behavior of structural systems for buildings

7/22/2019 BEHAVIOR OF STRUCTURAL SYSTEMS FOR BUILDINGS

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CEE 285 BEHAVIOR OF STRUCTURAL SYSTEMS

FOR BUILDINGS

DESIGN PROJECT

Professor H. KrawinklerStanford University

Submitted: March 22, 2!

"eam Members:

#immy $han

%s&hica $hhabra

#ennifer Moore

#ana "etikova

'ick (ann


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CEE 285 BEHAVIOR OF STRUCTURAL SYSTEMS

FOR BUILDINGS

DESIGN PROJECT

Professor H. Krawinkler

Stanford University

"eam Members:

#immy $han%s&hica $hhabra

#ennifer Moore

#ana "etikova

'ick (ann

BD Inc. Project: Palo Alto Office Tower 2


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Table of Co!e!"

P%)" *'+: SS"+M %SS+SSM+'"..............................................................................-. /ntroduction................................................................................................................-

. Pro0ect Pro&osal.....................................................................................................-

.2 /ndividual )oles.....................................................................................................-2. 1oad etermination ..................................................................................................3

2. 4ravity...................................................................................................................3

2.2 1ateral .................................................................................................................25. Structural esi6n.....................................................................................................2-

5. 4ravity System.....................................................................................................2-

5.2 Perimeter Moment 7rames ..................................................................................5

5.5 Shear (all esi6n...............................................................................................585.- $onnections..........................................................................................................-

5.8 7oundation...........................................................................................................-9

-. +"%S Modelin6 ; %nalysis and iscussion..........................................................8

-. Model iscussion.................................................................................................8-.2. Shear (all;7rame /nteraction.............................................................................82

-.5 +"%S Model and 7rame; Shear (all /nteraction $om&arison........................858. $onclusions..............................................................................................................88

P%)" "(*: %PP+'/< ; +S/4' $%1$U1%"/*'S................................................8!

%&&endi= % > 1oad etermination ...............................................................................8!%&&endi= > 4ravity System esi6n...........................................................................8!

%&&endi= $ > SM)7 esi6n.........................................................................................8!

%&&endi= > Shear (all esi6n..................................................................................8!

%&&endi= + > $onnection etails and $alculations......................................................8!%&&endi= 7 > %nalysis )esults ?+"%S and /[email protected]!



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PART ONE: SYSTEM ASSESSMENT

1.0 Introduction

1.1 Project Proposal

"o build a story office buildin6 in Palo %lto accordin6 to 99A U$ s&ecifications

kee&in6 the followin6 constraints in mind:

Site $onstraints:

Seismic 1oads: the buildin6 is located at A km from the San %ndreas fault.

Soil &rofile S

%rchitectural $onstraints:

$lear Story hei6ht should be at least 3.8 ft.

3 ft = - ft floor &lan

*ther $onsiderations:

/nsure elastic behavior of structure under stron6 motion earthBuake

$onsider foundation system

1.2 Individual Roles

/ndividual roles were 6iven to each team member:

*wner: #ennifer Moore

%rchitect: 'ick (ann

Structural: #immy $han

Mechanical: #ana "etikova

$ontractor: %sh&ica $hhabra

"he res&onsibilities of each are outlined below. +ach &erson &erformed research in

hisCher own area in order to 6uide the buildin6 system desi6n.

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#$2$# O%e&

"he owner wanted to have fle=ibility in the use of functional s&aces that can su&&ort the

unknown future demands on the structure as wells as to entice sales of s&aces. S&ecific

areas were chosen and desi6ned for heavier loads in order to meet this fle=ibility

reBuirement. "o increase demand, the owner also reBuested s&ecific &hysical

characteristics such as an atrium on the first floor and a restaurant. $ommercial s&ace on

the first floor was also set as a hard constraint in order to rent to retailers. MinimiDations

of costs were also im&ortant to the owner, who desired to have a cost efficient buildin6

system.

#$2$2 A&'()!e'!

"he architect res&onded to the ownerEs vision of the buildin6 throu6h an innovative and

&ractical e=tension of the atrium to im&rove the overall s&ace. /nstead of havin6 the

atrium at the first floor level, he reversed the seBuence and added a lar6e o&enin6 runnin6

throu6h the buildin6 from the !thto thfloor. "his lar6e o&en s&ace leads to a reduction

in the functional s&ace of the buildin6, however it allows am&le natural li6ht to enter the

buildin6, creatin6 a livelier atmos&here and increasin6 the &roductivity of its occu&ants.

"he ceilin6s at the first floor were increased to 8 ft in order to increase the 6randeur and

aesthetic a&&eal of the commercial area. "he architect o&ted a6ainst a basement. "he lack

of basement and commercial use of the first floor reBuired that mechanical systems be

&laced on the second floor, increasin6 the 2ndfloor story hei6ht to 8 ft.

"he architect desi6ned two continuous shear wall cores, one on each side of the o&enin6.

He has also &rovided for a restaurant on the fifth floor level, which &rovides for more

retail s&ace in the buildin6. "his floor was chosen because its central location would be

more accessible to the buildin6 occu&ants, which would ho&efully increase use. %lso, the

restaurantEs location on the 8thfloor would allow diners to look u& throu6h the o&enin6,

im&rovin6 the Buality of the lunchtime e=&erience. %dditionally, &eo&le at the to& floors

would be able to look down at the decorated restaurant.



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#$2$* S!&+'!+&al E,)ee&

"he mechanical and architectural reBuirements &osed as the &rimary structural challen6es

for the structural en6ineer. *wners concerns were addressed throu6h the architect and not

the owner herself.

*ne of the most im&ortant decisions that the structural en6ineers made was the ty&e of

lateral load resistin6 system. "he structural en6ineers decided on a dual system

consistin6 of concrete shears walls and steel s&ecial moment resistin6 frames ?SM)7@ in

both the +( and 'S directions. uctile shear walls &rovide e=cellent resistance to hi6h

lateral loads that are &robable in hi6hly seismic re6ions. "o achieve this ductility,

however, s&ecial attention had to be &aid to the detailin6 of the wallsE reinforcement.

%dditionally, the s&ecial moment resistin6 frames ?SM)7@ act as a Fbacku&G system

&rovidin6 necessary redundancy to the system.

S&ecial attention also had to be &aid to key areas for the heavy loads im&osed by the

mechanical system com&onents. "hese areas were strate6ically &laced in locations

a&&roved by the architect, so as not to interfere with the flow of the buildin6, yet &rovide

efficient service throu6hout. *ne of the most notable structural challen6es in the buildin6

has to do with the lar6e o&en core runnin6 down the center of the buildin6. "hisarchitectural detail &rovided many structural challen6es, be6innin6 with the dia&hra6m

that was assumed to be ri6id in this buildin6 desi6n. (ith a &lan discontinuity such as

this, the en6ineers would have to analyDe the dia&hra6m further to validate the ri6id

dia&hra6m assum&tion. Many other structural decisions had to be made throu6hout the

desi6n &rocess includin6 the use of com&osite beams, shored construction, and

fire&roofin6 around the stairways.

#$2$- MEP

"he structural en6ineers collaborated with the mechanical en6ineers to come u& with a

scheme for the ductwork, which will &rimarily run alon6 the interior corridor deck that

surrounds the o&enin6. *n the st throu6h 8th floor, ductwork will run under the floor

beams which are not very dee&. "he mechanical en6ineer s&ecified that two chillers and

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coolin6 towers are reBuired for the buildin6. $hillers and other *ri6ination systems will

be housed in the two mechanical rooms on the second floor ne=t to the cores. $oolers at

the roof are also located ne=t to the cores. 7our elevators are located in the buildin6. "he

shear core is housed around the stairway, allowin6 for most of the vertical &i&es to also

run alon6 the core. "he transformer and 6enerator which account for heavy concentrated

loads will be housed outside the buildin6 and hence do not affect the structural decisions.

"y&ical M+P features and loads can be found in "able 2;2.

#$2$5 Co!&a'!o&

"he &rimary role of the contractor was to &romote efficiency of the structural desi6n.

"his affected decisions on member siDin6, steel member and shear wall connections, and

concrete work. "he more similar the connections and member siDes, the more costefficient the desi6n. %lso, connections and members that are readily available in the

market are more desirable. 1abor was also a concern es&ecially related to the installation

of the doubler &lates which was avoided by increasin6 the interior column siDes. "he

contractor &artici&ated in the desi6n &rocess.

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2.0 Load Determination

4ravity loads were com&uted based on M+P load reBuirements, ty&ical dead loads, and

live loads based on varyin6 functional uses. (ind and seismic loads were determined to

com&ute total lateral load effects.

2.1 ravit!

Table 2.#$ead 1oad 1ive 1oads

"oads #s$

Concret+deck+misc. 0.065

Partitions 0.02

DL 0.085

Exterior Cladding 0.02

Roofing system 0.05

Sel$ %ei&'ts #l$

loor !eams 0.05

"irders 0.#

Col$mns 0.2

"ive "oads #s$

%ffices 0.05

Corridors& exits 0.#

ile Rooms 0.#5

Roof 0.02

"he chillers, which may wei6h u& to , lbs, were &laced on the second floor. "he

coolin6 towers are in 6eneral &laced on the roof for they reBuire a continuous flow of air

and are Buite noisy. Since at the time of conce&tual desi6n no decision was made as to

where e=actly on the roof coolin6 towers would be &laced, four areas of about 8 sBuare

feet where desi6ned to su&&ort loads u& to 5 &sf ?)ef. )oof 1oad Key Sheet@.

/n addition to chillers and coolin6 towers, another im&ortant consideration is the chilled

water loo& and condenser loo& which will &roduce a reaction of about 3, lb. at the

base of the buildin6.



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*ther 6eometric constraints arise from &rovidin6 the buildin6 with &lumbin6, storm, and

electrical system. "able 2;2 summariDes the M+P loads and considerations.

Table 2.2. M+P 1oads and $onsiderations

Ca!e,o&/ Rela!e0 Co"!&a)!" Ve&!)'al Loa0

#$ Ele1a!o& "/"!e

+levators and dumbwaiters ?1 and 11@ accessibility and fire&roofin6 2 = lb

2$ HVAC S/"!e

i@ *ri6ination System ; ;

$hillers

area of ft. = 2 ft.

-?I@ thick raised concrete &ad

2 ; 8 ft. ceilin6 hei6ht

5 &sf

$oolin6 towers

area of 8 ft. = 2

ft. hei6ht of 8 ft. ; 2 ft.

raised above deck

5 &sf

$ondenser loo& ?2 loo&s needed@ ' 3 lb

$hilled water loo& ?2 loo&s needed@ ; 3 lb

Masonry wall enclosures and

increased slab thickness for &um&s and

com&ressors

; &sf ; 5 &sf

ii@ istribution System

uctwork ; 8 &sf

*$ Ele'!&)'al S/"!e

"ransformers concrete encasin6 2 ft. = ! ft. 5 &sf

+mer6ency 4enerator 3 lb

-$ Pl+b), S/"!e

"anks and boilers ; ;

5$ F)&e P&o!e'!)o S/"!e

istribution lines and s&rinkler heads ; ;

% summary of the 6ravity loads alon6 with the architectural renderin6s of the ty&ical

floor &lans are included herein.



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BD Inc. Project: Palo Alto Office Tower !


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BD Inc. Project: Palo Alto Office Tower A


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2.2 "ateral

*nce the 6ravity loads are com&uted and finaliDed the lateral loads can be determined.

"he lateral loads are a&&lied in addition to the 6ravity loads and ty&ically control the siDe

of the members. /n our case, the lateral loads are resisted by a shear wall and moment

resistin6 frame system. (ind loads can be very hi6h in some re6ions such as near the

shoreline of a ma0or body of water, such as the Pacific *cean or the 4ulf of Me=ico.

However, the seismic forces im&osed on our buildin6 were much 6reater than the wind

forces, and therefore controlled the desi6n. *ther forms of lateral load, such as blast

loadin6 or im&act loadin6 are not relevant for the desi6n of an office buildin6 and

therefore were not considered in this &reliminary desi6n.

2$2$# 3)0 Loa0"

"he loads im&osed on the buildin6 were calculated usin6 the U$ formula 2;. %

desi6n wind s&eed of 9 m&h and an e=&osure cate6ory were used in the formulation of

the lateral wind loads. Usin6 the followin6 eBuation as well as "able !;4 of the U$,

containin6 values for $e, the wind &ressure at each story and at each mid;story was

inter&olated:

& J $e($BBs/ where ($BJ .3 I .8 J .5

"hen, as shown in 7i6ure 2;, the values of the wind &ressure, &, are avera6ed at each

interval and this value is then used as the desi6n wind &ressure over the entire half;story.

"he desi6n wind load was then re&resented as a line load over the width of the floor by

multi&lyin6 the wind &ressure of the half;story above and below each floor by their

res&ective half;story hei6hts and summin6.



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F),+&e 2.#: istribution of the (ind Pressures over the Hei6ht of the uildin6.

"his line load, ( in kCft, was then multi&lied by the width of the buildin6 to calculate the

total force im&osed on each floor by the wind. "hese story forces were then summed

cumulatively down the buildin6 to arrive at the story shear force. +ach story shear force

was then multi&lied by the story hei6ht and a6ain summed cumulatively down thebuildin6 to determine the overturnin6 moment im&osed by the wind loadin6. "he

calculations are summariDed in A44e0) A. %s e=&ected, the 'S wind &roduces hi6her

base shear forces and overturnin6 moments of -23 ki&s and 5,-2 ki&;ft, res&ectively.

"his is nearly twice the loads im&osed by an +( wind &roducin6 a base shear of 2-8 ki&s

and an overturnin6 moment A,98 ki&;ft. However, while these lateral load effects are



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notably lar6e due to the close &ro=imity to the Pacific $oast, they were ultimately

ne6lected in &lace of the even lar6er seismic loads.

2$2$2 Se)")' Loa0"

"he seismic loads im&osed on structures in the Palo %lto area are e=&ected to be

si6nificant. "he seismic loads were calculated accordin6 to the U$ ?99A@. %s

&rescribed by the code, the total base shear is calculated accordin6 to desi6n &arameters,

such as &ro=imity to an active fault, seismic Done, soil &rofile, ty&e of lateral system,

&eriod and the effective seismic wei6ht of the buildin6. "he seismic wei6ht was

determined in %&&endi= % usin6 many &reliminary assum&tions for material and

mechanical wei6hts. "hese assum&tions were later verified as conservative avera6es.

"he elastic fundamental &eriod of vibration of the structure was determined usin6 codeMethod % ?eBuation 5;3@:

" J $t?hn@5C-,

where $tJ .58 for steel moment;resistin6 frame was used. "hen, the base shear was

calculated usin6 eBuations U$ ?99A@ 5;- throu6h 5;A:

WRT

CvIV =

W

R

CaI8.2

CaW.

WR

ZNvI3.

*nce the total base shear was determined, the forces were distributed to each floor. Since

the natural fundamental &eriod was determined to be .5 sec .A sec, the whi&lash

force, 7twas determined accordin6 to:

7t J .A"L .28L,

"his force was a&&lied to the roof of the buildin6 to account for the wave reflection

which causes a hi6her inertia force on the to& floor. "he rest of the base shear was then

distributed to the individual floors based on their seismic wei6ht and hei6ht. %s was the

case with the wind loadin6, the seismic shear story forces were summed cumulatively



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down the buildin6 to determine the individual story shears and the base shear at the

6round level. "he story shear was then multi&lied by the story hei6ht and cumulatively

summed once more to determine the overturnin6 moment. "he results of these

calculations can be observed in 7i6ure 2;2.

F),+&e 2.26istribution of the Seismic 7orces over the Hei6ht of the uildin6.

%s can be easily seen from the results in the A44e0) A, the base shear for the buildin6

is ,53 ki&s and the overturnin6 moment at the 6round floor is 9!,!93 ki&;ft. "hese

results are nearly 5 times the lar6est values obtained from the wind loadin6, thus the wind

loads were i6nored and the seismic loads were used as the controllin6 desi6n lateral

loads. %dditionally, unlike the wind loadin6, the lateral systems in both directions

e=&erience the same loadin6 and thus must both be desi6ned for the same load effects.



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3.0 Structural Design

(.1 ravit! S!ste)

*$#$# G&a1)!/ Col+"

"he 6ravity columns which make u& all of the interior columns were desi6ned for a=ial

load only. "hese columns have beams framin6 into them and have sim&le shear

connections, which are modeled as &ins so that virtually no moment is transferred into the

column. "hus, in order to desi6n the columns we first had to determine the a=ial loads

due to dead and live loads only. "hese loads were based on the tributary area of the

column and 6ravity loads includin6 the column self;wei6ht. "he resultin6 loads are

summariDed in A44e0) B.

"he dead and live a=ial loads were summed cumulatively from the roof down to

determine the total a=ial load at each floor. "hese loads were then factored accordin6 to

the load combinations &rovided in the U$ ?99A@ to obtain a desi6n load, Pu. However,

before we could continue with the desi6n, two en6ineerin6 decisions were made. 7irst,

due to the column layout and symmetry of the buildin6 we determined that we could

reduce all of the interior 6ravity columns down to two ty&ical columnsN one on the cornerne=t to the elevators, and the other towards the middle of the buildin6 closer to the shear

wall. "his consistency &rovides a sim&lification durin6 construction. "he second

en6ineerin6 decision is that the columns would be s&liced at - feet above every second

level. "his decision is based on the trans&ortation constraints of the columns as well as

the constructability of the buildin6.

(ith these decisions in mind, the columns were then desi6ned usin6 a KJ , 7 yJ 8 ksi

and c J .38 for com&ression. $olumn siDes at each story were chosen so that the ratio

of a=ial com&ression from the loads to the a=ial com&ression ca&acity of the siDe,

nc

u

PP

, was less than or at most eBual to .. (e used (- sections for the 6ravity

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columns. "he final &reliminary desi6n of the 6ravity columns were taken as the siDes

desi6ned at the st, 5rd, 8th, Ath, and 9thfloors. "hese are summariDed in "able 5;.

Table *.#$ 4ravity $olumn esi6n

RA*ITY +O",MNS

-loor +olu)n +olu)n /

Roo$

10

)#*5, )#*5,

)#*-0 )#*-0

3

/

)#*#20 )#*#0-

4

)#*#5- )#*#*5

(

2

)#*x2## )#*#6

1

*$#$2 I!e&)o& G)&0e&"

"he interior 6irders are desi6ned for .2 I .! 1. )efer to the &revious load key sheets

for the various load areas. 7or interior 6irders only, we analyDed the 6irders with

distributed loads and tributary areas. (e looked at both the stren6th and deflection,

calculatin6 the minimum section modulus as well as the minimum / =before decidin6 the6irder sections. "he deflection limits for live loads and dead loads are 1C2- and 1C5!

res&ectively. Sam&le calculations can be found in A44e0) B.



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*$#$* Floo& Bea"

7loor beams and slab were desi6ned as a fully com&osite system to reduce beam siDes

and to take advanta6e of the concrete floor stren6th. 7loor beams were desi6ned with the

followin6 &ro&erties:

"otal floor de&th ; !.28 inches

$oncrete fill ; 1i6htwei6ht concrete ?fcEJ 5ksi, &cf density@

Steel stren6th ; f yJ 8ksi

Shear studs ; O inch diameter 5 inches lon6

Shored and unshored construction was evaluated with the followin6 assumed

construction loads:

(et concrete ; ! &sf live load

%dditional const. load ; 2 &sf live load

7inally, the choice of usin6 com&osite beams was verified by &erformin6 a cost

com&arison between com&osite and non;com&osite beams, detailed in A44e0) B$

1oads:

1oads were obtained from the load key sheets. "hree ty&ical loadin6s and three floor

beam len6thsCs&acin6s were used in calculations.

ead 1oad ; 38&sf

1ive 1oad ; Heavy J?8&sf@, Medium J ?&sf@ and 1i6ht J ?8&sf@

7loor beams ; 51on6 Q s&acin6, 28Q and 28 Q3;-R

)eBuired 7le=ural Stren6th:

"he fle=ural resistance reBuired was obtained from:

3

2wLM

u=

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where w is the load &er linear foot of beam obtained from tributary widths ?half the

distance to ad0acent beams@ and 1 is the s&an of the beam.

Select Section and Pro&erties:

%ssumin6 the de&th is the concrete stress block, a, is less than the thickness of the

concrete slab, the desi6n fle=ural stren6th, Mnis:

@22

? aydFAMconcysn

+=

where %sis the area of the steel beam reBuired, d is the de&th of the steel beam ?assumed

to be G for the first iteration@, y concis !.28 inches, a is the de&th of the concrete block

?assumed to be 2G for the first iteration@.

% value of 2 , distance from to& of the steel flan6e to the center of the concrete stress

block, is also reBuired. %ssumin6 the de&th of the concrete stress block is less then the

thickness of the slab, 2was obtained from:

22ayY

conc =

Usin6 these two values sections were chosen from the %/S$ 1)7 Steel esi6n Manual

5rdedition "able 8;- $om&osite (;Sha&es.

7le=ural ca&acity was check usin6:

@22

? aydfAM concysn ++= where

=

cediscenterline

beas!anb

tanST2.

T3.

minT2 and

bf

Afa

c

sy

P38.

=

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$om&ute number of Shear Studs )eBuired:

"he nominal stren6th of stud was obtained from:

uscccscn FA"fA# =P8.

where %sc is the cross;section of the shear stud ?.--in

2

@ , +c is the modulus of elasticityof concrete 6iven below ?238.5 ksi@ and w is the unit wei6ht of concrete ?&cf@.

P8.55 cc fw" =

7or a O in diameter stud the stren6th is A.-A ki&s. "he number of studs reBuired from

the &oint of ma= moment to its connected ends for full com&osite action was obtained

from:

n

ys

stud#

fA=U

Since the beams are sim&ly su&&orted this number is for half the beam len6th. "otal

number of studs reBuired is then twice stud.

$onstruction Phase Stren6th $heck:

% fle=ural demand for an unshored beam was checked usin6 the construction loads

assumed. 7or floor beams where the fle=ural ca&acity of the steel is e=ceeded, a lar6er

section was chosen and the number of shear studs recalculated.

eflection $alculations:

eams that are unshored were checked for deflection under dead loads usin6:

"I

wL

53-

8 -=

where unfactored load &er linear foot of beam and + and / are the modulus of elasticity

and moment of inertia for the unshored beam. (here deflection are lar6e ?V1C5!@

adeBuate camberin6 is reBuired.

eams that are com&osite were checked for deflections under live loads usin6:

5!53-

8 - L

"I

wL=



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where / is the lower bond elastic moment of inertia 6iven "able 8;8 of the %/S$ 1)7

Steel esi6n Manual 5rdedition.

$om&arison to a 'on;$om&osite Section:

eam sections were chosen by com&arin6 fle=ural ca&acity of the steel section to the

calculated fle=ural stren6th reBuired. Sections chosen were also checked for live load

deflections as ?W1C5!@. %ssumin6 Albs &er stud ?in cost@ the amount of steel increase

due to the beam siDe increase was com&ared.

SiDes for each of the 5 loadin6s ?heavy, medium and li6ht@ and for each of the 5

s&ansCs&acin6s as described in %, are tabulated below. % sam&le calculation can be

found in A44e0) B$

Table *.26 Section esi6n

5eav! 6"" 7 10ps$8 ,0/#0/

1ye of Const 3ection 3t$d 3t$d 3acing 4$ kft X4n kft

37ored )#2x,5 ,*9 e:ery 69 ,8*.5 *,-.5

;ns7ored )#2x,5 ,*9 e:ery 69 #** #-2


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37ored )#0x#- ,*9 e:ery -9 20*. 22*

;ns7ored )#0x26 ,*9 e:ery 69 #00 ##.*


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beams to the columns and eventually to the foundation, where they are dis&ersed into the

earth. "herefore, each member of this chain must be stron6 enou6h to resist the

ma=imum moments im&osed on it if the system is to carry the loads safely. However,

before we can desi6n the members we must know the ma=imum loads that each would be

likely to e=&erience. "hus, we can start with the &erimeter 6irders to determine the

ma=imum moments im&osed on them from the 6ravity loads. "hese can be calculated by

assumin6 the ends of the &erimeter 6irders are fi=ed and calculatin6 the fi=ed end

moments.

/n our system, none of the &erimeter 6irders carry distributed loads other than their own

self;wei6ht or the e=terior claddin6 which was assumed to be .5- kCft alon6 the len6th of

the beam. %dditionally, there are two &oint loads caused by two beams framin6 into the

6irders. "hus, before the fi=ed end moments can be calculated, the reactions from the

framin6 beams must be determined accordin6 to the load key sheet and beam layout

6eometry. "hese calculations are shown in A44e0) C$

*$2$2 G)&0e& De"),

"he &erimeter 6irders &rovide ma0ority of the stiffness in the Perimeter Moment )esistin6

7rames. However, we did not need to desi6n the 6irders for stiffness since the moment

frame is the secondary or Fbacku&G system. "he &rimary shear wall system instead

&rovides the reBuired stiffness. "he moment frame hence only needs to be desi6ned for

stren6th. "he desi6n load was taken as the ma=imum fi=ed end moments ?6ravity loads@

and moments due to earthBuake loadin6, which were determined usin6 the Portal Method.

"he fi=ed end moments were factored by . and used for a &reliminary estimate of the

6ravity moments. "hese assum&tions would later be checked by com&uter analysis.

%lso, the =factor used in U$ E9A for redundancy was i6nored in this desi6n, but the

load combinations &rovided in the code were utiliDed. "he ma=imum moment obtained

from the load combinations and the determined moments was used for the &reliminary

desi6n.



32/56

Usin6 the desi6n moment, we were able to calculate the minimum &lastic section

modulus, Y= that was reBuired. "he a&&ro&riate factor of .9 was used for bendin6.

"he eBuation used to &erform this calculation was:

Y=,min J Ma= Moment?from load combinations@T2C?.9T8?ksi@@

%t this &oint, it was decided to use the same 6irder siDe for all three of the 6irders in each

moment frame. "his consistency sim&lifies the construction &rocess and thus reducin6

the chance of beams &laced in the wron6 location. "he results of the &reliminary 6irder

desi6n are shown in A44e0) C$

*$2$* SMRF Col+ De"),

"he columns in the SM)7 under6o both a=ial com&ression and bendin6 moments. /t is

assumed that thereEs no bia=ial bendin6 e=&ected since the interior 6ravity beams framin6into the columns are shear connected. "he &erimeter columns were oriented such that

stron6 a=is of the column would occur. (e utiliDed symmetry and only two columns in

each direction of the moment resistin6 frame were desi6ned. %lso, we decided to use

(2- sections due to their lar6e bendin6 moment resistance.

%mon6 the loads im&osed on the &erimeter columns are moments and a=ial loads from

dead, live, and seismic loads. "o determine all of these com&onents we be6an by

calculatin6 the a=ial loads due to the dead and live loads. "he &rocedure for this was

e=actly the same as for the 6ravity columns, usin6 the tributary area of the columns and

the 6ravity loads due to all &ossible sources includin6 the self;wei6ht of the column. %

moment distribution of the moment resistin6 frames was also com&leted to determine

how the fi=ed end moments determined earlier were actually distributed to the columns

of the frame. "o com&ute the stiffness of each member in the moment distribution of the

frame, the moment of inertia of the columns was assumed to be .2 times the moment of

inertia of the beams. /n &erformin6 the moment distribution, a concentrated moment of

ki&;ft was used so that a sim&le &ercenta6e of the moments a&&lied due to the fi=ed

end moment could be used to calculate the actual distribution of moment in columns due

to 6ravity loads. %lso, an unbalanced loadin6 was used in the moment distribution to

re&resent &ossible scenarios of live load. %nother load effect obtained durin6 the



33/56

moment distribution was a continuity shear that resulted from the unbalanced moments in

the ad0acent columns. "his shear was com&uted by dividin6 the difference in moments in

the ad0acent columns by the len6th of the beam. "his shear in the beam is converted to

an a=ial load in the interior column and is added to the a=ial load due to dead loads. "he

a=ial loads due to dead and live loads were cumulatively summed as before to determine

the total a=ial load at each floor due to the dead and live loads. 7inally, the a=ial loads

and moments determined in the Portal Method are used to determine the ultimate loadin6

on the columns. "hese loads are summariDed in A44e0) C.

%ll of the load cases used in this desi6n were considered. However, since r=Cryis lar6e in

our case, we can i6nore the first case ?.2 I .!1@ and use the second case ?.2 I .81

I .+@ assumin6 K=J KyJ ., which is &ermitted by the seismic code, to determine the

ultimate a=ial load and bendin6 moment on each column. "he results of this factorin6

are shown in A44e0) C$

Usin6 the followin6 interaction eBuations siDes were determined from the factored loads:

.2.

++

nyb

uy

n$b

u$

nc

u

n

u

M

M

M

M

P

P

P

P

.932.

++>

nyb

uy

n$b

u$

nc

u

n

u

MM

MM

PP

PP

MuJ MntI 2Mlt

MntJ come from factored 6ravity loads

MltJ come from factored lateral loads

*nce a6ain the columns were s&liced at every 2 ndlevel, so that the column used were

those desi6ned at the st, 5rd, 8th, Ath, and 9thfloors.

*$2$- Se)")' P&o1)")o"

/n addition to the stren6th desi6n of the Perimeter Moment )esistin6 7rame columns,

s&ecial seismic &rovisions must be taken into account to ensure the safety of the structure.



34/56

(e used only the interior &erimeter columns for this check because they have two

moment resistin6 beams framin6 into them as o&&osed to only one. "he columns must be

stron6 enou6h so that &lastic hin6es will form in the beam before in the column. "his can

be accom&lished by eBuation 3;5 of the U$ E9A:

.@C?

ybb

cucycc

FZ

APFZ,

"his eBuation ensures that the &lastic stren6th of the column is lar6er than that of the

beam.

"he columns and beams desi6ned are checked for the stron6 column;weak beam conce&t

and where needed redesi6ned so that they &ass.

%nother seismic desi6n criterion that had to be checked for the Perimeter Moment

)esistin6 7rame is the check for Foverstren6thG durin6 an earthBuake, since column

bucklin6 can be a ma0or &roblem. "his &rovides an e=tra &rotection a6ainst e=tra a=ial

forces in severe earthBuakes, which are lar6er than those used &reviously in the desi6n.

Since a=ial loads &rimarily concern e=terior moment frame columns, this check will be

only for those columns. "his check should be used when-.

nc

u

P

P

. (e used the

followin6 code eBuation to assure that the e=terior &erimeter columns were &rotected

a6ainst overstren6th:

.2P1I .8P11?.-)@P+Z >cPn

/n &erformin6 this calculation the factored loads were added to .-T)TP+J .-T3.8T P+J

5.-T P+ . "his is a lar6e increase in a=ial load to &rotect a6ainst a rare event. "he a=ial

ca&acity at each floor is checked so that the above eBuation is satisfied and the column is

&rotected from bucklin6. %ny column that fails is resiDed so that it satisfies thisreBuirement. "hese results are summariDed in "able 5;5.

Table *.*6 F)al SMRF De"),

EAST 9 %EST -RAME NORT5 9 SO,T5 -RAME



35/56

+olu)ns irders +olu)ns irders-loor Interior Eterior -loor Interior Eterior

Roo$ )#8,5 Roo$ )#*26

10 )2#** 10 )#6*0

)2*#,# )2*55 )2*#,# )2*55

)2#** )2#**

)2#50 )2#**

)2*x#*6 )2*68 )2*#,# )2*55

3 )2#50 3 )2#50

/ )#855 / )2#50

)2*#62 )2*8* )2*#*6 )2*68

)2#55 )2#55

4 )#855 4 )2#55

)2*#62 )2*#0* )2*#62 )2*8*

( )2#55 ( )2#55

2 )2#55 2 )2*55

)2*#62 )2*## )2*#62 )2*#0*

1 1

(.( S'ear %all ;esi&n

"wo shear wall staircase cores resist lateral loads in the buildin6. "hey are 8ft =.8ft

?centerline dimensions@, and have wall thickness of 3 inches ?See 7i6ure 5;@. "he

stren6ths of concrete and rebars are 5&si and !ksi, res&ectively. )ebar siDes and

s&acin6s were determined usin6 sim&lified formulas, assumin6 a solid core with no

o&enin6s. oor o&enin6s 5.8E wide 3E tall were modeled on each floor in the +"%S

verification model to see the effects of this sim&lification. esi6n was &erformed in

accordance to a&&licable %$/ 53 &rovisions. )ebar layouts are shown in 7i6ure 5;8 and

described in "able 5;-.



36/56

F),+&e *.#6Plan Liew of Shear (all Staircase $ores

Table$ *.-6 Shear (all )einforcement

Shear (all )einforcement ?on each face of wall@8 ft +( core walls ?3G thick@ -Q3G horiDontal reinf

Q2G vertical reinf ?story ;-@

3Q3G vertical reinf ?story 8;@

3 ft 'S core walls ?3G thick@ -Q3G horiDontal reinf

Q2G vertical reinf ?story ;-@

3Q3G vertical reinf ?story 8;@

$hoice of 1ocation:

"he walls around the staircase were chosen as the lateral load resistin6 system because

the stair cores were continuous throu6h the structure. %nother reason for this choice was

the desire of the architect and the owner to maintain o&en s&aces and unobstructed views.

"he locations of stairs were determined by the architect for circulation &ur&oses. "he

atrium above the 8thfloor and the location of the elevator made shear walls behind the

elevators infeasible due to the inability to transfer shears near the o&en s&ace. %dditional

BD Inc. Project: Palo Alto Office Tower 5!


37/56

walls were also not desirable because of constraints for buildin6 modularity ?owner@, ease

of constructability ?contractor@ and aesthetics ?architect@.

Preliminary "hickness:

Since the cores were slender ?.8E width to 2!E total hei6ht@, deflection was believed to

control wall thickness. rift is limited accordin6 to U$ section !5.9:

[email protected]?A.

2.

A.

2.==

R%

%ssumin6 an avera6e interstory drift over the hei6ht of the buildin6 ?2!ft or 82 in@,

the total drift limit is 8.3 in.

7rom the calculated statically eBuivalent story shear values and assumin6 ?@ 3G thick

core walls with no o&enin6s, ?2@ [ the load 6oes to each core and ?5@ only fle=ural

deflection of the shear walls, the drift was found to be -.8in in the 'S direction and

5.5in in the +( direction ?)ef A44e0) D@. 7or these calculations, the moment of

inertia was modified to .A/ in accordance with %$/ $ode .. for calculatin6

deflections of an uncracked wall. "able 5;8 6ives a summary of the estimated overall

drift of the shear walls.

Table *.5: Shear (alls rift

1imitin6 drift 'S drift +( drift

8.3 in -.8 in 5.5 in

Pro&ortionin6 loads to each core:

)i6idities for each core were determined assumin6 only fle=ural deflection. "orsional

ri6idities were determined assumin6 a solid core without o&enin6s and a &oisson ratio of

.2. %ccidental torsion of 8\ was included. 7rom these calculations, it was found that

accidental torsion contributed to moments at each core. "he additional shear forces

caused by torsional moments at the core were determined assumin6 constant shear flow.

% summary of shear forces is 6iven in "able 5;!.

BD Inc. Project: Palo Alto Office Tower 5A


38/56

Table *.76Shear 7orces to /ndividual $ore

'S +(

Shear from direct shear .8L .8L

Shear from torsion .AL .!ALShear on each core .!AL .!!AL

Shear )einforcement:

Shear stren6th for the shear wall cores was determined usin6 only concrete shear

stren6ths and steel shear stren6ths in the walls in the direction of the load considered

?)ef. 7i6ure 5;2@. % factor of .A8 was used assumin6 only fle=ural failure of the

wall. Shear stren6th of concrete was determined usin6:

wccc tLfVP

= where

.2=c for .2WL&

7i6ure 5;2. Shear )esistin6 Portions $onsidered

7or most cases, it was found that minimum horiDontal reinforcement was reBuired. "his

minimum accordin6 to %$/;53 &rovisions is ]minJ.28. HoriDontal reinforcement for

all walls was chosen to be -Q3G.

endin6 )einforcement:



39/56

endin6 ca&acity of the shear wall core was determined with many sim&lifyin6

assum&tions. istributed rebar forces and com&ressive rebar forces were ne6lected. "he

distance from tension steel to centroid of concrete stress block was assumed to be .9

times the len6th of wall. Pn was assumed to act .- times the len6th of wall from the

neutral a=is. "he factor .9 was chosen instead of a smaller value since most of the

moment resistin6 rebars will be located in the flan6es ?)ef. 7i6ure 5;5@ of the core.

F),+&e *.*. Moment )esistin6 7lan6es of the $ore

7rom these assum&tions the relationshi& between a=ial load, area of steel reinforcement

in one flan6e and the bendin6 ca&acity of the core is :

nWysWn PLfALM -.9. += where

9.

un

MM = and

38.

un

PP =

%=ial loads were determined from tributary areas as shown below:



40/56

F),+&e *.-. "ributary %rea of Shear (all $ore

)eBuired area of reinforcin6 steel was determined from overturnin6 moment and a=ial

load data usin6 the above eBuations. 7or both 'S and +( walls, Q2G on each face

were chosen for reinforcement at the flan6es.

7or ductility reasons it is desired that the bendin6 stren6th be reached before shear,

therefore a check of MnCLn vs MuCLu was &erformed. /t was found that at hi6her stories

?story ! and hi6her@, the wall fails in shear. 7or ease of construction, the chan6e of rebar

layout was done at story 8 where the buildin6s layout also chan6es. 7or both 'S and +(

walls, 3Q3G on each face were chosen for reinforcement at the flan6es.



41/56

F),+&e *.5. Shear (all esi6n

(.4 +onnections

Larious connections were used in our desi6n and are described in this section. etail

drawin6s are shown at the end.

Moment )esistin6 7rame:

Several connection ty&es suitable for moment resistin6 frames in seismic re6ions were

considered. "he structural en6ineer evaluated welded unreinforced flan6e;welded web

connection ?(U7;(@, welded flan6e &late ?(7P@ connection, and reduced beam section

?)S@ connection. esi6n &rocedure and criteria were followed as outlined in 7+M%;

58 document.

"he basic desi6n a&&roach of moment resistin6 connections is to estimate the location of

&lastic hin6es and determine &robable &lastic moments and shear forces at the &lastic

hin6es, at critical sections of the assembly. "o be able to form &lastic hin6es in

&redetermined locations, i.e. within beams, connections are stren6thened and stiffened or

beam sections are locally reduced as in the case of reduced beam section connection

which were chosen for this &ro0ect by the structural en6ineer.



42/56

$olumn S&lices

$lose attention was &aid to the s&lices of e=terior columns which are &art of the moment

resistin6 frame. "hese members, in addition to 6ravity loads, are sub0ected to relatively

hi6h a=ial forces that are &roduced by overturnin6 moments caused by seismic activity.

"he structural en6ineer decided to use a combination of bolted and welded web s&lices

with com&lete 0oint &enetration flan6e welds, which can su&&ort a=ial as well as bendin6

forces due to earthBuake loads.

Shear $onnections

Sim&le bolted shear connections were desi6ned for interior column;to;beam connections,

beams framin6 into the shear walls, and the two beams framin6 into cantilever beam

which su&&ort the walkway on the !ththrou6h thfloor.

?)ef: A44e0) E for calculation details@

BD Inc. Project: Palo Alto Office Tower -2


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BD Inc. Project: Palo Alto Office Tower --


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BD Inc. Project: Palo Alto Office Tower -!


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BD Inc. Project: Palo Alto Office Tower -A


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49/56

(. -oundation

"he foundation of the buildin6 serves to transmit 6ravity and lateral loads as well as

overturnin6 moments to the earth. "o accom&lish this we have selected a combination

foundation system. Under each 6ravity column, footin6s will serve to transfer the 6ravity

loads to the soil. 7rom &reliminary calculations for the base &lates of these columns, it

was determined that the footin6s should be -2 inch sBuare. "he second &art of the

foundation carries both 6ravity loads and overturnin6 moments from the moment

resistin6 frames. "his was accom&lished usin6 stri& footin6s. "he stri& footin6s run the

len6th of the buildin6 alon6 the &erimeter and allow a &ath for the hi6h moments

6enerated in the moment resistin6 frame. 7rom similar calculations it was determined

that the footin6s should be at least 5! inches wide. 7inally, the shear walls will be

su&&orted by a mat foundation. "he &reliminary siDe of mat reBuired to &revent

overturnin6 of the shear wall base was determined from the overturnin6 moment and the

dead load on the core. )esistance to overturnin6 was assumed to come solely from dead

loads. "he reBuired eccentricity and therefore the reBuired half width of the mat was

calculated by dividin6 the overturnin6 moment by the total unfactored dead load

?includin6 self wei6ht@ of the shear wall. % -3E = -3E mat was determined. /nvesti6ations

on the use of anchors are reBuired to decrease the siDe.

Table *.5to Table *.: $alculation of Minimum Mat 7oundation SiDe

Table *.5

%all Sel$


50/56

Table *.7

;eter)ine Pu on %all

Dead load

Area B85sf AreaB50sf Bkis

#0 LRoof 8.5 ,-.,5

- L#0 6#2.5 52.06258 L- 6#2.5 52.0625

L8 6#2.5 52.0625

6 L 6#2.5 52.0625

5 L6 6#2.5 52.0625

* L5 8.5 66.-,5

, L* 8.5 66.-,5

2 L, 8.5 66.-,5

# L2 8.5 66.-,5

Total /3.4

Table *.Total do


51/56

4.0 ETABS Modeling - Analsis and Discussion

4.1 Model ;iscussion

+"%S was used to analyDe the buildin6. 7rom the +"%S analysis we were able to

com&are some of the actual load effects with the assum&tions made in the desi6n &rocess.

(e desi6ned the moment resistin6 frame to be able to resist 28\ of the total seismic

loads. However, from the results shown in "able -;, it is obvious that this is a very

conservative assum&tion. "he loads &roduced by +"%S are consistently lower than

those &redicted by the Portal Method. /n some cases the &redicted values by the Portal

Method are twice of those calculated by +"%S. "his discre&ancy is accounted for in the

interaction between the moment resistin6 frame and the shear wall. "he stiff shear wall

takes most of the load, so the moment resistin6 frame takes very little com&aratively.

"his can be &roved by the shear wall frame interaction com&utations it was found that

only about 8;\ of the total load actually 6oes to the moment resistin6 frame.

Table -.#6+( SM)7

-loor

!eam 4omentBinterior

Col$mn 4omentBinterior

Col$mn AxialBexterior

Portal E1A!3 Portal E1A!3 Portal E1A!3

Roo$ ##.2# 2-.288.28 --.#* *.8# #*.*

10 2-2.5 #26., #,8.0* -*.06 #5*.*2 66.8 ,,0.* #26 #,.8, #06.25 2,6.*# #20.0* ,6*.#6 #,#.2 205.*# #02.6 ,20.*8 #,.83 ,-,.6, #2-.8 2,2.- #0#.-# *06., 22./ *#8.-0 #2*.#

255.-5 #05.5- *-,.- 28#.5 *,-.05 ##6.2 2,.0 *.05 586.2* ,,-.884 *#-.8- -#.* 22.-6 *.** 66#.#* ,8*.6( *,#.,# -0. 282.* 6-.*- *#.#2 *2-.*62 *2.80 -.6 ,55.-, 5,.25 82#.5# *,.*1



52/56

Table -.26'S SM)7

-loor

!eam 4omentBinterior

Col$mn 4omentBinterior

Col$mn AxialBexterior

Portal E1A!3 Portal E1A!3 Portal E1A!3

Roo$ #*2.0 56.##8*.66 60.6* **.5* 8.#*

10 255.8 #55.,

##-.-2 8-.-, 88.85 ,#.6

2-.56 #80.-

#55.# -5., #,5.*2 5.2

,,*.62 #80.#8

#8.,0 #02.*5 #8,.-2 82.#

3 ,6.0* #8.*

2#*.6 ##0.*2 2,*.0* #08.-

/ ,-*.8* #8,.65

2,.8, ##5. 285.** #,5.0

*#6.-- 20*.0*

25*.-6 #20.,* ,*0.6- #65.#2

4 *,-.*6 #5.5

20.*6 ##,.,6 ,-*.06 #-0.

( *52.02 #60.8

2-.-8 #05.52 *5,.,2 2#5.0,

2 *-.66 #*,.22

,5,.** 8.88 5#,.05 2,.621

4.2. S'ear %all9-ra)e Interaction

(e evaluated the frame shear wall interaction usin6 the $om&onent Stiffness Method.

"his is used to find out the &ercenta6e of lateral load 6oin6 to the shear wall and the

frame. "he assum&tions made in the $om&onent Stiffness Method are:

. "orsion is i6nored.

2. 'o o&enin6s in the core

5. Uniform story hei6ht has been assumed. /n reality we have the stand 2nd story at

8 ft each, and all other stories at 2 ft so. %n avera6e uniform story hei6ht was

assumed to be 2.! ft

-. Shear deformations are ne6lected.

8. $alculations showed that seismic deflections 6overned over wind, thus wind was

i6nored in the final calculation of forces, deflection, and moment.



53/56

!. %=ial deformations very small, hence i6nored.

?)ef: A44e0) F for calculations@

Table -.*$Shear (all;7rame /nteraction Summary

'S +(

P to each frame 5. k 2!.2A k

P to each wall 5. k 2!.2A k

eflection 2.! in .A! in

*verturnin6 Moment --!35 k;ft -8-A k;ft

Le=t.col 8.58 k -.53 k

Lint.col 9.3 k 3.A! k

^Me=t.col 3A.!5 k A.A k

^Mint.col !.!9 k -5.-2 k

4.( ETA?S Model and -ra)e9 S'ear %all Interaction +o)parison

7rom the story drift data collected from +"%S, we were able to calculate the

deflections. "hese were com&ared to the shear wall frame interaction, as can be seen in

the followin6 table.

Table -.- to Table -.76 /nteraction +Buations Ls. $om&uter analysis

Table -.-

'S "otal eflection ?in@ +( "otal eflection ?in@

Shear wall 7rame interaction 2.! .A!

+"%S 5.8 .A38

7rom these com&arisons, it is seen that the assum&tions made in usin6 the shear wall

frame interaction formulas are verified throu6h the com&uter analysis usin6 +"%S.

eflections differences in the east west direction were smaller than in the north south

direction. "his can be e=&lained by the fact that door o&enin6s were modeled in +"%S

whereas they were i6nored in interaction calculations.

Percenta6e of the overturnin6 moment resisted by the shear wall core was also com&ared,

as can be seen in the table below. %6ain, the effects of the door o&enin6s account for the

differences between hand calculations and the +"%S model. Since o&enin6s were



54/56

modeled the walls become less stiff and a lower &ercenta6e of the buildin6 overturnin6

moment is resisted by the cores.

Table -.5

'orth South Half the uildin6*ver turnin6 moment *verturnin6moment one core Percenta6e of load6oin6 to the core

+"%S -35-9kft -23.53kft .35

Shear wall 7rameinteraction

-A9!.!kft --!35 kft .95

Table -.7

+ast (est Half the uildin6

*ver turnin6 moment

*verturnin6

moment one core

Percenta6e of load

6oin6 to the core

+"%S -35-9kft 59398.!3kft .328Shear wall 7rame

interaction

-A9!.!kft -8-A kft .9-

Half the buildin6 overturnin6 moment for the shear wall frame interaction was obtained

usin6 the story shears calculated from assumed seismic dead loads and the U$ E9A

code. "he same values were 6enerated from +"%Es built;in U$E9A code calculations

for the same assume &eriod of the structure but with seismic dead loads obtained from the

self wei6ht of the structure. "hese values are tabulated in the A44e0) F.

/nterstory drifts limits were also checked a6ainst the seismic interstory drift limitation

6iven by .55!. %s desi6ned, nowhere are the seismic drifts limits e=ceeded.

Floo& E3 ea&!(9+a:e )!e&"!o&/ 0&)f! NS ea&!(9+a:e )!e&"!o&/ 0&)f!

)oof .!53 .!!5

.5!2 .2-!!

9 .5!3 .2-9-



55/56

3 .5!! .2-A9

A .58 .2--3

! .5- .2535

8 .28 .29A

- .88 .383

5 .25 .8-52 .382 .9!

.!2 .--3

!.0 "onclusions

7or &reliminary desi6n of a re6ular story buildin6, sim&lifyin6 calculations were

found to &rovide sufficient accuracy for the initial choice of member siDes. y knowin6

the behavior of a structure, few detailed calculations had to be &erformed. "heassum&tion that &ercent of the lateral loadin6 6oes to the cores while 28 &ercent 6oes

to the SM)7 was also found to be a 6ood conservative a&&ro=imation.

%ssum&tions that the cores had no door o&enin6s si6nificantly reduced the com&le=ity of

calculations but also reduced the accuracy of the results. /n addition, rebar Buantities

were only calculated for a core without o&enin6s. )ebar layouts in the wall &iers as well

as in s&andrel beams of the core reBuire more com&le= calculations which can be

automated usin6 +"%S.



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PART T%O: APPEN;I@ 9 ;ESIN +A"+,"ATIONS

A##endi$ A % Load Determination

A##endi$ B % &ra'it Sstem Design

A##endi$ " % SM() Design

A##endi$ D % S*ear +all Design

A##endi$ E % "onnection Details and "alculations

A##endi$ ) % Analsis (esults ,ETABS and Interaction

behavior of structural systems for buildings

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