Department of Civil and Environmental Engineering Stanford University
A COMPARISON OF EARTHQUAKE BUILDING CODE REGULATIONS
by
John T. Egbert III
Report No. 42 April 1979
The John A. Blume Earthquake Engineering Center was established to promote research and education in earthquake engineering. Through its activities our understanding of earthquakes and their effects on mankind’s facilities and structures is improving. The Center conducts research, provides instruction, publishes reports and articles, conducts seminar and conferences, and provides financial support for students. The Center is named for Dr. John A. Blume, a well-known consulting engineer and Stanford alumnus. Address: The John A. Blume Earthquake Engineering Center Department of Civil and Environmental Engineering Stanford University Stanford CA 94305-4020 (650) 723-4150 (650) 725-9755 (fax) earthquake @ce. stanford.edu http://blume.stanford.edu
©1979 The John A. Blume Earthquake Engineering Center
ACKNOWLEDG»IENTS
The help of each of the many contributors to this project is grate-
fu~ly acknowledged.
The Seismology Committee of the Structural Engineers Association
of Northern California was responsible for providing the subject matter
Special help was received from Chris Poland, Ed Zackerof this project.
Bill Holmes and Eric Elsesser.
Funding for computer analysis was not available at Stanford Univer-
However, the firms GKT Consulting Engineers and URS/John A. Blumeatty.
and Associates both offered the use of their computers for this project.
The help of Ben Kacyra t Onder Kustu andThe GKT computer was used.
A very special acknowledgement to HratchPatrick Lau is appreciated.
Kouyoumdjian and Ed Haverlah for their effort spent checking the design
procedures, calculations and computer data.
The assistance with the calculations from Professor Helmut Krawinkler
is appreciated
The generosity of Professors Haresh C. Shah and Theodore C. Zsutty
for their helpful suggestions and encouragement is most gratefully ap-
Professor Shah and Zsutty's time was supported by thepreciated.
This support is gratefully acknowledgedNSF Grant No. ENV-77-17834.
Very much appreciated were the efforts of Laura Selby in typing
this dissertation.
The support that the United States Coast Guard has given is
gratefully acknowledged.
111
PREFACE
It is important to constantly review the building codes that are
currently being used in order to determine what improvements might be
For example, the formulae for obtaining base shear, lateral forcemade.
distribution and building period are continually being evaluated. Each
year design force levels increase in order to meet regulations which re-
Buildingsduce the likelihood of failure in the event of an earthquake.
must be constructed stronger and this may result in more structural re-
When a change to a code isdundancies, some of which may be unnecessary.
proposed~ the effect of this change on the variety of structural shapes
For example, a code change could affectand systems must be considered.
a two or thfee story concrete shear wall building much differently than
Rather than randomly increasinga twenty story steel frame high rise.
design levels or altering code requirements a code change should first
Thisbe examined for effects on a representative set of structures.
examination procedure is the subject of this work where the set of struc-
tures has been designed by current building codes and can be used for
comparative pruposes in evaluating the overall usefulness of a proposed
change and its value to certain structural systems
The Seismology Committee of the Structural Engineers Association of
Northern California (SEAONC) has studied a method which will standardize
and simplify the procedure for examining the effect of proposed building
The findings strongly indicate the need for the study ofcode changes.
a typical or standard set of buildings which would include not only the
general specifications for design of each building, but also several sets
of completed designs done by use of the most widely used building codes
This proposal offers a simple procedure that can be utilizedof today.
iv
to compare the impact of a code change against a code with a known per-
formance
v
TABLE OF CONTENTS
111Acknowledgements
IvPreface
viTable of Contents
ixList of Tables
List of Illustrations x
Chapter 1 SEISMOLOGY COHMITrEE PROJECT
14BUILDING DESIGN METHODSChapter 2
16Chapter 3 THE ATC 3 METHOD.
16172024262626272.727282830
3.13.23.33.43.53.63.73.83.93.103.113.123.133.14
31313232
Symbols and Notation. . . . . . . . . . . . . . .
Seismic Performance. . .. . . . . . . . . . . . .
Classification and Use of Framing Systems. . . .
Si te Effects. . . . . . . . . . . . . . . . . . .
Building Configurations. . . . . . . . . . . . .
Regular and Irregular Structures. . . . . . . . .
Load Combinations. . . . . . . . . . . . . . . .
Orthogonal Effects. . . . . . . . . . . . . . . .
Inverted Pendulum-~e Structures. . . . . . . .
Deflection and Drift Limits. . . . . . . . . . .
Base Shear. . . . . . . . . . . . . . . . . . . .
The Seismic Coefficient. . . . . . . . . . . . .
Building Period. . . . . . . . . . . . . . . . .
Distribution of Lateral Forces Along theHeight of the Structure.. . . . . . . . . . . . . .
Horizontal Shear Distribution and Torsion. . . .
Story Drift Determination. . . . . . . . . . . .
P-Delta Effects. . . . . . . . . . .. . . . . . .3.153.163.17
34THE STANFORD METHODChapter 4
343535373739394444
4.14.24.34.44.54.64.74.84.94.10
Symbols and Notation. . ~ . . . . . . . . . . . .
Base Shear. . . . . . . . . . . . . . . . . . . .
Zone Acceleration Value. . . . . . . . . . . . .
Mean Dynamic Amplification Factor. . . . . . . .
Building Period. . . . . . . . . . . . . . . . .
Structural Behavior Factor . ~ . . . . . . . . . .
Quality Factor. . . . . . . . . . . . . . . . . .
Structural Weight. . . . . . . . . . . . . . . .
Load Combinations. . . . . . . . . . . . . . . .
Distribution of L~~eral Forces Along theHeight of the Structure. . . . . . . . . . . . . 44
vi
TABLE OF CONTENTS (Continued)
4'454646
4.114.124.134.14
Building Setbacks and Irregular Shapes. . . . . .
Horizontal Shear Distribution and Torsion. . . .
Drift and Building Separations. . . . . . . . . .
Structural Systems. . . . . . . . . . . . . . . .
48Chapter 5 THE 1976 UNIFORM BUILDING CODE. . . . . . . . . .
48484953
5.15.25.35.45.5
Earthquake Regulations. . .. .. . , . . , . . , .. ..
Symbols and Notations. . .. , .. . . , .. . .. . , ..
Base Shear.. .. .. .. .. . . . . .. . . .. . .. . . .. .. ..
Building Period.. .. . . . . .. .. . . . . . .. .. .. ..
Distribution of Lateral Forces Along theHeight of the Structure. . .. , . .. . . .. . . .. .
Setbacks and Irregular Structures. .. . . .. . .. ,
Distribution of Horizontal Shear. . . . . .. . .. ..
Horizontal Torsional Moments. . . , .. .. . .. .. . ..
Building Drift and Separations. . .. .. . .. .. , .. ..
Structural Systems.. .. .. . . .. . .. .. . . .. . .. . .
Load Combinations.. .. . .. . . .. .. . . .. . .. .. . .
Essential Facilities.. . .. .. . .. .. .. .. . . .. .. .. ..
5454545555555656
5.65.75.85.95.105.115.12
57Chapter 6 THE 1973 UNIFORM BUn.DING CODE. . . . . . . . . .
5757
6.16.26.3
Symbols and Notation. . . . . . . . . . . . . . .
Base Shear. . . . . . . . . . . . . . . . . . . .
Distribution of Lateral Forces Along theHeight of the Structure. . . . . . . . . . .. . .
Distribution of Horizontal Shear. . . . . . . . .
Horizontal Torsional Moments. . . . . . . . . . .
Setbacks. . . . . . . . . . . . . . . . . . . . .
Structural Systems. . . . . . . . . . . . . . . .
Drift and Building Separations. . . . . . . . . .
S96060606161
6.46.56.66.76.8
62Chapter 7 THE BUILDING DESIGN
626464656565
7.17.27.37.47.57.6
Introduction. . . . . . . . . . . . . . . . . . .
Seismicity of the Area. . . . . . . . . . . . . .
Base Shear. . . . . . . . . . . . . . . . . . . .
Dead and Live Load. . . . . . . . . . . . . . . .
Fixed End Moments. . . . . . . . . . . . . . . .
Portal Frame and Me1'1ber Sizing. . . . . . . . . .
68Chapter 8 CODE COMPARISON
6868
8.18.28.3
70
Introduction. . . . . . . . . . . .. . . . L . . .
Base Shear. . . . . . . . , . . . .. . . . , . . .
Distribution of Lateral Forces Along theHeight of the Structure. . . . . . . . . . . . .
vii
TABLE OF COl~TENTS (Continued)
707577
8.48.58.6
Building Period. . . . . . . . . . . . . . . . .Load Combinations. . . . . . . . . . . . . . . .The Common Base for Comparison. . . . . . . . . .
89References. . . . . . . . . . . . . . . . . . . . . . . . . . .
viii
LIST OF TABLES
1-1 8Story Masses. . . . . . . . . . . . . . . . . . . . . . .Coefficients A , A , and Seismicity Indexa v 19
21Seismic Performance Category. . . . . . . . . . . . . . .
Structural Systems and Related Coefficients 22
25Soil Profile Coefficient. . . . . . . . . . . . . . . . .
Allowable Story Drift, A 29a
36Zone Acceleration Values. . . . . . . . . . . . . . . . .
Structural Types and Behavior Factor. B 40
Penalty Values, P . . . . . . . . . . . . . . . . . . . .q
Horizontal Force Factor, K . . . . . . . . . . . . . . . .
43
51
Occupancy Importance Factor, I . . . . . . . . . . . . . . 52
58Horizontal Force Factor, K . . . . . . . . . . . . . . . .
66Accidental Torsion. . . . . . . . . . . . . . , . . . .
69Comparison of Base Shears
71Lateral Load Distribution Formulae. . . . . . . . . . . .
8-.3 Distribution of Lateral Forces Along the Height ofthe Structure. . . . . . . . . . . . . . . . . . . . . . 72
74Proportion of the Lateral Force Distribution. . . . . . .
76Effects on Base Shear Due ~o Increased Period
78Acceptable Design Level
8-7 81Girder Member Sizes
8-8 84Total Girder Weight
8-9 85Section Modulus Comparisor . . . . . . . . . . . . . . . .
87Section Modulus Comparison. . . . . . . . , . . . . . . .
88Code Comparison Table
ix
LIST OF ILUJSTRATlONS
3SEAONC Standard Building Set. . . . . . . . . . . . . . .
1Basic Geometry for the Standard Buildings
38Mean Dynamic Amplification Factor
50Seismic Zone Map . . . . . . . . . . . . . . . . .
Plan and Elevation View of the Fifteen Story Building 637-1
73Distribution of Lateral Forces Along the Height ofthe Structure. . . . . . . . . . . . . . . . . . . . . .
x
Chapter 1
SEISMOLOGY COMMITTEE PROJECT
The Seismology Committee of the Structural Engineers Association
of Northern California has proposed a set of "Standard Buildings" which
The standardwill aid in evaluating the impact of building code changes.
buildings represent the basic structural systems that are encountered in
Simplicity has been incorporated into the composition of a stan-practice.
Each typicaldard building type in order to make its utilization appealing.
building has been specified only by plan and elevation dimensions, typical
openings, and story masses.
In this dissertation, all standard buildings will be designed by
(1) The ATC 3-06 Tentative Provisions for the Developmentfour methods:
of Seismic Regulations for Buildings (Ref. 1); (2) The Recommended Seismic
Resistant Design Provisions for Guatemala and Algeria (Refs. 2 and 3);
4); and (4) The 1973 Uniform(3) The 1976 Uniform Building Code (Ref.
Building Code (Ref. 5)
A standard building can be designed by any newly proposed building
code and the results of this design can easily be compared to the results
This manner ofof design obtained from the four methods just named.
examining a proposed code becomes a useful tool for evaluating the impact
of the change
A standard building is classified by its structural system (correspon-
ding to the K values from the 1976 Uniform Building Code), building material,
The standard buildings are ninety by ninety feet inand building height.
plan with four frames that are thirty feet on center in both principal
The standardThe story height is twelve feet six inches.directions.
building set includes one, two, six and fifteen story buildings with
1
structural systems of ductile moment resisting frames, dual systems, braced
Also included in the set are box systemsframes. and shear wall systems.
consisting of concrete shear walls, a one hundred by two hundred feet
glu-laminated tilt up, and rectangular "motel style" timber and masonry
The standard building set and the typical geometry are shownbuildings.
The typical story masses that were used for this
*:in Figures 1-1 and 1-2.
project are listed in Table 1-1.
As more experience is gained in working with these standard buildings
any deficiencies that become apparent can be eliminated by adding more
Such additions might include build-sophisticated buildings to the set.
ings with setbacks, small irregularities in plan, or an offset center of
The SEAONC project will thus become a standard base againstrigidity.
which to compare code changes and future building codes.
*Received from the Seismology Committee of SEAONC.
2
Figure 1-1
SEAONC STANDARD BUILDING SETPlan Views.
Ductile Moment Resisting Space FrameK = 0.67
ConcreteSteel
Tube SystemTube System
! I
1'.SN\Dnber of Stories:1SNumber of Stories:
Moment Resisting FrameMoment Resisting Frame
2,6,15Number of Stories:2,6, 15Number of Stories:
*Each plan view corresponds to one building for each building height
(in stories) listed.
3
Figure 1-1 (Continued)
K - 0.80 Dual System
Steel Frame/Concrete Core
Y IJ
Number of Stories: 6,15
4
(Continued)Figure 1-1
K - 1.0 Braced Frame and Shear Wall System
ConcreteSteel
Exterior Shear WallBraced Frame
I
2,6, 15Number of Stories:2,6, 15Number of Stories:
Shear Wall Core
ft"-rI
6Number of Stories:
5
K - 1.33 Box System
*MasonryConcrete
Exterior Shear Wall
2.6.15Number of Stories:Number of Stories: 2,6, 15
Corner Shear Wall
Timber**
Number of Stories: 2,62Number of Stories:
20' Tilt up with Glu-laminated Beams and Paneled Roof
100" X 200t
*The masonry."Motel Style" structure has a double bearing corridor,tr~Dsverse bearing walls, and concrete plank floors.. '**The "Timber Style" structure has a double bearing corridor and trans-
verse bearing walls.6
Figure 1-2
Basic Geometry for All Standard Buildings(Except tile-up, masonry, and timber)
-R
-2
-1
-G
Typical Elevation View
4 X 6' Openings Equally Spaced
0 ODD D 0 0 0 0,-0 0 0 0 0 0 0 0 0 6'
-- - - - - - - ..: - - - j;.t-j4L-j ;
Typical Exterior Wall
lOr. ..19" ~-I.
'-151~
Corner (No openings)Core
Typical Shear Walls
7
-cI
-c
QI
~Eof
'"'QJ
QJ ~m ~~ co~ bO ,d
~ ~
11-4~ -0
CO
QJCO 00
~ ~{/)~~ ,dtI) ~ Utl)QJ CU
~~~QJ~~~
~ tl)0- QJ ~0 E-c tI)~ tI)
U p.~ ~
,... .\0 CO
. CO0 ~
n11-4
~ 0
CO~~
:5
GJ...='...(J
~...tJ)
~(J......GJ
I>
MOJCd 1-44.1 ='~4.I0 CJN ='
-"'1-41-44.1O~
:d
roi .
~U~<J~ ='0 $.4
N~oritn$.4 I0 ~
=0 ~
.4.1 ~CJ QJ;j4.1~ QJ4.1 St/)0r4
I ~(: QJO~
'Z
,..00
.-tfa-
cdu0
1:04
10nn
~
a)
~0
c,
P$ '" ..,. ~ N .-4 C 0\ ~ \0 '" ..,..-4 .-4 - .-4 .-4
N 11'1r-. 11'1('1'\ ...T
~
~CO~~~\D\O~~~NNN 0"""""-NNN"'~~~
,... ,...0 0N N
0:: 5
q N N N 0 0 0 a) a) a) \0 10 \0 q~ '" '" '" \0 \0 \0 \0 \0 \0 ~ ~ ,... ~\0 ~ Q) a) ~ a) a) a)U) m m m M M
8
~ ~
&t\an-
0,...
..:J"(Cm
-'CQj='
~4J
8(,J-
,
Qjro4
~Eo4
~
\00.
0
~~,...
~
Q).0='
E-I
tIOc=
~~CI)
tI)~~ 0)
tI)~
~~~~C=Q)~~~~oCl)o=::E-ctl)Q)
~~~(J='
A
~~~U<J
.e~C/)
.-ttU<J
...fU~~
p
r-fQl«I ~~ ~
~~0 cJN ~
t~~~
~cn
.cG4.)4.)<J~ e04.)Nt/)-rot ,H ~
~ 0~
.~ ~(J GJ~~~~
I ~~ GJOP4
~
~4J0
fo4
JoI00
...~
m~~II!
:3:
aI
~0
C)
00000000000-~~~~t"\,.:f',.:f'-:ttnlt'\
n
2
~ Ir\ o.:r-- -'
~ ~
... N0\ ~-
0 -.1' -.1' -.1' -.1' -.1' -.1' -.1' -.1' -.1' -.1'«> \0 \0 ,.. r.. ~ «> «> 0\ 0\\0 «> ~ «> ~ ~ «> «> ~ «> «>
M N - 0 0\ ~ roo \0 11'\ .q M N-~
9
0.,...
.i:j" .i:j" .i:j" .i:j"0\000a) 0\ 0\ 0\
0\0
0 0\0 \0
n
N~~
-~4J
S~~
gu'-'
t.
.,M.0~
fool
QI
m~
~
QI,c:J
~
~
~+.IIt)
cn~~ (t)U)QlQIi ~+.I QI
+.I ~E C)
~ ~ §Oou~~
QI.-4
+.I():J
A
,...\0
.'0
.
W
Q)H~~<J
~~{/)
~CJ
-.of~~QI
t>
r-IGJ~ ~.I.J :s
~.I.J0 cJN :s
-rt~~4J0(1)
=
rot .t\S~~ (J~ :30 kN~
.,..C/]k .0 ~
:I: 0~
.~ Jo4U QJ='~
~~I Jo4~ Q)o~
z
J.I00
rootrz.
~u0
~
~.-f~
~
(0
j0
u
~ &1'\ -.:f" M N'" 0 O\~ '" \0 It)..,. M N.,4 - .,4
~ N N&1'\ ~~
0
00 00\ ~ ~
,...:0N
~~
10
C)
"0-
: §
-~~~.f.I
5u-.-4...-4QIr-I
~~
Q)
s 0
Q)U4oJ Q)
tI)(/)4oJ~>-,Q)CJ)CIJ""CIJ U
~ II! 5
~6u~o~~cocoCJ) o~
n Q)
~ Q)4oJCJ)
QIJ.4~.uu
~.ut/)
~u.uJ.4QI
:>
r-4QJ~ ...~ ='
St'N ='or-4 ...
~~°cntI2
.~~'" CJ" ~0",Nt/)
.to. "~ 0
Z.
.4.) ~(J GI='4.)~ GI4.) St/)~I ~~ GIOP4
Z
~00
r-frz.
~~0
E-4
In......
~
co
~r-I0U
M In -4' ~ c-. 0 0\ CO , \0 11'\ -4' ~ N... -""~"".-4
co-. '" c 11'\
~ ~
'"' ~ ~ ~ ~ ~ ~ ~ \Q \Q \Q \Q \Q '"'~O\O\NNNNN~~~~II'\CO ~~--
~ ~ ~ N-
,..0N
.-4 N0\ ~-
.-4 \0 \0 ... ... ... ... ... ~ ~ 4 4 4 ... ...N44~~~~~"""NNN \0 ~r-. 0\ 0\ 0\ 0\ 0\ 0\ 0\ 0 0 0 0 0 0 0
... ... ... .-4 --
NNNN\O\C~~~OON N N ~ ~
11
,..~-
,...0N
Na)~
'""''0OJ~
~+I6u--
,-OJ
r-I
~~
tIO~uCI) ~
~ ~CI)~
~~~4.1
~OCl)o~E-t-CI). .
~
QIH~'"'CJe'"'CI)
~CJ
oM'"'HQI
t>
""QItU ~~ ='
~~0 (J
~e~~Of/)rz:
~ .CIS'"." CJ~ ~0 ~N'" CI)~ ,0 ~
= 0Z
.~ H(J (IIe~~~
I H~ (IIOp,.
!z;
~00
r-Ir...
~4J0
Eo4
m...,...,
~
In
~.-I0
U
~ ~ ~ C"') N"" 0 0\ a)""\O ~ ~
~ ~~
~\D\D\C~~~~~~~N\D
~
~
N. N0\ ~~
,... «) «) ~ 0 ~ -:t" -:t" -:t" N N N ~ -:t" -:t",... '" '" 11'\ \0 \0 \0 \D \D ,... ,... ,... «) «) a>\D «) «) a> a> Q) a> «) «) a> «) «) ~ ~ M
t» t» t» t» N N ~-
12
N~~~~~~N N N
~ N
~ ~- ...
-'CQ)~~
or.j4.1g
to>-
.-4I
.-4
Q)t
~f-4
Qj~0
C.)
tI)~~~f/)tUQjtI):3=~<~QjXtU~~ Qj g
~.doof/)C.)E-.otl)o
.-
.~
QJ...~uu
~ucn
~u
u...QJ
t>
.-fatcd k." ='
g~N ='
"f-4kk."oC/)
~
I'"i .tOUU (J~ ~o~NU
-rit/)~ IQ ~
=~
.u ..() QI~u
~ ICI1o..t
I ..(: QIOP4
z
~00
~rz.
~u0
E-4
II)
co3
V)
g0
(..)
~ &f\ ~ to') N ...t' 0 0\ ~ r.. \0 &f\ ~
0 N~ \0'" \l)
-4" -4" In In \0 \0 \0 \0 r , ~ ~ ~-4" 0'\ 0'\ N N In In In In ~ ~ ~ --- ... ... -0 - ;..., ... - ~
N~~~OOOOOOOOOOO- N N N ,... ,... ,... t"\ -.1- -.1- -.1- \0 \0 ,... ,...
,...0N
N0\ CC
, 0\ 0\ 0 ID , , , , a) a) a) 0\ 0\ 0\MIDID 0 0 MMM-4""""'" O\N MMO\"""""NNNNNNNNNMMM ~-~ ~
13
~ N
N\D~
,...0N
N~"-'
Chapter 2
BUILDING DESIGN METHODS
Four methods of seismic resistant design will be examined in this
These are applied to the design of a standard building anddissertation.
the results are tabulated for comparison.
The ATC 3-06 "Tentative Provisions for the Development of Seismic
Regulations for Buildings" and "The Recommended Seismic Resistant Design
Provisions for Guatemala and Algeria" will be referred to in this disser-
"Stanford Method, II respectively.tation as the "ATC 3 Method" and the
the Uniform Building Codes will be referred to as the "1976 UBC" and
"1976 UBC."
The ATC 3 Method is meant to establish design and construction cri-
teria for the buildings that are subject to earthquake motions in order to
minimize the hazard to life and improve the capability of essential facil1-
ties to function during and after an earthquake.
The design earthquake motions that are specified for this method have
been selected so that there is a low probability of their being exceeded
during the normal life expectancy of the building- Buildings which are
designed to resist these motions in conformance with the specified require-
ments may suffer damage, but should have a very low probability of collapse
due to seismic-induced ground shaking.
The Stanford Method was developed for the countries of Guatemala and
Algeria in order to fulfill those countries' special needs for seismic
design regulations for buildings. Special attention is given to the struc-
tural qualities of redundancey, plan symmetry, regularity, and construction
inspection which sets this method apart from other design methods or codes.
Having good structural qualities in a building will result in the design
14
force levels being near those of the 1913 UBC, whereas poor structural
qualities will cause the design force levels to be near. or even larger,
than those of the 1976 UBC.
The 1976 UBC was derived by expanding upon the 1973 UBC such that a
more stringent code with much higher design levels has resulted.
15
Chapter 3
THE ATC 3 METHOD
3.1 Symbols and Notation
The symbols and notation that are used in the ATC 3 Method are listed
below:
= The seismic coefficient representing the Effective Peak
Acceleration.Aa
= The seismic coefficient representing the Effective Peak
Velocity.Av
- The incremental factor related to P-delta effects.ad
= The deflection amplification factor as given in Table 3-3.Cd
c - The seismic design coefficient.s
The vertical distribution factor.
= The portion of the seismic base shear, V, induced at level
i, n, or x, respectively.F i ,F ,Fn x
= The acceleration due to gravityg
= The height above the base to level i, n, or x, respectively.hi,hn,h x
.i . 1- The building level referred to by the subscript i.designates the first level above the base.
1
k - The distribution coefficient.
= The overall length of the building (in feet) at the base
in the direction being analyzed.L
= The torsional moment resulting from the location of thebuilding masses.Mt
- The accidental torsional momentt:a
= Designates the level which is uppermost in the main por-
tion of the building.n
= The effect of dead load~= The effect of seismic (earthquake-induced) forces.
QB= The effect of live load
'L- The effect of snow load.
Qs
16
R - The seismic response modification coefficient as given
in Table 3-3.
s = The seismic coefficient for the soil profile character-
istics of the site, as given in Table 3-4.
51.52.53. The Soil Profile Types.
T = The fundamental period of the building.
T = The approximate fundamental period of the building.a
v - The seismic shear force at any levelx
w - The total gravity load of the building.
w..w.w = The portion of W which is located at or assigned to levelJ. n x
i, n, or x. respectively.
- The level under consideration.
level above the base.
x x = 1 designates the first
4 = The design story drift
A - The allowable story drift.a
~ z The deflection at level x.x
a = The deflection at level x, determined by an elastic analysisxe
e . The stability coefficient for P-delta effects
Seismic Performance
Seismic performance is a measure of the amount of protection provided
to the public against potential hazards resulting from the effects of
building response to earthquake ground motions
A Seismicity Index and a Seismic Hazard Exposure Group are used in
assigning buildings to the proper Seismic Performance Category. The
Seismicity Indices range from 4 down to 1, where 4 is associated with the
most severe ground shaking. The Seismic Hazard Exposure Group classifi-
cation is from III down to I, where group III is associated with uses
requiring the greatest level of protection. The Seismic Performance
Categories range from D down to A, where category D is assigned to pro-
the highest level of design criteria.
1.7
The Seismicity Index is obtained from the design ground motion which
is defined in terms of Effective Peak Acceleration or Effective Peak
These parameters are represented by the two coefficients AVelocity. a
The geographical area of concern in this disserta-and A , respectively.vFrom the maps included with the ATC 3is the San Francisco Bay area.
* it is found that San Francisco county as well as most of the sur-Method
and A coefficientsrounding counties are map area 7 for both the Aa v
From Table 3-1 the coefficients are obtained:
-0.4Aa
- 0.4Av
Seismicity Index = 4
All buildings are assigned to one of the three Seismic Hazard Per-
formance Groups.
Seismdc Hazard Exposure Group III is for buildings1. Group Ill.
which contain essential facilities necessary for post-earthquake recovery.
These buildings and essential facilities which include mechanical equip-
and related systems must have the capability to function during and
immediately after an earthquake.
Fire stations. PoliceExamples of possible Group III facilities:
facilities, structures housing medical facilities capable of surgery and
emergency treatment, emergency preparedness centers, and power stations
or other emergency back-up facilities.
Seismic Hazard Exposure Group II contains buildings2. Group II.
that have a large number of occupants or buildings in which the occupants'
movements are restricted or their mobility is impaired.
*Due to their large size. it is impractical to reproduce these maps;
however. they are contained in Reference 1.
18
Table 3-1
Seismicity IndexCoefficient ACoefficient AMap Area va
0.40 40.407
40.30O!JO6
40.200.205
30.150.154
20.103 0.10
20.050.052
0.050.051
*Table I-B of Reference 1.
19
Examples of possible Group II facilities: Public assembly for 100
persons or more~ open air stands for 2000 persons or more~ day care cen-
ters, schools, shopping centers with covered malls and over 30,000 square
feet, offices over four stories in height or more than 10,000 square feet
per floor, hotels over four stories in height, hospital facilities other
than those of Group III, and factories over four stories in height.
3. Group I. Seismic Hazard Exposure Group I is composed of all
buildings that are not in Group II or III
4. Protected Access. Buildings that are sssigned to Seismic Hazard
Exposure Group III must be accessible both during and after an earthquake.
Where access 1s through another structure, that structure must conform
to the requirements of Group III. Where access is within ten feet of
side property lines, protection against potential falling hazards from
the adjacent property must be provided.
5. Multiple Use. Buildings having multiple uses must be assigned
the classification of the highest Seismic Hazard Exposure Group which
occupies fifteen percent or more of the total building area
The Seismic Performance Category is obtained from Table 3-2 and is
determined using both the Seismicity Index and the Seismic Hazard Exposure
The Seismic Performance Category determines the requirements forGroup.
design as discussed in Sections 3.3 and 3.6
3.3 Classification and Use of Framing Systems
Each building or portion of a building is classified as one of the
four types of framing systems which are: Bearing Wall, Building Frame
Each structural system is de-Moment Resisting Frame, and Dual System.
scribed in Table 3-3. Also from this table the Seismic Response Modifica-
tion Coefficient, R, and the Deflection Amplification Factor, Cd' are
obtained
20
Table 3-2
SEISMIC PERFORMANCE CATEGORY.
Seismic Hazard Exposure GroupSeismicity
IndexIII II I
c4 D c
B3 c c
2 BB B
1 A A A
'itTable I-A of Reference I.
21
Table 3-3
STRUCTURAL SYSTFJfS AND RELATED COEFFICIENTS.
VertlCl1 Sels~fc CoefflcfentsTvoe of Str'UCtur.1 Snte8 Resfstl~ Sn*..L ...f4-
BEARING WALL SYSTEM: A structura1 syst88 with Light framed wa11sbearing wa11s providing support for 111. or with shHr ~ne1s fiAt 4-.jor portions of. the vertlCl1 10.ds.
Sels.ic force resistance Is provided Shear wl11sby shear wa11s or braced fr~s. Reinforced concrete 4~ 4
Reinforced masonry]a. J
Brac~fr_es 4 ~ -
Unreinforced andpartfl11y reinforcedNSonry shear w.11s 1~ 1~
Lfght framed w.11swfth ShHr pane1s 7 '.
Shear wa11sReinforced concrete St 5Reinforced NSOnry 4It 4
Braced frames 5 4It
Urrefnforced andplrtia11y reinforced
-~- - Masonry sh~r wl11s 1~ 1..
Specf.1 ~nt f~sStee1 B litReinforced concr.te 7 I
r.~tnlry _nt f~sStee1 4ItReinforced concr.te 2 -Shear wl11sReinforced concrete 8 91Reinforced masonry 6~ SIt
J: Wood sheathed shear
Plne1s,j Brlced fra~s
BUILDING fRAHE SYSTEM: A structural sYSte8with .n essenti.lly c~lete Space fr-providing support for vertical loads.
Sei~ic force resistance is provided byshe.r walls or braced frames.
4".
--- -- -
MOMENT RESISTING FRAME SYSTEM: A structuralsys~ with in essentti11y ~lete SpiceFr- providt"9 support for ftrttcal 10ads.
Set~ic force resistance ts provided byOrdinary or Specii1 IbIIent Frl.s Cipableof resisting the toti1 prescribed fOrces. 4
2
5
,
OOAl SYSTEI4: A structur.l systen with .nessenti.lly ~Iete S~ce Fr.. providingsupport for vertical lo.ds.
A Speci.1 Moment FraMe shall be provide<which s~ll be cipable of resisting it least25 pe~ent of tile prescribed sef_ic forces.The totil seis.fc fo~e resis~nce is providedby the combination of the Special ItINnt FraN.nd shHr walls or bricld fr_s in proport i onto their relative rigidities. INVERTED PEHDULUH STRUCTURES. Structures
where the fr.fng resisting the totil prescribedsei_ic forces .cts essenti.lly.s isolitedc.ntflevers and provides support for vertic.lload.
Specfa1 ~nt Fr_sStructurl1 s tee 1 2.. ZItReinforced concrete 2\ ~
Ordf nary ftlment Fr..sStructura1 stee1 1~ 1\
*Table 3-8 of Reference 1
22
Where combinations of framing systems are incorporated into the same
building the R value in any direction and at any level does not exceed
the lowest R value obtained from Table 3-3 for the lateral force resistin8
system, in the direction considered
Any type of framing system may be used for buildings assigned to
Seismic Performance Categories A and B. Those buildings of Seismic Per-
formance Category C must conform to the requirements of Category B in
addition to the following requirements:
Seismic Resisting systems in buildings over one hundred sixty feet
in height must be designed with one of the framing systems listed below:
Special moment resisting frames which are defined as onea.
hundred percent moment resisting.
b. Dual fraIlling system
c. A system with structural steel or cast in place concrete
braced frames or shear walls which are so arranged that the
braced frames or shear walls in any plane resist no more than
~hirty three percent of the seismic design force including
torsional effects. This is limited to buildings not over two
hundred and forty feet in height
Moment resisting space frames which are adjoined by more rigid
elements not considered to be p"art of the seismic resisting system must
be designed such that the action or failure of the nonstructural elements
will not impair either the vertical or lateral load carrying capability
of the space frame
All structural elements that are not part of the lateral force
resisting system must be adequate for vertical load carrying capability
and the induced moments which result from the design story drift.
23
A special moment resisting frame that is used but is not re-
quired by these provisions may be discontinued and supported by a more
rigid system with a lower R value. However, the potential adverse effects
of adjacent stories with different strengths must be considered.
When a special moment resisting frame is required in these
provisions it must go all the way to the ground
Buildings of Seismic Performance Category D conform to the require-
ments of Category C except that the height limitations of Category Care
reduced from one hundred sixty feet to one hundred feet and from two
hundred forty feet to one hundred sixty feet
3.4 Site Eft~cts
The effects of site conditions on building response is established
based on soil profile types that are defined as follows:
Soil Profile Type 81 is given to rock of any characteristic with a
shear wave velocity greater than 2500 feet per second or where stable
deposits less than 200 feet thick of sand, gravel, or stiff clay are
overlying rock.
Soil Profile Type 52 is a profile with deep cohesion1ess or stiff
clay conditions including stable deposits of sand, gravel, or stiff clay
more than 200 feet thick overlying rock.
Soil Profile Type S3 is a profile with soft to medium stiff clays
and sands 30 or more feet thick with or without intervening layers of
sand or other cohesionless soils.
Site locations where soil properties are not known or do not fit
into any of the three categories use Soil Profile Type S2.
The Soil Profile Coefficient S is obtained from the appropriate
Soil Profile Typ~ in Table 3-4.
24
Table 3-4
SOIL PROFILE COEFFICIENT*
Soil Profile Type
51 82 53
s 1.0 1.2 1.5
*Tabel 3-A of Reference 1
25
B~ilding Configurations
For the purposes of seismic design, buildings are classified as either
regular or irregular structures, depending upon both the plan and vertical
When the geometry is nearly symmetrical and when the cen-configuration.
ter of mass and center of rigidity are nearly coincident, the building
is considered regular
A building is considered irregular when:
The building does not have an approximately symmetrical geo-(1)
metric shape, has re-entrant corners with significant dimensions in plan,
or has horizontal offsets with substantial dimensions in elevation.
(2) If the diaphragm at any level has significant changes in
strength or stiffness.
If the mass stiffness ratio between adjacent stories varies(3)
significantly.
Regular and Irregular Structures
Buildings of Seismic Performance Category At whether regular or ir-
regular, need not be analyzed for seismic loading. Regular structures
classified in Category B, C, or D must, as a minimum, be designed in
accordance with the procedures of the ATC 3 Method.
Irregular structures of Seismic Performance Categroy B are designed
However, those irregular structures ofthe same as regular struct~res.
Cetegories C and D must be analyzed with special consideration for the
dynamic characteristics of the building.
3.7 Load Combinations
Gravity and seismic loads are combined in accordance with formula
3-1 or as applicable 3-2 or 3-3.
(3-1)Combination of Load Effects - l.2~ + 1.OQL + 1.OQS t 1.OQE
26
Combination of Load Effects. O.8QD t 1.OQE (3-2)
When there are partial penetration welded steel column splices or un-
reinforced masonry and other brittle materials9 systems 9 and connections:
Combination of Load Effects. O.5QD:t 1.OQE (3-3)
where: QD = The effect of dead load.
QL = The effect of live load.
QE - The effect of seismic (earthquake-induced) forces.
Qs - The effect of snow load.
3.8 Orthogonal Effects
Each building must be designed to resist one hundred percent of the
seismic forces in one direction» plus thirty percent of these forces in
the orthogonal direction. The combination requiring the maximum component
strength must be used
3.9 Inverted Pendulum-Type ~tructures
Traditionally~ an inverted pendulum-type system has meant a single
degree of freedom system that is hinged at the base. However, as used
in the ATC 3 Method, such a system is fixed at the base and models a
structure having a seismic resisting system that acts essentially as an
isolated cantilever. The supporting columns or piers of the inverted
pendulum-type structure must be designed for the bending moment calcu-
lated at the base, which is determined by the procedures set forth in
this chapter.
3.10 Deflection and Drift Limits
All portions of the building must be designed and constructed to
act as an integral unit in resisting seismic forces unless separated
27
structurally by a distance sufficient to avoid damaging contact under
deflection. The allowable story drift is obtained from Table 3-5.
3.11 Base Shear
Buildings, considered to be fixed at the base, must be designed to
resist the seismic base shear V in the direction being analyzed as deter-
mined by the formula:
v = c ws (3-4)
where: c = Seismic Design Coefficient.sW = the total gravity load of the building.
The weight W shall be taken equal to the total weight of the structure
and applicable portions of the other components including but not limited
to:
(1) Partitions and permanent equipment including operating contents.
(2) For storage and warehouse structures, a minimum of twenty per-
of the floor live load.
(3) The effective snow load
3.12 The Seismic Coefficient
The seismic coefficient for a structure can be calculated either
based on the period of the structure or calculated independent of period
When the seismic coefficient is dependent upon period the equation
used is:
I.2A Sv
-;;"273c (3-5)=
s
where: A - Effective Peak Velocity from Table 3-1.vS = Coefficient for the soil profile characteristics
of the site, as given in Table 3-4.
R - The Response Modification Factor, as given in
Table 3-3.28
Table 3-5
*ALLOWABLE STORY DRIFT, l:J.a
*Table 3-C of Reference 1.
29
T - The fundamental period of the building as deter-
mined in Section 3.13
When the period of the building is not calculated, the value of Cs
is determined by:
A(3-6)cs
= The seismic coefficient representing the EffectiveAwhere: a
Peak Acceleration, from Table 3-1.
is less than or equal to 0.30 and the soil profile typeHowever, when Aa
18S3' the following formula is used to calculate Cs:
~
(3-7)A
C. - 2.0 -f
obtained from Equation 3-5 need not exceed the value ofThe value of Cs
as determined by either Equations 3-6 or 3-7cs
Period Determination--3.13
The fundamental period of a building, T, may be determined based on
the properties of the seismic resisting system using methods of mechanics
This calculatedand assuming that the base of the building is fixed.
period need not exceed 1.2 times the approximate building period, T .a
The approximate period is dependent upon the type of structural
For moment-resisting structures where the frames are not adjoinedsystem.
by more rigid elements or otherwise prevented from deflecting when sub-
is:jected to seismic forces the equation for Ta
= C h 3/4Tn (3-8)Ta
where: Cr - 0.035 for steel frames
~. 0:025 for concrete frames.
= The height in feet above the base to the highesthnlevel of the building.
30
Fpr all other buildings:
O.OShn
"~2
~
(3-9)T .a
where: L = Overall length in feet of the building at the base
in the direction under consideration.
3.14 Di$tribution of Lateral Forces Alon t of the Structure
The induced lateral seismic shear force, Fx' at any level is deter-
aiDed by the following equation:
(3-10)F C- vvxx
where:
(3-11)c .c!lrc\.I;!'vx nL w h k
i-I i i
Wi' Wx z The weight of level i or x
hit h = The height above the base to level i or xxk = The period related exponent
In Equation 3-11, the exponent k is related to buildLng period. Building$
having a period of 0.5 seconds or les$ have a corresponding k value of t
When the period of a building is 2.5 seconds or more the k va:J.ue is 2
Interpolation is used in order to obta!n the k value when bu!lding period
is between 0.5 and 2.5 seconds
Horizontal Shear Distribution and Torsion3~ 15
Th~ seismic shear force at any level V is expressed as:x
nV - L F
ix i-I (3-12)
31
and associated torsional forces must be distributedThe shear force Vx
to the various vertical components of the seismic resisting system in the
story below level x in accordance with the relative stiffness of the
The design must provide for thevertical components and the diaphragm.
torsional moment Mt' which results when the center of mass and the center
of rigidity do not coincide, plus the accidental torsional moment, M .ta
Accidental torsion is assumed to be the story shear acting at an eccentri-
city of five percent of the base dimension in a direction perpendicular
to the applied forces.
StOry Drift Determination
The story drift, 6, is computed as the difference of the deflections,
The deflection0 , at the top and bottom of the story under consideration.x
0 is evaluated by the equationx
(3-13)0 - C 0x. d xe
Cd = The deflection amplification factor from Table 3-3.where:
= The deflection determined by an elastic analysisqxeusing the prescribed seismic design forces from
Section 3.14 and considering the building fixed
at the base
P-Delta Effect
P-Delta effects on story shears and moments, the resulting member
forces and moments, and the story drifts induced by these effects are not
considered when the stability coefficient e is less than or equal to 0.10
P 6xe - v h Cdx sx
(3-14)
32
6 = Design story drift.where:
= Seismic shear force acting between level x and x-I.vx
= Story height below level x.
n= r wi' which is the total gravity load at and above
i-x
bsx
px
level x
When e is greater than 0.10, the P-Delta Amplification factor ad is
computed:
(3-15)ead - (1 - e)
The coefficient ad takes into account the multiplier effect due to the
initial story drift leading to another increment of drift which leads to
2still another increment, etc. The resulting factor is 1 + e + e + ...
which is 1/(1 - 6) or (1 + ad) and is multiplied by the design story
The story sheardrift to give the drift including the P-Delta effect.
is multiplied by the factor (1 + ad) for that story to obtain thevx
new shears
33
Chapter 4
THE STANFORD METHOD
4.1 Symbols and Notation
The units used throughout the Stanford Method are kilograms, meters
The symbols and notations used in the codeor centimeters, and seconds.
are listed below:
= Zone Acceleration Value.A
- Structural Behavior factor from Table 4-2B
- Mean dynamic amplification factor from Figure 4-fD
- The dimension of the effective width of the lateral forceresisting system in a direction parallel to the applied
forces.
Ds
a1= Deflection at level i. relative to the base. due to applied
lateral forces, rfi"
= Lateral force applied to level i, n, or x, respectively"Fi ,F ,Fn x- Lateral forces on a part of the structure and in the
direction under consideration.Fp
- Lateral force on a diaphragm at level x.Fpx
- That portion of V considered concentrated at the top ofthe structure in addition to F .n
- Distributed portion of total distributed lateral forceat level i.
Ft
£1
- Acceleration due to gravity.g
- Height above the base to level i, x, or n, respectively.hi ,h ,h
x n
Level i - Level of the structure referred to by the subscript i.i-I designates the first level above the base.
= That level which is uppermost in the main portion of
the structure.Level n
That level which is under design consideration.designates the first level above the base.
x = 1Level x -
- The total number of stories above the base to level nN
- Quality factor from Table 4-3Q
34
T = Fundamental elastic period of vibration of the structureI
in seconds in the direction under consideration.
. The total lateral force or shear at the basev
w = The total dead load and applicable portions of o-ther
loads.
e That portion of W which is located at or is assigned to
level i or x, respectively.
w., W1 X
4-.2 Base Shear
Every structure must be designed and constructed to resist the mini-
mum total lateral force that may occur in the direction of each main
axis of the structure but assumed to act nonconcurrently. The equation
for the minimum total lateral force is:
(4-1)V=ADBQW
4.3 Zone Acceleration Value
The Zone Acceleration Value A is obtained from Table 4-1 and is
determined by the Use Group Classification and the seismic zone in which
the structure is located. The three Use Group Classifications are:
Use Group 1: Essential facilities necessary for life care and safety.
Use Group 2: Ordinary coumercial, residential, public assembly, and
industrial buildings that have not been included in
Use Groups 1 or 3
Use Group 3: Facilities which are relatively nonessential for public
safety.
The seismic zones which are given with this method as it was published
However, the seismic zones I, II, and IIIare not for this country.
divide an area into zones of different seismicity. Seismic Zone III is the
area where the expected effects of seismic activity would be the greatest
and Seismic Zone I is for areas where such effects would be the slightest.
35
Table 4-1
ZONE ACCELERATION VALUES.(Decimal Fraction of Gravity)
*Table C-l of Reference 2. Thesevalues are for the country ofGuatemala; however, they can beapplied to the San FranciscoBay Area, as explained in Section4.3.
36
4.4 Mean Dynamic Amplifica~!onF!ct2!
value of the Mean Dynamic Amplification Factor. D. is a function
of period and is obtained from Figure 4-1. The value D depends upon the
soil type for a site. The soil type is determined from the average value
of shear wave velocity by the equations:
-.{fv (4-2)8
and
(4-3)EG. 2(1 + v)
where: v = shear wave velocity (meters/second)s
2G = shear modulus (kg/cm )
p = soil density (kg/sec2/cm' l,..
v - Poisson's ratio
2E - Young's Modulus (kg/cm )
Firm soil requires Vs
aeters/second, whereas soft soil has a shear wave velocity between one
to be greater than or equal to six hundred
hundred fifty and six hundred meters/second. When V is less than ones
hundred fifty meters/second or when the structure is of Use Group 1, a
geotechnical investigation must be performed to determine the seismic
site response characteristics.
4.5 Building P!!:iod
The building period T can be determined from the structural proper-
ties and deformational characteristics of the resisting elements in a
properly substantiated analysis such as by the equation:
(4-4)
37
fi
where: = Any lateral force distributed approximately in
accordance with the lateral distribution of forceequations of the code
0i = The elastic deflection due to ft.
In the absence of a period determination such as the one above, T
may be determined by the equation:
O.O9hn
~
T~ (4-5)
where: h and D..[D:
are expressed in meters.sn
Buildings which have moment resisting space frames that are capable of
resisting one hundred percent of the required lateral forces and which are
not prevented from doing so by more..~igid adjoining elements may use the
following equation in evaluating the period:
T = 0.10 N (4-6)
S_tructural Behavior Factor
The Structural Behavior Factor B depends on the type of lateral
The structure type number, definitions and cor-force resisting system.
responding B values are given in Table 4-2
Quality Factor
The quality factorQ for the lateral force resisting system of a
given building is a function of the system redundancy, plan symmetry,
elevation regularity, and construction quality control. The value of Q
is determined by the equation:
5r
q-l(4-7)o~ +
Pq
where: Pq is the penalty increment which depends upon whetheror not the structure meets a given quality criterion q
39
Table 4-2
STRUCTURAL TYPES AND BEHAVIOR FACTOR B*
Type or Arrangement of Lateral ForceResisting Elements
Valueof B
TypeNumber
16
1. Buildings with a ductile moment resisting space framedesigned with the capacity to resist the total re-quired lateral force. This frame must be capable ofcarrying all the weight of the structure togetherwith the entire design lateral load after it has beensubjected to deformations well beyond the yield pointdefQrmations of the structural members.
Buildings with a dual bracing system consisting of aductile moment resisting space frame and ductile shearwalls or braced frames designed in accordance with thefollowing criteria:
15
2.
a. The frame and shear walls or braced frames shallresist the total lateral force in accordance withtheir relative rigidities considering the interactionof the shear walls and frames.b. The shear walls or braced frames shall resist thetotal required lateral force.c. The ductile moment resisting space frame shallhave the capacity to resist not less than 25 percentof the required lateral force and carry the weight ofthe structure after the primary lateral bracing isdeformed well beyond its yield point deformation.
Buildings not greater than 5 stories in height with astructural steel moment resisting space frame thatdoes not necessarily satisfy the compact section re-quirement for a ductile moment resisting steel frame(type 1). The frame must, however, satisfy all otherrequirements for the type 1 system.
1'4
3.
1"4
4. Buildings not greater than 10 stories in height with aspace frame that is laterally supported by shear wallsor braced frames designed with the capacity to resistthe total required lateral force.EXCEPTION: If failure of the shear wall or bracedframe lateral force resisting system could result inthe loss of the vertical load carrying stability ofthe- space frame, the building will be classified asa type 5 Box System. The vertical supporting membersmust have the capacity to carry the weight of thestructure at deformations well beyond the yield pointdeformation of the lateral bracing system.
(Continued)
*Table C-2 of References 2 and 3.
40
Table 4-2 (Continued)
TypeNumber
Type or Arrangement of Lateral ForceResisting Elements
Valueof B
5. 13
Buildings less than 10 stories in height with a BoxSystem (i.e.. a structural system without a completevertical load carrying space frame) laterally supportedby shear walls or braced frames. The lateral bracingsystem is such that collapse may occur if the bracingsystem fails.
6. 1Z
Other Concrete Structural Systems for Buildings. All ,I
concrete sections must carry the lateral forces and theweight of the structure with concrete strain values lessthan 0.003. All elements supporting vertical load suchthat their failure would result in collapse shall have
1)
2)
3)
Shear strength capacity necessary to support ver-tical loads and develop flexural yield capacity attheir ends.Beam-column joint shear strength capacity to supportflexural yield capacity of framing members underlateral load conditions.Confining reinforcement necessary to develop con-crete strain of at least 0.01.
7. Buildings not more than three stories in height with aBox System as described for Type 5, but with standard-ized brick masonry panels in confining frames of rein-forced concrete.
2""3"
41
The criteria and corresponding P values are given in Table 4-3. Theq
definitions of the criteria which establish P at a value of zero areq
listed below:
1 Frame Redundancy Line. The individual frame and/or wall line
in the direction of the applied lateral load must have the following
measures of redundancy in all stories:
At least three bays having a relative width ratioFrame System.a.
of not more than 1.5. The frame bays may contain shear walls.
At least one wall pier with a story height to widthb. Wall System.
ratio less than or equal to 0.67, or at least two piers with a
story height to width ratio less than or equal to 1.0. The piers
must extend over the full story height and cannot contain openings
of any kind that can significantly reduce the stiffness or strength
2. Plan Redundancy. The plan of each story must have at least
four lines of frames or walls in the direction of the applied lateral
load. These lines of bracing elements must be spaced with reasonable
symmetry where the ratio of maximum to minimum spacing does not exceed
1.5
3,. The eccentricity between the center of massPlan Sytmnetry.
supported by any story and its center of rigidity cannot exceed fifteen
percent of the effective building width measured normal to the direction
of the applied lateral load.
In any story, the translational stiffness4. Elevation Regularity.
in line with the applied lateral load and the total rotational stiffness
against plan torsion cannot change by more than fifteen percent from the
stiffness values for the adjacent upper and lower stories. The stiffness
values must remain nearly constant or gradually decrease with height.
42
Table 4-3
PENALTY VALUES, P *q
Pq Value
Criterionq MeetsCriterion
Does not meetCriterion
1 Frame line redundancy 0 0.1
2 0 0.1Plan Redundancy
3 0 0.1Plan Symmetry
4 Elevation Regularity 0 0.1
s 0 0.2Construction Quality Contro~
*Table C-3 of References 2 and 3.
43
5. Construction Quality Control. There must be a provision within
the contract for the performance of inspection at the important stages
Theduring construction. inspection must be done under the direct super-
vision of a responsible design engineer. Material testing must be
in cases where dependable levels of quality are necessary for structural
performance.
4.8 Structural Weight
The structural weight W is the total dead load and applicable por-
tions of the other loads such as: Partitions, permanent equipment, and
for warehouses and storage areas a minimum of twenty five percent of the
live load must be included.
4.9 Load Combinations
The seismic forces and specified vertical load combinations as given
in Equations 4-8,4-9, and 4-10 must be resisted by member capacities
based on ultimate strength design for concrete and the equivalent of
ultimate strength design for steel, wood, and masonry.
U-D+L+E
U = a.8CD 't E)
U - 1.7(D + L) (4-10)
where: U = Elements strength requirement
D - Dead load effect on the element
L - Live load effect on the element
E = Seismic effect evaluated by using formula 4-1.
4.10 Distribution of Lateral Forces Along the Height of the Structure
The total lateral force or base shear V is distributed over the
height of buildings classified as regular structures or as having regular
systems in the following manner
44
nV=F+E Ft 1-1 i (~1.l.)
The concentrated force at the top, Ft' is found by;
Ft=O.O7TV (4-12)
However, Ft need not exceed O.25V and may be considered zero when T is
less than or equal to 0.7 seconds. The remaining portion of the base
shear is distributed over the height of the structure including the top
level as follows:
F (4-13)x nr w hi-I i i
4.11 Building Setba,c!.! and Irregu!a~ ~b!pes
Buildings having setbacks where the plan dimension of the tower is
at least seventy five percent of the corresponding plan dimension of the
lower part may be considered as uniform buildings without setbacks, pro-
viding that no other irregularities exist
The distribution of lateral force, in structures having irregular
shapes, large differences in lateral resistance or stiffnesses between
stories, or other unusual structural features must be determined using
or considering the dynamic characteristics of the structure.
4.12 Horizontal Shear Distribution and Torsion
The total shear in any horizontal plane shall be distributed to the
various elements of the lateral force resisting system in proportion to
their rigidities. Rigid elements that are assumed Qot to be part of the
lateral force resisting system may be inco~orated into the building
theirprovided that effect is considered in the destgn.
45
Horizontal torsional moments due to an eccentricity between the center
of mass and the center of rigidity result in additional shear forces that
must be accounted for in the design. Negative torsional shears are neg-
lected. In the case where the vertical resisting elements depend upon
diaphragm action to transfer the shear forces, the vertical elements must
be capable of resisting the total story shear force acting at a minimum
eccentricity of five percent of the maximum building dimension at that
level.
Drift and Building Separations
Lateral deflection, or drift ~f a story relative to its adjacent
stories is not to exceed 0.01 times the story height unless it is shown
The displacement calculated from thethat greater drift can be tolerated.
application of the required lateral forces must be multiplied by (1.O/2B)
This ratio shall not be less than 1..0..to obtain the drift.
All portions of a structure must be designed and constructed to act
as an integral unit in resisting the horizontal forces unless separated
structurally by a distance that is sufficient to avoid contact due to
deflection from seiSmic action or wind forces.
Structural Systems
Buildings designed with a structural behavior factor of B - 1/6
1/5 must have ductile moment resisting space frames. In zones of
high seismicity buildings more than ten stories tall must have ductile
moment resisting space frames capable of resisting at least twenty five
percent of the seismic force for the whole structure. All concrete space
frames required to be part of the lateral force resisting system and all
concrete frames located in the perimeter line of the vertical support must
be ductile moment resisting space frames.
46
All framing elements that are not part of the lateral force resisting
system must be adequate to withstand the vertical load and the induced
moment due to (I.O/B) times the distortion that results from the applica-
tion of the required lateral forces.
Moment resisting space frames may be adjoined by more rigid elements
that prevent the space frame from resisting the lateral load provided
that the failure of the rigid elements do not impair the resisting ability
of the space frame either laterally or vertically.
47
Chapter 5
THE 1976 UNIFORM BUILDING CODE
5.1 Earthquake Regulations
Every building or structure and every portion thereof must be designed
and constructed to resist stresses produced by lateral forces as discussed
The lateral forces are assumed to come from any direc-in this section.
tion and are applied at each floor or roof level above the base.
When wind loading produces higher stress levels, these shall be
Wind and earthquake loads need not beused instead of earthquake loads.
assumed to act simultaneously.
All allowable stresses and soil bearing values specified for working
stress design may be increased by one third when wind or earthquake forces
are either acting alone or when combined with vertical loads.
5.2 Symbols and Notations
The following symbols and notations are used in this code
- The dimension of the structure in feet in 8 directionparallel to the applied forces.
D
- Deflections at levels i and n, respectively, relativeto the base, due to applied lateral forces.Si,Sn
- Lateral force applied to levels i, n, or x, respectively.Fi ,F ,Fn x
= Lateral forces on a part of the structure and in the
direction under consideration.F
p
= That portion of V considered concentrated at the top ofthe structure in addition to F .Ft
n
- Acceleration due to gravity.g
h i ,h ,hn x= Height in feet above the base to levels i, n, or x,
respectively.
= Occupancy Importance Factor
= Numerical Coefficient from Table 5-1K
48
i = 1 designates the firstLevel i . The level of the structure.
level above the base.
. That level which is uppermost in the main portion of
the structure.
Leve 1 n
- That level which is under design consideration.Level x
- The total number of stories above the base to level n.N
s - Numerical coefficient for site-structure resonance.
- The fundamental elastic period of vibration of the buildingor structure in seconds in the direction under consideration
T
= The total lateral force or shear at the basev
- The total dead load of the structure, including the par-
tition loading where applicable.w
- That portion of W which is located at or is assigned to
levels i or x, respectively.Wi'wx
- Numerical coefficient dependent upon the zone as deter-mined from Figure 5-1.
z
S.3 Base Shear
Every structure must be designed and constructed to resist minimum
total lateral seismic forces which are assumed to act nonconcurrently,
The totalin the direction of each of the main axes of the structure.
lateral seismic force or base shear V is expressed as:
(5-1)V= ZKICSW
Z = The seismic zone coefficient from Figure 5-1.where:
K = Horizontal Force Factor from Table 5-1
S = The site-structure resonance coefficient and is
determined from the building period T and the site
characteristic period T .s
49
Figure 5-1
SEISMIC ZONE M.APS*
*Figures 1, 2, and 3 of Reference 4
50
Table 5-1
HORIZONTAL FORCE FAC'l'OR, K*
*Table 23-1 of Reference 4
51
Table 5-2
OCCUPANCY DofiJORTANCE FACTOR, r*
*Table 23-K of Reference 4.
52
TFot 1.0 or less
T s
T , T 12S - 1.0 + r - 0.5 Fs s
TFor ~ greater than 1.0s
s .
more than 2.5 seconds. When T is not properly established, the values
of S is taken as 1.5. The value of the product CS need not exceed 0.14.
5.4 Building Per!od
The building period T can be established from the structural pro-
perties and the deformational characteristics of the resisting elements.
One properly substantiated formula for this is:
I ( n n-1 '
JT = 2~1V\i:1 wiSi' ~ 8 i:1 FiSi + (Ft + Fn)Sn
In the absence of the period as determined above, T may be taken as:
O.OShn
.JD
~
T . (5-6)
Or in buildings where the lateral force resisting system consists of
ductile moment resisting space frames capable of carrying one hundred
percent of the lateral load and such a system is not prevented from
resisting the lateral forces by more rigid elements in the building. T
may be used as:
T - O.lON
53
Dtstribution of Lateral Forces Along the Height of the Structure
Buildings with regular shapes or framing systems have the total
lateral force distributed over the height of the structure as follows:
nV - Ft + 1: Fi
i-I(5-8)
The concentrated force at the top, Ft' is:
(5-9)Ft - O.O7TV
Ft does not exceed 0.25V and may be considered zero when T is 0.7 seconds
The remaining portion of the base shear is distributed to eachor less.
floor level as:
(V - Ft )w hx x (5-10)F .10. ,.'~ ,- .x n
r w h1-1 1 x
Setbacks and Irregular Structures
Buildings having setbacks of Which the plan dimension of the tower
in each direction is at least seventy five"percent of the corresponding
dimension of the lower part of the building can be considered to
be regular structures with no setbacks.
Structures which have highly irregular shapes, large differences in
lateral resistance or stiffness between adjacent stories or other unusual
structural features must be analyzed utilizing the dynamic characteristics
of the structure in order to determine the distribution of lateral forces.
Distribution of Horizontal Shear
Total shear in any horizontal plane is distributed to the various
elements of the lateral force resisting system in proportion to their
Rigid elements that are not considered to be part of therigidities.
54
lateral force resisting system may be incorporated into buildings provided
their effect on the action of the system is considered and provided
for in the design.
~o~1zontal Torsional Moments
Provisions must be made for the shear forces that result from tor-
sional moments due to an eccentricity between the center of mass and the
center of rigidity. Negative torsional shears are neglected. When ver-
tical resisting elements depend on diaphragm action t.o di8tribute the
shear at any level, the shear resisting elements must be capable of re-
sisting a torsional moment which is assumed to be the story shear acting
at an eccentricity of not less than five percent of the maximum building
dimension at that level
Building Drift an~ SeE!!:ations
Drift of a story relative to adjacent stories cannot exceed 0.005
times the story height unless it can be demonstrated that greater drift
can be tolerated. Displacements calculated from the application of the
required lateral forces is multiplied by (l.O/K) to obtain the drift
The ratio (1.0/K) shall not be less than 1.0
All portions of a structure must be designed to act as one unit in
resisting horizontal forces unless separated structurally by a distance
sufficient to avoid contact under deflection from earthquake or wind
forces.
Structural Systems
All buildings designed with a K factor of 0.67 or 0.80 must have
ductile moment resisting space frames. Buildings more than one hundred
sixty feet in height must have ductile moment resisting space frames
capable of resisting not less than twenty five percent of the required
55
seismic force for the structure as a whole. However, in seismic zone 1,
buildings more than one hundred sixty feet high may have concrete shear
walls in lieu of a ductile moment resisting space frame system, provided
that the K factor assigned is 1.00 or 1.33. In seismic zones 2,3, and
4 all concrete space frames required by design to be part of the lateral
force resisting system and all concrete frames located in the perimeter
line of the vertical support are required to be ductile moment resisting
space frames. The framing elements that are not required to be part of
the lateral force resisting system of buildings in seismic zones 2, 3
and 4 must be adequate for vertical load carrying capacity and the induced
moment due to (3/K) times the distortions resulting from the required
lateral forces.
5.11 Load Combinations
In computing the effect of seismic force in combination with ver-
tical loads, gravity load stresses which are induced by dead load plus
design live load, except roof live load, must be considered. Minimum
gravity loads must also be considered acting in combination with lateral
forces.
5.12 Essential Facilities
Essential facilities are those structures or buildings which must be
safe and operational for emergency purposes after an earthquake in order
to preserve the health and safety of the general public. Examples of
essential facilities are listed below:
1. Hospitals and other medical facilities having surgery or emer-
gency treatment areas.
2. Fire and police stations.
3. Municipal government disaster operation and communications centers.
56
Chapter 6
THE 1973 UNIFORM BUILDING CODE
6.1 Symbols and Notation
c = Numerical coefficient for base shear.
D = The dimension of the building in feet in the direction
parallel to the applied forces.
= Plan dimension of the vertical lateral force resisting
system in feet.Ds
Fi .F .Fn x- Lateral forces applied to a level i, n, or x, respectively.
= That portion of V considered concentrated at the top of
the structure at level n.Ft
- Horizontal force factor from Table 6-1K
Level i = Level of the structure referred to by the subscript i
- That level which is uppermost in the main portion of
the structure.Level n
Level x - That level which is under design consideration.
- Total number of stories above grade to level D.N
- The fundamental period of vibration of the structure inseconds in the direction considered.
T
- The total dead load including partitions.w
= That portion of W which is located at or is assigned to
the level designated i or x, respectively.Wi'wx
6.2 Base Shear
Base shear is expressed as:
(6-1)V= KCW
The factor C in Equation 6-1 is determined by:
0.05
;IT(6-2)c =
57
Table 6-
HORIZONTAL FORCE FACTOR, K*
Value of KType or Arangement of Resisting Elements
All building framing systems except as hereinafterclassifiedl 1.00
1.33Buildings with a box system
0.80
Buildings with a dual bracing system consisting of aductile moment-resisting space frame and shear wallsor vertical bracing frames designed in accordance withthe following criteria:
1. The frame and shear walls or vertical bracingframes shall resist the total lateral force inaccordance with their relative regidities con-sidering the interaction of the shear walls.or vertical bracing frames. and frame.
2. The shear walls or vertical bracing frames act-ing independently of the ductile moment-resistingspace frame shall resist the total requiredlateral force.
3. The ductile moment-resisting space frame shallhave the capacity to resist not less than 25%of the required lateral force.
Buildings with a ductile moment-resisting space framedesigned in accordance with the following criteria:The ductile moment-resisting space frame shall havethe capacity to resist the total required lateralforce.
0.67
Elevated tanks plus full contents on four or morecross-braced columns and not supported by a building 2 3.00
Structures other than buildings and other than thoseset forth in Chapter 23 of Reference 5. 2.00
*Table 23-H of Reference 5.1A Horizontal Force Factor K - 1.0 shall be used only for buildings where
failure of shear walls would not endanger the vertical load carryingcapacity of the structure. For other shear wall buildings, K - 1.33shall apply.
2The minimum value of KC ahall be 0.12 and the maximum value of KC neednot exceed 0.25.
58
For all one and two story structures the value of C cannot be less
than 0.10. All other structures must have a C value not exceeding 0.10.
Structures with a highly irregular shape, or large differences in lateral
resistance or stiffness between different stories or other unusual struc-
tural features must be designed considering the dynamic properties of
the structure.
The fundamental period of a building, T, is expressed as:
O.O5hnT. (6-3)
..Jii'
Lateral force resisting systems consisting of one hundred percent moment
resisting frames that are not prevented from resisting the lateral load
by more rigid elements which adjoin the frame result in a building's
period being determined by:
T - 0.10 N (6-4)
6.3 Diatr:1bution of Lateral Forces Along the Height of the Structure
The total base shear is distributed over the height of a building
by the formula:
(6-5)
. 0.004 V[~ 2(6-6)Ft
The value of Ft need not exceed O.15V and it may be assumed that Ft - 0
when (~/Ds) is 3 or less.
The above application is valid except for one and two story structures
which shall have a uniform distribution of lateral forces over the height.
59
Distribution of Horizontal Shear-- -
The total shear in any horitontal plane is distributed to the elements
of the lateral force resisting system in proportion to their rigidities
at the same time considering the rigidity of the diaphragm. Rigid elements
are not part of the lateral force resisting system may be utilized
provided that their effect on the action of the system is considered and
provided for in the design.
Horizontal Torsional Moments
Provisions must be made for the increase in shear which results from
the horizontal torsion due to an eccentrictiy between the center of mass
Negative torsional shears are neglected.and the center of rigidity.
When vertical resisting elements depend on diaphragm action for shear
distribution at any level, the shear resisting elements shall be capable
of resisting a torsional moment equivalent to the story shear acting with
an eccentricity of not less than five percent of the maximum building.d~en8ion at that level.
Setbacks
Buildings having setbacks in which the plan dimension in each direc-
tion at the setback is at least seventy five percent of the corresponding
dimension of the lower part of the structure may be considered
regular structures with no setbacks.
Buildings with irregularities that are classified as setbacks must
be designed differently. The portion that is set back or the tower as
it is referred to, is designed as a separate building. The resulting
total shear from the tower is applied to the top of the lower part of
the building which is then considered separately for its own height,
60
Structural Systems
All of the frames that are required to be part of the lateral force
resisting system must be ductile moment resisting frames. Buildings which
are greater than 160 feet in height must have a ductile moment resisting
space frame system that is capable of resisting at least twenty five
percent of the required lateral load for the structure as a whole. If
the building is more than three hundred twenty feet ti\ll, the frame must
consist of structural steel
All framing elements that are not required by design to be part of
the lateral force resisting system must be adequate for vertical load
carrying capacity when deflected a total of four times that which results
from the application of the required lateral forces
Moment resisting frames may be adjoined by more rigid elements that
tend to prevent the frame from resisting the lateral load where it can be
shown that failure of the more rigid element will not impair the vertical
or lateral load resisting ability of the frame
Drift and Building. Separatione
Lateral deflections, or drift of a story relative to adjacent stories
shall be considered in accordance with accepted engineering practice.
All portions of a structure must be designed and constructed to act
as a single unit in resisting the horizontal forces unless structurally
separated by a distance sufficient to avoid contact under deflection due
to seismic action or wind forces.
61
Chapter 7
THE BUILDING DESIGN
7.1 Introduction
The building chosen to be designed for this dissertstion was the
fifteen story ductile moment resisting steel frame from the Seismology
Committee's set of standard buildings. The building is symmetric in plan
with four frames in each major axis direction at intervals of thirty
feet. The overall base dimensions are ninety by ninety feet and the story
height is twelve feet six inches. Two beams within each bay transfer the
floor load to the girders. The floor beams, which are simply supported,
run only in the North-South direction and therefore rest on the girders
of the East-West frames. Box sections were chosen for the columns in
order to make the structure perfectly symmetric. All girder to column
Figure 7-1 pre-connections are one hundred percent moment resisting.
sents a typical plan and elevation view of the building.
The structure is assumed to be an office building located in the
San Francisco Bay Area. There are no structural interferences from any
parts such as elevators, stair towers, interior or exterior walls.
The San Francisco firm, GKT Consulting Engineers, donated computer
time and the computer program BATS, a modified version of the more well
known TABS, with which a static load analysis on the building was performed.
Computer output results were used to confirm that proper member sizes
had been chosen.
The building was designed using the procedures of the ATC 3 Method
which are discussed in the following sections. This ATC 3 design was
used as a standard and then Chapter 8 compares the results of this design
with the results of designs obtained from the other methods.
62
Seismicity of the Area2
The fifteen story office building is located in the San Francisco
and AThis location determines the two coefficients A asBay Area. va
well as the Seismicity Index.
- 0.4Aa
- 0.4Av
with a resulting Seismicity Index = 4
7.3 Base Shear
The ATC 3 Method gives the option of calculating the base shear
either based on building period or independent of building period. When
computed based on period:
5%(W)
and independent of period:
v - 12.5%(W)
Obviously there is a substantial difference between the two methods.
Calculations have been carried out using both values of base shear for
However, upon choosing girder member sizes itcomparative purposes.
becomes quite evident that 12.5%(W) is too large a value for base shear
and would not normally be used in practice for structures above three
The resulting values for the two base shears are:stories.
5% (W) = 640 K12.5%(W) = 1600 K
From this point on only the base shear of 5%(W) is considered..
The dis-
tribution of the base shear over the height of the building is shown for
comparison with the other design methods in Table 8-3 and Figure 8-1.
64
It was assumed that the interior frames resisted twice as much of
the lateral load as the exterior frames. However, the additional load
caused by accidental torsion was carried entirely by the exterior frames.
The accidental torsion was calculated to be O.lV. The resulting dis-
tribution of base shear to the individual frames is thirty three percent
to each interior frame and twenty seven percent to each exterior frame.
This is shown in Table 7-1.
7.4 Dead and Live Load
From the story masses listed in Table 1-1, an average dead load was
The buildingcalculated to be one hundred and five pounds per square foot.
contains offices which are assumed to have a live load of fifty pounds
per square foot and corridors which are generally designed for one hun-
As a conservative measure, a uniform livedred pounds per square foot.
load of seventy five pounds per square foot was used for the total floor
These results were compared to calculations that were based on a
*
area.
and at the point of choosinglive load of fifty pounds per suqare foot,
girder member sizes little or no difference was noticed.
7.S Fixed End Moments
The ends of each girder were assumed to be fixed. Moments were
calculated based on tributary area of the member and for the East-West
girders, the point loads due to the simply supported floor beams.
7.6 Portal Frame Analysis and Member Sizing
The portal method of frame analysis was used to compute column and
girder moments due to the lateral load. Assumptions of this method are
that the interior columns take twice as much shear as the exterior columns
and that the interior columns have no axial load.
*These calculations were done by Hratch H. Kouyoumdj ian of GKTConsulting Engineers.
65
Table 7-1
ACCIDENTAL TORS ION
~ - Torsional Moment
Hr is taken by the outer frame45 feet from the center
~ = ~ = O.IV at the outerframe
-L O.IV
45'
Typical Plan
USEV
!roT
0.17 V
VT
7Frames
0.21 VA and 1
0.33 V0.33 V0Band 2
0.33 V0.33 V0C and 3
0.27 V0.27 V+0.1 V
~Q1"6 v - O.l7V
2"6 v = O.33V
2"6 v z O.33V
1"6 v = O.l7VD and 4
66
Girder member sizes were selected based on these fixed end moments
in combination with vertical load moments as follows:
~ + 1.O~ + 1.O~ = ~
The ATC 3 Method allows a stress increase of 1.7 times the allowable
stress. Thus the quantity MTOT is divided by 1.7 to produce an allowable
moment MA. However, with guidance from the Seismology Committee it was
realized that, due to the combination of its height, structural system,
and configuration, this building would be governed by drift control re-
quirements. In order to control the inter-story drift the MA was increased
by one-third to bring it from the allowable to what is termed as an accept-
able design moment MACCEPT. From MACCEPT the girder member sizes were
chosen from the Allowable Stress Design Selection Table of the AISC Steel
In all cases the most economical section was selected.Construction Manual.
The column sizes were determined using the largest column moment
values which. indidently. occurred at the second story level. These
column moments received contributions from the lateral load and an assumed
twenty percent of the fixed end moments from girder dead and live loads
In addition to this design moment acting on the column, the ATC 3 Method
requires that thirty percent of this moment be applied simultaneously in
the orthogonal direction, along with the direct axial load effects.
Using the combined inter-action stress relationships in Section 1.6.1
of the AISC Specifications, it was determined that the column size should
be an eighteen by eighteen inch box-section made up of two and one half
inch thick plates
67
Chapter 8
CODE COMPARISON
Introduction
Having the building design, as completed by the ATC 3 Method as a
standard, the results were compared to designs of the same building done
according the the Stanford Method, the 1976 UBC and the 1973 UBC. The
procedures utilized in these other methods are similar to those of ATC 3
However, appropriate steps will beand will not be discussed in detail.
compared throughout the design process.
Base Shear
The different base shear equations and their values are shown for
Each equation is broken down in order to showcomparison in Table 8-1.
which variables are taken into account.
The equation used in the Stanford Method considers more factors
concerning the building qualities than do the other methods; thus, it is
able to deal with a wider variety of specific structures on a more accurate
One portion of the Stanford Method equation may pose a potentialbasis.
A component of the Quality Factor, Q, must judge the qualityproblem.
However, since this controlcontrol that will be performed on a job.
will occur after the design is completed, the designer must be able to
insure that the proper level of quality control will be available.
The Importance Factor of the ATC 3 Method is not directly included
However, this factor, termed the Seismicin the equation for base shear.
Hazard Exposure Group Classification, becomes incorporated into the design
when using the ATC 3 Method in determining the allowable story drift.
68
Table 8-1
COMPARISON or BASE SHEARS
'*628 K4.9%(W)ATC 3
692 K5.4%(W)Stanford Method
701 K5.5%(W)76 UBC
378 K3.0%(W)73 UBC
Factors
~~+'~
8
>-+'~.-IIU~
no
~4-J(/)>-
C/)
.4-J(J~1-44-J~
.~:3=
QJ,...:I~CJ:I,...~r"
I 00i , ~
gCo>
r
~~
I .-1-S-
OJ~0
N
CJ-rofSU)
-rofOJ
(/)
Formula GIt)
~~~
!
Code
~0
kQI
~
r"4~0
fI)
1.U Sv
-;;273wRATC 3 v s w A s T
v
wQ A B QSTANFORD, VzADBQW D DA
1 K ws c76 UBC v- ZICKSW z
K \'lcV=KCW73 UBC
*In the actual ATC 3 calculations the value of V = 4.9%(W) wasrounded off to V - 5%(W) or V - 640K.
69
Distribution of Lateral Forces Along the Height of the StTUcture
The manner in which the base shear is distributed over the height
of the building is shown for each method in Tables 8-2 and 8-3. All of
the methods distribute the lateral load as a function of the story mass
Since the top (roof) story is much lighter than the others,and height.
the special shape of the ATC 3 lateral force distribution is shown in
Figure 8-1, where the lateral load at the top is relatively small. However,
it should be noted that the distributions for the Stanford Method, the
1976 UBC» and the 1973 UBC all have an additional top story force which
Note that for the particularaffects the shape of their distributions.
building under consideration the distributions of the Stanford Method
The particular distribution ofand the 1976 UBC are nearly the same.
lateral forces by the ATC 3 Method varies exponentially with height where-
Except for theas the distributions by the other methods vary linearly.
top story, the 1973 UBC lateral force distribution is directly proportional
to the lateral force distribution of both the 1976 UBC and Stanford Method.
These differ by a factor of forty one percent as shown in Table 8-4.
Building Period
The building for this dissertation was designed with a structural
The buildingsystem made up of one hundred moment resisting steel frames.
period as calculated by the different methods is:
ATC 3 Method
3/4 T - O. 10 NT - 0.035 hn
T. 1.5 secondsT - 1.77 seconds
It is interesting to note that the method of calculating the building
period would have been the same for all four methods considered in this
70
Table 8-2
LATERAL LOAD DISTRIBUTION FORMULAE
w h kx xpoATC 3 Method ."'~,c'~'x n
I:i=1
L k
(V - Ft )w hx x po - O.O7TVtStanford Method and
1976 UBCP' .c"'"C~Cx n
t1-1
(v - Ft )w hx xFtF1973 UBC . .
x nt
1-1
71
Table 8-3
DISTRIBUTION OF LATERAL FORCES ALONG THE HEIGHTOF THE STRUCTURE
StanfordMethod
F
ATC 3Method
F
1976UBC
1973UBCLevel
xx
62 + 73* 63 + 74* 37 + 7*84R
74 4495 7315
69 41688414
3864637.513
3559586412
32545311 55
48 29484610
264343399
38 2231 378
193332247
27 1618 276
132222135
16 108 164
7111143
36512
*Ft
72
Figure 8-1
DISTRIBUTION OF LATERAL FORCES ALONG THE HEIGHT OF THE STRUCTURE
Lateral Force (kips)
75 50 25' 0100125ISO
~
>-~0~tn
~~~~~~~
13
Table 8-4
PROPORTION OF THE LATERAL FORCE DISTRIBUTION
(378K - 7K)(701K - 74K) 0.59.-;;~
(v:"Ft176
1 - 0.59 - 0.41
In percent. the 1973 UBC lateral force dis-tribution is forty one percent less thanthose of the 1976 UBC and the Stanford Method
74
dissertation provided that the structural system would have been other
than a one hundred percent moment resisting frame. It must be remembered
however, that metric units (meters) must be used in the equation from the
Stanford Method; however, the same results are obtained. The equations
are
Stanford Method
O.OShn
"\/D
O.O9hn
{D
~~
T -.
In order to compare the effects of period on base shear the equations
have been rewritten with T isolated in the denominator. The base shear
for each method is compared to base shear calculated with a ten percent
increase in period, as shown in Table 8-5.
The ATC 3 Method is the most sensitive to change in period with the
Stanford Method being nearly as sensitive. The 1973 UBC is the least
sensitive to period change.
8.5 Load Combinations .
The manner in which the gravity and seismic laods are combined, along
with any stress increases that are permitted for combinations with earth-
quake loads, will determine the required size of the members. The load
combinations that were used from each of the four methods are listed
below:
ATC 3 Method 1.2D + L + E
Stanford Method D+L
19'76 UBC D+L
1973 UBC D+L+E
(Note that E is different for each method)
75
Table 8-5
EFFECTS ON BASE SHEAR DUE TO INCREASED PERIOD
l:.:!:. ~ s w
!v = 2/3T
2/3 - 1.46
TATC 3 Method
*v = 2V0:3 ABQW
~Stanford Method
"T+ lO%T
...[i...JT + lO%T
76 UBC-v- -VT
O.O5KW
~~
-iJT + IOn
- 1.1473 UBC v-- 1.18
*For firm soil and 0.3 ~ T ~ 2.0 seconds.
**The values actually calculated were as shown: 628K and 4.9%W. However,the 4.9%W was rounded off to 5%W or 640K, which was used in the calculation
76
A stress increases beyond allowable is permitted by each method when
This isconsidering earthquake forces combined with vertical loads.
in order to take advantage of the reserve strength that members have
between the elastic design level and the plastic or ultimate strength
The permitted increases are listed below:design level.
1976 and 1973 UBCATC 3 and Stanford Methods
t.31.7
The CotJDnon Base for Comparison
live. and earthquake load moments as computed by theThe dead t
3 Method and as combined according to lo2MD + lo0~ + 1.0~ repre-
the plastic or ultimate strength design resisting moment requirements.
These moments were divided by the permitted stress increase value of 1.7
Throughto reduce them to equivalent allowable stress design moments.
engineering judgment based on the particular building height and the
rather fle:xible structural system, the allowable design level was then
This one thirdincreased by one third to allow for control of drift.
increase required to provide the extra member section and stiffness for
It would have been overlooked incontrol is an important factor.
a purely academic study, and yet it is a very real constraint for which
Only practical design experience (from theprovisions must be made.
The new design level which resultsSEAONC/GKT advisor) made this evident.
from this additional factor is referred to as the "Acceptable Design
Design levels from other methods were brought to this AcceptableLevel."
Design Level for comparative purposes; the calculations for this are shown
in Table 8-6.
77
Table 8-6
ACCEPTABLE DES IGN LEVEL
UltimateStress Increase
- AllowableLoad Combination - Ultimate
Allowable X 1.3 - Acceptable Design Level
ATC 3 Method
ULT1.3
(l.lD + ~ + E) X 1.3 = Acceptable -
1.7
Stanford Method- -
ULTCD + L + E) X 1.3 - Acceptable - 1:31.7 (Equivalent to ATC 3 Method)
1976 and 1973 UBC
(Equivalent to ATC 3 Method)(D + L + E) X 1.3 = Acceptable = ULT1.3
78
Member sizes were chosen using the Acceptable Design Moment as cal-
culated by each method. These moments for the buildings designed by
the ATC 3 and Stanford Methods were so close that the same member sizes
were selected. Therefore the resulting designs are identical. From this
point on, the 1976 and 1973 UBC buildings will be compared to the one
building that corresponds to both the ATC 3 and the Stanford Methods.
Table 8-7 lists the member sizes by story for comparison.
The buildings were compared in a more quantitative way by computing
the weight of the girders chosen by each method. Girder ~eights alone
were used in this comparison as they produce an acceptable, simple com-
parison without complicating the matter by introducing weight due to
columns or "in-bay" framing. The weights are shown at the bottom of each
page of Table 8-7 and are tabulated in Table 8-8. The total weight of
the girders in the building as designed by the ATC 3 and Stanford Methods
falls in between the value of the total weights of the girders found for
the 1976 and 1973 UBC buildings. This is an important factor from a cost
standpoint since the weight of steel is directly proportional to the cost
of a structural system
In addition to the weight, it is also important to compare the rela-
tive strength of the structures. The method developed in this disserta-
tion, though not unique, was deemed to be the best way to reduce the
strength of a building to a single number for comparative purposes. The
section moduli of the girders were averaged over every three stories,
except for the roof, for each frame. This was done in order to calculate
an average section modulus value for the structure. The results are
presented and compared in Tables 8-9 and 8-10.
In Table 8-11 the relative differences among the methods are reduced
to single numbers. The 1976 UBC building is thirteen percent heavier
79
and twenty one percent stronger than the building from the ATC 3 and
Stanford Methods. The 1973 UBC building is twenty nine percent lighter
and thirty percent weaker than the ATC 3 and Stanford Method building-
Averaging the percentage differences of weight and strength, it can be
in general that the design level of the 1976 UBC building is seven-
teen percent above that of the ATC'3 and Stanford Methods, and in general
the 1973 UBC building design level is thirty percent below the ATC 3 and
Stanford Methods.
In summary, the results of this study of one building system have
shown where the principal differences occur due to various design methods.
the study was limited to the framing system and its important details;
other factors such as the foundation design were not considered. The main
The equations for calculatingdifferences in the methods considered were:
the base shear; the way in which the lateral forces were distributed
the height of the structure; and the manner in which the loads were
The general results of this comparisoncombined for member size selection.
of design methods are considered valid for the fifteen story ductile moment
resisting steel frame building and can apply reasonably well to buildings
having similar heights, structural systems, and configurations
80
Table 8-7
GIRDER MEMBER SIZES
976 UBC
(Picked on the Basis of the Most Economical Section)
Fr. B & C Fr. A & DFr. 2 & 3 Fr. 1 & 4Level
W 18 x 35 W 14 x 26 W 24 x 61 W 16 x 40R
W 21 x 44 W 27 x 9415 W 24 x 55 W 24 x 61
W 24 x 68 W 30 x 9914 W 18 x 55 W 24 x 68
W 24 x 76 W 24 x 61 W 30 x 10813 W 24 x 76
W 24 x 84 W 30 x 116W 21 x 6812 W 24 x 84
W 24 x 94 W 24 x 68 W 30 x 116 W 27 x 8411
W 27 x 94 W 33 x 118W 24 x 76 W 27 x 9410
W 30 x 99 W 24 x 84 fIT 33 x 118 W 27 x 949
W 30 x 99 W 24 x 84 W 33 x 130 W 30 x 998
W 30 x 99 W 27 x 84 W 33 x 130 W 30 x 997
W 30 x 108 W 27 x 84 W 33 x 130 W 30 x 996
W 27 x 84 W 33 x 130 W 30 x 99W 30 x 1085
W 27 :c 84 W 33 x 130 W 30 x 994 W 30 x 108
W 27 x 84 W 30 x 99W 33 x 130W 30 x 1083
W 27 x 84 W 33x130 W 30 x 99W 30 x 1082
I wt/ft(lb/ft)
1070 1740 12941343
X 168'Fr. wt.(kips)'
180 292 211226
Total Weight - 915 kips
81
Table 8-7 (Continued)
GIRDER MEMBER SIZES
ATC 3 Method (V E 5%W)
Stanford Method
(Picked on the Basis of the Most Economical Section)
Fr. A & DFr. B & CFr. 1 & 4Fr. 2 & 3Level
W 12 x 22 W 21 x 55W 16 x 31 W 18 x 35R
W 18 x 35W 21 x 49 W 24 x 8415 W 21 x 55
W 21 x 44W 24 x 55 W 27 x 84 W 24 x 6114
W 21 x 49W 21 x 68 W 27 x 94 W 21 x 6813
W 21 x 55W 24 x 68 W 30 x 99 W 24 x 6812
W 24 x 61W 24 x 76 W 30 x 99 W 24 x 7611
W 24 x 61 W 30 x 108W 24 x 84 W 24 x 8410
W 21 x 68 W 30 x 108 W 24 x 84W 24 x 849
W 24 JC 68 W 30 x 108 W 24 x 84W 27 x 848
W 24 x 68 W 30 x 116 W 27 x 84W 27 x 847
W 24 x 76 W 30 x 116 W 27 x 84W 24 x 946
'W 24 x 76 W 30 x 116 W 27 x 84W 24 x945
W 24 x 76 W 30xl16 W 27 x 84W 24 x 944
W 24 x 76 W 30 x 116W 24 x 94 W 27 x 843
W 30 x 116 W 27 x 84W 24 x 76W 24 x 942
I wt/ft(lb/ft)
1535 11199111153
X 168'Fr. wt.(kips)"
188258194 153
r Frame Weights - Total Weight
Total Weight - 793 kips
82
Table 8-7 (Continued)
GIRDER MEMBER SIZES
1973 UBC
(Picked on the Basis of the Most Economical Section)
Fr. A & DFr. 1 & 4 Fr. B & CFr. 2 & 3Level
W 16 ~ 31WI" x 19 W 18 x 50W 14 x 26R
tJ 21 x 44W 14 x 34 W 24 x 6815 W 18 x 40
W 18 x 35 W 21 x 49W 21 x 44 W 24 x 7614
W 16 x 40 W 24 x 76 W 18 x 55W 18 x 5013
W 21 x 44 W 21 x 5SW 18 x 55 W 24 x 8412
W 21 x 44 W 24 x 84 W 24 x 55W 21 x 5511
W 18 x 50 W 24 x 61W 27 x 84W 24 x 5510
W 18 x 50 W 24 x 61W 24 x 61 W 27 x 849
W 21 x 49 W 21 x 68W 24 x 61 W 27 x 848
W 21 x 68W 21 x 68 W 24 x 94W 18 x 557
W 21 x 68W 21 x 68 1-124 x 94W 21 x 556
W 24 x 68 W 27 x 94 W 24 x 68W 21 x 555
W 24 x 68W 24 x 68 W 27 x 94W 21 x 554
W 24 x 68W 24 x 68 W 27 x 94W 21 x 553
W 24 x 68W 27 x 94W 24 x 68 W 21 x 552
I wt/ft(lb/ft)
887670855 1254
x )-68'Fr. wt.(k_~p~) .
149211 113144
Total Weight - 616 kips
83
Table 8-8
TOTAL GIRDER WEIGHT
1976 UBC 915 K 13% above
Reference level793 KATC 3 MethodStanford Method
29% below1973 UBC 616 K
84
or'~
GJ
~f-4
C/)~NHC/)
~
B-c,,~u 0
~.z
p~\0"'~~~
0'+.(
~ ~C/)M'0
Or:E.;(tU
M.. u
~E.<C/)HID
~~O~OHc/)MPu8E.<0-~
~H
t;~C/)
C")
.,a
N
~k
~
u~~,
$of~
-.:t
ca~
~~
~
~
lob
-<.
~rz.
CI)Q)
m~
fz4
.-of
.-of-II!
II).-iQ)>Q)
~
~~H
CI)
t!)
~
C/)
C!J
~
~A..,
C/)
t)
~
rz.HA
H
~~H
f/)
~<
U)
C-'
~
ra.HQ
~
u~
..-0...
It'\0N
0"
0t'f-
."N
..;r
~'"
«)~
.1i
~
Inct)
~
\0
-4'Cf't-
,...'"N
0n-
N~-
\0In...
u~
\QIt'\
-\CN
-
\011'\-.
-
0004
.co-.0004
.M
0\,...
Nj¥"\
0\
0U)
0M
\0r--
~0\-'
0\-cw,
-04'~
~0\-
M-~
Co)
~
N0N
00,
-4'
~~
0-
~
85
(X)
~0\
~
0-
"...
i
..-~
~,...,
~"'"
\0~
\Q,.,..
&f\
~
0~
N."N
0\\0N
u~
~~N
0\N~
~\0~
N
,
NMN
'"
A\0
Ar-.
'"~
...a)
0\,...
0\
0\,...
~od"
\0~
00\N
N
N
0,...~
~0\N
u~
0\N<'"
-NN
\0'"~
C'4
N
~MN
N-M--:t-
'"
...~
Mct\
0\,
0\,...;
\0
\0
~
00M
N
""
~N
0\N
~~
~
~.0
~coIU~~
~
l"-f'"
«)
~,..,.
~
G\,...
--cGJ:s
~u
gS0\~GJ
.0~
~
~~NH~
~
~H-C-' In
U~~ 0
~-B
M~
O\~~0
~~M~
U~E,c1 ~
.. M
~U~E,c1H
~~Cp.U S
~H
~M
S~~~
~HEo!U~~
~
~
N
r~
~
u~IQ
....
~
..
.~
rs.
Q
~
-<.
~~
CDaI
!~~.-i-<
co.-iGI>GI
...J
1.
rz.~Q
-.
rz.1-1Q~
rz.1-1A
H
C/)
Co-'
~
~1-1~
~
(/)
~
~
~H~
w
CI)
t-'
~
CI)
~
~
C/)
~
=<
Co)
~
04-0...
(;1
0N-
'"N"-'
11'\0N
-:to-.
U'\...
N,
~
11'\r...
In.n
Cf\co...
~r-..
&r\,...
In-.,.
,...~
M0\
'"\Q"-'
u~<
\DIf\-
~~.-of
\011'\~
woof
,...-
-\0N
.04
.04
AN.04
..M
M\0
MtOo
...\0
0\\0
~\0
~
0\l't\
~\0
0-
\0,
C0\-"
u~
N0~
~q-
,...~
0N
00M
86
CX)
~0\
..
C
N~
('of
\b
~\D
,...\Q
M
~N--'
,...U)
C")C")
0-:t
tI\....~
Co)
~
~
N
~\0-
N
N
N~N
"t'l'"'
11'\
.\D~
"'"
\Q\0
0\\0
.-4\0
~\0
r--~
~
04-04--I
N0
~~
~NN
."
."-
u~
tNN
\Q~...,
N084N
&f\~N
0\N
N
..~
..4
0\.n
-:r,...
an\0
Nt-.
;".!
t'\-
~U"\-
~~-
~11'\~
..,4N
\0\0
~~~
>-.0
QI~IU~QI
~
\0~
.
~~
0~
~
Table 8-10
SECTION MODUWS COMPARISON
AverageSection Modulus
Method
1976 UBC 21% above
Reference LevelATC 3 Method
Stanford Method
1973 UBC 30% below
87
Table 8-11
CODE COMPARISON TABLE.
LevelMethod
1976 UBC 17% above
Reference levelATC 3 Method
Stanford Method
1973 UBC 30% above
*This table is valid only for thebuilding discussed in this dis-
sertation.
88
REFERENCES
1.
Zsutty, T.C. and Haresh C. Shah, Recommended Seismic Resistant DesignProvisions for Guatemala. Technical Report for The John A. BlumeEarthquake Engineering Center, Stanford University, Department ofCivil Engineering, Stanford, California, May 1978.
2.
Zsutty, T.C. and Haresh C. Shah, Recommended Seismic Resistant DesignProvisions for Algeria. Technical Report for The John A. Blume Earth-quake Engineering Center, Stanford University, Department of CivilEngineering, Stanford, California, June, 1978.
3.
International Conference of Building Officials. 1976, ~niform BuildingCode.
4.
International Conference of Building Officials, 1973, Uniform BuildingCode.
5.
RQ