accidental eccentricities in the structure and torsional ground motions.
48. Optional analysis. When the maximum computed eccentricity in either orthogonal direction in any storey is between 0.05 On and 0.10 On' either the procedure outlined for uncoupled or for coupled analysis may be used.
DETAILING REQUIREMENTS.
49. The requirements that need to be followed for the design and detailing of members and connections are intended to assure appropriate strength and ductility levels in the structure. In general, the details have to be chosen so that plastic deformations and load reversals can occur without premature failure of the member or of the connections. Failure can occur by local or member buckling, or by brittle fracture. Local buckling can occur in the web or compression flange of rolled or built-up steel sections or in the reinforcing steel of reinforced concrete columns or beams. Brittle fracture can be avoided by appropriate choice of material, welding procedures and details.
50. The above principles are in general satisfied by following the design requirements for steel as given in CSA Standard SI6-1969, "Steel Structures for Buildings" and for reinforced concrete in CSA A23.3-1973, "Code for the Design of Concrete Structures for Buildings."
REFERENCES (I) Tso, W.K. and Bergman, R. Dynamic Analysis of an Unsymmetrical High-Rise Building.
Can. J. Civ.Eng., Vo!' 3, No. I, March 1976, pp. 107-118. (2) Rainer, H.J. Evaluation of the Dynamic Seismic Analysis Recommended for the 1975
National Building Code. NRCC No. 15479, July 1976. (3) Ferahian, R. H. Comparison of the Probabilities of Wind and Earthquake Loads in the NBC
1970. National Research Council of Canada, Division of Building Research, Building Research Note 72, Ottawa, 1970.
(4) Smith, W. E. T. Earthquakes of Eastern Canada and Adjacent Areas, 1534-1927. Publications of the Dominion Observatory, Ottawa, Vo!' 26, No.5, 1962.
(5) Smith, W. E. T. Earthquakes of Eastern Canada and Adjacent Areas 1928-1959. Publications of the Dominion Observatory, Ottawa, Vo!' 32, No.3, 1966.
(6) Milne, W. G. and Lucas, K. A. Seismic Activity in Western Canada 1955 to 1959 Inclusive. Publications of the Dominion Observatory, Ottawa, Vo!' 26, No. I, 1961.
(7) Davenport, A. G. and Milne, W. G. Distribution of Earthquake Risk in Canada. Fourth World Conference on Earthquake Engineering, Santiago, Chile, January 1969. (Also Bulletin, Seismological Society of America, Vo!' 59, No.2, April 1969, pp. 729-754.)
(8) Whitham, K., Milne, W. G. and Smith, W. E. T. The New Seismic Zoning Map for Canada, 1970 Edition, Geophysics, Reprinted from The Canadian Underwriter, 15 June, 1970.
(9) Ayres, J. M. and Sun, T. Y. Criteria for Building Services and Furnishings. Building Sciences Series 46, National Bureau of Standards, February 1973, pp. 253-285.
(10) Rogers, G. C, Milne, W. G. and Bone, M. N. The Strong Motion Seismograph Network in Western Canada, 1970. Publications of the Earth Physics Branch, Vo!' 41, No.2, Department of Energy, Mines and Resources, Ottawa, Canada.
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(II) Hasegawa, H. S. Theoretical Synthesis and Analysis of Strong Motion Spectra of Earthquakes. Canadian Geotechnical Journal, Vol. II, No.2, May 1974, pp. 278-297.
(12) Newmark, N. M., Blume, J. A. and Kapur, K. K. Seismic Design Spectra for Nuclear Power Plants. Journal of the Power Division, ASCE, Vol. 99, No. P02, November 1973, pp. 287-303.
(13) Newmark, N. M. and Hall, W. J. Procedures and Criteria for Earthquake Resistant Design. Building Sciences Series 46, National Bureau of Standards, February 1973, pp. 209-236.
(14) Finn, L. W. D. et al. The Effect of Foundation Soils on Seismic Response of Structures. Ref. (29), pp. 128-141.
(15) Seed, H. B. et al. Soil Conditions and Building Damage in 1967 Caracas Earthquake. Journal of the Soil Mechanics and Foundations Div., ASCE, Vol. 98, No. SM8, August 1972, pp. 787-806.
(16) WiegeL R. L., Ed. Earthquake Engineering. Prentice Hall, Inc., Englewood Cliffs, N.J., 1970. (17) The Prince William Sound, Alaska, Earthquake of 1964 and Aftershocks. Vol. II, Research
Studies, Seismology and Marine. Geology. U.S. Department of Commerce, U.S. Environmental Science Services Administration, U.s. Coast and Geodetic Survey, U.S. Government Printing Office, Washington, 1967.
(18) The Niigata Earthquake, 16 June 1964, and Resulting Damage to Reinforced Concrete Buildings. International Institute of Seismology and Earthquake Engineering, Tokyo, Japan, February 1965.
(19) Finn, W. D. L. et al. Sand Liquefaction in Triaxial and Simple Shear Tests. Journal of Soil Mech. and Foundations Div., ASCE, Vol. 97, No. SM4, April 1971, pp. 639-659.
(20) Seed, H. B. and Idriss, I. M. Simplified Procedure for Evaluating Soil Liquefaction Potential. Journal of the Soil Mechanics and Foundations Div., ASCE, Vol. 97, No. SM9, September 1971, pp. 1249-1273.
(21) Ishihara, K. and Yasuda, S. Sand Liquefaction due to Irregular Excitation. Soils and Foundations, Vol. 12, No.4, December 1972, pp. 65-77.
(22) Newmark, N.M. and Rosenblueth, E. Fundamentals of Earthquake Engineering. Prentice Hall, Inc., Englewood Cliffs, N.J., 1971.
(23) Wiggins, J. W. Balanced Risk Concept, New Approach to Earthquake Building Codes. Civil Engineering, ASCE, August 1972, pp. 55-59.
(24) Biggs, J. M. and Roesset, S. M. Seismic Analysis of Equipment Mounted on a Massive Structure. Seismic Design of Nuclear Power Plants, Ed. by R. J. Hansen, M. I. T. Press, Cambridge, Mass., 1970.
(25) Amin, M. et al. Earthquake Response of Multiply Connected Light Secondary Systems by Spectrum Methods. First National Congress of Pressure Vessel and Piping Technology, ASME, San Francisco, California. May 1971.
(26) Blume, J. A. Design of Earthquake Resistant Poured-in-Place Concrete Structures. Chapter 18, Ref. (14).
(27) Lin, Y. T. Prestressed and Precast Concrete Structures. Chapter 19, Ref. (14). (28) Degenkolb, H. J. Design of Earthquake-Resistant Structures-Steel Frame Structures. Chap
ter 17, Ref. (14). (29) Pekau, O. A. and Green, R. Inelastic Structures with Set-Backs. Paper No. 217, Session 5B,
Ref. (30). (30) Cherry, S. Basic Principles of Response of Linear Structures to Earthquake Ground Motions.
Pages III-7 to III-27, Proceedings of the Symposium on Earthquake Engineering, University of British Columbia, September 8-11, 1965.
(31) Cherry, S., Ed. Proceedings of First Canadian Conference on Earthquake Uni-versity of British Columbia, Vancouver, B.C., May 25-26, 1971.
(32) Proceedings. Fifth World Conference on Earthquake Engineering, Rome, 1973. (33) Proceedings, Fourth World Conference on Earthquake Engineering, Santiago, Chile, 1969.4
Vols. (34) Proceedings, Third World Conference on Earthquake Engineering, New Zealand, 1965. 3
Vols. (35) Proceedings, Second World Conference on Earthquake Engineering, Japan, 1960.3 Vols.
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(36) Clough, R. W. Earthquake Analysis by Response Spectrum Superposition. Bull. Seism. Soc. Am., Vol. 52, No.3, July 1962, pp. 647-660.
(37) Keintzel, E. On the Seismic Analysis of Unsymmetrical Storied Buildings. Paper No. 10, Session I B, Ref. (30).
(38) Tso, W. K. and Asmis, K. G. Torsional Vibration of Symmetric Structures. Pages 178-186, Ref. (29).
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COMMENTARYL
FOUNDATIONS
TABLE OF CONTENTS Page
INTRODUCTION. .. . . .. . •. .• . . . •. .••..•• . . .•. . . •.. .•..•.• 127 TEMPORARY EXCA V ATIONS .....•........•...•..•••..••. 127
Unsupported Excavations. • . . • . . . • . . . . . . . • . . . . . . . • • . . • • . . . 127 Supported Excavations . . . . • . . . . . . . . . . . . . . . . . . . . . . . • • . . . . • 127 Movements Associated With Excavations . . . . . . . . • . . . . • • . • • • . • 131 Underpinning . . • . . • . . • . . . • . . . . . . . . . • . . . . . • • . . • • • . . . . • • . 133 Factors to be Considered with Soil and Rock Tie-Back
AncOOrs . . . . . . . . . . . . . • . . . • • . . . • • . . . • . . . • . . • • . • . • . • . 134 Design and Installation of Members •..••..•..•....•...•...•• 134 Control of Groundwater in Excavations. . . . . . . . . . . . • • • • . . • . . • • 135
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SHALLOW FOUNDA nONS ............................... 135 General ............................................•. 135 Bearing Capacity and Settlement ........................... 135 Design Bearing Pressure .......................•......... 136 Estimates of Allowable Bearing Pressure .................•... 136
DEEP FOUNDA nONS •..•................................ 141 Introduction • . . . . . . . . . . . . . . . • . . . . . • . . . . . . . . . . . . . . . . . . . . 141 Geotechnical Requirements of Deep Foundations .••.......•.... 142
Deep Foundations End-Bearing on Rock or Highly Competent Deposits ........•...........•......... 142
Piles in Granular Soils . . . . . . . . . • . . . . . . • . . . . . . . . . . . . . • . 143 Piles in Cohesive Soils. . • . . . . . . . . . . . . . . . . . . . . . . . . . . . •. 143 Spacing and Arrangement of Piles and Drilled Shafts . . . . . • . . . 143 Settlement and Group Effects in Piles ...................• 144 Load Tests on Deep Foundations ............ . . . . . . . . . . . . 145
Installation and Structural Requirements of Deep Foundations . . . . . 146 Driven Piles . • • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 Cast-in-Place Deep Foundations ........................ 148 Location and Alignment . . . . . . . . . . . . . . . . . . . . . • . . • . . . . . . 151
PERMAFROST ..............................•..........• 151 REFERENCES ........................................... 153
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COMMENTARY L
Foundations
INTRODUCfION
127
1. The purpose of this Commentary is to suggest reasonable guidelines, compatible with sound engineering practice, to provide compliance with the requirements of Section 4.2 (Foundations) of the National Building Code 1977. Much of the Commentary material herein is simple, being intended as a first approximation dealing with routine problems of foundation design and construction. Neither this material nor the papers or texts to which it refers should be considered as a substitute for the experience and judgment of a person competent in dealing with the complexities of foundation practice.
2. The Commentary falls into 3 principal parts: Temporary Excavations, Shallow Foundations and Deep Foundations. The text within these parts specifically refers to relevant paragraphs of the National Building Code, Section 4.2.
3. The Commentary does not deal specifically with the identification and classification of soils and rocks, with subsurface investigations, with swelling and shrinking clay problems nor with frost action as related to foundations, as it is anticipated that all these topics will be included in a manual on foundation engineering being prepared by the Canadian Geotechnical Society. The Society plans to publish the final version of this Manual in 1977.
TEMPORARY EXCAVATIONS
UNSUPPORTED EXCAVATIONS 4. The safety and stability of unsupported excavations depends on the soil and groundwater
conditions and on the depth and slope of the cut. In granular materials slope failures will generally be fairly. shallow, in clays deep rotational failures involving not only the sides but also the base of the excavation are possible. It is also necessary to take into account the length of time the cut will remain unsupported.
5. Guidelines for treatment of open cuts in broaq soil categories are included in Table L-l. The selection of stable slope angles for Categories C and D requires that stability analyses be carried out. The selection of appropriate design shear strength parameters for such analyses requires a careful assessment of imposed shear stress levels, time effects, soil directional properties and uniformity and should be carried out by a person qualified in this work. The influence of groundwater conditions within the slope, or piezometric levels at or below the toe of the proposed slope, should also be investigated, as the resisting shear strength along a potential failure surface may be greatly reduced by hydrostatic pressures.
SUPPORTED EXCAVATIONS 6. Temporary shoring support of vertical excavation faces requires an assessment of a num
ber of factors including the length of time the excavation is to be supported in terms of influence on earth pressures, pressures from frost action or corrosion from aggressive soil or groundwater. The shoring wall elements may be either open, permitting full drainage, or closed, providing an impermeable barrier, depending mainly on the soil permeability and ground water conditions. Closed systems are designed for soil and full groundwater pressures, whereas hydrostatic pressures are not included in open systems where seepage through the wall can take place.
Design Eartb Pressures 7. For flexible and semi-flexible shoring walls commonly used for support of vertical faces of
excavations, and which may have a variety of support conditions, no satisfactory general theoretical solutions for prediction of earth pressures are available. The design earth pressure must take into account the method and sequence of construction and the tolerable deformation limits of the sides or faces of the excavation.
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Table L-l
OPEN CUT EXCAVATION GUIDELlNES*t
cate-I Soil G d I Typical Time to Refer-roun - . Remarks Type t FaIlure Failure gory wa er . Mode ences
I I
A Free- Below Shallow Gener- Rarely a problem if groundwater un- Terzaghi draining, cut or surface ally rapid der control and slope angle does not & Peck granular, con- or slope exceed friction angle of soil. Unsatu- 1967(1) non-plas- trolled wedge rated temporary steeper cuts rely on tic silts by ad- apparent cohesion and may slough
vance de- with time; cuts steeper than 45 deg. watering are not recommended; vertical cuts
more than 4 ft in depth should never be used
B As for Cut Slough- Rapid Uniform fine soils may flow for con- As for Category below ing to siderable distances if pumping from Category A ground- flow within excavation is attempted. A
water Slopes are controlled by hydraulic effects and may range from '/) or less to full value of friction angle
C Non-sen- Satu- Rota- Rapid or Analytical methods generally reliable As for sitive rated tionaI. delayed for prediction of stability in soft to Category clays. (see also Plane of depend- firm clays A Plastic Note t) weakness ingon and co- or com- per cent hesive posite of opera-silts surface tional
soil shear strength mobi-lized
D Sensitive Satu- Rota- Asper Extreme caution required; once ini-clays rated tional. (C); little tial failure is provoked, retrogressive
(see also Retro- advance action may effect wide area; reliabil- -Note t) gressive warning ity of analytical prediction methods
slides generally poor and as per(C)
Column 1 2 3 4 5 6
Notes to Table L-l: • Mixed soils such as glacial tills should be classified into Category A, B or C, depending on grain size, plasticity
and permeability and treated accordingly. t The stability of an open cut slope which is only marginaIJy stable at the end of excavation may be adversely
affected by such factors as the nature and magnitude of crest loading, vibrations, rainfall, the length of time the cut remains open or disturbance of the soil in the vicinity of the toe of the slope.
t Excavations through alternate layers of cohesive and granular soils or excavations terminated within a cohesive soil underlain by granular strata require an investigation of groundwater conditions in each layer, and the factor of safety against excavation base heave or slope failure as a result of upward water pressure should be assessed.
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8. The yield of one part of a flexible wall throws pressure onto the more rigid parts. Hence, the pressures in the vicinity of supports are higher than in unsupported areas, and the loads on individual supports vary, depending largely on the stiffness characteristics of the supports themselves and the construction technique.
9. The pressure envelopes representing the pressures that would normally be anticipated can be represented in triangular, trapezoidal or rectangular form, and the applicable design earth pressure coefficients will range between the active KA * case and the earth pressure at rest Ko,.* depending on permissible wall and soil movements.
10. Non-cohesive (granular) soils. As a first approximation the guidelines in Table L-2 are suggested in essentially granular soils such as fills, sands, silts, sandy silts, gravelly sands, sands and gravels or alternate layered conditions composed of such strata.
Restraint
Cantilever
Braced
Tied-back
Column 1
Notes to Table L-2:
TableL-2
ENVELOPE OF EARTH PRESSURE FOR DESIGN OF TEMPORARY SUPPORTS FOR GRANULAR SOILS
Design(1) Total
Pressure
I.OPA
1.2 to 1.3 P A
1.I to 1.4 P A
2
Envelope oil2)
Pressure Distribution
Rectangular or
trapezoidal
Rectangular or
trapezoidal
3
Ability to Restrict(3) Adjacent Soil Movements
unless wall extremely in dense soil
Generally poor where control of groundwater inadequate or where workmanship poor; can be moderate to good where these factors are properly controlled and bracing properly designed and tightly wedged or preloaded
Generally good where high total pressures are used; movements usually less than for braced walls and dependent on degree of prestressing, workmanship and wall stiffness
4
(I) P A theoretical total active pressure = IhyH2 X KA where y = unit weight of soil (submerged if below groundwater), pcf, and H = depth of cut. The figure of 0.2 is suggested as a lower bound for KA even in dense soils. Surcharge pressures and hydrostatic water pressures should be added where appropriate.
(2) After increasing P A by the appropriate multiplier, distribute total pressure over depth of cut as indicated in this column; triangular limits of trapezoid generally taken as O.2H to O.25H at top and bottom.
(3) Where greater control of adjacent ground movements is required, earth pressures should be computed using the at rest Ko earth pressure coefficient with prestress in struts or tie-backs to the full design load. Additional measures would include choice of a stiff wall and close vertical spacing of struts or tie-backs .
.. KA = effective friction angle of soil and the ground surface is horizontal.
... Ko l-sinq.'.
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II. Cohesive soils. For cohesive soils it is necessary to distinguish between soft to firm clays and stiff to very stiff clays. It is also necessary to take into account the effects of clay sensitivity and the factor of safety against base heave.
12. For stiff clay soils (Cu > 1,000 psf)**· including silty clays, sandy clays and clayey silts, the guidelines in Table L-3 are suggested. Similarly, for soft to firm clays (Cu >250 psf <1,000 psf), reference should be made to Table LA.
Table L-3
ENVELOPE OF EARTH PRESSURE FOR DESIGN OF TEMPORARY SUPPORTS FOR STIFF COHESIVE SOILS
Design Restraint Total
Pressure
Cantilever 1.0PA
but not less than
Braced or tied-back
Column 1
Notes to Table L-3:
O.l5yH2(1)
0.15yH2 to
0.4yH2(2)
2
Envelope of Ability to Restrict Pressure DistributionP)
Adjacent Soil Movements
Triangular May be poor depending on length of cantilever, wall stiffness, embedment conditions and clay sensitivity<4),(S)
Rectangular Depends on soil strength, sensitivity, or effective preloading or prestressing and
trapezoidal wall stiffness
3 4
(I) P A may be computed using short term strength, Le. P A = yH-2Cu if excavation open for limited period. Regardless of whether pressures are negative or zero, minimum positive pressures indicated must be used.
(2) Use higher range where clay is of high sensitivity. If the construction sequence or workmanship allow significant inward movement during any stage of excavation, there will be a tendency for build-up of pressures to essentially fluid soil values in very sensitive clays. With good workmanship, clay pressures are similar to those given in Table L-2. Strength tests taken on intact samples of stiff clays which are jointed or fissured may overestimate the strength characteristics and thus lead to an under-estimation of earth pressures.
(3) Surcharge pressures should be added where appropriate; hydrostatic pressures need not be included; total unit weight of soil, y, is to be used in calculations.
(4) Computed passive pressures below the base of the excavation should be reduced by 50 per cent to account for unavoidable disturbance due to strain effects and stress release.
(5) The factor of safety against base heave in stiff overconsolidated clays, as a result of high locked-in lateral stresses, should also be investigated .
..... Cu = 1h unconfined compressive strength.
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Table L-4
El\VELOPE OF EARTH PRESSURE FOR DESIGN OF TEMPORARY SUPPORTS FOR SOFT TO FIRM CLAYS
Design Envelope of Ability to Restrict Restraint Total Pressure
Pressure Distribution(4) Adjacent Soil MovementsI5 ).(6)
Cantilever 1.0 p .. Triangular Very poor; this type of support generally but not less than
0.15yH2(1) to be avoided in soft, sensitive clays
Braced or 0.4yH2 Rectangular Depends on clay shear strength and tied-back to stabilityi3i
0.8yH2(2)
Column 1 2 3 4
Notes to Table 1.,..4: (I) P A may be computed using short term strength, i.e. P A = I'H-2Cu if the excavation is open for a limited peri
od. Regardless of whether pressures are negative or zero, minimum positive pressures indicated must be used. (2) Higher range should be used where clay is of soft consistency, and lower range where clay is of firm consist
ency. This value may be conservative for non-homogeneous, non-sensitive sandy-silty cohesive soils
of firm consistency. If stability number N +
------''- approaches 5 to 6. use higher range. At Cu
this depth base heave may also take place and therefore suitable precautions should be taken. (3) Design of a suitable shoring and bracing system in soft to firm clay conditions is not a routine matter, and the
advice of a specialist should be obtained to establish design pressures, to check overall stability and base heave and to predict adjacent soil movements.
(4) Essentially t1uid soil pressures in very sensitive clays may be realized as a result of unavoidable wall movements prior to insertion of restraint supports.
(5) Computed passive pressures below the base of the excavation should be reduced by at least 50 per cent to account for unavoidable disturbance due to strain effects.
(6) Additional precautions in soft to firm sensitive clays would include (a) insertion of the top strut or anchor prior to excavation beyond 5 to 10 ft depth, and (b) where the excavation area is of limited size, placing of a 6- to 12-in.-thick concrete mat at the base of the excavation, where practical, immediately on completion of excavation.
MOVEMENTS ASSOCIATED WITH EXCAVATIONS 13. Movements associated with excavations are primarily related to construction technique
and commonly consist of lateral yield of the soil and support system towards the excavation, with corresponding vertical movement adjacent to the excavation walls. Both lateral and vertical movements due to yield are generally of the same order of magnitude; however, if very flexible vertical wall elements are used, lateral movements can be grossly increased. Where construction technique is poor, erratic movements can also occur due to loss of ground or erosion behind the wall.
14. Movements due to yield of cantilever walls are related to the wall and soil stiffness. For most flexible or relatively flexible wall types the lateral deformations will exceed values required for mobilization of active soil pressures. For most soils and particularly cohesive soils, therefore, there is a danger that a further build-up of lateral pressures beyond active values will take place as a result of loosening due to strain effects. An exception would be where design soil pressures of an at rest Ko magnitude or greater are used in design, and an appopriately stiff wall, such as large diameter cylinder piling, is provided, embedded in competent soil.
IS. Movements due to yield in strutted excavations are, to a large extent, unavoidable, since they are controlled not by design assumptions but by construction details and procedures. Such movements develop in each excavation phase before the next level of struts is installed.
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16. The yield movements of anchored walls are controlled more by design methods than with strutted walls. The number of anchors and the vertical spacing of such anchors, playa significant part in controlling the degree of lateral deformation. In normal practice, movements due to yield of anchored diaphragms, sheeted or soldier pile walls are usually less than for strutted walls for the same depth of excavation.
17. For general guidance Table L-5 summarizes the approximate range of vertical and lateral movements to be expected. It should be recognized that, in certain cases, more favourable results may be achieved with proper design, good construction workmanship and careful field supervision, including monitoring of behaviour.
TableL-S
VERTICAL AND LATERAL MOVEMENTS ASSOCIATED WITH EXCAVATION
Granular Stiff Clay,
Soft to Restraint Wall Details Soils, Firm Clay, Remarks
% depth % depth % depth
Cantilever Conventional Moderate Moderate May Movements related to stiffness to large collapse wall, soil stiffness and em-
bedment condition
Soldier piles or 0.2 to 0.5 0.1 to 0.6 1 to 2 Struts installed as soon as sheet piles support level reached and
Braced prestressed to 100 per cen t design load
Rakers or struts 0.5 to 1.0 0.3 to 0.8 >2 Poor workmanship could loosely wedged result in greater values
Soldier piles or 0.2 to 0.4 0.1 to 0.5 1 to 2 Prestressed to pressure sheet piles between active and at-rest
Concrete dia- <0.2 <0.1 to 0.5 <I t02 Prestressed as above, phragm walls since wall stiffness and
Tied-back design earth pressures are normally greater, move-ments generally are less than for soldier piles or sheet piling; little data available
Column 1 2 3 4 5 6
Notes to Table L-S: (I) Indicated movements apply directly behind wall; for granular soils and stiff clays, movements would be
expected to feather out in approximately linear fashion over horizontal distance of 1.0 to 1.5 depth of excavation (H). For soft to firm clays, and assuming average workmanship, this distance increases to 2.0 to 2.5H, and with poor workmanship to greater than 3H.
(2) If groundwater is not properly controlled in granular strata, movements may be much larger than indicated, and loss of ground could also result.
(3) If the factor of safety against base heave for soft to firm clays is low, large deformations will result. (4) Upper range of movements usually applicable for highly sensitive clays in either stiff or soft to firm category. (5) Experience indicates that movements are reduced by using close vertical spacing between strut or tie-back
levels and by careful at~'!ntion to prestress details.
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UNDERPINNING 18. Structures adjacent to excavations will frequently need to be supported. The need for
underpinning will depend on the location of the structure, the details of its foundation support, its sensitivity to settlement and lateral deformations, cost of underpinning or provision of extra excavation face support and other precautions, as well as the cost of repairs or consequences if the structure is not underpinned.
19. The geometry of zones within which support for adjacent structures is usually considered necessary, as a result of adjacent excavation through soil, is shown in Figure L-l. Where adjacent structures are founded on bedrock and excavation is through rock, less underpinning and more face support should be considered.
20. The general order of magnitude of movements as a result of excavation with various support methods in different soil conditions has been summarized in Table L-5. This table may also be used to assist in judging the necessity for provision of underpinning.
ZO NE A:
TIGHTLY BRACED/TIED EXCAVATION WALL
BASE OF EXCAVATION
FOUNDATIONS WITHIN THIS ZONE OFTEN REQUIRE UNDERPINNING. HORIZONTAL AND VERTICAL PRESSURES ON EXCAVATION WALL OF NON-UNDERPINNED FOUNDATIONS MUST BE CONSIDERED
ZONE B:
FOUNDATIONS WITHIN THIS ZONE OFTEN DO NOT REQUIRE UNDERPINNING. HORIZONTAL AND VERTICAL PRESSURES ON EXCAVATION WALL OF NON-UNDERPINNED FOUNDATIONS MUST BE CONSIDERED
ZO N E C:
FOUNDATIONS WITHIN THIS ZONE USUALLY DO NOT REQUIRE UNDERPINNING
Figure 1..-1 Requirements for underpinning
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FACTORS TO BE CONSIDERED WITH SOIL AND ROCK TIE-BACK ANCHORS 21. Anchors are usually inclined downwards, transmitting the vertical component of the
anchor force into the anchored vertical member. This force should be considered in design, together with the weight of the vertical member itself.
22. Forces which resist downward movement due to the inclined anchor load are skin friction and the reaction at the base of the vertical member. When soldier piles are used, vertical forces are concentrated in the piles. Only minimal friction, if any, can be mobilized. Such vertical forces must, therefore, be supported at the base of the pile. The vertical and horizontal base capacity of the pile must be checked; otherwise, unacceptable vertical and horizontal deformation may take place.
23. Settlement of vertical members produces some reduction in anchor loads, with a consequent tendency for outward displacement of the supported face. It is, therefore, essential to monitor vertical and horizontal movements at the top and bottom of the excavation at regular intervals throughout the course of the work.
24. The performance of soil and rock anchors is dependent, not only on minor variations in soil and groundwater conditions, but also on construction techniques and details. Consequently, the prediction of anchor capacity by theoretical calculations is not reliable. Anchorage capacities must be established by test taking into account the load deformation and "creep" properties of the soil, and each anchor must be proofloaded during construction.
25. The overall stability of a soil anchorage system should be checked by analyzing the stability of the block of soil lying between the wall and the anchorages. In general, the anchors should be extended beyond a I: I line drawn from the base of the excavation, and no allowance for any load carrying support should be assumed within this line.
DESIGN AND INSTALLATION OF MEMBERS 26. Members such as walers, struts, soldier piles and sheeting should be sized in accordance
with the structural requirements of Part 4 of the National Building Code 1977.
27. The depth of penetration of the vertical wall member should be 1.5 times the depth required for moment equilibrium about the lowest strut.
28. For driven soldier piles, the maximum horizontal force on the flange of the soldier pile below the bottom of the excavation may be taken as 1.5 times the values computed for the width of the flange, providing that the pile spacing is not less than 5 times the flange width.
29. For piles placed in a concrete base, the diameter of the concrete filled hole may be used in place of the flange width as discussed in the preceding paragraph.
30. The selection of material and sizes of timber planks or lagging should conform with good practice, and the lagging should be of good quality hardwood. Lagging is installed by hand after a depth of several feet is excavated. The maximum depth made each time before a section of lagging is placed depends on the soil characteristics. Soft clay and cohesionless soils must be planked in short depths to reduce the amount of soil moving into the excavation. The depth of excavation below any lagging boards that have not yet been placed should not exceed 4 ft. Lagging must be tightly backfilled or wedged against the soiL
31. To minimize the possibility of erratic loss of ground in local areas when excavating sands and silts below original groundwater, it is essential that straw packing, burlap or in extreme conditions, grouting be used behind the lagging as it is installed.
32. The design of all members including struts, walers, sheetpiling, walls and soldier piles should be checked for several stages of partial excavation when the wall is assumed to be continuous over the strut immediately above the excavation level and supported some distance below the excavation level by the available passive resistance. This condition could produce the maximum loading in struts and walers.
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33. Where excessive stresses or loads would result from interim construction conditions using regular construction procedures, trenching techniques can be employed to advantage.
34. The design of members should also be checked for the condition when portions of the building within the excavated area are completed and lower struts are removed. Consideration must be given to the possible increase in loading on the upper struts remaining in place; also the span between that portion of the building that has been completed and the lowest strut then in place must be considered in relation to flexural stresses.
CONTROL OF GROUNDWATER IN EXCAVATIONS 35. Good practice requires that the following conditions must be fulfilled when dewatering
excavations: (a) A dewatering method must be chosen that will not only assure the stability of the sides and
bottom of the excavation but also prevent damage to adjacent structures such as by settlement.
(b) The lowered water table must be kept constantly under full control, thus avoiding fluctuations liable to cause instability of the excavation.
(c) Effective filters must be provided where necessary to prevent loss of ground. (d) Adequate pumping and standby pumping capacity must be provided. (e) Pumped water must be discharged in a manner that will not interfere with the excavation or
cause pollution. (f) For most soils the groundwater table during construction must be maintained at least 2 to 5
ft below the bottom of the excavation so as to ensure dry working conditions. It should be maintained at a somewhat lower level for silts than for sands in order to prevent traffic from pumping water to the surface and making the bottom of the excavation wet or "spongy."
(g) Adequate monitoring of groundwater levels by piezometers or by observation standpipes should be maintained.
(h) Where impermeable strata are underlain by pervious water bearing layers, depending on the depth of excavation and the hydrostatic head in the pervious strata, it may be necessary to lower the head in the pervious stratum in advance of excavation, to prevent a "blow" or excessive disturbance of the base as a result of upward hydrostatic pressure.
(i) Pumping from sumps or ditches inside the excavation is normally carried out where dense low permeability soils, such as certain glacial tills or cohesive soils, are present or where the excavation is in bedrock; this method is not recommended for excavation in semi-pervious or pervious soils, such as silts or fine sands, since it often leads to extensive sloughing of the excavation sides and disturbance of the bottom.
SHALLOW FOUNDATIONS
GENERAL 36. A shallow foundation means a foundation unit which derives its support from the soil or
rock close to the lowest part of the building which it supports. The depth of the bearing area below the adjacent ground is usually governed by the requirement to provide adequate protection against climatic or frost effects; vertical loads on the sides of the foundation due to adhesion or friction are normally neglected.
BEARING CAPACITY AND SETILEMENT 37. The design of a foundation unit normally requires that both bearing capacity and settle
ment be checked. While either bearing capacity or settlement criteria may provide the limiting condition, it is normal for settlement to govern. Distress from differential settlement as evidenced by such occurrences as cracking and distortion of doors and window frames is common experience. The drastic effects of a bearing capacity failure are rare except perhaps during construction where shallow temporary footings are frequently used with falsework.
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Bearing Capacity 38. The bearing capacity of both cohesive and non-cohesive soils can be determined with rea
sonable reliability by assuming that the strength parameters for the bearing soil are accurately known within the depth of influence of the footing.
Settlement 39. Cohesive soil. The settlement of a structure on cohesive soil can be calculated with less
accuracy than the bearing capacity. Such a calculation is affected by a number of complicating factors usually requiring judgment to assess. The most important of these is an estimate of the preconsolidation pressure, that is, the maximum past consolidation pressure on the in situ soil. Because of the various uncertainties, errors of a factor of 2 should be expected in the calculation of settlement.
40. Non-cohesive soil. The settlement of a structure on non-cohesive soil can normally only be estimated by empirical methods. Such an estimate usually is taken to mean the settlement directly related to the load, but this settlement generally occurs quite rapidly; frequently, such settlement occurs during the construction period. Post construction settlement in such a case will be negligible and may be considerably less than the predicted settlement.
41. Post construction settlement can occur for a considerable period after construction, even after a period of successful performance of the structure, as the result of vibrations or changes in the groundwater conditions, whether natural or man-made, due to earthquake or blasting, flooding or groundwater lowering. Settlement of this nature is not usually included in an empirical estimation, but should be assessed.
DESIGN BEARING PRESSURE 42. The design bearing pressure is limited by 2 considerations:
(a) the foundation must be safe against shear failures of the supporting soil, and (b) settlement must not be excessive.
43. The design bearing pressure is the lesser of the values dictated by these 2 requirements.
44. A detailed flow diagram for the design of shallow foundations is shown in Figure L-2. In many cases this can be simplified; however, it illustrates the factors affecting the choice of design bearing pressure for most structures.
ESTIMATES OF ALLOW ABLE BEARING PRESSURE 45. Universally applicable values of allowable bearing pressure cannot be given. Many fac
tors affect bearing capacity, and the allowable load will frequently be controlled by settlement criteria. Nevertheless, it is often useful to estimate the allowable bearing pressure for preliminary design on the basis of the material description; such values should be recalculated for final design in keeping with good geotechnical practice and normal analytical procedures.(i)
46. Estimated values of presumed allowable bearing pressure and notes are given in Tables L-6, L-7, L-8 and L-9. Such pressures should be considered as the maximum permissible under the total dead and live loading and treated as first approximations only.
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r- --I I
FLOW DIAGRAM FOR FOUNDATION DESIGN
SHAllOW FOUNOAT IONS
------r---l
• THESE FREQUENTLy I..-Or-..7ROl FOUNDATION
Figure L-2 Flow diagram for design of shallow foundations
I I I I I
t I I I I , I ,
137
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138 Table L-6
ESTIMATES OF ALLOW ABLE BEARING PRESSURE ON ROCK
Allowable
Rock Type Rock Condi tions * Bearing Remarks Pressure,t tons/sq ft
(a) Massive igneous and Discontinuities Goints. 100 metamorphic rocks in minor cracks) at wide sound condition: gran- spacing (>3 ft) ite, diorite, basalt and
Discontinuities at moder- 20 to 50 gneiss a(espac~
(b) Foliated metamorphic (i) Discon tin 30 Foliations approximately rocks in sound condi- wide spad horizontal tion: slate and schist
(ii) Discontinuities at <10 Foliations approximately moderate spacing (I horizontal to 3 ft)
(iii) Foliations tilted to the Potential sliding along horizontal foliations. Potential lack
of support adjacent to cuts on excavations. See Hoek, Bray (1972)(2)
(c) Sedimentary rocks in Discontinuities at wide 1 n tn 4n Strata approximately sound condition: ce- spacing (>3 ft) horizontal mented shale or silt-stone, sandstone, lime- Potential solution cavities
stone. dolomite and in limestone, dolomite.
heavily cemented con- Variability in cementation
glomerate of conglomerates. See (b)(iii)
(d) Compaction shale and Discontinuities at wide ,~ . Strata approximately other argillaceous spacing (>3 ft) horizontal rocks in sound condition Argillaceous shales are
subject to some swell on release of stress. All shales tend to soften on expo-sure to water and certain shales swell markedly
(e) All closely jointed Discontinuities at spacing - Can only be assessed by rocks including thinly less than I ft apart. detailed investigations bedded limestones and Random joint or crack and examination in situ shales patterns including loading tests if
necessary
(t) Heavily shattered or - See (e) weathered rocks
Column I 2 3 4
Notes to Table L-6: • The spacing of discontinuities is critical to the bearing pressure allowable on a rock mass. Discontinuities.
such as joints or cracks, are presumed to be widely spaced if greater than 3 ft apart and moderately spaced when greater than I ft. It is further presumed that the thickness or width of such discontinuities is less than 14 in. (or less than I in. if completely filled with soil or rock debris). Where such conditions do not exist, types (e) or (I) must be assumed.
t The values of bearing pressures given above. except for (I), are based on the assumptions that the foundations are close to the rock surface but carried down to unweathered rock with adequate frost protection and that the foundation is greater than I ft in width.
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Table L-7
ESTIMATES OF ALLOWABLE BEARING PRESSURE ON NON-COHESIVE GRANULAR SOILS
Allowable Soil Type and Bearing
Potential Problemst Remarks Conditions· Pressure,t
tons/sq ft
(a) Dense well-graded 4 to 6 The density of sands For general reference see: sands, dense sand and containing large sizes or T erzaghi, Peck (1967)( I) gravel gravels is frequently over- Peck, Hanson and
estimated when inferred Thomburn (1974)(4) (b) Compact well-graded 2 to 4 from standard or cone
sands, compact sand penetration tests only, and gravel Fletcher (1965)(3)
(c) Loose well-graded 1 to 2 Potential settlement when sand, loose sand and subject to shock or vibra-gravel tions. See (f)
(d) Dense uniform sands 3 to 4 Density usually better See Gadsby (1971)(5)
(e) Compact uniform I to 3 defined by standard or Tavenas (1973)(6) cone penetration tests, as Tavenas, Ladd and
sands compared to (a) to (c). LaRochelle (1973)(7) However, considerable caution is required in interpretation of test data
(f) Loose uniform sands <1 Even where very low See Terzaghi (1955)(8) bearing pressures are used, settlement can occur due to submerg-ence, vibrations from blasting, machine opera-tion or earthquake
(g) Very loose uniform - Subject to possible sands, silts liquefaction. Should
never be used for sup-port of foundations
Column I 2 3 4
Notes to Table L-7: • The density condition of the soil is assumed to have been established in conformance with good geotechnical
practice. t The values of bearing pressure are based on the assumptions that the width of foundation (B) is not less than 3
ft and that the groundwater level will never be higher than a depth, B, below the base of the foundation. When the groundwater level is, or could be, higher than a depth, B, below the base of the foundation, the values listed should be divided by a factor = 2.
t Long term settlement of foundations on compact to dense non-cohesive deposits is normally modest provided such deposits are not underlain by compressible cohesive deposits at depth.
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Table LoS
ESTIMATES OF ALLOWABLE BEARING PRESSURE ON COHESIVE SOILS (for sensitive clays, see Table L-9)
Allowable Soil Type and Bearing Applicability for Support Settlementt Condi tions· Pressure,t of Shallow Foundationst
tons/sq ft
(a) Very stiff to hard clay, 3 to 6 Good Settlement is normally es-heterogeneous clayey timated on the basis of in-deposits or mixed vestigations, sampling deposits such as till and laboratory test data
(b) Stiff clays 1 to 2 Fair to good For general reference see:
Terzaghi, Peck (1967)(1)
(c) Firm clays 0.5 to 1.0 Poor except for minor Bjerrum (1967)(9)
structures little affected Crawford (1964)(10)
by distortion Schmertmann (1963)(11)
(d) Soft clays o to 0.5 Very poor not recom-mended
(e) Very soft clays No
Column I 2 3 4
Notes to Table L-8: • The strength of cohesive soils is assumed to have been established in conformance with good geotechnical
practice. t Cohesive soils are susceptible to long term consolidation settlement. For Types (b) to (d) inclusive, considera
tions of such settlement often govern the applied pressure rather than bearing pressures based on soil strength. In the case of Type (a) soils, heave can take place with excavation and consequent relief of stress.
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Table L-9
PROBLEM SOILS, ROCKS OR CONDITIONS (No bearing pressures can be presumed without detailed investigations)
Type or Condition k Examples References
Organic soils skeg terrain: estuarine organic silts I MacFarlane (1969)(12' and clays
Normally consolidated Lacustrine deposits and varved glacio- Milligan, Soderman, clays lacustrine deposits in Manitoba, Rutka (1962)(13'
Northern Ontario, Northern Quebec
Sensitive clays Marine clay deposits in St. Lawrence Crawford (1961, River Valley, Eastern Ontario, Quebec 1968)(14)(15)
LaRochelle, Chagnon, LeFebvre (1970)(16)
Swelling/shrinking clays Clay-rich deposits in Alberta, Hamilton (I965){I7) Saskatchewan, Manitoba
Metastable soils British Columbia loess Hardy (I950){I8)
Expansive shales Western Canada - Bearpaw and Quigley, Vogan (1970)(19) Cretaceous deposits Hardy (l957){20)
Eastern Canada weathering of sulphide minerals accelerated by oxidizing bacteria
Permafrost Northern Canada, Arctic Brown (I970){21) Sanger (1969){22)
Column I 2 3
DEEP FOUNDATIONS
INTRODUCTION 47. A deep foundation is a foundation unit that provides support for a building by transfer
ring loads either by end-bearing to a soil or rock at considerable depth below the building, or by adhesion or friction, or both, in the soil or rock in which it is placed. Piles are the most common type of deep foundation.
48. Piles can be premanufactured or cast-in-place; they can be driven, jacked, jetted, screwed, bored, drilled or excavated. They can be of wood, concrete or steel or a combination thereof. (Drilled shafts of diameter greater than about 30 in. are frequently referred to as caissons in Canada.)
49. In the design of deep foundations, it is essential to recognize that loads which may be applied to a deep foundation are dependent not only on the properties of the foundation as a structural unit (e.g. the shaft strength of a drilled shaft determined on the basis of CSA A23.3-1973, "Code for the Design of Concrete Structures for Buildings"), but also on the properties of the foundation soil (or rock) and of the soil/foundation system (e.g. pile capacity as a function of soil strength; settlement of a drilled shaft as a function of contact pressure, etc.). Thus, the designer must distinguish the structural from the geotechnical capacity of a deep foundation unit or system, analyze each very carefully and define application of such loads which may be carried
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safely, both from a structural and a geotechnical point of view. In many applications, geotechnical considerations may limit the permissible loads to levels well below those which might be arrived at on the basis of only structural considerations.
50. Geotechnical criteria for assessing permissible loads on a deep foundation are determined on the basis of site investigations and geotechnical analyses. However, in most cases, the quality of a deep foundation is highly dependent on construction technique, on equipment and on workmanship. Such parameters cannot be quantified nor taken into account in normal design procedures. Consequently, as implied in NBC Subsection 4.2.7., it is desirable to design deep foundations on the basis of in situ load tests on actual foundation units.
51. Criteria relating to structurally permissible loads are defined in the design sections of the National Building Code applicable to the structural materials used in the deep foundation unit. However, it should be noted that the standards referenced in the NBC were written mainly for the purpose of designing elements and assemblies in the superstructure. A structural consultant involved in the design of deep foundations must recognize that installation and quality control conditions below grade differ from those above grade (as in the superstructure); the permissible loads determined by usual structural design methods may have to be reduced, sometimes to a marked degree, to account for these differences. It is obvious that permissible loads can only be selected on the basis of close co-operation between the geotechnical and structural consultants for the project.
52. In this section of the Commentary, suggested values of permissible loads are given for several kinds of foundation units. These values are listed solely for the purpose of providing the reader with a first approximation of the probable loads which, under routine conditions, might be applied safely to a given kind of unit. In each case, both geotechnical and structural evaluation and analysis is mandatory. However, as discussed above, since construction procedures often have a dominant influence on the load/deformation behaviour of the deep foundation, the choice of a permissible load is always subject to judgment and experience and to the provision that appropriate inspection is carried out as specified in Article 4.2.2.3. of the NBC. Inspection must be considered an integral part of the design process.
GEOTECHNICAL REQUIREMENTS OF DEEP FOUNDATIONS Deep Foundations End-Bearing on Rock or Highly Competent Deposits
53. Deep foundations which are placed on rock or on a dense basal deposit, such as till or hard clay, are bored, drilled or excavated and cast-in-place, and are commonly referred to as drilled shafts. In this case, the area of end-bearing contact is known and, provided this area and the character of the foundation stratum can be defined by inspection, the geotechnical capacity of the deep foundation can be evaluated on the basis of the allowable bearing pressure of the foundation stratum. (Refer to Tables L-6, L-7 and L-8, on shallow foundations.)
54. Rock sockets. Frequently, cast-in-place foundations are socketed into rock, either to obtain higher end bearing capacity at depth or to transfer load to the rock by adhesion or bond along the walls of the socket. Adhesion is highly dependent on the rock type and on the socket wall condition after drilling. Design values used for adhesion in sound rock lying below weathered or shattered rock range from 100 psi to 300 psi; however, much lower values have been observed in practice, where the construction methods used have produced a poor contact area. Careful inspection of all rock sockets prior to concreting is essentiaL Socketing may also be employed to provide base fixity and resistance to horizontal movement.(23)·(24)
55. Deep foundations may also be driven to rock or into dense basal deposits. In this case, which includes H-piles, pipe piles driven closed-end or precast concrete piles, the exact area of contact with the foundation stratum, the depth of penetration into it or the quality of the foundation stratum are largely unknown. Consequently, the determination of the load capacity of such driven deep foundations should be made on the basis of observations during driving, load tests and local experience. (Refer to Table L-IO.)
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Piles in Granular Soils (Refer to Table L-IO) 56. Piles which are driven into granular soils derive their load carrying capacity from both
point resistance and shaft friction. The relative contributions of point resistance and shaft friction to the total capacity of the pile depend essentially on the density of the soil and on the characteristics of the pile.
57. It is commonly assumed that pile driving in granular soils increases the density of the deposit. Because of this, it is generally economical to drive piles in granular soils to the maximum depth possible, without causing pile damage, in order to obtain the maximum working load on the pile. However, in some granular soils, such as fine sands or cohesion less silts, the pile capacity may decrease after driving. This effect is known as "relaxation." In contrast, in some coarse sands or other coarse grained deposits, the load capacity of piles may increase after driving. This effect is known as "freeze." Neither of these effects can be assessed quantitatively except on the basis of redriving and load testing.
58. Compacted concrete piles. Compacted or rammed concrete piles in granular soils derive their load capacity mainly from the densification of the soil around the base. The capacity of such piles is, therefore, entirely dependent on the construction technique and can only be assessed on the basis of load tests and detailed local experience.
Piles in Cohesive Soils (Refer to Table L-IO) 59. The load capacity of piles driven into cohesive materials is governed by the adhesion
between the pile and the soil and, to a much lesser extent than in granular soils, by the point resistance. This is particularly true for soft to firm clays.
60. The adhesion is not always equal to the undrained shear strength of the soil since, in some circumstances, the effect of pile driving markedly changes the character of the soil. In soft sensitive clays, complete remoulding of the soil may occur on driving. This effect diminishes with time following driving as the soil adjacent to the pile consolidates. In some cases, it has been observed that complete in strength to the original undisturbed value has not been attained even after a considerable period of time has elapsed.(32)
61. Because of the slow rate of regain of strength in certain cohesive soils, it may be necessary to delay load until several weeks have elapsed after driving.
62. In stiff to very stiff cohesive soils, there is considerable evidence to indicate that, in driving, a gap is formed between the pile and soil; this gap is not always fully closed with time, thus minimizing the adhesion to the pile relative to the high shear strength of the soil. For this reason, an approximate limit of 1,200 psf has been suggested for the adhesion value, even for stiff clays (Table L-IO).
63. Drilled shafts in cohesive soils. Except for shafts drilled through stiff or very stiff cohesive deposits, the major portion of drilled shaft capacity is derived from the bearing capacity of a hard or dense stratum at the base. For a first approximation of bearing capacity, Tables L-6 and L-7 should be used. For a more detailed assessment of bored piles, see Burland et al (1966).(33)
Spacing and Arrangement of Piles and Drilled Shafts 64. The following should be considered during the spacing and arrangement of piles and
drilled shafts: (a) The overlap of stresses between units which influences total load capacity and settlement, (b) overstressing of weaker zones at depth, and (c) installation difficulties, particularly the effects on adjacent piles or drilled shafts.
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65. In most cases the spacing, D, between the centres of driven piles of average diameter. d, should not be less than 2.5 d.
Table L-IO
LOAD CAPACITIES OF DRIVEN PILES
Pile Type I Load Capacity Recommendations Notes
(a) End-bearing on High to very high, but Ultimate pile capacity rock, dense till dictated by driving usually high but or other similar conditions, conditions of load/deformation can only materials basal deposits, pile types be assessed by load test
and stiffness (ASTM DI143-74, Method A)
(b) Piles driven into See (a) See (a) Meyerhof (1956)(25) dense sand, Berezantseu et al sand and gravel (1961)(26)
(c) Piles driven into Medium to high, part First approximation to See references loose to compact point resistance, part skin load capacity, use skin above. sand, sand and friction friction (pst) = 1,000 ± Vesic (1970)(27) gravel 500. Define by load test De Beer (1963)(28)
(ASTM DI143-74, Method A)
(d) Piles driven into Medium, but "relaxation" See (c). Essential to define Yang (1970)(29) compact to effects must be checked by load test dense silts
(e) Piles driven into Low to medium, First approximation, use Tomlinson (1957)(30) cohesive soils susceptible to long term skin friction. Soft cohesive Eide et al (1961)(31)
settlement soil = 0 - 600 psf. Firm to stiff cohesive soil = 600-1,200 psf. Define by load test (ASTM DI143-74, Method B)
Column 1 2 3 4
Settlement and Group Effects in Piles 66. In practice, piles are frequently used in groups; however, most of the published literature
deals with the behaviour of single piles. It has been stated by Leonards (1970)<34) that, "there is no consistent relationship between the settlement of a single pile and the settlement of the pile group at the same load per pile. Therefore, selecting a design load on the basis of the load at a given gross or net deflection, or at a given fraction of the ultimate pile capacity, is equivalent to accepting an unknown factor of safety with respect to satisfactory performance of the foundation." This statement is certainly valid for all piled foundations where the piles derive their support from skin friction, or from combined skin friction and end-bearing; however, it may not be as critical where piles derive all of their support or the major portion of it from end-bearing on a relatively incompressible stratum. An example of such support is where piles are driven through weak deposits to end-bearing on rock. For this case, the engineer normally relies on some means of assessing the dynamic resistance during pile driving complemented by load tests to define the deformation characteristics of the piles under load.
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67. In contrast to true end-bearing pile foundations, where the load/deformation characteristics of individual piles are of significance, the use of friction pile foundations is generally governed by considerations of group action and, for cohesive soils, long term consolidation settlement. The actual capacity and load/deformation characteristics of individual piles are not significant in this case. The purpose of friction piles in the upper part of a deep deposit of cohesive soils or of granular soils (or silts) is to reduce the intensity of pressure acting at ground level and to shift the zone of maximum stress to the lower levels, where less settlement will result.
68. In the case of an individual pile or where the building is narrow in relation to the depth of piles, the zone of pressure increase is spread over a large area in comparison with the width of the foundations; in contrast, where the building is wide, friction piles spread the load out very little, and the effect of the pile foundation on the soil is practically the same as that of a raft foundation without piles. In this case, the total bearing value of the piles in the foundation bears no relation to the carrying value of an individual pile by itself; the settlement of the foundation is, therefore, governed by the character of the subsoil, not by the load capacity of the piled foundation.
Load Tests on Deep Foundations 69. Use of load tests. As previously indicated, load testing of piles, as specified in NBC Sen
tence 4.2.7.2.(2), is the most positive method of determining load capacity. Depending upon the type and size of the foundation, such load tests may be performed at different stages during design and construction.
70. Load tests during design. The best method of designing a pile foundation is to perform pile driving and loading tests. The number of tests, the type of pile tested, the methods of driving or of installation and of test loading should be selected by the engineer responsible for the design. The following points should be considered:
(a) The test program should be carried out by a person competent in this field of work. (b) Adequate soil information should be obtained at the test location. (c) The piles, the equipment used for driving or other method of installation and the procedure
should be those intended to be used in the construction of the foundation. (d) As a minimum, the head of a pile should be instrumented to record the total pile and soil
deformation. Where possible, deformation measurements should also be made at the tip of the pile and at intermediate points to allow for a separate evaluation of point resistance and skin friction.
(e) The driving process should be observed in detail and, wherever possible, stress levels in the pile assessed (e.g. by means of the wave equation method of analysis).
(f) The piles should be loaded to at least twice the proposed working load and preferably to failure.
71. Routine load tests during construction. It is recommended practice to perform load tests on representative deep foundation units at early stages of construction. The purpose of such tests is to ascertain that the allowable loads obtained by design are appropriate, and that the installation procedure is satisfactory.
72. The selection of the test piles should be made by the engineer responsible for the design on the basis of observed driving behaviour or installation features.
73. Load tests for control. Where full advantage is to be taken of Clause 4.2.4.L(l)(c) and Sentence 4.2.7.2.(2) of the NBC, a sufficient number of load tests must be carried out on representative units to ascertain the range of the pile performance under load. Load tests for control should be performed on lout of each group of 250 units, or portion thereof, of the same type and capacity. Load tests should also be performed on lout of each group of units where driving records or other observations indicate that the soil conditions differ significantly from those prevailing at the site. Selection of the deep foundation units to be load tested is the responsibility of the design engineer.
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INSTALLATION AND STRUCTURAL REQUIREMENTS OF DEEP FOUNDA nONS 74. In most cases, the maximum allowable load on a deep foundation unit is governed by
geotechnical considerations. The design capacity of a deep foundation unit determined from structural considerations represents the maximum axial load which theoretically could be carried; however, this load is generally less than could be applied to a comparable unit if used in the superstructure of a building because;
(a) the actual placing of deep foundations frequently deviates from the position and alignment assumed in design,
(b) once in place, deep foundation units often can neither be inspected nor repaired, and (c) the placement of concrete in cast-in-place deep foundations frequently cannot be done with
the same degree of control as in structural columns.
75. In Tables L-il to L-13 guidelines are given to assist in determining a reasonable axial design capacity for deep foundation units under common conditions. In using these tables it should be noted that they are not a substitute for structural analysis and design, but are intended only to provide a conservative guide for the routine situations which may confront a designer, where a unit may be considered as a short column and where axial load governs the design.
76. The flexural capacity and ductility of piles should be considered when, under certain soil conditions, the soil either does not provide lateral support or could cause lateral loads to be applied to the piles.
77. Frequently, economies can be made by using higher capacities or different techniques. Such higher capacities should only be used in conditions where they can be justified as suitable and when quality can be ensured by an adequate program of inspection and load tests.
Driven Piles 78. This type of deep foundation unit may suffer structural damage when being driven.
Determination of capacity is generally made by comparing driving resistance (blows per inch) with the energy or size of hammer blow and relating these figures to the results of previous experience or to the behaviour of similar piles subjected to static load tests. For this purpose, observations of pile driving must include:
pile length and weight, hammer type (e.g. drop, diesel, ram weight), hammer energy applied, type and thickness of packing, and blows per foot or inch and elastic rebound of pile, or acceleration and stress at head of pile.
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Table L-ll
GUIDELINES FOR DRIVEN PILES
Type of Normal Typical Structural Installation Size Pile Load, Notes Pile Range tons
Considerations Considera tions
(a) Timber 7 to 10 in. 20 to 50 Must be checked in Cannot be Preservative tip accordance with NBC inspected. Sus- treatment nor-
Section 4.3 ceptible to dam- mally required. age during hard (CSA 080-1974) driving. Tip re-inforcement rec-ommended where driven to end bearing
(b) Steel 8tol4in. 40 to 200 Must be checked in May be dam- Tip points often sections accordance with NBC aged during required for (H, WF) Sections 4.5 and 4.6 driving bu t load hard driving.
End bearing: allowable capacity not Average thick-working stresses usually necessarily ness of flange or ::} .3 f when driven reduced web, t 2 :Ys in. to end bearing refusal on Projection of rock or dense strata, but flange ::} 14 t
(c) Pipe 8 to 24 in. 40 to 200 higher stresses possible Suitable for in- Normally driven sections diam. under specific controlled spection after closed-end. Tip conditions driving. Con- reinforcement
Friction: usually working crete quality or drive shoe stresses are governed by highly depend- required when geotechnical considera- en t on place- driven open-tions and rarely exceed ment method end. Pipe thick-12,000 psi ness> 1,4 in., In pipe piles, concrete but:Ys in. strength does not normally recommended contribute to pile capacity unless the pile is driven to end bearing
(d) Precast 8 to 12 in. 40 to 120 End bearing: capacity Cannot be in- Refer to ACI concrete must be checked in spected. Careful 70-50.(35} sections 12 to 36 100 to 300 accordance with NBC selection and Possible tensile
in. Section 4.5. Normally driving method stresses in con-r c> 4,000 psi required to pre- crete during Friction: the capacity of vent damage 'soft' driving. friction piles is normally High compres-governed by both instal- sive stresses in lation method and geo- concrete during technical considerations; 'hard' driving. the average compressive Tip reinforce-stress under load rarely ment usually exceeds 1,500 psi essential
Column I 2 3 4 5 6
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79. The assessment of pile stresses during driving by means of the theory of wave propagation or by the "wave equation" method of pile analysis is a useful tool. By assigning appropriate elastic properties to such parameters as the pile/cushion system and the pile/soil system, it is possible to compute the penetration per blow and pile stresses for a given hammer energy; however, it must be emphasized that these results and also the extrapolation of the penetration per blow to a definition of ultimate pile capacity are, at best, only approximations. The "wave equation" method, in common with all empirical dynamic pile formulae, calls for the exercise of judgment and experience. No method, in itself, can be employed to provide definitive values either concerning driving criteria or concerning load/deformation characteristics of a driven pile. Pile load tests are essential to confirm the driving criteria used and to assess load/deformation performance.
80. Damage to driven piles. Piles may be damaged by attempting to drive to an excessively small "set" per blow or to an excessively large number of blows at high resistance. This is known as "overdriving." The driving set required should be established so as to achieve a reasonable performance under load without incurring the risk of serious damage. Driving stresses depend upon the hammer, blows, size and type of pile, length of pile, cushion material and upon the soil conditions. These factors must be examined for each situation and acceptable "set" criteria determined on the basis of previous experience and load testing.
81. Piles may also be damaged by driving through obstructions, such as boulders or fill material, or by sloping rock surfaces which may deflect the pile or create high local stresses leading to serious deformation or to breakage.
82. Excessive bend or sweep may be experienced when driving long piles (e.g. 100 ft or more). A discussion of allowable bending of piles is given by Fellenius (1972).(36)
83. The use of steel reinforcing tips is strongly recommended whenever there is a possibility of end damage. Tip reinforcement may also reduce the incidence of damage through overdriving.
84. Movement of adjacent piles during driving. Where a group of piles is to be placed through silt or clay, measures shall be taken to indicate any movement of each pile during the installation of adjacent piles. Horizontal and vertical movement should be recorded.
85. Piles which have suffered vertical movement should generally be redriven. Piles which have suffered horizontal displacement must be investigated for structural damage.
86. Jetting or pre-excavation. When jetting, predrilling or other pre-excavation methods have been used during pile installation, the pile tip should be driven below the depth of pre-excavation to the required bearing. Care must be taken to avoid jetting, pre-driving or pre-excavating to a depth or in a manner that will affect the design capacity of piles previously placed. This is discussed in detail in ACI 70-50.(35)
Cast-in-Place Deep Foundations 87. Cast-in-place deep units can be divided into 2 main categories: compacted expanded
base piles (Table L-12) and drilled shafts (Table L-13) ..
88. The placement of the materials forming such units is crucial. In general, it is difficult, if not impossible, to ensure the same level of quality in placing concrete in such units as in a building superstructure. Careful attention must be given to the methods of installation, of concrete mix proportions and placement methods, and to the degree of inspection possible. The allowable loads on such units must be adjusted accordingly, in keeping with sound design, engineering experience and judgment.
89. Concrete cast in place. The placing of concrete in pipe piles, expanded base pile shafts and in drilled shafts can be classified in 2 categories:
(a) Concrete placed in the dry should be placed by guided free fall, bucket or chute. Segregation may occur if concrete is allowed to fall through a reinforcing cage or similar obstruction.
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Table L-12
GUIDELINES FOR COMPACTED, EXPANDED BASE PILES
Normal Typical Type of Size Structural Installation Pile Range,
Load, Consideratons Considerations Notes
in. tons
(a) Rammed 14 to 24 50 to 150 Concrete quality Cannot be Allowable load shaft highly dependent inspected. frequently
on technique Contamination of determined on the concrete. 'Necking' basis of energy of shafts. Possible required to expell damage by adjacent measured volumes piles of concrete at base.
Highly dependent on judgment and experience. Possible heave of all piles must be continuously monitored
(b) Steel 12 to 20 50 to 175 Where the pipe wall Less subject to See (a) above pipe thickness < 1,4 in., damage than (a) shaft, the structural above. Shaft can be concrete contribution of the inspected prior to filled pipe should be filling
disregarded
Column 1 2 3 4 5 6
Concrete of more than 4 in. slump placed by free fall of 15 ft or more in non-reinforced or lightly reinforced shafts receives adequate compaction and does not require vibration. Placement by tremie methods is necessary when a considerable inflow of ground water is present or when there is standing water in the hole.
(b) Concrete placed under water should be placed through a tremie pipe or by pump in such a way as to eliminate any contamination, washing or dilution of the concrete by the water. It should have a 6 in. to 8 in. slump and vibration should not be applied. (Refer to CSA A23.1-1973, "Concrete Materials and Methods of Concrete Construction.")
90. Reinforcing steel for cast-in-place units. Reinforcing steel is generally placed pre-assembled as in a cage. During placement, it may be subjected to severe handling and placement stresses and to impact. Placement cannot be made with as high a degree of accuracy as in a superstructure, nor can it be easily checked.
91. For the design of cast-in-place foundations, the provisions of CSA A23.3-1973, "Code for the Design of Concrete Structures for Buildings" should, therefore, be amended in the following respects:
(a) Reinforcing steel assemblies should be designed and constructed so as to withstand all handling and placing stresses without deformation which would impair the structural performance of the unit.
(b) Weldable steel should be employed, in most cases, to permit construction of rigid and strong assemblies.
(c) The clear distance between longitudinal bars should not be less than 3 in.
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(d) Ties or spiral may be welded to the longitudinal bars. Welding should be in accordance with CSA W59.1-1970, "General Specification for Welding of Steel Structures." Welded spirals or ties should not be of wire less than 0.28 in. in diam., with pitch not more than 12 in. and with not less than 3 in. clear space between ties or spirals.
(e) The possibility of misplacing the reinforcing bars should be considered and allowed for in the design, and reasonable tolerances established for field performance: e.g. 3 in. of correct bar location in plan,
:±: 6 in. of correct bar location in elevation. (f) Generally, longitudinal steel should be uniformly distributed around the cross-section, as
twisting of an assembly may occur during placement.
Table L-13
GUIDELINES FOR DRILLED SHAFTS
Type of I Normal Typical Structural Installation Shaft Size Load, Considerations Considerations Notes
Range tons
(a) Uncased 12 to 27 30 to 50 Good concrete Where shaft Not recommended plain in.diam. quality not always diameter < 27 in. for normal concrete shaft possible normally cannot be application where
inspected, thus caving can occur permitting only low allowable loads < 50 tons
(b) Uncased. 30 to 60 50 to Generally good Can be inspected. Usually under-Rein- in.diam. 5,000 concrete quality However, where reamed to provide forced shaft possible with temporary casing belled base. Bell or plain fc >3,000 psi used to retain wet, sides typically at concrete. <5,000 psi. caving soil, high 2(V) to I(H). Often Under- Can normally be slump concrete may not under-reamed reamed designed in be required. where bearing on or accordance with Precautions should sound rock straight NBC Section 4.5 be taken to prevent
(CSA A23.3-1973) possible contamination of concrete
(c) Cased. 18 to 60 50to See (b) above. Must Can be inspected Usually not under-Perm a- in.diam. 5,000 be checked as reamed. Generally nent shaft composite unit in socketed where steel pipe accordance with taken to rock. lining NBC Section 4.5 Design for
(CSA A23.3-1973) complete load and Section 4.6 transfer through
socket. Essential to seat liner on rock bearing surface. Drive shoe usually fitted to pipe liner
Column I 2 3 4 5 6 I
-- --=:::oor'
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Location and Alignment 92. The exact location of each deep foundation unit should be staked in advance and
checked immediately prior to installation of each unit. After completion of the installation the location of each unit should be checked against design location and permissible deviation as indicated on the design documents.
93. As required in NBC Article 4.2.7.5., permissible deviations from the design location shall be determined by design analysis. In practice, it is usually possible to position piles and shafts within a tolerance of 3 in.; for practical reasons smaller tolerances should not be specified.
94. As required in NBC Article 4.2.7.6., where a deep foundation unit is wrongly located, the condition of the foundation shall be assessed by the person responsible for the design and the necessary changes made.
95. During and after installation of any deep foundation unit, its alignment should be checked against the design alignment and the permissible deviation as indicated on the design documents.
96. Current practice is to limit the total deviation from design alignment to a certain percentage of the final length of the deep foundation unit, 2 per cent is a value in common use. However, such practice does not ensure proper structural behaviour of the unit since it does not take into account the length over which this deviation is distributed. It should be recognized that:
(a) the total deviation from alignment of a deep foundation unit has little influence on its geotechnical capacity unless it reaches extreme values greater than 10 per cent of the length of the unit,
(b) practically all piles, particularly when driven, are more or less out of design alignment. A straigh t pile is a theoretical concept seldom achieved in practice, and
(c) only the radius of curvature of a deep foundation unit is of importance for its structural and geotechnical behaviour. The maximum allowable radius of curvature should be determined by design whenever it is specified that such radius be measured during inspection. A discussion of allowable bending of piles is given by Fellenius (1972).(35)
PERMAFROST
97. The lines on Figure L-3 indicate the approximate southern limit of permafrost and the boundary between the discontinuous and continuous permafrost zones in Canada. The distribution of permafrost varies from continuous in the north to discontinuous in the south. In the continuous zone permafrost occurs everywhere under the ground surface and is generally hundreds of feet thick. Southward, the continuous zone gives way gradually to the discontinuous zone where permafrost exists in combination with some areas of unfrozen material. The discontinuous zone is one of broad transition between continuous permafrost and ground having no permafrost. In this zone, permafrost may vary from a widespread distribution with isolated patches of unfrozen ground to predominantly thawed material containing islands of ground that remain frozen. In the southern area of this discontinuous zone, permafrost occurs as scattered patches and is only a few feet thick.
98. It is emphasized that the lines on this map must be considered as the approximate location of broad transition bands many miles wide. Permafrost also exists at high altitudes in the mountains of Western Canada a great distance south of the southern limit shown on the map. Information on the occurrence and distribution of permafrost in Canada has been compiled by the Division of Building Research, National Research Council.(37).(38)
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153
REFERENCES (I) Terzaghi, K. and Peck, R. B. Soil Mechanics in Engineering Practice. J. Wiley & Sons Inc.,
N.Y., 1967. (2) Hoek, E. and Bray, J.W. Rock Slope Engineering. Inst. of Mining and Metallurgy, 1972. (3) Fletcher, G.F.A. Standard Penetration Test: Its uses and abuses. J. Soil Mech. Found. Div.,
Proc. Am. Soc. Civil Engrs., 91: SM4, 1965, pp 67-75. (4) Peck, R.B., Hanson, W.E. and Thornburn, T.H. Foundation Engineering. J. Wiley & Sons
Inc., N.Y., 1974. (5) Gadsby, J.W. Discussion of 'The Correlation of Cone Size in the Dynamic Cone Penetration
Test with the Standard Penetration Test.' Geotechnique, Vol. 20,1971, pp. 315-319. (6) Tavenas, F.A. Difficulties in the Use of Relative Density as a Soil Parameter. Am. Soc. Test.
Mtls., STP 523, 1973. (7) Tavenas, F.A., Ladd, R.S. and LaRochelle, P. The Accuracy of Relative Density Measure
ments: Results of a Comparative Test Programme. Am. Soc. Test. Mtls., STP 523, 1973.
(8) Terzaghi, K. Influence of Geological Factors on the Engineering Properties of Sediments. Economic Geology, 5th Anniv. Volume, 1955, pp. 557-618.
(9) Bjerrum, L. Engineering Geology of Norwegian Normally-consolidated Marine Clays as related to Settlements of Buildings, Seventh Rankine Lecture. Geotechnique, Vol. 17, 1967, pp. 83-117.
(10) Crawford, CB. Interpretation of the Consolidation Test. Journal of Soil Mech. Found. Div. Proc. Am. Soc. Civil Eng .• Vol. 90, SM5, 1964, pp. 87-102.
(II) Schmertmann, J.H. Estimating the True Consolidation Behavior of Clay from Laboratory Test Results. Proc. Am. Soc. Civil Eng., Vol. 79, Separate 311, 1963.
(12) MacFarlane, I.C, Editor. Muskeg Engineering Handbook, Univ. Toronto Press, Toronto, 1969.
(13) Milligan, V., Soderman, L.G. and Rutka, A. Experience with Canadian Varved Clays. Journal of Soil Mech. Found. Div. Proc. Am. Soc. Civil Eng., Vol. 88, SM4, 1962, pp. 31-67.
(14) Crawford, CB. Engineering studies of Leda clay. In: R.F. Legget (Editor) Soils in Canada. Roy. Soc. Can., Spec. Publ. No.3, 1961, pp. 200-217.
(15) Crawford, CB. Quick Clays of Eastern Canada. Engg. Geol., Vol. 2, No.4, 1968, pp. 239-265. (16) LaRochelle, P., Chagnon, J.Y. and Lefebvre, G. Regional Geology and Landslides in Marine
Clay Deposits of Eastern Canada. Can. Geotech. Journal, Vol. 7, No.2, 1970, pp. 145-156.
(17) Hamilton, J.J. Shallow Foundations on Swelling Clays in Western Canada. Proc. Intern. Res. Engg. Conf. Expansive Clay Soils, Texas A&M Univ., Vol. 2, 1965, pp. 183-207.
(18) Hardy, R.M. Construction Problems in Silty Soils. Eng. Journal, Vol. 33, No.9, 1950, pp. 775-782.
(19) Quigley, R.M. and Vogan, R.W. Black Shale Heaving at Ottawa, Canada. Can. Geotechn. Journal, Vol. 7, No.2, 1970, pp. 106-112.
(20) Hardy, R.M. Engineering Problems involving Preconsolidated Clay Shales. Trans. Engg. Inst. Can., Vol. I, 1957, pp. 5-14.
(21) Brown, R.J.E. Permafrost in Canada. Univ. Toronto Press, Toronto, 1970. (22) Sanger, F.J. Foundation of Structures in Cold Regions. Cold Reg. Res. Engg. Lab. Cold Reg.
Sci. Engg. Monogr., Vol. III-C4, 1969. (23) Coates, D.F. Rock Mechanics Principles. Mines Branch Monograph 874, Queen's Printer,
Ottawa, 1967, p. 358. (24) Tavenas, F.A. Controle du roc de foundations de pieux fores a haute capacite. Can. Geo
techno Journal, Vol. 8, 1971, pp. 400-416. (25) Meyerhof, G.G. Penetration Tests on Bearing Capacity of Cohesionless Soils. Journal of Soil
Mech. Found. Div. Am. Soc. Civil Eng., Vol. 82, SMI, Paper No. 866, 1956. (26) Berezantsev, V.G., Kristoforov, V.S., and Golubkov, V.N. Load Bearing Capacity and Defor
mation of Pile Foundations. Proc. Intern. Conf. Soil Mech. Found. Eng .• 5th, Paris, Vol. 2, 1961, pp. 11-15.
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(27) Vesic, A.S. Tests on Instrumented Piles, Ogeechee River Site. Journal of Soil Mech. Found. Div. Am. Soc. Civil Eng., Vol. 96, SM2, 1970, pp. 561-584.
(28) De Beer, EE The Scale Effect in the Transposition of the Results of Deep Sounding Tests on the Ultimate Bearing Capacity of Piles and Caisson Foundations. Geotechnique, Vol. 13, 1963, pp. 39-75.
(29) Yang, N.C. Relaxation of Piles in Sand and Inorganic Silt. Journal of Soil Mech. Found. Div. Am. Soc. Civil Eng., Vol. 96, SM2, 1970, pp. 395-410.
(30) Tomlinson, M.J. The Adhesion of Piles Driven in Clay Soils. Proc. Intern. Soc. Soil Mech. Found. Eng., 4th, London, Vol. 2, 1957, pp. 66-71.
(31) Eide, P., Hutchinson, J.N. and Landva, A. Short and Long Term Loading ofa Friction Pile in Clay. Proc. Intern. Conf. Soil Mech. Found. 5th, Paris, Vol. 2, 1961, pp. 45-53.
(32) Tomlinson, M.J. Foundation Design and Construction. John Wiley & Sons, Inc., N.Y., 1963. (33) Burland, J.D., Butler, F.G. and Dunican, P. The Behavior and Design of Large Diameter
Bored Piles in Stiff Clay. Proc. Symposium on Large Bored Piles, Inst. Civil Eng., London, 1966, pp. 51-71.
(34) Leonards, G.A. Summary and Review of Part II of the Symposium on Pile Foundations. Hwy. Res. Record No. 333, 1970.
(35) ACI Committee 543. Recommendations for Design, Manufacture and Installation of Concrete Piles. ACI 70-50, ACI Manual of Concrete Practice, Part 3, 1974.
(36) Fellenius, B.H. Bending of Piles Determined by Inclinometer Measurements. Can. Geotechn. Journal, Vol. 9, 1972, pp. 25-32.
(37) "Permafrost Map of Canada" (a joint production of the Geological Survey of Canada and DBR/NRC). August 1967, NRC No. 9769.
(38) Brown, R.J.E. "Permafrost Map of Canada." Reprint from Canadian Geographical Journal, February 1968, pp. 56-63, NRC No. 10326.
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