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Srnuctunm. ENGINEERING REFERENCE MANUAL 'I='r
"
SIXTH EDITION
Alan Williams, PhD, SE, FICE, C Eng
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Tfw Clmin? "1'-.-"Pr L! Milfinn J %'I-Iif".-=r=i(1n-.1|§-3 ,
Benefit by Registering This Book with PPI I H151, i'|nt_|l{ ll|'i||;-'l[e.\} :-'l.['|i'i l_!|1]'|‘+?|_:[iu['|!'1'.
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Report Errors and View Corrections for This Book l"PI is grateful Lu every reader who tiutifies us of :1 possible error. Your feetliuick tulle-ws us Lu inipruve the L[Li£llil-1|-' JL[1l.i :1r:eun\e1,' of our prutiucis. Yetl can reg:-urt
e1'1'>1rn mid view |.:n1'1'|.>t:rin|1.== m.www.]11>i2|1ass.c01n.ferrata.
STRUCTURAL ENGINEERING REFERENCE MANUAL Sixth Edition IIT||r;n-1-|| F:-ri;|',|||;|_1[ -':|'1hi:u-|li1i-:'-||:
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<.‘<:-it-].'ri_p,iL| E! '_'i'II'l'_', l:~].' E-‘T=:-I41:-isi-.-11-.11 [*".1l-Ii-::u|it:-lls. |:u;-_ l:l"Pl'i'. All riglitri rt-5-:'r1.'-r-:1. I\3=:~ |'-srl ~:-f 1111s put-lit-ali-I--||
[nay i:-0 r~::]:-tr.-rl1|-::r--:l. stun:--I in a |'1=trir\'.i1 sfcsl-.=m. -12' t|'¢1|1s1*.|it|»:--:3. in my I-:1-rn'. -1.-r b_\' ¢1n_\' mu--.t|1s. 1:]:-~:-lr-.~||it-. lm"-t-[mil-zzul. ].-l|-.:-1I|-t:-.:|~f|'il|;..[,, |'1-:'-:.-l'|l'il|g| |It' 1,111--r'|I.'im-. 1.'|'l[l|-:.-lli ii|.|- |-rim-\\'|-itli-1| ||~.'1t||is:-ii-.:-|| |IE' ll|~' ||'|Ll|llsl|1-I". l]IIil|1I.'I.l lll Lil-.' r._lll|ll'll f'i-l;'1[i-5 :.~f .-".]':|i-l'lI.::'1_ l’l"l l‘_'5ll F'iITh .-'I.'.':~|||||-, ll|~|:r|:-n1._ (13. l-l'1lJll'_l
(4?-:'1~|] 5?-HH 5:111:-a 1'.1w.'.;=|:-iE;;:~uss.u-=1-|n l|‘-l[ll'\‘I "T9-l-?|!"lLi'?--i.lTli-Tl _L||1ri|.|'_'|' rt-|'iT| |;|u5_|'|‘-:::=. (l|'||'||[||] N||r[|l‘-|-[; '_i|l] ] !.1-I-]‘;'.|'l'.7
Table oi Contents Preface and lcinowlndgmenta . . . . . . . . . . . . . . .1; lnlrorluciion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\'ii Goclea and Befanelenae . . . . . . . . . . . . . . . . . . . . . . tun
Chapter I: Relnie-reel! lionerete Design l.
Strength Design l’rinciples . . . . . . . . . . . . . . . . . . 1-1
3.
St-rt-113111 Design of ril1.‘lii.ll.lIC1.‘l.l (.‘onc|'ett> Hearua . . . . . . . . . . . . . . . . . . . . . . . . . 1-Ii 5H|'L'i<.'ea:l'.>ili[._5-' Ri.‘l.[|.|l]‘¢.‘|ii'!.‘ill5 l'H|' B¢.'el|||s. . -
L'|J-"LU
I5. ‘F.
.
.
.
.
.
.
=2
l-'33
313'-
St-ri|.> F|.|eLim-i, . . . . . . . . . . . . . . . 2-l laoloiod Column with Square Fooling . . . . . . . . .2-5 ].'<|||:_'11r'!:'] fl|'ll1iI‘i'I.l:l \\'li.h ]'i,'t"i':l:_'||'|;I[I||:_'||' F||ul.i|'|g. . .
L15-LOIIG
B-Ill
Combined Footing . . . . . . . . . . . . . . . . . . . . . . . 2-I2 Strap Fo-nli|1g . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-iii
I5.
Ctmlllever l1I.'iuini.||g Wall . . . . .
T.
L‘ounierl'o11 lielainhig, Wall . . . . . . . . . . . . . . . . .2-1-35 R|']'|-'h'|'|-:'|~s,.,. ,. .... ,.,
,
. . . .3-El ,., .2-ET
I_:*::n:t'|:l
F“
I1.
Eit»lL|iiI.I11s................
. . .3-I2 . . .3-I7 . 3-E2 . . .3-I-BB . . .3-B8 . . .3-J31 . . .-‘l-‘ii
D".-si;-{II fur Fic.-sun.-. . 3l\I "LO
. ..
lJesig|1 for Shear . . . . . . . . . . . . . . . . . . . . . . . . .—--... - -—|. L>—'r—I|—
. 5 -1
.5-Li . 5-9 5-I2
Design for Flexure. . . . .
5-115 I’?
[_.l:'-Rim] |'||"l.'lu||,tu'u.:I.i,|'|]‘|.‘.' . . .
Heie1'ent!es...........
5-:5
l‘J:|1.rI lee PrI.rlIlI'lI|s- . - .
=3-3|?
Snlntiomi............................
5-2?
l'J~e-sipm r|l'5lel1r'le|' Waller. . . . . .
. ll -1 . Li—Ll . Fi -B . l'i-Fl
6-13
Design ol"1\.nel1or H-olts. . . . . . . . D:-si,|-111 uI' Ph-st-r|:sH=.-<.l lvla|.::<>tlr§-' . . . . . . . . . [J11oiil}' .'l|!iS|.|.l‘i‘lI'||f:I2, Tosiing, nnrl [|:la]1eciio|1
6- I Fl ii-Llfi ti 3]
Hel't‘renees.......................... Pmcliee Prnhltems. . . . .. . . .
ii--l[i 6-12 6---I2
Solutions
ll-'1-1
Ghapter T: Lateral Feroee Part 1: Lelerel Foree-Reelellng Syeieme . . . . l =2
lntrrnclilr-1inn.....
..
Basie Components. . . .
$LrI.u:lur-2|] Sysi-er||s . . . . [}iapi|ragms.......
....3-32
Chapter 4: Structural llool Dnaign i. lillI|T>l.lLll.'l-lI'.>[l............ . . . Lo-:1cl{Ic-n1bin:1tions _ . _ . _ . _ . . . . . . . . . . . . . . . .
-I -Tn
i‘:
l'.l|=-aigii Stages . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-l
. ...... . ...... .. . ...... ......
=l -159
[U1-'-J‘)
chapter 3: Preetreeeeti G‘-onorete Design D|.~sig|| for Shear and Torsion . . . l"|'es1ress Losses _ . _ . _ . _ . _ . _ . . . . . C|.un]msil-I: Cunslru<.'1iu|| . . . . Loncl Lialancing Procedure . . . . . . . . fii.'|.i.i<-.:1|l3'l|'|:l<'-Iei'|i'|li‘|i1il'efir.r|u:l.||r|'es. References . . . . . . . . . . . . . . . . . . . . . i"|':1r:r.i-r-.r= Pm-h-Iems . . . . . . . . . . . . . . .
- 1 -455!-
l'J?||.?l ice l"tul.IlI'lus. . . . ."§-rulntiolis
Design for Flexurt-.. . . .. .. D¢.'si,|-111l'-:>r Elieur. .. .. . . .. .. ilesigli nl' 3-iaisniiry IE.‘-olnnins. . . . Design ul‘Sl|e-or ‘ilfznlls . .. . . . .
Pruotitc Problems . . . . . . . . . . . . . . . . . . . . . . . .2-I33 Snlnlinn.=< . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-Bill
l.
=1 ii-1
Rr-ice|'nm:es. . . . . . . .
Chapter Gt Reinforced ilaeonry Design l'1<'-.-:ig11]‘|'i11=-i1|lm'-. .. .. .. .. .. .. .. .. .. .. 2
4-15 =1 -:33 =1 sfl =1 -1 -i -I -51 --1-5'?
De.-si,|;n let Elieur . . . . . . . . ilesigii for FIon1p|'|'e:'-sir|1i . . . Design for Tension . . . . . .
Chapter 2: Foundations and Retaining Structures l.
Design ul l3
Chapter 5: Timber Design .-H|'lj|.|sr.|m-nl Fm:t.ur.~:. . . .. . . .
'l"a.'o-Way‘ Slab Systems . . . . . . . . . . . . . . . . . . . . l—i1 Rl'!l_i"|t'!l'l'f"(‘!i. . .. .. . . .. ... .i-16 l*ru.t'li1:e Prt:-blen1s . . . . . . . . . . . . . . . . . . . . . . . . l-LB Solulinns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . l--1.3
Design offiompression Members. . . . . l"lusli<.'D1.~si:-i|| ilesigli nl'T¢'|1sinn 3.-1e|ni1e|'s . . . .
IU. l‘laleGirdors................ ll. C||||\|n|.\.'i_i<_~ Be_-n|'|'|.~: . ,
. - . 1-9
Elusiie Design lIrl1:lhud . . . . . . . . . . . . . . . . . . . . l-ill Shear and T‘n1‘sinn . . . . . . . . . . . . . . . . . . . . . . . . l-i=1 Cr.\||ereI.|: Columns. . .. .. ....... .. . . . . l-E6 llevelopmelii nnri Splice 1.englh of H1*lr|l'I.||1:|:tnI.'l\l. .
H.
5 ii T 8 fl
—-:|-.. n-1-1 I-Q._._-._-
..
T-l-1
Pari2:$eiarr|ieDe5ign................. 5 Equivalent Laier.-1| Force Procedure . . . ii T
VI.-1'1iI.ra|l D551:-ilmlinn <.1['5I.'is111iI; Fm-tI.rI.'s . lliaplimgm l.o.'11'ls .. . . .. . . .. .. . . ...
S
5'~l.ur_1.' Drill . . . . . .
l\i-t-3 "-3:;|:\-7.1-1T.
T-illl T-3|]
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FTIIIICTURIL
ENGINEERING
REFERENCE
IIIIIIII.
TIMI! 3 $C?N?<'IIJ-E‘ IOF 3&1‘?-Sftlf-B-' el1a]it1'1'
number
subject
l
Rtallliintxall i.'lul|.1:r|'.-1.|Ie Du.-clg|;|
2
Founr.latio||.~= unti Retaining Slruetures
ll
Pres! rt-ssoii Concrete DI:-siglt
-I
5| i'iIlTl lli.'ii.l Fiiuerl llhrsigli
5
'l‘i1ul.1er Utsign
Ili
Rei|u'oroutl :\lrL\itJiiT_\" Design
T
T.-'ilr!rul F||r|1'_-c
ti
Bridge D‘l.‘>il,l.£ii
You must rernnin sharp for eight hours or more. If you plavml a spa-1't hack in school. your em-it'll trie-.'| to put
-lime to
time to
:i[4tl'i
finish
you in g;an1e—rolatori situations. P1\o|.i=.a1'ing for the Struc-
Clieek PPl's u.'elisite for last-minute up-dates anti errata to any PPI Imnks _1,'o|| |ni_:_rht have anrl are lwingilig to the I.‘.\nun.
tural SE] einnn isu'l- uulch dilTere'ui- l'ru-in |n'e]mriug For a l:-ig gslite. Sonw part oi your preparation slnnilrl he
Obtain u st‘]I\i\i'4'tit'* tr|'.>[r_v ofthis hoo]-:‘s imlos. ‘:'ou niav be
11'-alist.ie anri rep1~0sentat.ive of the e>:=nn onviIon1nent..
nhle to jiliotoeopy the actual intlex: i|lii.‘1'[iHi.l'i.'i.‘l}'. you may fiurl the index as a riowlilosrl on PPl':=i W‘F'litEiil|I!.
Tlierv: are several things you Ci-i]'.l tlo to rnuke your review more |'npres.e11i.aT.iw=. For socarnple, if you gnT|1e|' inost of
Ii you i|ave11't alreatl]: rlnne so, marl the “.-lttlvioe from
your 1~o\-iew 1~t-sous."-I."-s [i.e.. books] in advance and try to use them exelusiveljr during your review, you will lwenriin mn-|'n l':-unili:-u‘ with thelu. [GP 'i‘?fli]i‘£-iI'!, you t_::~1n
also atlri to or change _vour roferenres if _vou fintl
Exnaiiiiiees“ seet.io|1 of I-‘I-‘Is wolisito. ll you ioiwift. hnmi ioiin-wing almig on the l-"lngi|1re4n'ing E.~o'|.1n Forum o|| PPI's 1.vr_'-lisil-u. use tlie st-arrl| i'luu:l-ion to locate relevniit discussions.
inutleq\|nL'i1."s._) Ii'it's eo11\'e11ient_ visit the exarn lu-cation in urtler to liud
Learning to use your time wisely ia one a-F the innsr.
the huilrling, parking areas. mzain romn, anti t‘I.'iiiTl'flfliI|1:-i.
iiiiptu-lnul. lllssoiis you eon lea:-u (luring your rt-view.
If it's not oonvt-nieul.. you uni find tlriving tiizeeiions
You will LllltlIIJtllJlIi.‘Iill}' encoiint-er questions that entl up taking much lolig-or than you F".\i‘[11i"€‘T-Hi. ln some i11stnnI;=¢.'s. you will I.‘-ntlse your or-"n 1.lelu_\-‘s hy sporuling too nineh time looking tllrough h-uoks for things you marl [n-1' just. h_v looking for thr: hooks. [.l|n|nsr-l\'os.!].
antl'."or site maps on the web.
OI:he1' timt-s. the questions will entail too nnleh work. Ii is important that n port-ion of your 1\evieu' invol1.'1.'s snlving problems so that you learn to i'IZ!II![Ii.1‘.l'Ji2£! thr-so
sitluuious tuui so that you can make intelligent. (l1?f{‘-lfilflii-"5
Tnln: the lintit-11,‘ uover oil your r_'nl1:ulni.ur and i:lu:i:k to
make su1'r- you are liriligiiig the otn're-:1 size repluoenioin
iiattei-ies. Some calculutois ieqliive a (llilt"l‘(‘!l1i- kinrl oi‘ hnttery for their "]n:rrnnru:nt" nu:r||ories. Put the cover hack on and ii-€!Et1Il1'l" it witli a piece n-F 1118.‘-'-l-iZii‘l_i§ tape. ‘Ll.-'1'itre _'i."fl1ii‘ na1nr- on the tape to irlr!miF_1.' _\'onr calrrlilamr.
if _3'o111' s]i-no ealeulator is not the ssmie as §.'o1.u' ]n'irna1'_v
about skipping such t|ut'stio1:|s tliiring the exurn. Two realist-in review hooks that _vou to-n1 use rlnring your oxani p1‘r:pa1'aTim1 to pl'artinv solving ‘|'|-1'~|'rl‘i-l!“1i‘lH il‘l1‘Elll.|'ll".' Si-r1rt'hn'ul Eriyiri-rr*r'nry Sol-slot! FI‘tllPli'Tl-!-'5 (pull-lisluirtl |.1_v Proitrssionnl Publications. lne.}_ anti Sirnei-urr.Li Sample
yn-nr spare calculator is Functional.
Qn-e'=.-ztimts mid Soh:iior1_-i [plllilislinrl lay the National
FIFIEFIJIE YOUR Bill
Collueil oi Einuuintrrs for El1gi11ee1'il1_g on-I1 5tlrv|.‘}'i|:|g,].
t'nl1:uluior. sp1:1u.l at few niinutes iauniliurizing yourself with how it worlrs. In pnrtietilnr. you shunltl verily that
[ I Untiu.-r snow Lrluiins. shovel, aunl Lnrp io lie on while
WHRT ‘I'D DD I I-‘EH BITS BEFORE 'I'I'IE EXAM Tlier-re are a few things _von should rln :-1 week or so bnforn the exnln. You should arrange for ehiltlcart: and transportation. S111-re the exam clam not al1.va_v:=< start or -nnrl at the
dt-sigu:|.I.u1 time. nu-nke sure that 3,-our chil1lt:u1~e anti transportation srrnngemeiits are fleitilile. III
e
new-er.ppil||aee.een|
installing chains.
Ulierk tire prewttrcs. Clieelc your car's spare tire. Clieek Fm‘ tiro ilistallntiori t.£vt'|l5-.
't"1:1'ii'}z t-hut you have ilie veltiele ununiul. Clieek iluiri levels [n-ii, gas. water. hrako Fluid, iruilsrnissiou fluhl. wlttllow-wttsliiitg soluiio||). Fill up ear with gas.
Cheek |_:ut.t.t:rv an<:i charge il' 1'|t-er-ssu1'_v.
nnreouueruon I Klrow sonic-Lliirrg about your [Lise system {where they are. how to replace them, etc.]. I Assenililo all requircrl maps. I Fiat anything that rnight slow you clown (missing
wiper hlaries. etc.]. Check your car's taillights.
two slnall plastii: lJ-oi-ties of water travel pack of tissue {keep in your pocket} I I lianrlkorcliicf heatloehe recrrtedy I I persoiial rncrlication
I I $5.00 in rniscellaneou.-1 change
Allis the recently arriverl Dhl‘|r' license st.icl~:o1'.
I I hack-up roarling glasses
light. oorniortable sweat-or
Fix anytlring that might. get you pulled over on the wuy to the exain {l.ruruetl-out taillight or ln.'ai.lli,g,lit.
' loose shoes or slippers
broken lenses. hairi tires. missing license plate. noisy
I I cushion for your chair earplugs wristwatch with alarm I seyeral large Lrasli bags ["raint'oats" for your lioxes
muffler}. Treat the insitle windows with anti-fog solution. Put a roll of 11-u|1cr towels in the back sent. Gather exact change for any hrirlge tolls or toll maria.
I Put 52f) in your car's glove hox.
of bnol:s_]
I I roll of paper towels _ wire coat hanger [to hang up your jacket or to get
hack into your car in an en:c|~gcncy_I I extra set of car keys on a string, around your neck
I I Choc]-: for current 1\egist.rat.ior1 anti] proof of insurance. Locate a spare door and ignition key. Find your ."i.~i.!t or other 1iiJilLlt5Iltlt.‘-ti.'.55iEl-k1[l.1.1‘- carils anti phone nurnhcrs.
I I Plan out alternate routes.
The second kit eotrsisl-s oi the [olloa-iiig items and shoulrl he left in a separate hag or h-ox in your car in
they arc neorletl.
Seconrl in imponancc to your scllolastic pn_-paration is the ]nit1pu1'at-loll of your two eituiii l-tits. The first kil-
copy of your application proofof-r.leli\'c1'y liglrt lu.ru:h hir-vcrago in tliornms or caus
consists oi a hag. hox [plastic milk cratts hold up hotter
surrglr-lasts
lililiiilflfi ‘@'"|.‘l...51..-Ell‘
xv
...........................
than calitlhoarti in the rain]. or wheeled t.ra1.'£'l suitcase containing items to he brought with you into the exam roorn.
extra pair of prescription glasses
raincoat. boots. gloves. hat. and umbrella street uiap of the t_":tutn area
this hook
parking permit. lntt-l-L'ry-pLm'e1io|l desk latnp your coll phone
other text-hooks and reference books
piece ol' rope
let-tor admitting you to l-he exatn photographic identification (_e.g.. rlrivor's license]
regular tlil':tiE1i1fl|'y scientilie,-'L'|rginceri|ig dict-iouary review course notes in a three-ring hintler
cartiboarti boztcs or plastic milk crates to use as liookcases
]n'imary calculator spare calculator
instruction hooklets for your calc|_||at.ors extra calculator batteries atraighterlgo anti rulers cotn|1a.ss protraetor
scissors stapler transparent tape uiugnilyiug glass small i]ewolor‘s] scrowrlrivor for Fixing your glasses
or tor rcrnot-lug hatter-ies l'rorn your calcu|.ato1I unobtrusive {quiet-] snacks or candies. already
unwrapped
PREPARE FDR THE WORST All of the ocrnrrrcrioes listed in this suction have happened to exaniirrens. Grarrte-rl, you cannot prepare For
every eventuality. But oven though each occurrence is a low-prol.ml.iilit_v event-. taken together tlicsi: oL~l.1ur're1u:es are worth considering in advance. I I
imagine getting a flat tire, getting stuck in tralfic. or running out of gas on the way to the -m-ram. lmagino rain anrl snow as you are carrying your
cardboard boxes oi books into the exani room. Woulil ])li.ti5l-i'LT trash lings be lu:lplul‘.*
I
imagine arriving lute. Can you get into the cxiun without having to make two trips from your car?
I
liuagino having to park two hlocks from the exam
site. How are you going to gel ct-erytiring to the ("xatn room? C-an you actually carry 1:‘-\'c1'yl-lrillg that
FII
e 1e1eer.ppl!||aee.:ee|
lurnuuutrlou
lmllpraint pvns and full-tip ||mrlrr'r5 is pruliihitrrri Eur an-nr:\l l‘l'!:-‘|."-lfl-11:‘-l. If yuu finish the uxuru curl]; ruul thrzrc nrc still rnurr: than 30 1ni|1urr-:4 |'rmmini11g, }'l.'1ll will hr! |'1r!r|uitTr-rl tn lczwu L110 1'u0111. ][ you finish lvau llmu 3|) t||i11ul-us l.H;'l'urI.'i-hr‘ curl nf the rrxaln. you run)’ ii-l: rrquirnri to l'{‘lIl.ll1l[l miril the renrl. This is r|r_mn [.0 lie r:r)t1e¢ir|e|':;1l_.r_! of the
gyfi
Dial _','m| 1;1um'I.‘rl- bet-'|v1;1:il rnniius mul rl]z'I.|||I.'-lI."1"i' Dial _','uu 1;'<.|m'I.'rl- l.H.‘l-'Ni.‘(.‘ll l'1.1'l- and i|1r‘l1L's? Dl1.l_‘r'Ulll.‘<.ll]\~'L‘I'l- Iruru gugu LuillJsull|lc|Jn'::rs\|:1's':'
Dlill yull (‘1CI]]\'II!l‘T- l;»<\t.\\'-em kPa aml Pu? Dirl you rr:c:lu::r:l-1 all {lain 01:-l.aim:>=:l lrom ulllcr l5(JlII|‘CE.‘H. tnblrrs, and figr|rcs':’
people wliu urc sl-ill wu-rl-ring.
When yon: luau-0. you i]'1l|:sIL rulurn _1_-our cxmu lJ<'.lUiil(!l-. You 111113: not lrccp t-he cxaru buoklct. fur lutcr r1:vir:1.v. If t.lmrr.* are any |'|lLi':=lT'l0ll:i t.lmt. _vm_| rliinlr wr'n_'- l'lawor|. in r.'r1'u1'. 01' I.l.ll5l;Jl‘J‘lllJl1.‘. u.-sir ll |mur_'1ur fur 4| "‘rI.-putting liurlu“ on wliicli _\'r1|: can submit _\'r:||r CIIIIll1Il1'lE!1'lL.\i. Fullriw }"Dl1l'
11-i‘o<'t<1r’:= ruivicre in ])ll(!I‘niI'lt1B; tl1i.~'.| ¢.lo<.'1.1me|1r.
SIIIDIILII YOU 'I'l.I.I{ TU DTIIIEH EXIHIIIEES IFTEFI THE EXIII? Tlir: jury is u-uL on l-his qur':~l-iuu. I-"L'upl1: l'L'uci_ quils:
rliffrerraiii-ly tr: the mmln rrxprrriqmcrr. Some puripln arr nrinrgiznrl. Most are mclu-iilstnri. Snrnu pnripln um-.~rl tr:
imwilul by iallrilig with oilier {'J
ruul p11':[r:r lo j\I5L gel. into :1 hul Luh Lo mimk and sllll-l.
l-low To sn|.\r|r n|uL'r||=|.e-\':r|n|r:|r 9"|§.5T|.9"§...
l'|.I0.~it r:ngiur~r'r:a. l~].[)plJ.l‘C‘[l.ll}'_ l-:11: in t11i:i1utt1_~r cutcgury.
\lr'lu"u yuu brrgiu l'_‘l1l'll screiiun uf the |:':cru:||. ul::sr_'1'\'c the fnllnwing silggnaiiniis.
HIZJII hr! viralating yrmr "DI-Ii-ll. oi ailrrncrr" if yrau talk +111-mil
I
vxulu. Il's \'.]llEL'lIli.- nut. Lu risk how su11||:r.1ur_' 1:151: npprmurluad n f]lll'!5ilflIl‘.l tl1|~1i- hurl _\-"nu mmplornlgr
I_.|5r_! m1|_~,' rlio pnlicil prr_1\'irlml_
I D0 not apciirl an ll‘I1I|T‘(lll1.HT-E amcmm 0t'ti1ne on an}; singll: q|||_-st-iun. If yruu |lil\'L‘ nu-L u11:=w1:rul n qucstiurr iu u EL't'l>il.l'lll~\l.l'lL‘ zunuuut ui Lilnu, llmiu: u 1lUiI." of it urul l11l'}'\|'[! D1].
I
5-PT your w1'is|tw:-itrli a.lru'm fin fi\'r' 1i1i1111T.0-H l1r!i'n1'n rim
eurl 011;-4u:l| [mix-lluur an-:.=:siu||. alul 1:;-=0 Llmi rr-uminiug tirur to _!.,'11r:>s:; at all uf tlir: rr_'|m1ining (‘|_‘l.lL"l=‘i-l.UT.ll5. Grids
Since I.'1.'1.'ry.'\uJ1c 1.\'l1u tuulr the I_'.\rmu lms arr-1:11 ii. yuu will
the will?!-tlllfrl with crt.lu::r £!Xi"IllllllIT!II'-‘.1 i111|11e<:li=.itel__v after the st_u||||1r-Ii. How:-vrer. kr:cp in minrl Llmt. it is 1-'01-_',' rlisqui+:Ling Lu Lhink you :\||r~l\~r-ml 1: r|nr:s1.i(|11 rcurn-1;-il_','. u||]_v ILL: lmw: :au:nr_'uur' t-1:ll you wiu:rr' _\'m| went. wrung. To emsurrr you rlr: not viral:-1l»1: t-lu: nuiirlizaclmiilrra |-1grr:r:—
1]‘||I!1‘IT ymi siigunrl liol'n-re taking rim exmm nmkr! snrr: _vn|| rlu nut. [|lHI'll.55 any I.-ruuu pi'u'Li|.'r||]urs ‘Nil-ll |1(-u['i|u wluu lmw: not also tal-r1:u i-hr: rrxsuu.
arr! rlmt. you will ii-P !-illl‘\E‘l'!!i.'i.Flll with alm||l. L!-]'l{| of fl-'Dlll'
gllII."_*.iH1'_*R, anrl t|ir.':=i.' prliiits will nu-01? rliam iimlm up fur l-iu: l'4.-w puilirs 1-lml. gm-u iuiglu I.-n1'ul:§' 1.\'url-riu_|;, Lluiriug tiw 1:1:-it l‘|\'1? lninutras. I
Maire rmental nntmi ulimil. .nn_\' r|\|r!sl;inme. inr wliirlr you mlilinjrt. find .1 r*c|rl'r:|:l 1'0-_s].i-|2|1i.~.
erurl during llw scoring |m.|<1'ss anti ill.5(‘Ull1ll-["1 from thr: |::u|.1n: so it. is Illlirlf. |11:r~|:s:;nrg.' to tcll ymrr proctor. lint l‘|4"' :-zurr- in nmrlr ilm 1'|1‘lP! lH":=lT nu:-lwnr li¢\l'n-rre luu-viug nu. 9
lllulru sure illl uf your IL'l5]JU]lHL1:i un llu: zunswr-1' siwcl. are durlr. and L'Ull|.[J|L'i.El}" [ill the l‘Jl.llJl.ll\‘_‘S.
§°|=.ll.'|5 'l?l.\1|.5.§'|'|!1.-'.'|"|¥i.F4\l?!.|.5F!!.|-|-.?.'.. ...... ...... I'|l£ll1:¢' 11-ui:1l:s arr: luz-l. in Cil.l'L'lL'5ti[l1.‘dS. |\'cr:]1 Lllr: l'ullu1-ving
iiouui in miurl wlmn _1,'c:=\| arr! 5rilviu|g Lhn r!||rl-nl'-c]1.npior
r.;11r-=s't.io11.<.<. H<:»])1=.l'||ll_v. t.l|r:sr- .=.n||g;g0st.l0|1s will |fIIZ! suito111.1! la: |.l'm-lug I110 c.\um'|. I I l)i.r.l you rr-clicck yuur lIla1L|i|I'1]mli(ri1l eq1mlirms'.’ I I D43» llie unilrs cmirr-1 1:-ul. in ynur (1ill(‘1ll€tllI.'Jll5':'
AFTER Tl-IE EXLII
‘r'e-l. t.l10rr- is r--0ln|::illi1ig Lu Iilu ait.r-1- rile exam. lklrmt. ]JI.‘\U]Jl.U go hu||1::, i-ll]'UW t-huir cxuru “kit-5' iutu llu: CDIl1l'!l'. aurl crillapfin. A 1.\'m*k later. whflu tlmy can lwar
lu thin}: alnom the (‘?L[JI.‘]'lII!]](‘?(! agaiin. ll1c_v 5liI.l'l- inlegruting tlwir uxuin kits lmclr int-u i-llcir uurmul livus. The carlculaturs go lmrlr into L111: rlrnwrar, tlu: lmulrai gr: liack on Tin‘: 5lH".'l\‘i‘H. Illfl S-'3.l]l] in clmugre goefi imrtlc inmliu: piggy |.|aul=.. zlml ill] oi l-110 |||]:srr."]luuI."uI|:|s stuff lirmrglit tn tilt! ox:-1ru Ll; pill: ilflflk wlu!rr!vr!:|' it cninu frrmi.
Hr-1\.=.'.*s wlmt. l 1".lllgE£{‘=ii- 3:011 (lo as 5~I)IIl-ll as _\'m| get. llIII-I111). hr-f
which you sigiml your agrermlrviit. I I (fall }'nu|r ni||plu}'e|- and tell liiinflinr that y-mi nfleci lo Lnlrc E1 111r_'nl-ul |lL'k‘lll-ll day uu Llulirizly.
FPI
l u|unur.ppl!||aul.:om
gvlfl
arnuerennt eunntssnrue aersasnce unuuar.
A few rlays later. when you ean laee the world again. rlo the following. I I
lllake notes ahont anything you woulrl rlo rliffereutly it you. liar] to take the esain over again. Consolidate all of your application paperwork,
eorresnoiulenee to,-“from your state. ant] any paperwnrlr that you reeeiyerl on exam clay.
I
If you took a live review eumse. call or email the
I
Visit the Engineering Exam Forum part of PPI's
instructor [or write a note] to say “Thanks.”
there were two answers for sneh-anrl-sueh question—o1' even, perhaps. that suelr-ant!-srleh qnrstien was missing
horn their exam hoeklet alt.eget.he1'. hlaeh of thrse claims nn1sL he L‘-Ll'll5itl.1.‘1"D2.l as a potential nr.ljusl.un_-nt to the 1.-ut score. Then the exauns rnnst actrlnliy he graded. Sinee grading nearly 5l'l.II.‘rlll'l exams {eounting all the FE and PE
exams} rerntiers spee.ializerl eqni]7nnent. seft.wa1'e. anti twirling not normally ].\ossessetl by the average employee. as well as time to do the work [also not
normally possr-ssecil hy the average einpioyrz-e','|. grnrlirrg
website and see what other people are saying abcnlt
is invariably oulsonroul.
the exam yon reek.
Ourseumerl gr-arling eannet. begin until all of the states
I
H.etnrn any hooks you Ii-on-owrsrl.
I
Vlfrite tliarrlr-you notes to all of the people who wmte letters of rieeonnnenrlatimi o|' |'ei'erenre for you. Finri and rearl t.he -f‘.llFl.‘|‘l-i.l':l' in this hook that onyers el-hits. There were no ethies questions on your SE exam. hut it rioesn't make any riifferenee. Ethical
have rt.-lurrn.-11 their score sheets to NCEES anti XCEES has sorter], separated. organized, anrl ennsolidated the
I
hellavior is espeetetl of an SE in any ease. Spend a few minutes reficeting on how your perlormanee
Iehligatiens. at.t.itur.le. ]?n~esentation. lieiravier. appenrnnee. ete.] might he about to ehange once you are ii-neliseri. Consider linw you ane going to he a wle lno-tlol for others itrountl you.
I I Pnt all ofyeu1“1‘eview hooks. hin
seore sheets into wh.:1te\'e1' “secret sanee sequenee" is hr-st. During gtmliiig. seine of the score sheets “pop out" with any ]'.lLllIIllJL‘f of alnionrialities that rlernantl manual searing. filter the inrliyidual exams are seoreri. the results nee analyzerl in a variety of ways. Home of the analysis looks
at passing rates hy sueh tlelineator.-s as tlegree. nntjor. university. site. and state. Part of the analysis looks For siuiilaritirst hetweeu physically arljaeent roraminees [to
look for elleatialgj. Part of the analysis i'lJUi'b:i for exnltt sites that lIl.l-1\'l1.‘ statistically alinormal group performanee. Anti some of the analysis looks for exam ques-
tions that have a r.lispne]>e1'tie-iiate ii-action e-l' sueeessfiil or llilsliecesslttl eiralllinees. .~‘|.||y1-say. you get the idea: Grariing is not merely putting your exam sheet in an
eleetronie rearler. All oi' these steps have to be eernpleterl for lDl]5"E of the L-xalltirtus helore any results can go out. FIll.l.I.L‘I"
Onee NCEES has _g1'ar.|eri your test. anrl netiliecl your
By l-he l-ilne you've "'u||rlo||e" all of your peeparnl-ions. you might liave thought of a Few things that eoulrl help
fttriire examinees. If yon have any sage eonunents about how to prepare. any suggestions about what to do during or hring to the exam. any comments on how to
sl-ate. when you hear ahout it rleperuls on u-‘hen the worlr is clone by your state. Some states have to
flP|TIl'\O‘-'11‘ the results at a I1-eartl meeting; others prepare the eert_ifieat.r-s before sentling out notilieali-ens. Sente states are Inore eoinputerizetl than others. Sorue states
have fill exanrinees, while others have lll,ll[lll. Sn-tue
i1n]>t'e'-"e this I:-ooh. or any funny aneerletes abe-nt ye-nr experlenee. l hope you will share these with me.
states are shut rlewil by hllzzanls and iltlI'l‘lt‘€t|lt's:
Waiting tor the exam results is its own form el'rnetn:1l
The EKHJII rrsnrlts are not released tn all states simulta-
others are nrlrninistratiyely ehaliengl.=ri—ur|rlerstafl'r.'ri. inarler|uat.ely trainwl. er over hnrlget. There is no pattern to the puhlie release of results. None.
torture. l‘|.lLl1ough the net-uni nu'n.'l1ine grn-Liing “only lakes seeonrls." eousirler the following laets: (a} NCEES prepares
lnnltiple exams for eaeh administration. in ease one heeornes unusable {i.e.. is i|s1pprop1'iulely reie1.\setl] hefore the exam rlate.
Sines! the actual \'e'rsion of
the exarn used is not known until after it is finally given. the cut. more eileterlninatien oeeurs alter the e:-tam iilnte. I weultln‘t he stirnrisecl to hear that NIL‘-EES reoei»-es riozasns. if not hundrerls. of elaims from well-rneaning examinees who were llll_l"}E- eertain that the exams they
neously. [The states with the fewest examinees often receive their etsults soonest.) They one not releaserl aiphabetienily hy state or exarninee name. The people who failerl are not n|'.I-tifierl first [er last}. “'r'on|' coworker might 1r;1;'ei\'e his or her no-l-ilienl-ion today. aunl you might he waiting another three weeks For yours.
Some sl-nl-ts ]J<.|sl- the names of l-he stl<1'¢e'.-:sl1|l -esalilillees. iinsueecssfui examinees. or lioth on their oifieial state
wehsites hefrme the results go out. Others uprlat.-e their wt-lisitts niler the results go out. Some slates tlon't list much of anything on their weiisitcs.
took were fatally ilawerl to some tit-glee-—tl'iat tl1en.'-
Er."-meniher. too. that the size or tlliehness of the r.'-m-el-
wasn‘t a eorrret answer for sneh-anti-sueh q|:|rstion—tl1at
ope you reeeive front your state does not mean anything.
nrrnouu¢noa Some st-ulna send n big cungmt11]afi0ns Imckrlgu and t.1r.!r1.il'ir.!=-1t.n. '[1'tl191‘-=1 .=u=.11rl :1 hig pavkago with :1 nnw appli-
5.!|P..!l'|'|.!.!' I9‘-|...!.'l§§ ' .............................
rsatirm to velmeat the mcana. Some states send a 1)-0st.ca1'(l.
[ ] Cclulmnltc.
Sulur: 5|.-ml u u11r_--pngr: l1:l.L|.-r. Su-nu: 5141141; sq.-ml yuu an invnirrcr Fur your |iE!l'!Il!-3-E fans. (A1111. what :1 welcnms! lrilll]
[ ] Xulil'_v 1111-. |1I."l.'.‘|[J|[! who wrur.|;- l<:Lr.|;-n< ul
You just have to upcn it to fiml out. (llmck I110 E||gil1-ce|'i||g Exam FD-l'll]]] on the I-‘Pl w:-lrsite nvgularlgr 1-0 llnd unl which :.-:Lalx:s lmvc ruluazecd tlwlr 1'l.‘till||Cl:i. You will flntl lllany uthcr anxious URI-1]Tlll'l'E‘l.‘ti Tl1f!|'|'!. And aJ1_\' number nl'l|11nmm|:s mnsplr:~1.cj,' t.l1nm'ie=|
and ruulum.
3;];
mcm11nmndati<:»n or rnfernncn For ynu. [ ] Rrmd "‘F.|'LQs about 'WhuL Hnppvrls .-'Ll'l,#:r ‘Y'all Pass; H10 Fl:-:an1” nn PPFH wnhrsitn. [ ] Ask your un1pl»o_1,'c!r for a mi:-nu. [ ] Tull Lhc full-as uL PPI (W110 luwc l.1¢_'uu ruul.in' fur _\'n11 all alm1g] T-I1-n gnarl news.
'lVhilu yuu am: wzlilillg. I hu-pl: you will l.|ccu|||I.' 21 “F'orun1" 1'eg'|1]ar. Lug nn tmfbnn and help at-hm" nxamilloefi l1-5' rah:-11'ing 3:-0111' knnwlrslge, mz]-|e1'ic!11cc-5, and ‘Ni!-i|I||I!l11..
Amil. ifycn: he-ar any gounljcnkt-_~1 an wurk. I hope you will slum: them as wull.
FII
0 v||uur.ppl!||aul.:ol|
Iinrv-rlx
Codes and References CODES
A|neri|::=u1 5-1:-ci<.*t._x' -:rl' Civil E5|||_.'_:i|ut=
:"|.uu.-riL'uu .-'L>sucizLliu:| u[ Stem: Hll.',].l1|\'-£l.f." nml Trams]1uriuliun Oflirrilllfi. .4.*l5'I.|'Tf) LHFD Brr'r1'_qc D|'.‘:'1ig]‘?l Spurifirrrliiun-1. EH1 \'.'r|- QUIT). [.AF\!":iH'l"[_'l]
Auu::ri|:rn|1 'L'T0:1r;-:1-1.0 I11:-t.il1|Ic:. H-uilrliri-y -II.-‘mh h’-::q-rn'r-r-
Lt:-uri-4 fur" Bml-:lm_qs and Uliwr S!-r1:-rh:r'rr-s. 2l]U5. [ASCE] B||i]:li11g' Sr.-imuic Bull.-L3" (_‘uu:u.ril. NEHHP fi‘-:-rm.n-rr1r.'nrIr.'r.l'5'r.-im*r1ir Pr01I:.umn# for N¢".w B'm'ld'1'r|_r,Ia and Ofhcr .';li'1-amt.-n'r=-.-a. 2|](_l!§l. INHHHF]
rru:'nL< for Sf-r1:c!z.rr'al C-'0n4:r¢'£r.' and If-'mr|rm'n!rn'_r;. EIHJS. [.I\C‘[]
Inn.-|'lml.io|m1 Uqrlr: C-m1m~_i|. l'ru.wm=zéu.-ml Builriing
Alllcwicrml Fc:m'-;t- and Papvr Asscrlnticlll.
Pl'r'rn:-at-_."l'-‘rm-ahrcl:-uirwl Cczrlrrrcrtc 1111-itilutn. PC-‘I Dcaign
1'1-1.-=.ig-r1 Sfrr-r:Jfir1r1Hr1rL fur
Natianrlf
H"rm.-i Cr?-ma-l1*ur:firnL A.S'U__.-"
C'rJ-dc. 2'l](][l'. IIBCI Hrmrfll-|ml.'.' Pf‘r‘.r1r't.'rf mu! J'-'rr--_-aI:'r--.-1.~¢r:rl (_.‘r)Tl.r:J‘|'-'l¢?. Gill 4?-(I.
LRFD. urilfi -C-7urrurwrr-Em}! mu! Huppfr-'rru.'rr£. ZDCI5. [I\'D5|.
21101. ]PL':|]
:\uu.-riL'nu Forest. auul I"'np-|:r 4“LS!EL'H.'l.l'|l.-lLllJ. Spa--riu-I D:-.-saywa .P1'f)I.'L\.iIG?T-'1' fur" Wind rmri 5'-rria"rre-iv. 1r'ilk Cr:rr1rr1r.'1r£rn1r. LZIKIH-. |SDP\\’S]
T110 Dllawljr-|'|l‘j.' .‘:iu|.'i|;rl_\'- Blrihlirag; C-‘aria-' R-vq'r¢t'r'+-1r4r*rrl-< rem! .5-'pr."r.'l,Fir.'r1l-irlrl-i far M-:11mnr;,r 5'£1'm'.h:rr.':i. Qlllllfi. [l\lS.lC']
A|um'im|1 I||stir.'|:|10 of Stu-nl Cn|1st1'ur:l:irm_ Hr-!.i.-ml.I'c D¢'-‘Eyre 1'l-l'r.m1m-l’- 2lll]fi- [AISC 3E'i'|
n_|:|=En|:_|_|c|:a
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l"'|.l:u.'riI."a|u In:e.l.il.l|lc uf 5LL'1.'l (_'-u-u:
C-ur|J.~.= uf E-lll.',iIll\‘_'I‘.'Il"aL 51'!-wrur D:'.s'iyn-fur" Briilifirlyn. U5.
for Slrurrl-uT'r1-I rmrl Slaw! Brn'lrIir|g.v. 2005. [.-USU L’l43[l|
Cu\'c:r11u1mu: Printing Officrn. 19515;. [NAVFAC]
:\uu:riL'nu ImaliLI.|1c of Slur] Cu|1>,"l-r1:|r_'liun. Slrrr.-I Cruz.stmr.-l1'rJ1'l Mrlnmll. 13:11 arl. 'i'[]ll'5. [.-\I5lf.5 }.Iruuml|
Si111]1eiuu Strcmg-Tie C0|np:u|};_
llr"rmn' Crm.utr'|u1lzan
Cn1Jf1F'rr?01'&_ (.'nmIn_r; C-2111!. 2[)Il.
fiuunl'im1|1 lrrm nml Fitrvl ln.~;l.itnl.r!. l"h"m'H'r »hnc1"J'm11: $}"""'_,.I'itf:rl-iurlfor flu: De-.-
l-mu! 1'|--l':~mIrr'r'-s. QIIIT. [A151]
PPI
l vru|ur.||pl2panl.:nn
Iinrv-rlx
Reinforced Concrete Design 1.? = 1.2D+ 1.1111" + 11_r.L'
1. H-1rv11_L1T|| D11:-iigll l"ri111'i]1|1~.~1. ... . . . .. .. . . . . 1-1 E. 5[11~1|1__',1l| Du~'i1z_,11 r.1l1'l1'i11l'<111.'='rl F_'u11|.'r|.'l<* ]]4~111n:-1 . . . . . _ . . . . . . _ . . . . . . . . . . . . . . . . . . .
-
. .“'_§-11l"I.-'i.1'?1‘1!lrilll_\' H1':|11i1'1\|11r111l:-1 lhf llr1:11||:-1 . . . _
-
- E121-.~'1i<' D<'1\=i1_;_||1\[1'll14.|1l. . ..
..
.
5h1'111' 111111 Tu-1'11-1:111. ... . . . . .. ... .. Fifli rl-L;
.-
... .
(‘u111'1'1~l1~ '('0]11111|1:i . . . . . . . . . . . . . . . . . . . . . _ .
_. _1|_>- - r,‘-_,'__.;:,.;i—,; 'DG
. lI11‘-\‘1'!lu]'|-I111‘-|1|' :'1l11| §_l|:-|i1'11'- |.1;'1'|;.§[ l1 1:-l'
14519-4|
|_Acr 9-§| 1ACI§I-5|
11=11.1111 + 1.1151 + 1.1111
1.41:1 s-3
i\5Nl"‘lIlll]_\'. 1111-:1 ;1n'11.-1 11.'l1:'r|~ {.5 |l'J|'l l|1'l_."'l|. l|7l|'|1]1u'r* l.lill"\1.'il|1 |.§i ll"\'.'||r'11c' 1l|r' 11-.-i111| ln.-1rl. l11|.~' ||r:-I
l*l1'-t'1'err'11:'\":-'~ . . . . . . . . . . . . . . . _ . . . . . .
. . . . 1--'l[i
ii-1'-:-11 In:i11<'|xi i11' -.1 r.ii|1i':-1iu1|1||i1_\' I111-1111'.
P1'11|1'li|:'1' ]’|'ul|-|1~|||.~: . , , . .
... .
‘I11.-|1]:1.ru l.llI§ wi.ll1 l. LE 11.']|.1':1~1.-;1.1'l]:1|1|.:|.lu-|.u:|.1l L-1l1:1_-11-1|.
l--lll
5§ul|1tiu1ua _ . . . . . . . . . . . . . . . . . . . . . . . . . . _ . .. l--15
1111 .-u':'1"||'r' |1'1.'r'| .-.1:-i.~41|1i1' lr>1'r1|'s.
Example 1 .1
‘I. STRENGTH DESIGN PRINCIPLES
'l'l'|I' I'll-||I>'-\'ill1L' illll-iH‘:1l.i>m1 _-=l||>'|'-'1-1:1 l\'||-i<'=1| |'|'11|||v nl'a| sitir~l
Noam‘.-||c]at1.u'~e Ilf.'1lIl I121».-1121 1-;111]|.qI.l;|.lu' 111ml.
1-iipr-i ill‘ lllf kip:-1 ul: |.||f
I-:u|1| :i1|<' 111 1.1."-:'i_|1||1 .=111|l |11'1:\-.1||'1* r>l' ll|1i4|1=
‘kip-4 111' |||'l
luml 1iu<- 1-.» ]11'1':a1=1|1'1- -.-t'1=uil
}:i|1:-111' [III
1'n0t' |i\'1~ lcmcl. .ur,-__.
li1-'1' ]lli\ll r111|[ !lw |1|:1||.
};l|Jt- ul' lllf Icipc-1 111' l||l
lluur I.l1'aHl luaul. i11I.'l111l]11§__',
-;1~1"1.'i[r- [1-\'r-I l'n|'1'1."
l€i|1-énr II11
lmul duv 1-.1 I1-'1il|'.\':1l1'!
};i|x- ul.' [hf
“'1-"=2Q_!"'f -:*P=:
:1|1<:-vr l-:1u1.
1ci|1~'u1' l||l Icipn 111' llrl
-li1=11'il-111:--I ||:>\-1-:1
}1i|.r-=,~'|l
ll’
\1.'1|.|d 1u:1.||
Iilpc-1. ul: |.||f
S3,-||1l1-ul:1 "1 r_>
+111.-51L-,. 111- 5111- 13';
1-‘ = 1211+ 1.1"11-J‘ +1151.‘ -11.2.5‘ 1_.==11.11D+ 1.1111-" + 1.1111
‘HI.-|1]:1.1'I.' lI|.5.1'. wi1h l.l]1'. Tu! ;_{;|11-1;_;I.':\. |1]:1.|'I.z-11fplll1llI."
]'i1'i|1l'»:1rc'r.'11|1~|1l . . . . .. .. .... .. ... ]-I13 H. T'|'.'4|-\‘1‘11}.' S|:1l1 Fij.'.=>H'-111:1 . . . . . . . . . . . . . . . . . . ]-~'ll
U
Concrele
1'<'|uF1l|'::a:I |u:'|-1|. 111:-lm|i11|;§
cl1uldi|11_I, 11111.1 111111111115. 111,11, — 1.17! 1-:1]1s,-‘Tl = [ll ki]1|,-"fl
1'|111ldi111.I, 1‘1ll{l.l'1i1]1111lll:i. 11.11, = 1.[i 1:111:-1,-"fl |'l11u[" ]i1.'|1 Iuml. 1r.';_
= L2-'3 I-:i|m_,I"f1
]1<1rizc111111l \I."111d |11'1.~:+111r1~. 11,-, _ 1.ll k'1]11~",-‘Tl 1.'r-Hi:-al '1.1'i1'|:| ‘|'11‘1".\-l:i1l1‘1". ,-1, = [ll] ki]1_,-‘ft l)1~h'-1'11fi1'|:- rl1r- ||1:11ci1'|11|||1 um"! 1|1l11i11111||| 1]:-1-i_|.511 In.-11!:-1 11-1| H10 1'11‘-.~'l-l'|u1.>1' <'u]1111|||.~' Suilefr-:1-11
l
— —
T]1=- aaxiul l<11ul<.111 u-111.‘ 1'11-lutn11 1.l111- lu 1l1m-1.11-zl.|.l luzul i1~' llf :11-",9, + 5111,-,~] Lei L!
Ruqulrad Strength 'l'l'|:~ 1:-:|11i1'r~
Q, I11ll|rl]1|ivt| lr_\' 1||1* :1.]1]1I'u‘|)l'l1‘|11" |-:1:'|1l
l'm't<1r>=. 1.. T]11- 1'o:|11l1'w.l .<.l1'1-n|;I.|1. U. is :11-l'i111-ll hf." .M"1' S-114*. FLE mi
L-' -— 1 4113' + F] U — l.'.?[D -1- F -l- T] -|- l.Li[L
1 11.5|jL, u-1' S or 111
$1619-1| H}
jncr 9-2
. . . 1211 11_|{1.2
k'
'
jAc1 9-;1_
li'
'
L? .
1111 l-il]}fi
'l']11\ :-'|xi;1l ln-:11] 1111111111 (:r>||111111 1l111' I11 the t'l1'm1' li\'1*l1'1:-1=:l is Il;51r',| jl 11:? 2 {Ill l'[}'(l-5 . _ . :~llr|'i1H'I(.|-271 . _
L" = l-217+ l.[il:L,-1.11" 51.11" R}
+ -:11 5L‘ u-1' 11 s 11--'1
+ 15>.-ml-11~11(1.11
H
2 = C12.-5 I-:i|h
PPI
O
v|\|1Ir.|I|rl2|Ia1I.:n1II
1-2
S‘I'll\|¢T|IlllI-.
ENDINEERINH
REFERENCE
lI-l.Nl.Ill-
.|*ll1.1sfr1211'-1:111 for Ear. LI 2DT‘l -nip
Pv
1" as-
_
| r1
L i [B11112 11!] - T2 I'l
: P|-1:3
i
—o—
1'1
is
—1.1-—
-qi
l‘ T111.‘ 11111111 |u1'11.l 1.1t1u|11' ('1.1l11111|1 1.11111 11.1 1111: 11.11.11 ll‘-‘I3 11.11111 i1~' Lr :
i
111.1 L1 . .
.
i
u-qi
.1
= l_l.2_1|:‘J2 l-zipsjl + 11.611129 [1 111111-1 — E1 l1i|11.
1.111111.-1:11.l11:er 111111111111 111111 i:-2 [1;i'-'1.-11 1131'
+10-511*] 1-:j|1s}+1[I.5][[12.-5 l1i|11~'_}1 — Z1‘--13 1111111
(1 @)112 11.1“
=
fl . _4; '°]12El 1'1]
T1111 111i11i1n11111 1-1lr1111gtl1 l11v1'-l 1l115ig|1 luarl 1111 1-1 11111111111 i:-1
— |I[l.'J][D'2 l-1111:-:] I {1.If1]1
'l'l111 .1u:111l 1111111 1111 1'1-1111 111111111111 11111! 111 11111 \'111'li1::1| wi111l |11'11~"111|1"1.' 1:1 1_1l1i11.i111.-11 |1_1' 1"1'.:11.1l1'it1g 1'1_111:‘1.'11 111 1111: 1111.111||11t1
= — 133 I-111111 pl}
2
T111‘ 11111xi11111111 11lr1'|1gtl1 10"-'1.-1 111".-111;11 11.11111 1.111 11 1_'1.1l111|111 is
Z -11,1=1.211 ~. 1.11.1 -11.5.1. = {1_'.3I:|1I'El1'! 1»:i|11-1] ~ [l.li)[li2.1i 1»:i]11-1] —'— (H.511:-I 1-E5111-1]
= 2|‘! 11111-1
:1'r1111pr1-.~1~1i1111_'|
Z -,Q=1.211 + 1.111,. + 11.11 = {1_'.3.'-IIIYEIE 1»:i|11-1] + [l.l1i)[1l 1:11:11] + (H.511: [Tl-"11 1111111-ii = 113 1-121111-i
|1c-11115011]
1:111 11}
ll
2 = -F1 ki|1.~1
129.15 1-zips]
1 [l.li}1[-5 ki]n1}1
11.1111-111-1 and is 1.,'"1v1!11 by
(11.5
|11111"|1p1'1:111111111:guv1~1'111-]
Z -_.-1.1- 11.911 -1 1.111-11,-_. + 1.1111-",.
— :1L11].l.i ki].1e1
W
|r11|11111'1'1=§i1111]
Z -11.1=1.-211+1.1111* + 11.11. +1111.
T1111 axis] 1111-111 111:1 1.1111" 111111111111 11111.‘ 111 l1111'i11:1111t11l 11111111 ]1-1'c~11111111'c- is 11111115111111 I1}.-' l.11ki111.1 |n1m11111t.~1 111111111: |:]111 11111111.
=
. 1
= ‘I15 1111111
= -1 11i]i1-1
,
1
+ 10.311129 G 1-1111+: — 1.1 11111111
kip
2
P1111 LT
1.1
Z-11,1=1.111:-+1.111..+11.111-1-' =11.:2,1|j11-2 111,1fi,1+1:1.1111_1111]1.~1_1
-1 fl:I1(U.1.- _ -11-11 fl)
.H‘),
1.1
:|'11|1|p|11'_-1-11011]
Design Strength T111: 111.-.111-;11 slrr.-11gl]1 1.11 11 1111111111.-1' 12.'1'.llIhl:-11.5 1.11 1111: 111.1111i11:1l. 111' Tl11111r1*1lr1a1 111111111111‘. :-1tr1111gt11 111' the |11111111111."r imiltiplirerl Ii}; 1.1111:_1|ipr1_1|11-i;1t11:-:1111_111;.11|1 rr_1|'l111-1i1_'m l':'|1_*t1'n'.
1:1. T111" 1'c1l11tllu11 1'111'1u1' is 1l1'fi111:1l in AC1 501'. 9.3 1111 1.‘i= [l.l]U
[l'1_1r ll1~:1:11r1' 111' t1'||.-111111-1-111111111113111 .-'1'1r1iu11.\1]
131 = [l.'F5
[fur 1111111-1' 111111 10111111111:
1?1= 11.111
[Fur 1111111111111 -1'1t|1 .~'|1ir111 11-i|1i111r\1-1111-111]
1.-"1= [H15
[Fur 111111111111-~' witli 14111-rnl 1i1_~==.:|
1.-"1= 111.115
[fur l.11.~<'1ri11|.1 1111 1'1.1111'1r-11' -'~1lrl'11r.1='§|
sluroneeu eenensre IIEIIGII
2. STRENGTH DESIGN OF REINFORCED ODIIDFIETE BEIKIIS
..' .-.',,,,_,
1:-|1:=im| rr.-i|1furr:-||1|."ut imi|.~x. |r|_r],_.-'I_' 1||mci|1m1:|| r.1':||-=irn| rl~iul'11|1'|."11u-||t inrlvx
1-3
—
in n Ifi'[4l.|'lg'llL|l.|.' |nI'|\l|1 with t1:1|.1-ii-1|-1:
Nomunclat-um
n'i|:f|||.-|1-|u|'|:lI llIll|_'|'
ll
-:||'||l|'| -::-|' |~c|||i\'i1l|~1|.l |'|'l'|il|1p,Il|=||'
"1|||n.1
uL:Lx'L|uu|n am-:1 <:|' [1*1L'iilZIIIl
slnzxw ||]|||-1:
.4 _ .-1-1 .4
rs-i|1fr.»1r.r-u1c'|1L ,-1--'-.-Ii
Beams with Tension Reinforcement Only
:'|.| 1.-:\ uf uulllplurc.-si|.:-1:: \'|.-i!||.l'u|.'1:|.-|'1|.v|:J|.|£
- 2 an . -_an
TI."ilI|fu!’IfI‘ll]I2‘l][ area to -:|r'-'clu]: thr-
Ill‘
illlfil ||f1l'||ni11l| |‘
In n::c:n1'(lm1n~ with AC1 Sun. 111.2. n r
fllul il iH "IND aui-wl.lt|\I.‘-1|. 1|'m1 tilt! ll.'11-.~'i(||'| l'lffi.ll|[l.l|.'lL'k'l]II.']1lluau; :L"iL"l(lL‘l|..l'2 The 11u111i1u\] fl¢:x1:|:m] 5111.-n|gtl| uf u ructn||gu|:11' Immn in rlc!rivr2ci"' as
<.Il11:\[:\l:|-:ii.l 1;; |'|:|J||.';|n
rc-i1:fum'|nc|:r arm t-:1 h~n|mu:c- thr-
_ -3 Ill
I1:-_~:id\l:|.| l1|ul:ul'l'1l
0 fi..
111.. = .4.;,»1(1_‘_’"“j;ff,)
\\'i:il1|.| uf |;um|1I-:1-.-:\iun f:u:0 uf m»z:u1lmr
i|.|
u1'|1 '.1.'i||T]|.
in
rii-=h'||1r<- :frH||| <'n:1r|.~1:|1' r\n||1|=r¢--wir|-u film! to |)l"'l‘llil'|\l :1:-[is
in
G.
|:'41[|1]:|1'x~
I-zip:-'
ri
-:|L-"|:||1|‘1! {ruin -:'x1|'|‘|:||¢' cx:||1p|‘<'_\'
in
I’
|l'
fl.
It-i|1Ic>m-111-:-|n
llqlmfiug tlw H"ll.!-iilt! nlul ru111pr:rs:-:i\'sr furcru:-= acting nu 1111: HDC‘lLi[hll ,g.,'"i\':2ee- the {lupth <11 thc! lI![[I.li.'I."Ji](!Il]l L'c!r:t.angul:-:1"
=at.|'c-_~1=< 1:»|ur_:l-: :1.-4 H _ .-'1 J).
u.s5j"b
-4-J»("'5)
in
11
l1:!i.l1Iu!u:!t||u|1l
t‘i.Ill'l]J|.\l!!i:ii.\'1£ 5-1L'|."lI||.§[|.| uf m1||;-1|:-tr
1ur_,-'m-’
Ii
=-:~1rc~.~:.~:» in EIl'1IIl[HII"-\‘-i~iI.'IIl 1'<.'il1i'r.I-1'H.'11|t'l|T
lhl,-'i11"
JR-
_v.-iul-:1 :¢lr|~n|.|,rh -:>|' r1'ir|[|::-rct1"Jt|:'r||
||.r,=m-’
Hmlgu cit-pth
not 0.\::!c!:!d rt-uU,,_ Fur n Ln:|s:in|:-n|111IL'ullr-rl :-;r~ctim1.
il.|
dc-;+ig|1 mum:-ut Ill:-run". 11l,,,'-bri’ rI|.~=-i|L|| nululr-uf --11|*n|:!i| HF thr:m1suu|:ii|1g l1n1|gu-:» n|u::i|num rlw-:
1|.r_,-'ur‘
r,-1 = [L9 amjl. |u1|'|1:n?.
fr; If, .1-I;
-'~!.....< I-L.
uuluilull "(‘Illl'!l| :-:~1rI:~n|:th 4:-t' n
1I|1('1lJlJ'L‘l'. or mini1111u|l rc<]ui1'ul mu|m'ni slrI.'||gLl|. slmll
in-I11F II:
Mn =11.s'r.w..
ft-kips in-|11F III T1-kips iu-lhf -L»:
'l"h:_- rnq||i|'nr| |'ninfurr:r:||mm r:1r.ir,\ {En a ;.5i\.'n|: F:1<_‘tn1r1"l mu|||r.:nT is tI1=.*1'|
m|:mI:|c~r
‘....
r~:'-4ir.lun| 11m|11|?11t {AL — .'lJ',,,,_,,}
AL,
Fm-umrrl mumseut cm 1111: Jmuannbcr tc~|'nei|.1~ furue in the 112il|fuIc1!l1|»:'u1
in-ll:-E -1»: I1-Rips in-lhf ur I1-kips Ripe-
_...
. . :_|r.e-..Jf_)(1xi,I. 1- an
ft-I-:i]1s
.1-I,
Tu
'l'h:_- mz1!iln'|1l‘n p-c-|'|||is.~sil:lr_! l';1r:tr_>rr_e|'l mmnmmt on tlm
;
If
I :'\'
=&
H
-[Ida
Tlmew mqn'r-fission:-c nmy lm msulilj.-' prngmnilnud using :1 ]'1i'lt||.|-|:||I!||.| L'i'll(T|.lliI1'l_l]‘." A]1<.~|'tL1'|T._i\'I.'rl_\_»'. mliwigll l1'||:l|I1-4 !)1a'|.j.'
Symbols :1‘, :t|1t|1]:Il1!:1sl::-u
he ll:iL'£|.'H.'" nml r1:nn'm1g.',i11g tlu: L'x|Jrcniiuu" in t1:1'ms-:~ of the H'1‘I:-ii1'H‘l rvi11Fm'nr-lnmlt index. ....-. give-c
ZUIIU fnriui
9.-
:~1::-ziu ul cant-|'|1:-11 |I1L:l'1i[|]'I|I'.\-e-iL|!l. film"-1'
1.-1 ||.u|
I]ll|.Ki.l'|1|.ll]l F|Il'llil] :11 [‘IKl"I'lll\l l'Lllll'|Jl'4.‘14<*3i.4Jll
—
film. [|.|'Jl'Ji5 5.1
atmiu in lc~nsiu|: III'i12|fI.'It'BII'll]I."lI|[
p
.-11'nir| in lT‘Ul1l[l"|'l"-"-"'\-‘illll r|"ir|fr=r<'|"|||¢'r|r ratiu of TE‘l1F~ilJ[l L1'il1I|:rn'I'|L|c'l|T. .-I,,|"-'1-'-'
Pl-
|1!i|:fi|r|'u||||'|1t riali-:1 pru-z|ucri|||.g 1|::l:L||t:1'|l
|flI:‘_\Jl
-itrzlin I:-:1-1:r.li1iuL|.\' 11uuci1|||1n1 tr-nsinn rr'i11F<1rr1'I||1"||t mtirr in 1| |'r.‘4.'r.|I.|1|:1.l|l-\r1.1|.*».1||| '-1'll.]|Tc'm=i-rm
||7'|-- |||
miuinm|1: :-11luwuIrl»:- l'1'i||fmc~c|L|c-llt mun»
—
F|
TT!i1'|l'||r|'r'lI1|~|1t rnti-:1 p1'rx|||:'i|1|1_ an t<-r|.~:i||:||-
—
=1
I ‘
ff. —
It-i1|t'u|u:|m~1|t uni}:
4':-lltrcallul fiL‘1I'[iIIHl
1% = -.».'lfU-‘J — [|'.529=k».'} . r‘
)"L|>p1_-rulizc .'\ |II]‘U‘--'i[|L'E- n 'l.|.4.‘eiE|g[l aid l-hnl- la|n1]em_-5 u ugzxiln-.~l .'U'.._-",|':I|4|"3.
Tension-Controlled and Compression-Controlled 5-ectlnns A:-= :==p~_'('il1|.-xl in ACI SI.-In 1U.'2.3 zuui shuwn in Fig_ 1.1. the um11i|u|] l'l1~xuml eitrrllgill of :1 nwmhur i:-i rc!n1:h0:l PPI
l v|u|uv.ppl2|:|nnl.:en|
Cuncr:-He
1-4
§'|'lll.l¢TlJllll.
ENGINEERIIIU
REFERENCE
ll-lllllll.
Figmve LI Recranwgwar .5‘\‘.'ess B|'c1:11" crass section 9
atram 1:l|11lr|1:-utlon =c — 121.003
I
I
I
atreaa duatrlbutlon @351“-
I
G
I -l— 'C|.B5abf,-I
I <1
Ii-1fl—-q-q
*1
1-1
I
.1, 3-
/I/
+—— -c
H 1
——
CHI
1-»'r-»1r—! u s-9
.-.112
M
—I———#E
1.'.']1c11 t-I11‘ st r11i|1 i11 1111: 1'.\:tr1:111r_: ('U'lll.[JflI!i:}iI.'|.I-ll I'1h1:1' r1:111:l11:1-1
uf 1,- ; U.l'.][Il!. Fur g_',1'111l1: GI] 1'1‘i11[1Jr1:1:|111:11t I11-11':i. .\\C'-I
:1 valuv 11iII.lI]lIl5. D1:|11:111ii11g 1111 t]1<::1t1'11i11 i|1 t-I11: I-1~1uii1111
S1:1:. lII].ii.l§ 1m1'111111:1-= :1 11'tr11i|1 limit 11f
r1I.r:r:I. 1I11= :+1'»rTi-r111 ii-I 1:l11.\'1:eiIir~1'I 11:-1 1':I.lI]11'T‘ r.r:|1:ai1111-110111.111]Ir11I
1, — 11.11112
ur ('u111p1'L':i::~iu|1-1.1.111I-rullud 111111 ll1|.' st11:11giI1-1‘01l111'liu11 f111:t1:r v11ri1~:-1 Fr11n1 11 1.1111111: 11F ILENI I11 (].[iI':.
1"'1C'| $511‘. 10.3.4 1i1:Iit1u< 11 l1:11:~'iu11-111111111111-mi 1,1-1‘iiu11 11:.-1
Il1:'111:<:. the 111:1111'1aI 11.1-:i1-1 1111111.]: r11Li11 11-: gi\'1~11 I1_1'
5 _ 11.111111
11111: in wi1i1:i1 I:h1: st-1'11i11 in L111: 1'xLr1:1111: t1:11:ii1.111 st.1:1'l
11,- ‘I3 fi.iiII].'] 11'l1m1 1111' m111'1'1*ln r1=111:|1r:5 in-1 11ITi11111T-re :-1T1'11i11 uf 1,-= [|'.i][i3. H1:11u:. [rum Fig. l.l. I'u1' 1-1 1'11I111- uI' 1,- - D1105. 1111: 111'11Ir11l il.‘iIh' 1l1:pl]1 r<1liu is givvtl I:_1'
1!
'l']1I.- :st.rr.-11g! I1 1'1::1:l111-1i<.'111 I'=1ct<;n- f1.>1' this 1r1'.>|11;li1i=.'111, Iiirr 111c111I11:1':-1 with 11:ci1111g11]21r st-ir1'1111:e.. in giv1:11 I131‘ AC‘-I FI1:1:. 1-1.3.2.2 1-1:-;
-r =
E
..'_.
iii.-111')
,_-1 = 11.1-1:1
T111: f11ll11wi11g r1:111ti11|1:1]1ip:1 are 11hI:ai1111.1l. r1 = i].3T"-'T>."f,_1'1I'
1",, = 11.11111.-11,11 1,11
F'i5!__ HIl.3.LI 11.11
. ,1,=11.:11s1.-1.- 1 1*‘J,’
4,5) = I].-Hi + H31‘;
11-= 11.3111.-.1, 1:1, = 11.15 |;’,. <_: 1111111 11.-1_.~"11-2]
j11|1|11l|11,1'm'-' -: 11
‘I’
0.2.’
E
111111151111! 1-ir.1'1:111!,ti1 i1-1 ]i111iI1\1I I1}; ACI 5111:. l[].H..'1 L11
1111111 l1=1‘_,'111*'|
:- -‘_"ZIlZIIIJ]I1l'_."i11-’|
'I'I'11: H1111:-l113TI1 11.~; 13' = ILIHI
I11 11 I-1:11.
1]1_:fl01_~tin1111 are 111111-rI11r:r11l, p,"i1.'i11g 11<|w|11:1T1'- 1\':1r11i11g n-I‘ i111|.w:111li|11=; [11iI111'1-. AITTI S1111. 1li.3.3 1Ir~fi|1n:-2 :1 1:0111|1r1::-.:=1ir111-1:11|111'0-II1'1I 1-1re1".1i1'111 aue that in wI1i1=l1 l-I11: :sLr<1i11 i11 l-I11: 1~111111-1111- lc11,2
.
[i.lUf'..»l_,,. 1111- 111i11i11111111 1==1|111_~1:1I'1l|1: 11111 t.1::11:¢il<~ .~1I1-:1i11 =11.
111‘ = 11.115 -i 20.111111 LII“
= (1.65 |11]11i111l1||1
=
Fur l1u.\111rz'1| 111:.-|11l11:r:1 11121! [1111-'1' 1111 1111]11l I:.11'uI uf P,, €
J’, - -1111111
III
l-'ur :1-1:1:ti<11'|:< H1111 lie in TI1(*: 1r1111:=iTi1111 111girJ11 l1r.:n-.-1.-1.-11 the 11.-1111iu11-1'111111-11111-1| e1|11i cu||1]1r1:1111iu11-1.'r.111t1'u-Ilul Ii111il>.=. 1111: 1.-=tr1:11gt]1 rcd111:l-iu11 I'11ci-111' is 11i1t11i111_'1i I'1'1.1111 AC1
nun-w.ppilpar|.:ern
1-, = 11.11114 H1_\11-11', H11: 11m111':=1I 1-1:~:i:1 1I1'-|1r.I1 r11t.ir1 i:-1 giwll I1);
511' — 11.1211 T111: 01.11'l'L'-.<]1ul11ii11_g 1-1I11:l1g,II1 1'1.~1I\lL'Iiut1 I'1|('-l.u1' is r;-I = I]-El? The 11111xi1|111111 11]]11\1'11I1l1: r1'i11i'1.11'c-1:111.1.~11I. r.111i11 i:e.1]1:ri1'01l {M111 Fig. 1.1 11.11
1
If
yam“ — H.311-i.-'_1‘| F |.|
nsluroneeu eenonsre IIEIIGII
Example 1 .2
1-5
[1]] Tlw 1111|11i1111| 111r.11111:11t of 11.‘:-ii:1t11111:1: is
A 1'1:i11f11r1:1:1i 1:11111:1'1:t1: shah I1-1 si111pl5' s11|1]111r11:1I 11v1:r 11
:<[::111 r.»I' 12 ft. TI11: :1]=_1|1 I1.-Ls 11 1:01":-1:1'1.111: <‘1.1tl1|11\.*.~Hi\'1T:
E
.11, _ .-1.1,.(11-
sl-r1'11gL]1 11f3i][H] ||1i',<"i11"'. z1|11i 1111: r1:i11D.11'111.'1111.-11l 1'u-11sist:1 11l'1111. -l grmh: GU I1111".-1 at 11 i111J11 1'1'1:1l1_'1' with 1111 1:IT1'1'tiv1:
111-11th nf ii i11. 'l"l1n 10111] rlcmtl I11n.1I_ i11nl11r|i11g 1.h11. scall-
1'fl.‘_'-.'2 i113](fit]
w1']ghl uI' l-iIL! :
=
[11] f_'4.111;-'i1|1'r 11 :~'|11I1 with 11 12 I11 wi1l1I1. Wluni is I-I11: 11:u:ii1111 r1'~i11l'11r1:r:1111:|1T 1111111 ]'11'111'i1i1:1i'.’
= 11:11:» 11-111111
{I1} \\"]1:11 L-1 L111: 1InptI1 11F1.h1: 1'1:c1.1111|g11I:11' :-1T1'11s1-1I1I11ck'." [-1*] \'1.-'I111T is T|1r- In\'1\1'-r1r111 11f r.l1r1 i11m1'1111| rr:si:1r.i11g 1111.|1111'11I-'1’ [1I_I' \\"]'1111 is LhI_: l1u-|11it1a'1I Ii1;:11l.ll'1'1I :<[11.:1'1g1I1 uiil I2 in whirl:
(5.78 511]
1-.1 I1.
(1'] 'I'hn lh11iti11_11, 1'ni11I11r1:1'1111'11T 1'1-11i11 F111" .11 r.r111si1111I.'u11l.|ul|I.‘1| -—11'1rliu|1 i-:1 fl‘
1- = II.-'_ili];'.I I}-P — I1
sI11I1':’ [1:] \'I1"11:11. is tiw 1111111i1|111111 1-1-1:1"111is1='iI1Ir~ 1I0sig11 F1-11"t11r1'\1l
111111111,-111. 1111 11 12 i11 \\'i(I(: s-I.-111'.’ [Iii \"\"hi1l i-H Lilli: 1'1|II]I1III.:1:I [i'1[rtIJr1I'I.| 1I(:i1=I |I.mr.i t1i1.>l111.':t1t I11
AC‘-I E11. 9-2 1.111 11 12 i11 wi1l1' :1l11I1';’
:10-1111 : 111.;1111j1111.11:»1 7' 110.1100 ltl.
— 11.111-I
[11] \'I1'|111|; is H11" 11111:ci11111111 |11:r111issih]1: 1-itr1!11gI:]1 I1:\'1:] iivv
T111: r1:i11iiJ11:v.-1'|1<-111. 1-=11_.i11 |.11~u1-'i1.l111i is
]11111I 1111111111111 1111 1-1 12 in wiclv sI.11h':' |:I1} "|.\-'I111t is I.l111 111111ci11111|11 ]11!r111issiI1I1= .~11'~1'1.rin1"- I1*\'fl] live
11 = A" hr! _ 11.22 111*
]u11<.l 111011111111 1.111 11 1‘! I11 wi~1Iu:sI11I1':' [i] \"1"|111l I:-1 l-ilL' |)L‘l'll1iH$iI'JiL‘ 5L'l"\-'iL'L' ]L‘\-'L'| li\.'1: 11.11111?
1:12 i11][[i i11]
S11-ii-1b'1111
—- D.iJ[II3
[11] ('.I1111_si1i1:1' :1 12 i11 1.1'i1i1: slab. ': P1
Th1: 1111'-11 nFn11re 1111. J. I131‘ is [LEE] i112. T111: 1'ni|11'ir11'1'1'1111~111 1111311 1'1-1'u1'i1i1'
H¢.~|'11‘~:.~, 1I11i::<1I:1rLi1_=t1 is 1Ir|'1:
4 = [(|.2[li11'*I}I_l2 i11] l 'I ll in
,1. = 11.11
— II].'.7!‘Z in:
T111: 11111_\1i11u1111 p1‘-r111i1-1sii1]1: 1I1"si|;11 F111:iu11:\1l111111111:11i i1-1 III1} Eq1111Li|1g H11: t1:11siI4: 211111 cu|11]11'1':1siv1' [1.11"1.11."11 11|.'1i11g 1111 the .~1r~rI.i1111 giw-s the 1i1:]'1th of thv r:q11i\'1-1111111 1111:11111g11]:~11' 1-111-11:-:1 hln-1~I1 as
1-1,, = .1.-11,, _ 111.111111.:m11-111,».-1 _ 5.13! ft--hips
.. . -_. }[u11.11|]u .. 111 H: fun = [1112111 5*-’-W1-I’
(11.5-'3) (301111
1 12 111} 11]’
= [I143 in
I_l'_I- Thu e1|1]1]ic1I i'111'lur1'1i 1h'a11i 1111111 1111.|1111'11L is
Mmzl .2 :1: 1“
[1:] T111: ]1:1'r:r-111'111 11-E Th1'- i|111rr1111I 1'1::si1-1ti|1|'_§ 11111111n11t is
uht1'1i111i:1i l'11.1111 Fig. 1.1 11.1
_
1I—g=fi 111%
{1.2](1_1.l2 IE)|j12 111’ I1 11
= 2.1111 11.-111,111
1211 -1-I11.
PPI
l vru1ur.||pl2|:1anl.:e1n
C11ncr1-1
]_-is
5 ‘I I ll i: 1' ll I I L
E ll I I ll I5 E I I II I
I E IF E I E ll i> E
[14] Fr:1111 AC! Er|. I]-13!. the 11111xi11111111 pv1'11111a.~1il1|r r'1l.t‘|I!1‘|fl[]‘| |1wr~l liwe I-n:11'l ||1n-111-1‘-111. is-1
II ll ll ll Jl l
.‘1'r1I|.1!1011 T111: 111.‘--1]g11 1114.1-1111-11L [u1'"l.1.11' 1:1
.'1I.._r__ _ M" — .'1I..;1 =
.;."\
11'" =
—-1L-G ft-kipea — 2.59 Ft-l~;l[15
- 11.1-"1 fl-I-iips
hr!
_ 111 |l1f 1j1=,111"1.-1<111{1(12 E) (11111-11 FD)
{I1} T111: 111=.1:~:i1n11111 |1-1-1'1ni:\-
[12 1111111; 1111“
111111110111 is
-V.-.=
= 51341 ll1f~'i11"'
.11
’
1.“
,. -_ -. 1111'
H
-11'.~[1 j
ii = i =11.“-1-T?
= 3.14 l'r_.-I-:i|11~1
-'1'_
1H
,
]'| F 1111111 A Ill“
_ 1.116 ft-kipea I-'1'n111 A|1p. .4, :1.-§111111i111.{11141111111111-m11T1'-nllml :-1|~rTim1. Tlm 11'1_1-1'r1_->11-u11:li111; lL'1Jh-'iUll 11~i11l'1_1-lu-1111-11! 111111.-11 is
[ii] 'I'l|1'1 11-1}1'111i>=1~i|1|1_1 1~1_-1'1'i-no lm=1_"1| |i\-1"; lnml in 1,1L = 1-Hf
.11 — 0.25-3 T111: r1.'11|I.1i11'd 1vi1|l'1.11'111.'1111.-11! rut-iu is
_
I:'2'§'H1.E'Pl'i ft-111]):-i:}(1|Hl[) M
11111
_
J
[I2 Ft]:
1'P=T
= 11121 1111,.-E1
.
'
H.251’
lhf
Iilllllll —
= it::|[
Balanced Sir-Iin Condition
1-11.111111
.171 '|1.r1]11|1r:r-(I .~1t.mi11 r11111di1.ir111 is 1u~|1ir~\'11'~c| 11']1s'11 thv I:c1111-.~'i1.I]1 l‘1‘i|l[L>l'l.Tl.!lilll'l|1 _1'iL‘|1|:s Hi[ll.ll]1£LI]L‘Ull5]_'|' 1'-'i1|| lhu 111111»;i11|11111 >=t-111111 i11 the c'u11cr1:t1' 1'1c111'h'111g :1 1'1-1l111‘ (1fU.U|.lZI.
‘[110 rc!i11lh1'fi*111v11r. 1'aTin rc!q:1ir1':l 11:1 ]11'r1-1"|11c:re r1 I1.-1]:111r:rerl r11.r:1i11 -r*1:'|11:Iit.i|'1-11 in give"-11 I111"
1111) 111-
= []_|HL-EH
'l']1u 111111111111; 1'r1i|1fc1m:!111c'11T 1111.511 Fr:-1' 111011511111-H1111rr1|l1‘~r|
1.-r:c1i<111 is I.
. flu = |:|i.5'_r_|
$1".[)|]C|.'i
flq = H.-'i]1],!1| —'_
I1
_|'__‘.|_H1'.U'||U — "‘-'1 E_, H-. _ ,.-P
I11 11c!1'ur{l1111n~ with AC‘! SH‘. 1U.-:1. L111! 111i11i11111111 ]'1<1r1'111i1-:».~
:11-1111 M 11-11.111111
L.
.‘?- p
"l'l11\ r11cr111-|1tic111 is that the» 111i11i11111111 rni11fi11'-P01110111. tlfififl 11=_II '{‘Jif.'L‘l.'l.l -iilifii 1111.111: l||a111 H1111. lr.'1]11111e_-1| I13’ illli\]_‘1'h-'i5-
F01" 1s111|11a 11111l l'11<1ti111.5.~=. ."'1C'l 51:11:. 7.12 11:q11i1'1~s 11 1111111-
I[i.‘1l|"1£.‘. t]1¢r511c:ti:111 is [[!lI!-'\iI1]lIl-[‘H-11H.'IIZI|.|.{‘{|.. T1111 111i11i1111||11 .11.1]:1w:-1l1l1'- 1's1i11fm'r1r-1111111! r11ti1'1 is
1111||11 1'rei11fc1r:!re111n11t r;1Ti<1 F111‘ _1.{1':1r]c' HI] c|reF1'1|'111n1'l 11:11:11 1'1-F
21111
|r1min _ U.U[]1S
III‘ pl|1_11 = T D
Exz1111p1c.-. 1.3 A 1'1=-i|1['r1|"r:r1rl nc111c:r1~tr~ 114111111 11:11.11 1111 :'fl'n::r.ivn (Ir-|1|'.]1 r1l'
21111 M i11'-'
fiH(]H lid]-"1112. ]'J:'11*1'111i11n Thn :-11'n11 of 1:111:-111111 1'ni11fi1rr<1-
1111111111 = 11.11033
1111*1|L rI.'q|11111] il' [110 11111111 1sI1|1[1u1'l.~.- 21 lutall [u1.'lI.1-1'I.'I.l
-1'. 1'1
15 in 111111 11 11'ill1I1 u[ 1? 111 is l'I.'l11furn'L't1 with 14111111‘ EU 111m-1 1111:]
11111; 11 r1:1111:1'ct1" 1"11111]1r1*1i51vc:
1111111111111 11f 15lI ft-kipei.
Ill
— 0.11136
._ 21111 .r1...1.. = 311'? - 11-
= 1;11.:1111]111.115'1
1e-11't'11gt|1
uf
111'
:2-5|-i1i5fl\l'T(l-T"|.']
lleluroiloeo oouonsre 1112811111
T1111 r1!111l'1.11'c‘1~1111~11I: 1-111111 1'1!1|111r1!11 11-1
511111111011 I11 Ex. 1.3. 11 1'-'11: 111111-11"11 111111 1111: ||11111i11111111 1111111111111111:11.~111.111 1'1"11:11'11r1::1:11111111 1111111 111 11 111111111111-1111111'11ll1*1l 111-11111
.-'1, - 1'1-5_,.rl
1.1'1ti1 11 1*11111::1'1.‘T11 1-iLr1r111.1t11 111 H-1111111 11111111‘: 111111 grmln 111)
— i'(].l112S][12 111111111 1111 _-
1.7
11,-111fi'11'111_~.11|1'1|11t 11:11-11 L-1
i113
C1'.112n1:.r1-1 ,0, — D.i]13fi
'l']1:.- 1.~u1-1'1‘-_+]1u1111111g t1':11:~i=.111 rr.-i111'1.111<-1~1m.-111 1111-:1 is
Beam: with Compression Reinforcement 11 1'1*i|11'1.11'1'1*1| 1‘1.1|11"r1rt1~ 11-011111 with 1'11111p1'1~s1;i1.1|1 1'l‘i.Il-
-*1-..., = 1'1..-rim
1n|'1:n11111111 is 11111111111 111 Fig. 1.2. (.711111]1-|'11e'<-111111 1'1:111f111"1:1!-
= 112 11111111 i11j11_11.111;1111 = 2.1111 1111
111011! 111111 1u.111il111|1z1l 11111111111 11~i11l'u1111.-1111-111 21111‘ 1'1.'1[1|11'1.'1l 1.9111111 1-1111 f11rL11r1:11 1111111111111 1111 1111* 111111111111" 1'x1'1'11111-1 1111'
111'-.~11g11 1'11‘-1c111'=1l 11t1're11gt|1 111' T1111 |11r:111i'11~1' 11.11111 Tlm .~111'11i11 111 11111 11111511111 .~1r1_-1_-1. ¢",=[1.[H]=3. ']‘111- rosi1i1111i 111111111-1'|t. i.~1 gi1'1'11 I13."
'I'111_- 11111'1'r~_-a]111111'!11'|g rr11111i1_111 |'|'_!iI1'r(lY'(_1,‘1l'|1_‘l1I 111111111: 1.~1
.1-1,. = .11, - .1-1',,,_,,
_
pin
_.
1111111
111 .1 1 111_1_=_1{r.1 I i fig)
AJ = i = 1.
ff
T|'|1.- 1111.111-1 1.111.'I.1t11|.I111_-:1:-111.111 Il.'11'1|i.1111I'1~|111-111. 111111 11111111 11.111111
3 1111111 in?
i1:|1:111111 1'1:i11f11r1'1'||11'|11 1111' = l1.‘2Tl A, =
-111,
'
1_?'1J|':{rI — 11"]
F111111 App. .11.. 1111' 1:11r1'1:1-11111111111111, 111111c111111111 111:14ig11 1111:111r111 s11'1~11[;1l1 is
.11,,,=., = 11.211.'11'f_1,.d*
|4|i
' ., fj _[111.111111
1111
(1
111.21]-3f|(3(J1I11.1 %)1_12 1111110 1111"
£1‘
_
E 1', 1- _ 11.:115r1
K
1111' ' 11! — in)
1111111 i
11111) Ii
ft
= 157.-1| 11.-111111-1 '|'1111 1111111111111 111111110111 111
E1ca|'11]:1le 1.4
1'11, = Mu — 111'“-_L\
A 11-11111:-|'r:n1'l 1-1_1111'111-to I11-11111 11.-'1111 1111 1,-i1'r11":111.'r1 1|c1p11'1 111' [[111111111l:11\'111l|1u1l2 111 i11111'i11Fur1'1'1| w1l111;1"11111~ U1] 1111111
= ]T"‘11 1'1-kipei — 151'.--1 it-1:i|11-1
111111 111111 11 1:11-111~1'nr.111'111111|11'r-111=\i1'1! 1111'1111gl11 111' 111111111 I111",-'i11.
= 211.11 F1:-11i|1111
'1'|'|=.~ l1l'.']'I1|| 11_1 l|'1I.~ Iir1f!l1l211<.|1I1 1'1-1' till‘! 1?'<.I111]'I1\1_':-11111.11! r1-i11i'1.11~<:1.-
1110111 is Z1 i|1_ D1't1_'r111i111' 1111: 111'1-11>: 1:-1' 1111111011 111111 1:11111]11'1':41111111 r1~i|1F111'1:n111n|11 1'11q111r1111 i1'1i11‘- i1r~1-1111 21111111111121 11
1111111 F111'-l.r11'r11l 1111111111111 111 ii-‘H 1'1-1-1i|1.11_ Figure 1.2 BE-am 11-1111 If-‘M1171-'5-s-s1'1:1n I?e.1'.'Fc1rcaI'r.151r1r"
I"
D111
‘I _| 1'.|'
11 ear;
1, — 11.11113 E9
A“
C
_
. .Asr-1
.1'11',|‘; Amu
1, — 11.11115
.- _ T
T
0
PPI
ry
T‘
0
_p-
1 IIlI!.|I|I|I|I1lI-l.GI|II
]_-B
$‘IlIl.l¢Tl.|IiI1I. ENGINEERING nsrznsues Il.l.Nl.ll~I-
The 111:]¢liti¢1l1nI 111111-1 uf tcr11:1i1.111 rc!i11Furn"11u*11t 1'1=q11ir:!:l is
T111! r:':|l1ir1:!d 111'r'11 :1l'I.'11111]11'1*-.~11ei:111 r:1i11f11r:::!1mr11t is
U’; =1 '1
-If
Alix
IA
1‘:
|,D.J-J2 111 _I-(GU in!
-':1_1"_\.[rI— cf)
1211.11 11-1<1pfi'1{_1-2 [11.u) £1111
43.511
in?
= 11.1.1111 11F
(111 in :1 in]
Flanged Suction with Tension
= [L3-E12 ill?
Bainfurcamant \\'|111|1 the 1'n1:m11;::|||:=11' .~1t1'c'.+1 hlmk is \\'h\!1]]}' r111mt:—11i11H| i1| 1111- [l1ll11_{.r:. 41. l1u1|g1'|.l ::=1\1'li1111| 11111;,‘ |>1- 1.l1'-1igt11'1l 2|-—= 21 HTt11|1gul11r ]bl"l\I|11.
T1111 tuml 1'r~q11i1'nrl 1-11'-1111 m"t1*|1:"-1ir111 1'1~i11f:11':rn||1r1|11
.4. = .-1,,,,,,. + .4, = 2.1111 in” +11.:152 111’ = 2.1-111:1 in’
\\'|11~11 H11‘ :l1~pI:]1 of the 1':-:'ts111|;11l1=|1' 1-1trc!1+.-1 I1lu
The (|[‘]JH.l 0| L111: 5t1'|.*s1e- |1]|::»1'k 1'1;
11:1 I1-111111111‘ I111: {‘U1ll])l'L':ibi'u'l1‘ [u1'1'1: in Lhv 11|.1l>.=l11111li1|g
flalngmi i_~a _ _ _ -. _ kip:-1 [l'.l1ll 111'](l1l|'
Almxfx r1=?HFyr
'-" -'"’
1 _ 11.1-1r1j_T11J-[:1 - 11,.) 1 IX
-' 1r.
I
111.-1_15j|(:1
112 1111 T1111 111u1'l'v-1111111111111;1.l1r-iigtl ||1~u|||1.*|1l Hl!1.*1|g1I1 is
= 5.12 in hr
$1171" = r_'J.=|,;ffl
rf —
The nc:11i1'nl El.I'11i:i 1l1~pL]1 is T111: 11:11:11 wvh |1111>1t tl1'w:lu]1 [hr 1'1'1ai1|1111] 111111111111. rt = [|.3T-51!
w]1ic:h in givc-11 hy
= l:U.l5T5][lU ill_:|
111,- = .’H',, — M,-
= [LI] i|| Thc: \'11l||v of 11f,_."ff_BL.a': L11 £1("H."l'lI|1i11lT121.
the m]:litiu1111I nron of rz-i|1f:1r<:c1111111t rirqllirwl to 1111]:-11111-1‘ 1|11* rt‘:-1i1'l1ml 1111111111111 1:-1
_ —~ M _iP) ,rj-{1~1.111111m:)£_1
= {11?.11r.111
- [Lil
' '-
4
. ,,,
= ,;:hu rIf:_
L
in The total area of rc!i|1fnr:r11111011t 1':-q11iru:l L\1
= 4:11.011 l -11",-"111"
xi. = .11.; + .-1,... Flynn 1.3 F-'='|r|;;r-51:1‘ Scrcrmn W'l1'1 Tr_:r1$fL-‘fl F!::1r1f=;-*rcur-'mn'=|“" 1:1.
H.033 +
1|
,\
X C:
j‘
bw
E|.S5.l';_
11'
I
T"
C r
cw.
C
Cf
'1'
DB5 fl:
I
__ Cw
‘ A1
Thu cur-
1t':-ip-u1|
'I'l1=.- :¢T1'r'.+1@ in 1111- 1:u1'|||'>1'r1:=:~i111'| am.-I in
T’
nlaluronceu 1.':1:1u¢11E'r£ 11-115111111
Example 1 .5
1-Q
T111! 1'1"i11i11r1!1!1111111i 1'1!q11i1'c1l to 111111111111 H11‘ 1'1r11i1l1111l
P1 T11_\i11i'1'_111'r:1'11l 1_'1'_'1111_:r1_-111 l"|:'1|1g1_'11'| l'1-1_\:1:111 11-ir_.l1 :1 fl:1|1g1'11'1'i1|i_i1
1111111111111 is
4
r.1l'2-i 111. 11 1'-1-1.1 1\'i1il-h 1.1-[ 12 in. 11 fl11|1g1: 1l1:11t]1 of I1 i11. 111111 an 1*Ff111:ti\'11 1l11pt]1 11f lli in i1-I 1'11i11F1111'c'1\1l 1.1.'iii1 1.1111111! iii]
-
_ 1.1.1£1,.1i_fl'_ El‘. Z
fu
r1~i11F111'11n1111'1|1t. If Tl11'1 1!1:111"1'r1t11 1111|11]11'1~.~a1ivn 1-1r1'n1:1gt]1 is
Conc12rc-1
1;_(J.'.?5T}{l2 11111111 1111
i.il]'i][i ]i.1i',-"i113. 1i1:l.11r11'1i1'11.~ 1|11- =.'11'11:'1 1.=i' t.1':1111i1.1|1 1'1-i11|'1.1111.111c11i- 1'1'q11ir1'1l tu 1s11[1pu1't 1111 11ppli1'1l f111'lu1'1'1l 1111.11111:11t 11F '.!:':1ii ii.-i1i]11-1.
1111
Srriraizlrm
HI‘
= 2.1? 111’
1"'1.-111111110 H1111 H11‘ 1.iL']11-l1 ui 1111- l.'L‘l'lEllli-_f,|.ii.iil' :11-|1'1>'~' I1-lurk 1!x1'1‘1~1L11 1:111: 1i1'pt]1 11ft]11! Hs111g1.‘.
'i'i11_- r.1'.=t1_1| 11.*l1.~1i1'.1-11 111‘-i11fi'.1r1:1"1111r1|1T 1_'1|'1'111 11.-c"|11i1'1_'-1| i.~1 xi. = .-"1 .; + .-L11
T111‘ z1r1.'11 of ic111=iu11 1'1"i11f1.1r1'L'111r.'111 1'u|11i1'1'1l 11.1 i111]11|11'L'
— L-53 in: + 2.1? in:
1l11'1 1:11111p1'1*:-2-151111 i'111'1‘11 in 1:111! F11'1|1|'.11‘- is
- =l.[i'|] in: I).-'35_i':..I'1;{l1 — i1..:i -4.1.1 = 1 11
T111: 1111111-I1 of il11' 1'1[11i1.'11]1_'11i- r1!1_'i11|1g11l111' gi\'1.~11 by
hluck is
.-1.1..f -11- E”
F ki|11s1. ..,_). [[II.i'i.1'}1(£i [3 i11[1|_2-l 111 l‘.. i11] 111~
11.11.-1ff_b
1111 LT,“
12.-1? i1111(1111
111-
= 1.53 i113
1111.5-511 (3
iii
11:1 1111 l|1'
1"'1:-m11111i11g lhl: >.11:1'1iu11 is l1-1111-i1.|11-111.111l.1'uliL-1L H11: cur-
= 1.1.11 111
111.~1~=;11.:111.ii11g_,1i1.*'.~=i,1:__11 1111_11111.'11i slr1.'11gt]1 is
'.“=- 171.1
11— 11 >.Ur\,1 r'_€ 1 ii"
1_1'_"-3
--.
i-'11! 11 T(‘!i11-iil'Jil-(‘l_'lii|Ti'1'bi|l_'IZ| 111-1_:1i1_111. ti1r1 111;1xi11111111 -rlnpl I1 oi" .
iiJ.'J_||_1.5..i 111 ](_i.1ii
ililifi
.
(16 111
liin
1|11.- 121.|11i\-"1111.-1'11. 111.'r1::l..:'1111;11i111- 1=1.1'1.'-111 1.1i1.:1::i1 in gix-1.-11 11,1‘
2 J
11, = 11.111.71.151-1= 111.11."-.3j|{11.1111)[ 11,1 111}
12 E f1
= 5.1!] in 1:1» 11
= !i‘i]_i"1Ii it-115111-1
The r1':si1i1111l 111r_1||11'11i 111 I11: 1i1:\'r.']1_1;11.'1i |1_v H11: 1\'1'i1- is
111. = 11-1" - .11, = 2511 11.1111“ - 1111.1_1:1 1'1-1111-11 =1s11.1111..111,111 - - -. 11-1.1|1111[1z _. _ _ 111 lur 1_1511.11 H) f:"""'F =
:11.~1;11\:\1|111111i]
$3112 11111111 1111*
= 111.196 F‘1'n111 .~‘1.|11]1. .111. Llm 1:1'111'm11]1<11111]i11g 11~1111i1'1111 1'ni11i'1'11-1-1111111111 i11
|T|1r! s1*1'iin|l is 1_1~11-:i11|1-1'1111t1'11||1'1| 11_~' 1:1.~e<1|111r\1|-I
3. SERVICEIBILITY REQUIREMENTS FDR IEAIIB Nomenclature .-I1 1-I,
111‘1'11 111' i111|i1'ir|I111] lull‘ 111-1-1\1:1i'11'111=i1_11:1 111-i11fr_11-1.-1'1111'111
in: in“
.—L1
1111111 111' 1-kin r1~i:11f111*1:1-111.1111! 111:1" 1|11i.|
in:
|11!igl1l 111 111111.-1i1i1' |'111'1'
.-!,,
111‘1'11 111' i]I.Ill|.1IlI‘?-TIII‘HF1."li 1‘1'i11i'11:r11'1111'111
1:‘.
il'1 1'1 li1" 1'i.1':\:' (JlI|'1'l"T I111 l1'r1:-.i11|1 r11'E1r1|'1111‘1'1-'11111r1|
in: i11.
r1',1
11111111011-1' of I:-111'
i11
E,
|1:1111il1|ll:=- 1:i'1!]:1_~1i;i1:ii_'.' 11f1;1:11l11;'lz1[1!.
|'i1|:'_1"i.l'1:'
:s:111-_'_ " 1,-“,1: E.
111111'i11i111-:1 1:i"11i11.-1ti1-i1j.' 11E r1"i11ti11'1:r111111'11t.
i:i1111_1"i11:
2!.|.lIl|)i]
1.11 = iiifi?
J’,
11111r|11l1.11-'1 1:-i i'l1]IIll‘iIl'l." 11t' rrm1'1'1'r1'.
|i1t'.1"i112
1.51,.-T’ _|':
1'11L1"11|.=1ir11I .~si1'1-.-1-1" in r1~i|1F111'1'1~1111'|1i 11i
i1i11:1‘1"i11‘
s1'r\'i1'1'- l1:1111|1-:-
PPI
l I1lI!.|I|I|I|l1lI-l.GfiII
1-lfl
ITRUGTIIIIIL Euulusznluu ne|=:n|su¢£ Illll.IlL
I1
nrc-rail] rliuu'||-iimm |.|i11u':||h|.~I
in
.l',,
l|'1uIlt|('l|1 uf int-|1ia uf :-1':u;};c-|I
iul
Ffgum 1.4 Tenmm H‘eu1rc:n:ernefi.' 1'.i~er&.'.'s
t|':|.||:-im:|m-|| m-ri:||:|,
I|,,|:l.'|1'II:‘_-"55 - H.--l,|I_<|'— It-'1'_1" L
|'ff£~cl1'|'|'- l|]u|:||I;'||1 nf i]M'Ir\i.:|.
illl
-[J
n|||1r|c'r|l <>Fi|1|'|11:: uf 3|-cam c-||r|ctr1'||* .~;|~rrlirm. ¢':L_.|'.-"_,-'1':
in‘
L"
1|-:'I.m:-1] axis -ilrptli l:|c'u:|" at !iI."I\'ilIi' In-mil.
—
1'."Q,ur1 + [,rm:l2
I’
span I-mlgth u|'In:-|L||1 or u|n'=I.\'n_\' slain.
it
p|1.>]::|'1§|||t| ul' |.'.'|.|1|!l|u'r|-1
.\-I,
r|1n:
in-lhi 111' fl:-kipv-
.l.l'_.,
1-I:-in-kilip, lllulilfllt. 2_f,I~,_."J‘r
in-ll:-I'm-
r1 -.<
u1r_|r.l||]nr rmiu. 1':-'. n"-mr-|-tn-rn:-|'m'-1 .-]1a|;-ing ut'1c-miiu||
iu
la.i.J ==
l_t-kip:-z
H“'lllrU|'('l"‘lIli'll|
r.'.'_
||ni.I '-1.'|‘ig‘l|I nF r1::~|1rrt'h'
|]\F_."it:‘
Symbols
Example l.fi Thu |>|:n11| 5]m1.\'n is H.*it1[umc'd with right 110. H g_',rm|t' Lil.)
heirs. Clear vu\'r_'r of 1l_-‘rs in is pm1.'irlL'cl to [hr nu. -1 siirriips. ]'.'Ir-tr-rminu 1lu'- skin l'IZ!iIl1F1'ITH"l1l-l"lll. mqiiirml. fllul c']1r:I.'k ilmi thv :~'|=nn']1|1.5; ml Ll|.|: |1:i||l'|.rl'l\\-luulll ("unf0r|||:i lu ACI Stir‘. 1lJ.lj.
H
||:'ߢ'|-Iillll
in
£
ti|:u:-r1nl»:'L|t l'u:'t<_"|L' Eur >iu.~tai|u'rl
— ‘I3 In
|.u:u|
A,‘ ,1.-"
r|1ul1ip|iI"1' I'<1|'1H|rlili-"mul |r>|1|.:-1in|r' ck-Hr:-tiull 1'1:iui1:-lumn»:-ul mliu fur t‘ul|]])l‘1!5:iil.:I|)
— NO. 4 5‘lirl‘L|p:i
—
n~1:||'n|1cr|~1m'|:|l , .-1:,-Tu!
Control oi Crack ‘Widths
45 in
In ncnrnrdmacrtr with .-\C7I Sm". 1U.!:i. uracil: wiilth is mn1|'|'|-llucl lay limiting Hm 5]i.1r:i|\g -:11" T-r-miinu |'nini¥'|rrt=1m~11t
lu i\ \'a11|:* g_i'-'|.'11 |.1_1.' 4"|l.[:l E-1.1. ll]--I. \\'||I.'rL' I. is in |.luil.s L:-l'
1 In clear
ki]1:s,|"i112.
i
[iflfi — 2.5-=1. .-i = —
L
I 0
i
'
I ,_
|_15 lnclearcuver l
-1% _J', As 5]1lI]'\'|‘l1 in Fig. ].--|.. .-1 is the (rf'|.ll'.|I!Il'-TI."J—(‘1!'11l.1'!l' squaring. in ]1'|<']|<-e<. uf lhu 1{‘l|h-'il_lll r:']]1li.I|111'l|l1'l1[. l|1.'4\11'=
."Fu.|'n.Ur.v.va Thu €]II!éll.' r_'uv.'1~r pruvidcrti tu lht: i1:||:iiuu rc:i11fu1'u:|1wllt is
given h_1,'
c!xlr1:|1w t1:u.:iiun fnccr. mul c, is tlw crlcrnr m11~::r1:tv cm'01'. in i111!]1irH_ [ruin thc: n:!nrr'si :-suriacrv in tr'|:u+i<:n Lu thr-
:-@||ri';u:n nf Ihn I.rm:aiun re-i11frn'r:n||mnr. \.‘I.'lm|'r: t.hms- is unly unu hair l1l_‘&|l'l.'Sl lu lh4.'1.'xlrI_'|m- ir:u:
tlw width uf the i.‘I'\1lt‘[!I|]]E! tnmaiun Farr. (.7m1I:rn]]i11g the :-¢|unr_'i1ig ui tre||.~iir:n n_*i|'|i'|'>|'ra'!mm\T limits t.hr- wicltli of Hill‘l'm'I.- 1:L'nc]m iu m1 il1.'I2.'IL‘]J'|.|1]J'|.\." ]|.":|.-l. T|'|=.- Hllim-4 i|| E111: r1.'illfI.1l‘L'Ij'||2|I.'II1 iii M.'!'\‘ir.'|.' |¢.I='Hl mi'|_\' hr.-
uiilwr cn]:'||1zLt:'d ur zu-zsunu-{l irqiml to |:2_,"3]f*_ ‘H-'lwt1 i-lw dcrptll ul the |)|.‘H]]l t'Jcuxrd>i liili in. _-'LC.'I
(1, =
S_ 1 ".5
The 5-1l'l".‘i!-1 in tlw 1'r~iufurc:c!11:(!11T M E-'~£’!"|.'i\"E? lcmcl i:-a 1'1:-esilllllfll I.'t]Ni'||. lu
I, = = [§}(|1n
Sew. lf).fi_T r:eq\|in':-c Llmt Hki" |'ni|:ii:irr<'1m~11r. lm ]i|:lr:nrl ulI.|-lug hulh :-.~i-:11: fuI.1_'.-1 uf llu: 1'-‘I.-|1. ill I111‘ lu\.\'L'1' half uf lhl:
licralln.
ill
= '3 ill
I -LU ki|:e;_."iui
|lI|=l:||l¢|=.u cnllcnrrs nzslnnl
1-11
The iiuucimiml nlluwnlilir lmr spncriiig is givvu lJ_1.' .-'LC.'I
l'_-"2Z1lIIl. Tlicr tutnl rlcrflrrtiuii n-cc!11rriug.§ sflvr ilu: Elll:‘lL‘]1llll?1'li-
Hrl. lli--J :1_s
iii‘ :lnilw:timi srensiiiwe |'!i.1':|ll1"lll_\i is li||1it.m'| In i|."4i_i[].
Fur lllJl‘ll'l-ill wr:lgl|[- [ruin-.|'|.*.m =.1l|1l ;:.i‘=\=|<- GUI rcinfurr.-Imir.-111.
mu
i"iCl Ti'1i>i.4.! El.-5[zI.i [:r|.1\'i1i|i--H H[Ii.ll|._-'|Ii'l.‘|Il'l|l L'i'1l.-ius i1|1|1liur||>l1.r in 11‘I\L‘llli)L“l'S s11]1]xJrt-ing I|1UllElI!11Hill‘l|'l‘ crlvimriits. Tlll."H'i.“
.¥= %— 2.1-_H",_
mti-as :-111'-sli-nwii in 'l':1lil(- l.].
=
mm§$
|j2.!.'|][2 in]
Tabla ‘l.I 5par|.vDap\:n F|‘a.'|i:ls uml. 1'1:-mliliilti:-4
|:n::n:||
Hiilll
I
2“
in"
1-
—1Uiu 'l'lw ;-lrtunl lml simczing is giwm h_\' .1
NZ
| |
2-i|:||]:|_'. s1|||p-0| ZN
16
rmnr 1'[|
mm-mmsm—mmmm-mam
I
L
' F l-5.4
I-l
butli fllilli cv:-iiiiuuuus
Ii
= 4.213 in Siuur -Lil] in is l-ms than l[ZI in. this lmr sparing is snti.~:F:1r:h'i|'_\.=.
E
I
i
?l
EH
E
L
B
l[l
-:'|I.||iil1-1'r'|'
Fur i;1'4ir.lr ll) 11'iufi.>L'L¢L'||u'||1. lill.‘ lulilllzllul \'ailu|:s ill't'
The E|IIf]IIli.l ul the lurmu is
11:|11|tiplit'(| by tilt‘ fl-icriur [J.l'i. For ligllt.wr'i|g|1t. -D2)I|](!1'lI'll‘.
ilw mli11l=1rnci 1.-'sl1u=:-z :m- mulii|ili-ml Ii}; tlw l'm:mr
h = -'13 in
1?- 3~{i in
R = 1.55 - 11.1111-.'m=,. 3 um
T]1irrcFnrt'_ skiu rcillftirrrrllitrlii is rcqiiiruil. Using nn. ii imrs, tho m.-1.\.'i|uu:n sllnwnliln :-i[]:-'l(‘ill_|{ is
Deflection lletenninatiun
-24.; = lD111
Slmrl-h:1':n ilcFlc't'I:im|s nmy lit! riilcriilntcrci bf.-' using ilw
'I'|'|1.~ |=-:11:-i Hlmll ¢.~.\<11.~|14| fur at |lir~"t=.'|||(=i.'-. -'t_,-"'2'. Dull] Lin?
nl'Fr~rr.iw~ ll|.|'|-|ll1"'l|.I’. nf im-1'r.i:-1 givmi l:_'_i' .-\l[Il Sc-tr. El.!_'|.‘.!.Ii ruirl i||||st1':it.-ml in I-iig. L5 .-Ls
ll'l|Hi|_>ll l'i1r."I;-.
Tlw mi11Fm'c:mumLt ln_'m11i is slmwn in tlw l'nllm.\"ing
l]ll|:
Jr, —
MW" lr:.’.+
(1 —
MW“ )1,-,
]A\lCi 9'8]
Ailditimml lung-tsrrui ulirllr-rtiml is rasiimstwl From .*'i(.‘I
Hr.-r-. 9.-5.2.-5 hy |||ulli]i»l_'.'i1'u,; tl'|r.- -llluri-T:_*l'tll 1i1T!ill"II1Ill.1ll hy ilu: miill-ipliur C
Ad = s,
|ACI 9-: :'
1 -|- u-Up
II-N0.3 -in
\
jlflin llflin
I I
—
i 1 _ T15 lI'l ulnar cover
'
L is llu: Ii1m-|.lL-pr.-ml¢:||L i'zu'I:ur i'u1'sus1ai1ml iIiJill.i. ill.-i'||1ul in AC1 Sm‘. 1'l.fi.E‘.5n11
.{
Eil] ['3 ii
‘Lil l.-1 LL?
Ii
l Ii
Dlfllctinn Limitation: Tllv i\]]U\\'i\|J]L'. lJllJlll.‘(ilillL' r.lr:llm'l]|.=-ll ui lll'.~
'l'l1c_- iii,-ilfl*l_.i1'|-|| is r::'1lc_*n|:m_~<] l'r_>|' n:=|r_'l1 |<_'m¢li||g (‘.'iwe_'- |_|:-ling
'l'ahlre §l.!_'i{l1-1| as ll,-"IS/ll Fm‘ ilai rrxifs nml i_,-'3[_i-il l'r:-1' ilrmls (luv lu llir: npplil.-|.l liw lUi1Iil. The lulu] ili-Hi-Lrliuu1.w.'|.'||rri||g ziflcrr tlw £l.lCHl{‘illl.|.1"lll of nun:-Irlisitivcirlcrilicvlits is i.i.lllilHi in
Thus. Lin! slmrt-h~1'm clceilzrtriiiiii J” inn}; bu crslciiiaiihcl Fm‘
lill.‘ u]1pruprinl1.' visllw ul l-luv L'il'1.'cli\'I: [[lLl'lll1.‘ll[ of iiicrtiu.
liifilli lu.-ui |_>nl_v nml Lhr» sliuri-h.~1'|r\ ilnfle.-c.-Tim‘: -'=;;;_,-_; PPI
l IIlI!.|I|I|I|l8I-l.GfiII
Concriss
1-12
$1'RuI.‘:1un:|. Ellullusznlllu nsrsnsuci Illlllll.
Figun: 1.5 Sem'r::e L-::-um’ David.-r|'nns
imMis;s 5-ectlan
strain
I __. "' |
stress
i"'|_
b
e
_
;
translorme-:1 saclinn
ltd
I’
I
1:
|*—*‘1 i
r'i'“'I
qip {:1
‘u
L"F=li.L7|.lii'l|.-1.‘l.i. l'u-r Llil: l-ul-ul zimilicd luml. Tilt‘ livu luzul
Fmm ACI SI.'I.'- 5.5.
(icflu't_iull is ilwu givrzi l:_\'
l
_ E,- =
as.."."[15i1
(liiliiljl
\'|"'u.|'-‘U’: =
5'1. = {lglm Ll - ‘5'I.I
lllilll
- 3323!] lii]is_-"in?
Tlw film] mtsl rlrel'ls!cii:m, ilicrlliciiiig H|Il(iii.i|'ill:-ii |ri|ig-
i1'|'ln 1lfil'lI.'i=lir_1l|. is gii-'I.'l: i1_\'
E, _ 2ll.IJlllJ kips.-‘iii:
451" = iiulil + -5‘|.m_i + fir.
Ex
20.000
"
mu
lll‘
| --
1!=F= =h.l'-‘i
_ 15;,|-1-1;. + 91.15::
_ -'1. _
Example 1 .7 A 11~i||l'ul'L‘|:il cu||L'r\r_'li: liumu of nurllizil weight CU-ll1.'l‘L‘[L' and s|mn|iing 12 it ]1.n_s an nifnrtiwi rinpili cal’ lii ill. an I.Il\'1.‘l‘iiii i.iE![Ili]l 111' I5 ill. and em l.'I.>lu[:n.'s~'i\'1*- H1 l'l.1llgl.il 1.:-l' 3I]iJll ll:F_."i|1L'. mul it
rt_'i11Fu1'i:ul with tliru: nu. S gratin
(ill lmrs. The lmsm is 12 in wiciv. The liomlin|:; nimnmit ri1|-P tn susmimlcl rlrsul Irmcl is [ill ET-kips. .\‘¢'g|r:r:t. rim wr.'ig.hl ui lln: muiill.-l'lI.'I.'liu|| :~'I.'||:=il-iw: I.'lI.'||1|.'nls. whii.'h arr! sit-mrliul i1i11lu\tlisi1~l_'-' nftsrr nrlliiwilig t-ht! fnlsvwurk. T111: l-rai!|si¢11l- iluul" li1.'I.' luurl [lIU'llll.'[lI is 31] l'l-kipri. Coin]}.urc l.|:|c' iicam ticflctt-iuiui wiill the nlluwnlilv vi-ilmrs I-‘lll{i
IIi£3Tl.‘I.'IllflI|I|€! Llm final |]lI!fl.[ll. :i¢rfli~rLimL dis: Lu lcmg-term r_-il'nr:r_s nml l..t'F.'ltl:il("I‘|T |:_m<"ls. S0|'ui:0n
Tim nllciwa-ili-I0 liver lnml rlnilmsinli for lln-nrs is givr-u lay FLCI 'I'=.l|.I]|.' ii.-"}lf:i.|-II =1.-l
1 fi;_ _
III‘
2.3? in?
_
.
‘F bud _ [12 in]|[lli mi _ "mm pi! = [lJ.lJ123][S.i'l3i = 11.1113 I-'mm A1111-. 11. tlw mm'spnnrli|ig m-i1t|':1l sxis rlnpili fi\r.'lur is ii‘ = lliifiill
'l']1v l'l'lI:'|I|]'l|I‘11T -n-l' iimriia uf tim r:|'nrl-wt] i.rm|sfi'|i'||im'| s:'c:-
iiuu is _
.l
1., = Lg"-5 - ,..4..r.i - i-irjfi (12 mi-(|ji1.::['i1'11j|{1zi m[|}” =i + {-*3.T3]||j2.3T i||'3j|{l6 in — ljlJ.3fi!!1]i:1fi in]}-3 = 2932 in‘
in‘
(12 fi.}[1*_= _
_ U.-'lll' in
Thu: mu:l|.|l|.l.+ <11" rn]1~1.|.lr|t-. 1-\'|'|0|~c A = 1.1] i'<;n- nuriiml The iillmwlbln IIl1T'flD[‘l'.i[ill flET1?T attaicrhinrem. (if lli}1‘li-il"l!l$l-
1.'.-'L'i|ghL L'L‘I[ll'l'L'l.\'_‘ [AC1 Soc. 8.6.1). is gii.-‘I.-n lijr AC1
river nlmnnnts is
Eq. Fl-lli as
F1 III
0
:12n}[12 E) -i-in -000"
""-“‘“_2i:1_
mu
wurw.ppiIpar|.:n-In
_ '
"'
f, _ v.s.\./’_Ij' _ [?.5){l .lJ}1||||i'I3[HJli = 411 |i1r_.»'m1'
Iuroncsn concurrz nisln-Ill
T111.‘ crrarkillg |11:1mr'nt is |;i\':!11 I13." .~\CI Eq. 1]-ii as
T111! illllltiplirr for llcirlitiuiull lnllg-tcrrlu tllrfliwtitill is giwli 115' AC1 liq. El-ll 1-is
llf1 .. lll',l . H __2u_q_ l2l(11l F}l»s12 "
'l'li:_- :11.‘-1li\.lj:[.i|"_l|l r|l1r_- tn Hiil'_I|'|I-1fl'_!Il‘l'| |i\'1_* l(l:u'ls 111111 |n1'|gicml llelui iulliis is
— 22.131't—kipi-1
[Sc~<:l:i11ll is ('l'2'l('klI‘i1.:
#|.m+,'_.|
M
:1
%'
£11111)
M
I ~
1 -
N
(11511) )
-_ I
.
11,- = .1l,._.(l - .\..] + 11. = 111.1112 i1l}{1 + 2] + 11.11114 in = [l.l'1-ill 111
:l
+ (1 -
)1-2932 ll.-‘jl
4. ELASTIC DESIGN METHOD Nomcnclnhirc
= 3Ui"B ill‘ T112 cru1'r:!spl.l1111inlz_. sill.l1't-tl:r111 cici'll.'1ctil.l11 |:1ul: t-1.1 cicrzul 1:1:-1:1 is _
i?‘iill'iF.'1.=lt‘1.l‘lF_\':
L'i1'ocls is
I.-,
22.11-ift-I-c' .- "... . iciiilill lll'j|
_
.,
.
.
_ . _
-_:-
M= 11-4.11314‘ ,_,_1_. = 1:1-5[Il_H_lJl| .i_L—i(l[‘lé1:l|_lZ Ell = M52 in E
-=61 [Hill ill
T111: final 11l:[ll.'L'liull 111.14: iu iu-1l1.',-t|.'r11l i|.ll.l.1. sliurl-turlll
:l'
i"'
= .1_.a.. - 11.. = l_2,\il1.ls2 ill} +l1.us1 ill = i_1.3E'\S in
T1111 flE1¢'flTi\'t' llllcilllmlt 01' i11
I, =
' I‘
(3321:
E
_ -E _ 2 _ 11 _?____ -" 1-:1-.u,=r 1111
lls lll.~(l2 %)l_|lJU'|J 11.1:
-:2 iii] it-1ii]1s
1-13
.
.
I. l_2i[1T:5 ill‘:|
L.
iil'11lil.1.'iil\1':i.‘i il1 lI!]lllI1l'!!ll"
l l1_.-'11.‘-’
I.
|l|l.‘T1l.|\i l.1'Il>ii1l." =-11'n-as ill rlrillii:-l'<'l.~l1l1.'|lt
i| \1_."‘iIl-"
j
11!’1.'IJ'l'-:l.l.‘|l1 i:'l£'t<1l'
_1',..,
lmlmli-1-<1 lr-\'m'-min l'=u':1ur
1.'|__,|
lm|;11l|l'rs1 12lI‘l!ll'l'il.i 1l.xislI:r[l-111 Fm-lrir
:11’
sL'r1.'i|:\l' r.i1'si1.;li lill:-limit
E:-lcips
1'|f|..| il_._|,
1ilil1i'lJIl'|.'(] .-I.-l'*.'i<:v 111':-igIll. tllmllluztll |'11l'r|'|1'm-:i1'l|:' rt:-|1r'|1:'l_1~ si rl‘:<.'<
i11'1_."i||"i
il“.
pi:-|_'||1'r."-'i'|1|-:' suwr-I slrr-.-s
T111: ~.'iTi'r."li'-'r.' lllUHl¢.‘lli uf illL‘l'liEI. 11.11" L110 1101111 iualil pill.-'
fl-|l1|1-i
i|li_."i|l’
1i‘l't! iflilti is -
:1
1.— Li")1 - 1 (11-1'1 l'3'+-ll
Symbols
:|.
H i
(L5-'1 -'11-:1:-1.:
1....
_- 22.1511.-111». "‘.ifiblil |.lil_i . . 22.1.:-l-ll" .~ "‘ . _ .
;1|,,.|
1'!vfliF‘l1Il'N:i illllsilllrl l‘<'illirrrrl1'rllr!ll1 'n'l1il1.
—
P. i£‘|...|.~"3.l*-.-
Dntlrlninltiun of Working Stress Ulluas T111! vilistiir {irsign ltll."[1][II[1. is fII!iE?1'l'i."lI| to in 151.CI S-N". 111.1 as Llw >1ll.nrn:m\ rlnsigli 1m’-ilmcl. Thu slr:1ip;hl-lilln i1ll.‘UF_‘|'. illllslrzllvci i11 Fig. 1.5. is llH.'121 Lu ralltlllllic iilL' ii-‘l-l'['5."-id?)-i in .l-1 11ilr11li>m' ‘llllii-Pl’ 1110 111:tilJ11 of the sp]'1-iifil
= 25175 in‘
s1.-1".'ir:0 |t.'1:-11:12‘-l Fllllji 1.1.1 0ll.~l\m- tilst. l_l1r_es1.- R1f.t‘l'_'5.'-if"!-1 rlr; lm-t.
T110 L'ul'|'r.'s|1-ullllirll-; sllu1'l-l-l.'r|11 111.-1lccl.iu11 11111: iu I110 tic-zul 11:11.11 1:-llis liver illlillii is
'
'. 1-ll" .-
~_1"-'
61.11-.I.| _ {s1HjlJ[[J‘]_T ipqm I T} -11.2313 ill '
k .' . (11211 #3 l_2s1:':l i1l"'_.| lil-
Tili.‘ 511I1Jl'i»-i1f'1'[!l llrflclcrtinli lint! in U'H]]Hi.i.‘[l.l. livr ins-:1 is 151- a|:||_:|+{__| ""1511 _
ill ' ' ii|.1.-52 ill
liexiixt-lsl ]:|=.~l~lnLs:~iI=l1i= vulllli-.~l. "1‘h1:= |IH?rl'l:IllhHiiI1IIl H[]1.‘H-ill-l lililff 11,1, = liulximlllll ]IH."l'l:lli51~'i|I1l'.!I-4ll‘1?H-1 ill the |tn:rl'|1.*l'1t:tr:
_i].-'15]:
11., = nulxilmlm ]IH."l'l:Ili5hi|11l?! slllvs-1 ill the l'f!illIifl!‘CII!II|1€!1]1'. = 2|] 1ii]1l-.1,-"11l'*r
[lgrsrlr -ii] 1'r~il1fc|rr\l'|ll~:'llt]
= 2-‘ll 1-{i114-illiill-‘P
|:|.;l.':il11' Iii] :l'l'il:ll'll:l'l1u|m!lll]
I-'rmn Fig. l.5, iilr: l|1'l|ll'.I:'|.i axis -l'il'![‘!I1'l i':ac_'i<'|I is 1'1f:l'i'\-'-|'s'i ss
= Ill]-‘3-1 111
is
-T. £1.10 in
.5: = ‘|i."l2||'H'l + [,-.111)" — lrrrl
[slltisl'1u'lu1}']
PPI
l v|u1uv.ppl2|:|nnl.:nn
Cuncrs
1-14
trnuctunnl. z||u||||zzn||u:| lIEFEREll¢E Illll.IlL
Apprndix B t1\l111]atc::s v:-tllurs uf k ng:1i:|_\it pn. In addi-
1",“, = 1- ta = | - %:?21:' .5 = mas:
tinn, tlw ]nw:|'-;\r|n fact-:'|r is |'|nri1.'re|'i :-1.»:
.-_
_E
1-]
.‘ . 1 E Mhdl Z .n1.._, Z {tn ft. _ 1
:1
.
-
Pail»-Id
£24
[DISQHIB in]
The :-.4Lrr.':-.¢< in Lhr: l'L‘]Jl[LI'1'l.‘1_‘lll1_'[ll dllu tu an |1]1|.1ll1.'1l.1I.'rvir;'L'
lnmlmnt M is-:»
= 11¢: in“ M
frfi
I‘
'I'|'|t- 511‘:-.-ts in tllr c:crm*1w.*.t.|: is
_ an I" _ _@t-{Mr-'
Z
2%?’ M.-rs l
‘I
:2}¢_1.m in‘-'](24.U(]U M m) ¢12 i11](III.3'lfl](1t3i|:]
= I334 l|'Jf_."ttl2 -'21 pm
]:
For >1 hnlanuml dmiiglt. t-ht! strc:-at in tlm rui1:fiJrcsr1111r11t
nnri t.l|re n:n.\ti|||ltm :
"P.-u |h|l‘|| = i I-'.~r _ "-1". [.
5. SIIIELII lllll TORSION Nomenclature r|:|.
.-<|||'1|.|' .-<|1;11t. |]i:
fr
.-1, _
lnml amrl Fxnlrre uf :=1l[t1mrt.-' uflI:~ctiw: <'l'tJ!'\~i-&il!t'[iU1|.ll.|. 4111!:-1 of 41 strut in n
in“
strut-i-|n||-I iu tuullvl t:\kt'|| |1|'1p1~1|.1|il'|:|:|.r
Lu
.Tl|r||_1 _
tn thv mtis 01' thlr Mlrut
‘IT!
.-1,, Pu": =
3‘: n|
_p,d
Mlml = *‘3>1_|“1:1‘1,1_'1*|,,.|\'i
|u't!a r-11¢-Imam] lay: u|1tsidr- [r€'l'i1llt!tL‘1' ::l'
. -| ll'l'
l'l.HI|'I|.§| 1! l'|'|.H\H E\|.H".i.iJl|
.-1|»
il.l'I'i! n|' |1:!l||fn1'r
t'I:fi'|J.=ti1|1.: l'nc‘tc>rr.‘1| mun1I:~|1t .-1;.
:|.l‘1!a 1.1-T:-|]P!tl' ltrlllfultlrtllvlll ]Ja.|.':|.l|E'| lu-
tu-l.|'l -.-
H1“-Y'|I|'||-I H'[|Hi||ll rl"'il|rU|'\('|""||l1'l||
Example 1 .8
.-1,
J"|. 11~i|tl'I.:~l'I.rI."|.l ¢.“u11<'11*lu b<*at|:1 with utt l‘.|TL'L7[-i‘r'l.! tlupth L:-l' lfiinu11
am! has .1 cm1c'r0t-n r:_\;lin:!c!r s.1|'rs||gt.|: -m° iifjflfl lhF|."i|1'2. Using I110 clamliir 1lL'-sigtl 1ut*1llu<|. 1l|.'t|."r1||iu1.- thr: art-at uf
11:11:-iicm 1':-i:|fur(::!111t!11t wqttircacl if the I:-emu SIl[II[JLIl.'(5 at mm] sn~.|r\.-ir_:r» n1<_'|1110nt. <_'|f]-1.1 E1-kips.
t1:-tnl nrw. ui luitgihaclilutl url|1fc»Ic1'|11r-|1t to
un-
t:‘1!Hi.-tl l-:.Il'.-~iu!|. .4"
:|.l1!:a ur |\:!i.l|1'|.rI|u:!t||vl|1 ill lm-|I.t|-u-1 ur -::||rl|ul
1115'
r1.'1~i~=li1||: t|."n~=i|r' FI.Irl.'r' N...
.-1,,
ufivctllrc 4-L'm"\+e+ut-tiultnl urua uf the Face
. -| I.l'l'
IIE H Lllllljll XIII"!
.-1,.
j.ED2lH'1'tl1'I.‘v.‘l r'1:t"lr»'-1.11 lly >'hc'<1r flrrw. lJ.l55.-L,“
.-1";
turn -t'l1<'lr_ns-tvl In]: t-1'*1|t1'tlinc~ of th-I‘
i||
uutorlnueit clusctl 1rnn.w1:reu.-tun-1iu1|:||
.S'r|-I-'r.g.tim.:
t'1!it|l'-::-lwcrmlllrlll "' t|1-r- mnrl111nr mtir: is gium r l-"|'-mu l-‘Ix. 1.4. :|.-a
u = 3.73
'I'h=.* |n:-rn"|i.~t-¢ih|=.- Lvo|1cre|;n and r1~i11l'|)1'c:-nunmnt .-m'(:*ts:.-:- urn
.-1.
ll-l"l'l\ n-f |1n1t[n'rr\itrr--1-I-ll hI'[l!‘~il.lll l'L*it|l'<:|'<1*1m't|t
. -. uv
.4,
:|.r-11:: uf -::|||u |.¢e|.', uf :|. |']um~1.l :1ti|'n|.|| |1::si:~.l::|g
-l.ll 2
»1,.
rm“.-eirm within R rli.-‘r='|1|r:' .-' ltwn u-f:-;l1I:~41r rc'l|1fr.rn'r't|1c'|1t ]:»t"1'|:-|.'|Ldi|.'1|l,|\|'
. -tn-
um fluxlmral um:-iu-1: IDillf1I|l'4:f'J!l.1!lll
p,_‘,= I350 lhfl.-‘in’
.-1“;
am-as u-|':\'|1|'.=|r-|'|"i::|in-1| r|-i||l'1:||*1'|'|m-||l
l.ll
;|,, = 24.[lI|JD |l.>f,-"in?
.-1"],
|u'1'n rl-f .-'|1|~<'|r rr'i|1:fm'rt-r|1n|1t 11|tr|t||r!| tr: t1ux1mtl turn-iun
in:
-‘.h.|t'fi=?i:-1n. n.t:|i:ura1|::_y' is |'.:l:lai|||iu'| by -1'1.-‘*~'il.ltlliIlg that. t.t|.»:=
El
wlfllll uf it cilrlp ||t'.'|.||:
].It.‘1l|.-l'i|.l axis tl|.'|1tll Eau:lu1' I.'t|unls tlu: |JH|4l.lJI‘.'L't| 'r'it].l.lL'. Thml.
rl
'|\'iIhI|. HE |.'!J|lIp|'I'.'C"\'ill]I Elli? III |]|I'II|]||"|'
in in
II“
wv'l.\ 1-.-i(lt|1 or di|u|1r~tr'r ut' :'iIr.'I1l|tr >=u'tiu1|
i||
E‘
1:t'|:n|1rmaai'>'r- fm\t:r- m:ti|'|;2_; un :1 nudnl -zumr
kip:-
_f.,.
1~fl'u1'ti'-'|~ ('llIll]I|I'1'5i!ii'|'(‘ :~1r|-|:||.|_th n|' |-cml-rule!
l|rL"i||
In
. um (B. .... 5;. (13.50
HM ml =
fr, + I-';|_.
-
H
=
. __ E _ _ -. -.. . ,- E (ammo W) | ¢h...s)[1.m W)
= (1.329
III
0
an-w.ppilpar|.:n|'n
~ 1
in 41 strut ur llud-1'
_f_,‘.
_'¢l1:11| .-tm|1;;_1lt uf !t'iJ|.fi.I|.'t:|."|]H!]|.l
L,
_'>'i.vl!]|| :-tlL|L'l|;;1||. |1flt‘:||:l:-\.1!t':-an |ui|'1fi|h1.!l|1t'l'1t
1|.:_.-mu
it I,
m-|~r.-11| thirrl-rr|r-_~r< nF |||r!r|1b-vr |tl1|:-lmmgo lvugtl: nf at rcil|li:m:'i|1g bur
in in
l||L"il|.
IIIFGIIGEII collcnrrz nsulnu
wirlth 01' h|.~<1ri|u.t pltitv
1'.» I‘.
rlc-at b-llflll. tttt-mtttrctl l':=|t1t:-tu-futrtt uf
itt it
Wlwtt
the
sitmtr
rt'!i|tfi:Jrtrc!111:!11t-
Encturui titutiimit at :ent'ti-:2-I1 E:-ttttmtul It'll!-ii|.t! furue :i]Jp1i.1!t|. at tup uf
r1..f ti
1-’. : i s
it-kips
kip;-1
rx:-r1||~1
in
1--'. = st»,.t.¢’_rf.
Pt-
p-t:t'1|tu!1t'1' 111' t1.:lt1t'|'|it|u u1' u-||l'.1:!|'|ttue~1 t:|.
R
etttpp-tart rmtctiutt acting cm :1 |1uc1|t1-zuttu
kipa
5
rtput|::iu|; u-1' H111 utr ur l<:||1-titut l'wIt|'c:||1::|~t||-:!l:|l in dir-|-trlimt |:t:t|';t|h-1 ln1|utt',il|:||1i:t:t1
in
tact-tint:
1imit1.=
trltrt.-.1.-1'r.~a_~ tm1<'|ur|<'l1 1'l.'?11lFl.lFl.'F?111l.“1l[
rt"ilt1"urt't:'11t1-Itt :tt'm|::1|1|;, t>1' litrtiztrittttl l‘1!1.11ftrIt\!lI.|0l11
in
H-1t.|1 trrrlm i1t:| inp, mt it :|t0t1;|1 zmtu
]ci]:t<
ttmitinnl turtiit:-tml ttttmtt-|tt strrttgtlt Enctumd 1L11'1i14Jl1€I| lttumc-1tt t-‘ll ti0t'tit>1i
it-kips I1-1:111;
‘T-f"'5"'3‘-i 1‘
|:tt:lJ|i.|'t::] :t|:t::nt' :tLt“-t:|t,g.1|;|] |'tru\‘ithet1 1|}:
kijm
1-‘.
r1::-|‘lr.?l't!l1.' tlt)|]l1.l]t-1] s1t¢.'nt' titt't.'|t,t;tl1 ]1t'u\'it'1c~c1 11):
}ti]:e=
If tithlitiuttttl shuttr t'a]mt'ily is 1't.‘\l|_1l1l'L‘L1.. 1-hu s'tz.t: u-1 1-ltt: t:nttr~t'r!tr! Hmrtinti tttmat lm 1I11\'!1‘l=\.1\1-WI]. AC1 SH‘. ll.-1.5.1
limits tlw 2-i['1r‘t(‘1l1gt]I1 tho 5tit'r11p:=t tn :1 tum-ziiittttn vulttn 01' r1'_."2 or E-1 in. and wlimt Lltt! vnlttu 111' 1-",
= 21,1121 VIII
:t|:|ui:r rt'iIt|'ul1:|-tmrltl
rt -,
t~11|:!|'1'|\'|' wi111|| l1El1\tJlllTl'!!N' ttmt-:r1~1t| ritt
1ti]1~¢
iu
with tt tir
Symbols H
nttgh‘. b-t!LWr':!tt im1"]il|t'\t] :-1i1'1'll]J.-t tutu]
:1‘,
ft-tctur tu ttcmtiltt 11.11" tho cifoct of the
t11!|.',!rt!:et
1t1r|$¢iIIu1irwl encifi '1iIF1I1F!l1l|K!l'
[AC1 1:-3]
This '|.'1I]1Ilt! it-s DtJI|1H1.‘1'\'|-J11-1.\'i.‘ and is ustta1]_1,' sttfficitr11t.1].' at-rrmtt-at.n. .-1 tiium prflri:-"=9 1-'al1_|t= is pmvirlnrl 113; AC1 St-L‘. l1.2.‘Z.l zus
P [G\_,-I1-t 1-’. — (1.n).._.#1', +
,t-' . ~:' 1
1...:
_ _.-ac: 11-51
-1
1: ;i.5t...t\.=_r_i t--' , ,¢t T" 32 1.0
:1!L1:|tu|.';tg_1: ti-.1 lite-t ult l]:||' ttfftittlilt-1: |;t'_
jncr H-l‘5_
The lltlttlillrllzihttt-11' strmlgtlt nf tho :-iltn:-tr rt'\itt1'c:run1nc!nt is
ttttta-111:! ]>t~ri[|1|~.h:er ||F1||1_' rx:||1rrr1:'t1* :;|11~w
E! '.
AC1
in
rt. ,.
titrtrrnwi ¥-ht*+.1r in-r=\1.~ at :~z~|:1i|.1t| 011:-rti\'t~ wititlt 01' strut ]t|t"|'p1'1tr.|ic‘|1I|tt' tu tht! =1:-tin u1'tl'nt- t-strut
vurt-ica].
Elna. I1.-1.T.2 giv-re‘-t the tt-rmiitt:-1| 5|1I"\.'1.I r::=t|1.-tt':it}' as
ett||t|:-url:-:
tr,
is
1-15
r.'r.=|ttp1'r*.-2-'i1t'r' 1ill‘1.'l1,1!,1.1] rt-111 tic:-dnl Z0111‘ E:-tc-tur tu ttcutaultt for th-:- cfioct uf crnckittg
.,,=T;'_ 5 um l|>E,.*in'1
and truttfiititig IL"111flJ1.‘C€'l'|Z|E'1!lI on thrt!m!t'l i\'t! l'll|lL[lIl'l!~h-Cl‘l'l!311111131“ t|[1]|.1-
.1111“ 12-i the fttcttureed tltnimrttt ct-m:111'ri1:g 5-i]111l1.|L:-11100112-i|.}'
fUl1lI‘l'£'|Il' ill 11 F|Il'l11
with 1",, at tho 1-'-€!C11t]I|] lining :1|t:»1l_w.n1.
A
c-unt‘-t:ti::|1 1':'tt:tut' twtlatutl to ttuit wt-igiit ui
11
tr.»-:'11'tt'11'itt c-1' frirtiuti
II) 1:11-.<.|Ir|m1:.*:r Witlt AC1 Eq. l1-l mttl En]. 11-2, 1.lt13 cutttbiltutl sltcttr cstpttcit-_1.' uf the fl.l11t!I|'l.“1I-1.‘ aiuctiutt mttl
[J
rtritthultnrlluettt rtttitr. .-L,-'|'J_.|l
thn :-thn:-11' railiftirriuiimit. i5 qi 1-"..+ ¢,i»1."_,, an-rl this tttmtt
—
Ix:-|1rtrc!|1'_ :|.-t gi't'|e|| i|| HLCI Sm. H11-.1
lillslgn for Bhnar
nimnucl 1-"',,. it-'1tit".lt is 1:110 fartnml 1-ilimtr fnnwv applifil tn the st‘-t"tiu|1. Wltctt 1-",, is 1t-ta l.1tt1|t £11-",_.-'2, th(- 1;~u11t‘11t-1.u szrctinn it-i tttluqimttr Lu carry the 2-i1tr'tar witlmtlt m1_\' 2-iltt-tar
The ttutuinztl -¢=1tt:at- capa'|ci1._t- u1 the ittulittuti :
Tl'.‘111F1)1'fi?!|11(!llI-. Witltiu the 1't:11I,g(! t;-H.-',._,-"2 5 1=',, 5 qt-1-',.. =1
sltuwit in Fig. 1.1115 givctt by AC] Sm‘. 11.-l.T_4 tut
minitttttltt ttt'I.'ti u1'sltt't11' t't'itt1'urcr_'11tc1t1- is sjiccifitxl by AC1 Sutr. l1.-1.15.21 J11-1
.*1,.f\.,tfl'.Bil'tt'r — K11-tfl}
t-’_, = i
|ACI 11-16]
.4.........;. =
H
u."r 1,,
'
Figm 1.8 Emm wt:-'1 -'mwr.~t1-0 St-Wt-1:1:-‘
_
_A~:=r 11-1:,
._ i -5|)-[1,,..~.-' i
lg.-
3
1.1-'|ir-I1
1\\\>\\1I"
fgr
:=~=l.4;1 kip.~t,-"i112. AC1 F§r|. 1|-13 gnvm"n.~t.
Wltctt the :slt|1]JuI‘1 t"L‘ut1.14.|-1'1 plutlltwts at curt|.|m-.<
Eiuc. 11.1.3 5-'|'K‘\t‘1fi1"Ji tzhnt tlw |:1rit.ir::-11 2-1-t"\"T1t'|1'| fur :-1|1t"1iJ' i:-t lutatctl at at tli:-.ltut(1'~ l't'u-ut 1.||t- itttp-t'>ut'L I.‘-t|ttul Lu Lltu c!1ft:~ct-it't: dept-h_ ltt ttcidit-14111, fur this ctaiiditiu-11 to apply, PPI
l 1Itllr.|II|I|lII-l.GQII
Concrete
1-16
$1'RuI.‘:1un:|. Ellullueznlllu nsrsnsuci Illlllll.
111111111 tttust lw t1|1]1]it1d 11€.‘1ll'Ut' 1-1t-t-hr‘ 11.111 01 tlu: hqrttln tuul 111101-111-1-01111-=1t.r11'1 I1-1:111 tm1_1t- 1'1-1~r111' wit.l1i11 =1 1|i.~:t.11tr:r1 Frrattt the 1<11p|1r_:-|'t tfrrltlatl to t_.l1r1 <=11't-t_:ti1.'r_~ 1'l|'![1I|‘|.
G
: w(l.9M|_,E. + 2.'.1111$..1-"'...1) Mi
11.11111 1.111 11'1' :1111_1-1.1 E t|1-
Figwl 1.? C1.-11'1£a1'.‘17.e.':.'.-0.-1 J01 Shear a'— — |
“W7
— —-.—
+ 1'.2r11111j1[11.t115j|(EI 1.1;...-j1{11'1 11.1 1211 11-1.1|..j1(12
Tl'H11|11111l1l1T_ I |
1./'_
urthcul suction
x [1'.1i11_1[]t11tt) - - 1111' 1 111.1 — U kip
I“
:
_
beulln uluvuliun
— 18.2 liijm
¢wp|:1e-rt
2- 21"]. I
Tufiflml I!“
}
shear lnruu
Ht~||('t*. ilt 1wc1.1t:11t11t't- witlt AC1
11.-1.'[i.l. >l1('111' ruin-
fiarctrntcrnt. is nut l't!t]llI1!'L‘\I].
1:11] Bt!lI!r'l1L1'l'! 11> 1"',._,-"2' <' 1",, -=1 <11-",. L111! tt1i|1i11111|1t 1-tltrv-.11" IE'111F1'r1'flt"1|I1":l1L 1-tpnrzifitltl lay AC1
Example 1 .9 A I1,~i111'r,-|'[:(11'l -:_'t'_1|1r_:n;1tr.~ l1q1:.111| 111' ttr_1|'1|1;1| \.\'cight (:(1-1101171111 willt 1111 0111.-r_'ti1.'L' 1lL'|J1h uf [[1 itt 1111:] 21 1-1'it|11t uf ll? ht is
A=l|11|t1j1 _ -'_1|HJ,,.
i— i .-1 fu
r1~it1fnt't:r1cl witlt gtwttlo [it] h.11n-1 11tt1'1 11:11-1 11 t1c1t1t:rt1tz1 mm-
].11*(:-1:=ivr_1 .1t|'1:e1tgt11 01' 3111111 lhf,-"i11"'. L1'1tet.c:r111i11-0 thc: $110111“ 111-i||1'|.>t'|;rI.1t|1I.!||1 I=.':]11]11t'
1111,1111-11
111r.1||1I.'|11 M.,=N F1-1ti|1s. 211111 thL' t'L'i111'u11t'c11|t*11l
_
ll.l'
=11.12 t11“_."f1.
rtttin p" = 11.1115
[111 Lhu 1'11c"tu-1'-1111 14110111" Ftlrnr 1",,= 1-1 kips
Shear 11:iufurL'L't|1t'|11 tuilsistiltg u[ twu arms 01' ttu. 3 11-tuti
[t:] 1-ltl: Ytictumtl 1s1tt:11r furct: 1-"U; -I-1 k1[ki
at H itt aiparittg |1rt11.=itlt15 11 rtri11fut'nt*tttt*ttI: nrmt of
1:11} 1111:: f1‘1C|IL1I‘l‘(]..\ih[‘1-11‘ furur 1-",,_ T1 1-tips
[tr] t-111? Fnrrttnrzrtl sltmtr furct! 1",, = 1211 hips
If
= 0.11:1 11.3.-"rt
Thu 5111-ltriitg of 1'1 in 1:111:15 nut c!x1:rt'\t\rl 1-i,>"'.! 11111:] is
5'01-11 11111.1
=1.-1ti1-1'111:tc11'_1'.
[11] T110 :i|!I'1‘ll' :11-1'L'|1gt-I1 pruviclctl 11)’ 1-111' 1-1.1-|1t't't‘tt' is-1 givvtt h-3' AC1 Eq. 11-11 as
1;-1". = 1.-"_., — 1311",. = -'1-1 kips —
(2}{11.r1.1[12 11.j1|j11'= 1tt}{t.11} ,~":1111111 ‘f
1111111
111'
,_1 Ln FL
11111121
= 1'12 1£1}'!t!i
1111'
= 15.8 kipu
¢'.' 2191",
Ht~1|4:c. i|t i1ct'1.1t't1z1t1t'I.' with .-‘LC-I 1:11.11‘. 11.1.5.1. .-11i1'r|1]11~= arr‘ rtrqiiiwtl at 11 ttttaximtiut 1-T|'1\1lIZ!iIl1{.'; of d,1"'.3!=1'1 in. T110 :11'r1:1 01' 111111111 rr1i11t‘nmt~111t-11r. 1'r1r|11it'r11"l i.~1 git't_~11 11].-' AC1
c 21-"U Using AC] Flq. 1]-F1 to \-'-r-1'iI'}' thr! sr1c:ti1'1|1gi\.'r111
1-g_.4_ {s11<1p..1(111111'1 M * 1211 Ft-l
1):] T111:1etL'tut'L't1:11||.'111' [urcc I.'.\tt'1.1ct]s 1111: shvur :e=1rt'|1gL|1 uf
t11trrvt1n1:rc1ttr. 11111] the slimtr 1-itrc111gr.h 1'1‘-q1|it'w1 {ruin 1-them‘ 1'E!111fi'|1'-1‘\!'1]1€'11T is givntt l1_-.' A{'.‘l Flq. 11-] mtrl Ffq. 11-1! 1-11-;
01",-= '.1¢|b,_. r1}. \,-"if:
0
_
[£11-'.1"|'111~]
{E11 %)1j12 11.1(1-2
[11] tl11=- f:1r:t.1'1|'r11'| 1-111r111|' 1°01‘-1111* 1-"u=51 kips, thtl 1'11-1':t.r11'r1rl
III
11.-1.1_i.3 is I'|I'(.|‘l]1fl"€|.
tuul l-11i.~.- its t-;i\'t*1t 11;,"
|:~'.'t1 11111-llf|(Jl'j':
wurw.ppiIpar|.:n-In
E111. 1|-15 11:;
Ar
Q1,-_
“
°m"r*"
. .. ._ _111 12-1.2 141]»-_i{l2 E)
{t].'1"!T1j|[lf1i11)([1t_1
= 0.41 1.1‘-Km
111'
IIIFGIIGEIII cflllcurri nillnnl
1-1'?
Silcnr Fl‘i[L1£)I£!(!I1]I!I1i nu11:1'i:iti11g nit-wu:ln11:1' of nu. -I iil-\1':i
Wiwll a sxrriirs of £51']11!|.1|}-' spiatrcrd bvnt-up imni is ll!€1I!II1, m-i
at B in si|mr:ihg ]n'm-'i|'ln:-; =1 W-i|1i'm'r:nn|r!nT >1|'m-1 raf
slmwn in Fig. 1.5, l|11*11u|11i11.1|.Hi1:'nr c:>1|mrriT_\' is ;|!_i1.-‘rm by AC1 Hi‘,-1:. I1.-LT.-1 :|.-i
£= [I.[i[] i||°;'n
F
A
.-1,fL,{>iir1r‘r ~ cn:an]d .
:- u.4.- mi,-"E1 [:-mi:ai=-"|c-tm'_'.'|
1.46! II-16] H
[1l,'I This slum!" .~.-l-rvllgl-11 ruqllircd [will Um shear rr.'i11filnrsrlilirllt is givnn by AF] Eq. 11-1 and Eq. 11-2 n:-i
FIHLIN 1.3 B[!fl-I‘)? wilfi |'r::.1'|'r|(:d Hiirfi
r.'.I 1", = 1"“ — |_ir iv",
= T1 kipu —
=
\,‘_,-1‘Z-‘I
‘L1
|
2 i-tips
.“.> ‘Zr;-I 1-" ,. “("1111", in nctrrmrclinluzrc! wiih AC1 S-Hr. ll.-l..":.Ii-. 5Tirr11]'m arr; 1'(a|'|1_|il'|'!f|, at :1 irunciniiml 2-ip:1(*i11g 1_1f'rI|."-1=-1 in. Tlrm
arr.-an uf r.ehL'm' r\'_'i11l'u1'+.1"uu'rlt l'UI.|_llil'L'L1 is given 113' .~\C-I Eq. 11-15 as
4|
.
Q
. ,_ . _, |.ll |_5.1.2k1p@.)(12 H)
M.‘
-1 .
WU’-“'
[U.T5]|f1fi in)(fi[]
Duly thv c!c'||tc'r 1ill.'l£‘lI‘—[U-llI.'E11H ul the in:'lin:'cl hm‘ is c:|'>||sirim1-cl r-Ff:-crtiw; this; limits: Llm 2-‘quitting. I|1‘|l"FL'i11T-Ni in il1ii.l'L‘l.?[1LJ[L Jmreillisi lu lhI." ]ut|glll|di|m] ruit\[urr:L'1ur.'ul. in a mnxiuuun -.'.u]uc: uf
- -
-\'.._... = U.3T5r.I[1 + rut. u,'|
I-
= H.112 iifiifr
Tliis \'eI.lI.u: ia h|1]w.1l. in m.'u.|r:iauu:r.' wil-h AC1 SI.~<:. 11.-1.5.3. wlmu 1",, E!Xfi!(‘.i'i..*i =l.ir,,r1'\,-"FE.
§_-iiw-hr l‘1'!iI:|.f|II|t'|If(!!l]Z|f!I|]T fx'|1l:-ii$|1ill_L{ uitw-n:1rn1:+ n-F ma. -1 in-mi
ill 1 in .~'|Jzu.1ing ].ll‘UY1[1L'R$ 21 l‘1.‘il|.i.-L>l'L‘L'lllL'Il1 ill'L'i‘l 01'
In :1|':rx'r1'c|=-111-no with AC1 Snrt. 11.4.1.2. ilw nlinimnnl ]1r.'1'|uiLIL'd angle ul illclimlliull u[ I111‘ i||r.'|im'cl bars is 1111"‘. \\"]::!11 &i1](!fl.I 1'0i:1[c:|'c:c!111»:!11t. ::u1|_\ii:;t:i of heat]: 2-ifiTl‘ll]]H
.4, . — =1-L':‘u|3_."[I n 11> (1 92
ixfi
nnrl inr_~|im~="l 1l1'll'5, the T<_'|1.11 <.‘u|||lfim_\.ii.-HllL‘L‘ti u[L'i1c]1 1-_\'pL'.
:24:-11ie=t'n|:-tr.>|'_\']
The numi1u\] zvulniriluxi nlmnr TH-ii5Tli]1l![! shall not c!xc‘u¥l 5{1,.rI-\,-‘if.
[19] 'l‘l|+_"e Hi!i|'!:'1l' s-:m?||p,1|| |'|7:r1Llirr_-ri i1'\l)1T| t.hn s-:l:r_!:_1r 1'l'_!1II|ii_'lN,‘\!.'— 1uc1|l- is 3.',iv+.'n lay AC1 E-q. ll-1 EllIl(| Eq. ll-2 mi 191-". _" 1" .,
Q i"
Exarnple 1.10 The 1':-i11furc:z:c] cuurrcrtv huam of i1ur||m1 wcriglut camr:n=I.n :-:i|ru'|.':n in rim fr:l]n\\'i11g ill11:-|t|':1r.inn has an nfFnc:iiw: :11.-plli uf 16 in. an whlth ul' 1'2 in. 21 1'.'4_|-|u_'ru~L<.::0:||]11'r':=..*-aivcr eitrungth ul'liUlMl ]irF_:'i1:2. uml is rtvillfurcrul
_ 121] I-cipe; — 15.8 kipei
-— l[H.2 iRi[ki
with g1'.~\¢|n GE) l'|-:a1's. |](at_.m'|t||i11!_'- thr: :l(:=iig|: .=ii1r_~m' |:_'.1]mc:-
:- -L-:1
iiy pruviciul ul. .51-cliun A-."'|..
Ht"llL'\L‘. in nccur:1a||L-u ‘W111i AC1 Sn-L-. 1] .=1.T."J. the :iL'L‘lI1U[l size is im1-rlnquatv.
Inclined Bars ‘When él siilglc. I:-writ-up imr ur |;ruup uf burs L't|uit|isln1|l
.5'r1.l'u1in.|iThu 11u||1i1w.| ie-]||:zLr 5|.I'L‘11:_'_,l]1 uf l-hu l.'U-1lL'l"l.‘l-L‘ ire giv.'1:u lay AC1 Eq. 11-H as
— 2i»..¢:~\,»’,Tf
fmlu Thn :-:LLp|ml'T in 115111 mi s]m:1r rni||fnrm11w11t. The
]'ll.ll1]1llil1 -‘i1IL'i'll‘ 11':\]1a'1L'ril;.-' is given l:__v .-KC] Sift‘. 11.4.7.5 an
= .»i|,.fv:'-\i:1r'|
5 3 E», r1 \.=";7f_
inc: :1-r?|
_
|j2j|i12 in][ 111 m';|j|.u':- ;":im|u 1;
_
|u
[hf llJ[H] kip
= 21.!) k1[J5
PPI
l v|uuv.ppl2|:|nnl.:nn
Cuncr2:-r
1-18
$1'11u1.‘:1u11:1. Euulueznluu nsrsnsuci Illlllll.
11111.-1-1f1'r111'11r1 fm‘ Ha‘. 1.11‘?
A
ND. 3 ‘E E111 0.13.
1—N0. E C1l'.'| I
1
1
.
The 1111111111111 11111-111‘ 1111101111111 U1 1110 \'1‘.‘Il'1-1L'1-11 :1l1r1"11|1>.= i1-1
giv-1~1111_1' AC1 Eq. 11-15 1-11-1 F
|_
Arr.‘-Id
'1|>.1|;- =
,1;
(115.1
‘\~
T111: 1111111 1111111111 is-111:11r 1.'11]1111'i11' 111. :1L'1:l.iu|1 1"1-."'|. 1:11
._:- = 1:11 1-’. + 1--',1= {11.1'.'11|121 111111 + 1111.11 1111111] ill:
_
1-E11}?-i
.
._ _
= -171.5 1-:i|11-1
(1111 FDIIIE1 111]
=
,._, 111
1
E1
D001: Beams A:-1 1-:11nw11 in Fig. 1.51. :1 111-11-".11 111--rim. 11:1 111111111111 i11 AC1 51'1". 1U.1'.1 111111 51:1‘. 11.1.1. 1:-.1 11 111-21111 111 1.1'11i1i'1| 1111- 1111111
- 211.-1 1-111111
T111.~1111111i11111 s1111r11r strvngtli 1111111: i111:1i111:11 1111111; givrri 111' P1111 Er]. 11-IT .1111
111' 1:112:11‘ 1-11-11111 1:11 11'1'1:r1111 111111111 1111-1::-1 11111. 1rx1:1\1~11 -"1. D1~1:p 1111:1111 1!111111iti11|111 1-11:-111 1111111)" tn 1'1'\1.1'i11|11s 11111111111111 11111111111 wiili ("11_'|11l{‘1'_'111l':_'|1j.1_'Nj1 1111.-11111 wi{.11i11 t.1vi|j11_': [.1111 111',-11111 1l11|11||
. . . -1- . 11' ' - . - ,, 1-'_.,_1,.,; _ :1.-_r',_.:11|111 _ I11].-I-1 111'_|([11J 1111111111 ] ' 111*
11'u1|1 11 >.=11[1pu1'l. Thu 1111111111111 5111-111" st-r1:11g.',l11 1.1111 110011 1111:1111 12-i li111i1.1111 113.1 AC1 S1111. 11.7.11 111 11 m11_~1i1111111111f 1-'1" = 1111J||-1E11rI'1lf‘j
_ 111.2 kipei
151:-1 i1111i{'1111.111 111 Fig. 1.51. 111ihi|1111111 11r1!11:i 111 1'11rii(*111 1-11111 T111: 1"u|||1.Iit1L-11 111111111" 1.-l.r1*1|1;,11| u1' 1111' :1-'11I.'11r rI.'11|1'ur1"1*-
11111111 111
111".1ri>:1.=-111111 rr.1i11f'01‘1‘1~1111.-111. 1111'! .=1p1:-r_:i1i1_\1| i|| AC1 E1111:-. 11.7.-il 111111 SI.-L". 11.1.5 111 01111-1‘ tu 1'L‘a'1]'1l1]1 1'r111'11i11|a'_.. ."11lL'r1111-
ti1'1!1j.'. 1'11in111|'1:1!1111211t 11111]: 1111 |11'111.-1111111 1-111 511-11111111-11 i11 1"’-1 = 1'!1|.-1rj| '1' 1"-1:-l:1uJ|
AC1
.~'1.:1.I5.
= 1151.11 111111-1
I11111-1~11r=|11111:'1.-11-i1|1 .~'1.L!1
-:. 21-’.
1iusig_',111:11 111111111, 1:11.111-r 11u-1111111.-111' a111111_\'11i.~1 1.11" 111' 1111- afrai1'1111'1-.F.i11 1111'-1.111111 gi1.'n11 i11 A('1 111111. A. 1n 1111* 1-111'111-111111-
1l.?.‘2. 1l1:11:ep 11111111111 1||11:-L I111
ii1' 111111111111, >1 11m11111-1'-1' i.~111i\'i111'1|. as 11111111111 il1 I-‘i_1.{. 1.111. 111 111:1:u1'111111c'1* with .1\C.'1 S1511. 11.-1.11.1. 1-i11fT1l[II 1-q'1111:i11g
111111 e11.~.=1r1m1'.i1r111ll‘y. 1.1r D-1'1-11111114". in 1'-'11i<‘11 1111* 111-11111
11111211 hn-I. 1-1cr:r1r»11 r1_."'.! = 8 ih, :1|111 11111 11|1.~1rri|1g p1111-'11"1r111 i:-1
t111.111r_1' 111'151C1 S»1.‘{‘. 111.2 1111111 11111 11111111.’. 111111 B-r11gi1111:-1
1111111:-=1a1L'lu1'1'. T111: 111i11i|||11111 1.1111.-111'1'1:i111'urI:I_'||1|.'|11 1‘0l|ll11'L't1
111 11'11i1".11 111111111 Tl|m1'_1' r11"1r:=1 111111-|_\'. I11 111l1"lirir1|1. 1111' T1111 h-1-l'lI1-11111.1-111.‘ 1111-111u11 11.1-111111111. 1111- 111-1-11 1,w:11111 11111111 I111111-1111r11 1-111 111111 r11111prr'11si1111 1-11.111111 111111 111111111111 1112111111111
is 5|:-1~ci1'|I.'11 |1_\' AC1 E11. 11-13 1111 .11..
51111.,
— = i -" .1-1.1
|--111'1:nu-1] H
= (.1111 ::%§){12 i111[11
1111.11-1111 1-1 111'
=11.12 111*,-“E1 -5.11.1111
III
0
[:1:|.li:\1;11tl1|r_\']
1nurw.ppiIpar|.:11-In
11111 1111-111:-1 111111 1:111! 1i11]'1pn1'L11.
A»: .~:111.11-1'11 in 1-‘i1;;. |.l1. 11 1111111-111111-Tire 11111-1101 11111_11 I111 1'uns-1r111:1.1-11 111 1'1.-|11'1:111-111- 1111- in11:1'|1a11 1'1.1r1_'1_'s 111 11 111:1:p 111111111. C1_1111]1r1'1e11i11|:1 :1tr11111 1111' 1111111011 in 1111: 1'11111'r1:t1* 111 I1‘:-1151 n1'1111pr1*.~111i\'1~ 1'n-|'1:n11. 'l‘|1n .*1t1'n|1;|1_t11 111 1.1111:-in :.-1|'l.llr.- 1:-.1 g1_11'|_‘r||1~11 11].’ [111*1l'1'1t1:1\'1-1'11‘ 11111.-111111 1iv:\'1‘1-1111-1.111 11)" 1111* 111t1*rs11 s]'1r1'11(1 111' 1111: 11p|11i1.11 c11111pr1::-11111111 1111'1.'1:.
U:-11111; 11:11:11 r:n11t1'r1l |'r:i111'n|'1r1'11111\111., 11.11 11|1re1".ifir~r1 111 AC1 S1-1:. 11.1 rr.-:1i1el- 1111: l1'm|:
nE|u|=|:|I¢u=.u <:n|u'.:n:'rE nsnluu
1-19
Flgum 1.9 M.-:1-."r1um SJ?-es-.' Re-n-‘a*ca'r1a0r rcw a Deep Beam _ cr _
.
.5 >. — >. ‘I2 |n
|~—> 5
-4,. :¢ 0.002515;
1/
Concrclr e
d
_
s;'=§'=12|nL
'3' n
‘Ir/I‘
aw, :< 0.0015113, TBDBIO-I1 |'G|I‘||lZ| |'G6I\1Bl'|I
.l'“'-7.-|1|'|
Figure 1.10 b‘- and LJ-Ifeg|rms
\ %
Ti:--'5 cu:1si.~:l u[ lI.'11>=iu-n rL'i11f0rcr:1||1:nl and l-hv s-|1rru11|ul-
~\
W
D-region
_|
B-ragiun
H
|
\
ing c'0u:'r»:!Tr~ that is. c:u|:\c:c!nTti:! with Lhr axis nf r.]11r tiv. [J-ragiun
| /
|
1 Jr
|_n4 '
Tlw c:rmc:rs*tr~ dun:-c 1101 cr0n1ril111tn In tlw e-"~m*||gtl: 0|" 1||1_! li|_!.
."¢'mI¢"=.-e r_|-:rc11r 1.\'|'|:_-11* they meme ah-.t.r11t:-c, tim,
5:22:11. Tlu~m1glr- hr-tv.s'
f1'= E5" i|| ur|1l.'I' 1-1| lllltigillu ¢.'1'1I.I.1Ritlg. 'I']n'_- c_-fl'r:|':rivr: |':|'r|||prr_-5.-:i\'4_'estluf-||g1I| r:-F the -r_*:_'|1'|:_-11'-ta‘: in :'|
>-1_ru1 in 5p<-ciliual in ALT! Sc.-c. Ala‘-.2 as
{H = 11.:-4."-,3,ff_ Figure LII Srmr-ancr-Tue .'.-'rc||:|'e.' 2h
|_-
3
—“-' 2h
-_|_-
_ 1 H
' "
-_|
W‘
J
'
[flu ;u| |||1r|~i:ll'||r|-(211.1
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.-. :_. -1\JW ' H4; : fl
*
fur :1 .-elrm uf unifurm flu:-Iei :~('['1i|.|!l.. ms in l]|.|- rn||||m-.-c-aim:-|| x||n1~ n|' :|. h|~.=||n
_ [Hum
‘ _
A
[ACI A-3'
|1|.Ilil1'---Impvrl s1rut Fur -1 ||r|-l1]|~.
Ii.
.
.
.
-'i_ _ u.-m
H[l'llt:-I~ ll] 41 u'~1m1:-1| u"|c~mlwI [ urlur l]|.1' lam:-eiu-|:| |'l;||1|.',|' III :1 ll.ll'llIl|.H!I]
" , - U.Lil]
SE:-I all -::t|1c-r r-4|:-1-:-'|
5
.3. - 1.1] [fur 1:-Jruml '.\'r~igl:r I:-um'11‘1c~| ri/-‘nod’?
auut -\z
nud,a,.."'
J
_, /'
"‘--. -._
strut
I
-. '\-\.
J
“H
$= [L35 [Inr ~¢|\:|<'i-|i|:|Ltwvi|2l|t -:'m|<'n~Ir'I .3 = [LT-5 [lnrnull-ligl:w.'c'ig|11 1'-:mr1'r.-tr:
'“‘-._H /r
é’ L-
/-D-rcgiun
“-.._H_‘
“MB
-
|
.
1
In a|1:curdzl:1cI.' wltll .'\(_'| bu". ."\..$.l. lhI.' nullunul com]]1‘l3':-i.*ii‘L-'lI' z-iLr»:!11gt]1 uf :-1 511'ut is;
aa25"‘1'““-~__ \-_ m,
= ,r,., .-1,.
|ACJ A-2]
= Ir, 1r',|'1
it.
PPI
0 v|u|uu.ppl2panl.|:n|n
1-Zfl
trnucrunnl. zlluulsznunu lIEFEREll¢E Illll.IlL
T110 st-rnngtla rc!d11ctiu11 factor for st-rllt-zuul-tit! [ll|'.K1l.“i:i
In flL'€Ul‘(iJlI|1(!II! with .'\C'| S11‘. A.."1.l. t-ht! nnluinal vuln-
is _l._§i1.-‘ran hy ACI SH‘. £l.Z}.1!.E_i AH.
]1w-.~:sii1.-'|': .~:r.rv11gt|1 nf a ||n-wlai zrmr: is
0 = i].Ti'J
J’-i||.': = Jr-1r'AllZ
'A'?i
= f,,_1|r,.!-I
In 21 |'r.'i111'1.|-11.1:i:l u:.|11<'11:l-1: i.1I.'4:m. Lhu llumilml 5111.-[lglil ui at 1'L'ir1[urL'i11g hm" uvliilg as H iic is givcu iJ]." .~\(_‘-I Sec. A.-l.1 as
Tim l'4\|:‘I.'.~i uf Ll|I.' uuciui win‘ .'>'iIl.U\\'l| in Fig. 1.l'.'-I uru
F“, = .~1_.,_f_\.
]1lnt.r!_ aml the Imigtlis ml‘ rim Paws nrn in :li1i(>:_-t ]1m|1r_:|'rir_>||
Ii Lhl: i)t‘ll'c-i in u l-iv arc in IJllL' lnyn-r. aue. 0-1|uv.\'n in Fig. 1.12. ilw wiritli nf the tin nmv he ta!-it-11 mi tlw rlii1l1wtc!r of the
all imam-i and is terrlluacl a .Fe_|,|'drr.\.u!+zfi'r.' rmdnl ac-nrr. Tho
]1c!r]1~:!11:iic:11]ur to him £1.31‘?-i of tim strut. Liv. and ii-lralring lu Lin: l'u1'1:c1-.= incl-ing. Hccilcu. l-|lL' uudr: has L‘1;]llili sl-1'I_'.1:er:>.- un
r:lT0cT.ivr_: wi<;|t.h =.'|frhr.- ='-4liI‘1.|T- :
ii»-elm in :I1=.~I;i0 plus twice t.ii|:e<1.1\'~.*.1' L0 the .-m1'f=.10o.*. 0t" t.h0
1r.'. = ur, cure-H + J';,:iin I?
imrs.
The r.'J.'.*r.-nrfr.'rI rmdai zone: :i|]EJ'|7.-‘ll in Fig. 1.12 is that
]1r.1r1i<.'m of the 1m*ml.:0r |.>0uurl0rl lay Th-0 i11tc|'5c:crtir.1il of
Figunl 1J2 N:10'aI'Z0r|a
tin: L‘iTL‘L'|..i"."L‘ strut. wiI.ll]1 and the r.'fl'u:l.iv1: Lil: width. As sp-wcifiwl in AC1 Finn. .-L-1.11.2. thr! r'Lll.{‘iIl[l-‘H-1j!',|I! l0u|:;th of
.-W"
the rr.-i11|iJ1'0c|1|1.*.|1L is 111=?.1.~=1.11'ca:l from the pcvim of interW:
V
-l- If
#5-<_‘i'_'iiUI|1 uf lhr: hm" nntl the L'xtr.'ndr_'ti nu-Ila] 10110. Tlw n:i11fum:uu:uL may he H1ll.'i.|.UI‘1J(l by H ]}]£l|IL‘. by hunk:-s. 0|" la}; :1 :-:r.mig|1r. (l1w¢~|u]1111r-11t. |F11gT|1.
.-"
Exalnple 1.11
”‘\
A rc!inl'nr0Hl ctrmcrutse bnaiu of 110-1'm>1l wreight m11|:t11~Tr-
T
-—r-
w,.'2
\'-'iT|'| 0 clear spun of G ft. am :::Efi~.*t.iv0 ~:l0pli'| of 2G in. a'm1'l :1 wi1lt_l1 of 1'2 in. as .~=]10v-1| in the 1'0I|u\--ing illu:s1rul_io11.
W,-'2
]I|éL\i :1 {~u11c11:h: {‘fl]Il[!l.'[‘!55i‘|'I1.‘ strcrngtil of-15110 ||Ji',>"in2. Tlu:
- i - iQ—hI
"“"- mclnn dud nodal zone
5'
n-0|:Ia1z0n&
i-i—|-I
I.
-0.-
fnctnrnri app-liwl lhr-:20 of HI] kipea inclnrlms an :-1iit‘|\\'r'l|:\ft1'! fur I]'|(- 1~il".v1_-igill.uHl11_'1.w;~z1|||- D:-11.-1't:|i|:¢ t]1£~|11|m|:»:r ul' grmlc [ii]. nu. S lmn-1 rrquirwcl fur I:|::n:='iu11 1'rin[urc:»:r1n::11t mlrl rriinnk T||.~11. Linn -I‘~l'|11i'\'-'l.il'!llT rrnncrrntv strut and nnrlal zrmc .11 the left s.1_||>pm't. r;|:|-inpiy winh t|1c1'-0q1|i|'r:|nm1tS of AC] 1fll.]}[). A. Hn.l'r:Iin.Ia
."'|.:i (i'L'fi1I|L'[] in .-U11 SL'L'. .'\.l illlli 5|lLJ‘1‘."[l iu Fig. 1.12. at
nodal zrmr: in the vnlumv uf ::nuc'rvt.~:: :-;|Lrrm|n:iiug ii nucin that is ;L-=.-:|.L|mT:rl I0 t.r:_1||:-'.i'c:|' sit1'1l£-an-rl-t.i-ire fiji-mo:-: t.i|r0\|gi| the :||.:w.lI.-. Thu uudc: ii.iLl:i11'lli.1.‘1.i. in Fig. 1.12 is L']il.':ih-i[i.L'Li. zue C-C‘-T. wiih Lwu of U10 111r:111|1-cm ucl-in|; on U10 I|10li.L' in r-0111111?-.=i5i0|: and tim third nmxniier in tv|min11. Simi-
larly. v--11»:-11 all l]‘|l‘(N?! lucmhers acting on l]1=.- 1'|:Jdr;- are in cu:n|:1'0s.siun. the nu-ila: is 1.'i-ll..."55i.E|L‘[| ma C‘-C-C. The r!ii'r:|".ti1.-'n rn||:|]i1'r:=i5i\'0 :-itrr~|1_q1l1 0f 1hr~ c!riur:l'0t0 in a nc:-rlre
The C'i'L"Jl1' :;|'m11-to-1l~L*pt]1 reitiu is given by i
"'2 in
1'1
23 in = Eli -=2,‘ -"i.
::1:al.i_-sl'|:e:| ."\("[ Sm. li..t'!-.1]
T110 i=1:-ellizml :str||1-mul-t.i0 inmlcl is .-shown in the illuslrai-iu11. nntl blur: u:|1g|L' ix:t.'n.'L'1:l|. l-ht‘ Hlflll-5 mull the i-it‘ is
irs :.|;|-c-c-iii01.l in AL‘! Soc. .~'|..-5.2 am
9, .
1,, _ u.s5_.-i,,,r'f_ _.i,
|
' "
=
I H .
for 11 1\ur.|4l| rum‘ h<:I11u|<'r.l I.lil nil Filii‘-5
. . .
= [Hill . .
by :ill'|1l:i 01- h-uarlug iirl"'\|lL“i u|.' buth
T110 t'r[ui1.'u]
fur =1 110-da] mum! n|1|;-Inning
:-1|u'l-tin n1-ru.'|!\l :-1:4
||||1' liu
[ -
0
= :» 2-5" [:-enti:=fi|:=:~ .-1.01 5.-.. .-..2 5]
_
=E]-E4]-..
III
|ACJ A-81
H = um"
fur .1 uu-c1:11 zum! ;|.|||.t|u|-|'.i:|1_!.{ ['||'|'1il [IT |'l]|llTl:" iiicii
urn-w.ppilplsl.:nm
T = {-"ID kip:-s}{=1L'.* in] Eli in = 64.62 kips
nslnrunceu cuuunzrz nzsluu
1-21
Hinsfrrziion for E1. LII + 90 kips
|—i
| ConcErc-r
d Ifiifll
n-- 2a in
_
'
beam elevation
\ 1; in cave:
12m
:,- ram
12m
+80 Kips
Er”
1'5‘?
25."
,.-IQFP I3
—
w, -- -1- I|'|
,0 — 31.3"
1 +9 t-10 kinsi r—a1s2m ' D 5 R 4-0kips+ _
I-84'“
_
I
mrllmti-;:n
i'acmr
is
givun
| :_\'
_.§_('j]
¢.—(]_T5
_ _ _ _ 1']|<.- l1I.'L'l.'-i.“-i\I'_'v' l'I.'IIJiU.l‘1.'¢.‘l|ll.‘ll|. il]‘l.‘4'l IN j_._',J\'L'Il
_
P1
1,,—2.-ism
in_-
.J,.
Ii, = wiilth of :!q11i'.'>1l¢~1\t 2-mppurt strut _ "Mmlfl
_
in
|r.I_ _ width uf ::q11i\.'nlm\t c-u1u'u~tr strut. ,,.r =i
plfu
_
Plfldfli ZIJIIE
— [-i111:llnu31.B"'
A ,=i ii
|:,'|:|-4|‘?
01.02 ki||> [[i.?-3} (00 |.|\'
= ]__]_| in‘-'
_ = mu in Till‘ .11|1u-4.“ in l||I.' u|||i\'el||.'||1 Iiv ir=
Urw l\I.'u- nu. S lam‘-.~'. ‘v1.'i|.il.'il. i_4i\'|.-as nu urvu uf
f-,-- -
.4 = 1.r.ra in’ 2° '4’-*
T
'3
3tl'I.|‘l- Bfifl-‘lifl model
T110 .~atr<:ngti1 iwv. !-}..i.2.l| :-L1"
,. »r§;i '~. -1QL '-
i_
:"“"i“r‘“'1"T7"-i
.'\:i .~;]1c:\I.'n in tin: iiill:-iLI‘4lii(J]1. tlw-:liuu'u:aiu|1:sufflurmmciui mun :m' £lT_- - u|l|i\'ulL'n1 tit width — ch, I Er
=
T
Li-[.62 kips
In.-if
-- - I . . - . {_l'.. m_||f_-1 |||_|
l.3.'r ki]1.~:|>"i112
Fur n |11.'(|ru*.-llilir nmlul natal.-
f.- = :~"1rI.-1:» in I I11: I.-qui1.'ul1.~ul u.u|r.'H.'lI.- r~'t1"ul _ _ If .|,. - 1.35 |ii|x~=_."i|1'*i f,,- — Ei.l'L':i5 in 1111::-qui1.'nl1:ul -§i11].l].\vLII‘|. strut
= | i..+ [2]-11.-3 my
=1.-
= -i in
= 1.35 iii]:-:~'_-"i|1'.5‘
I
0 v|uuu.ppl2p.nnl.|:n
1-22
trnuctunni. ziiuiiiszninu lIEFEREll¢E Illll.IlL
For 1111 11111'0iuh1r1!r\1l. h-utt-1r‘-11'1111p1~1l st-r11t with |10r111ul
Flgum 1.13 1Z'cr0eJUer.s1+s
wt-igiit ::n-11-r.|'m.n. L119 rlmaign cn111]1|'r~_~i:ai'.'¢* 1m'n|1gt.|1 111' 1.1111.
r_-r;ur:rr_1te.- in t.l1c_1 Ht1'11t is givmi 111.-' .-RC1 E1]. .-11-31111 beanng
¢.f_., = 11.H.'1<::'1__;'1 - [1J.E15;|[[1.?5,‘|{1J.ti](1.D]£15
= 1.72 1.1115111.“ I'> f.-
I
Plillfl N“ r_ V“ _i__‘_
H
[-=11tir
Tl11:t1r_-1.11.1411 1.'0u1|11-caaivi: :1t11:1|1.I,1i1u1'z1 [1LK1Hi zuu4:1\111_']10ring 01111 l:1_\_'1rr :11 rc!i11f111'ri11g 1111111 'i1'it]1c1111 |:1uufi11i11g ruin-
"‘
8
A, [primary
reintcmr-eme|1|:] Vu
-4» [closed stirrupsi
di"“" * 1&0 , ll—_1 1“ ‘L1 —1'ra|-ning her 10 anchor
i'01~c=.~1'1|¢.-|1t i.~1 151‘-1:11 l.1_\.' AC1 liq. A-8 :1.-1
:1ir|'up:
1:-1,, = 111.55,.-1_._.1j i
_ [U.75_‘1{1J.=55j|[l1.Ei](1.5
.
r0i11fn1'n~11w11L 1-min it-1 1-apnrifiacl 113: .'\(‘l 51110. l1.H.3.2
= 2.311 kip.-,-'11.": ‘I>_|'i‘-_-
1111111 1.|1‘1l'i\'1?{1 1'l‘I'.>l1l AC1 E11. ll-2-'3 as
1.-111.ti:\'l'1u'l||:|'}']
.»1.-, -— <1-I.11
The zI.||t'l1ur1|g,t' ]I:11g,th El\'i\1]£L|J1L" fur lhl: Lil: rL'i|11'u11‘c111-11111-_ using 2 iu 1:111] II!lI)\'tf'1'. i1-1
11- rt
1.1
.-
Alan. fru-111 .-FLCI Star. l1.H.l5.2.1. tho E1-1.t!1|JI'1I'{i 1-1i!lt'!1-11' Fume 1.111 t.hr.! :-11.‘v{‘.t.i1I111 1:-1
-
E,, = i. Mn” — — 2 +t1 111 — 2 111 _ 25 iu — 26 i11 —
Hm31_H_:_
.
2.48 in 2
.
+13 111
.
2 111
V“ 'f- III.'2c:.1f.1!.I..rI ‘E 1431] + 'l].1]B,f‘:_}|r;11r..-r.!T
= 13.4? in
'I'|1=.* lit-v|::l0|>111|:=11t length 1:11 11 graniliie [ii]. 110.
|>.-11'. with
2.5 iu sith: 1:u1.'I:r zinti 2 in clul I:u\'t'r11111l with 11 st-11111111111 Elli" 11::-nit, is [given 113.‘ _-!1.(IIS-Pr. 12.5.2 11:1
- ._-
<_11.._1(|21_1-1,1
i“” =
ll 1' g) .1. in-
5 1G[iD-£111.-rt 11- t'L1c[fit'iL'i|1 111' Friciiuii zit fziu: 01:11:11)]:-1Jr1-.
:01 pgivi-11 h_1,' AC1 Sim. 11.6.1.3 = 1.4.1
|Fc11' runr:r1-t|~ piFltZ|'i1 111nr|0|il1|i:r11.|i§.']
The L~u1'rL'L'tiui| Eu1:tu1" 1'1:1111.t"1l Lu 1111' uuit wL'i1;11L uf cun-
{11.7}{|21u1 %){1 111} :
ll
' _
Mg’ 1.11111
-
111
c:rc!11~ in l'1[!fil‘ll’\{1 h_1,' AC1 Sac. 11.11.-1.11 11:1 .3. — 1.1]
I101 1101'111nl wt-i.g._:l|t cu11c1'~:-tr]
I I3 —-1l:;I
Ifur all li|.1l1t1\1*i|z,]1t t~m|::1'c-t-:-]
= 12.5 in
'l']10 tc111.~1il-r- 1'01‘-11* ."|',,_. 111:-1_1,' mat. hr! |n=L~1 th.'u1 11.21"". 111111 Tim
I-* 1"
C'Ul'l’L'>.~jJ'U1l(i1llg alrvzl 01' rL'i111u1't1*1111:11l- K111111111 is given 11}:
|:\|i1'1|.ur:i|.',_|'11':11.p_ti:| i.~1i|1.'i-:1uq|.|;|.l<:.|
UNI: 1111 £11111 [llul-(1 11.1 11|'11;'-i11;|1' 11111 1:111:11.
AC1 51:11:. 11.8.3.-"J us I’
\ .. ,1" = ii
-cu’,
Oorbols ."'1:1-s]11.111'|1 i11 Fig. 1.13 111111 a'|JL'L'ifit.‘ti in AC-I 501:. 11.3-. L111:
T111: 11-1111111-<1 1111.-:1 01' pri111ar_-.- Ir.-11:siu11 rui11l'urI:t'|11t'|11 is
H1lt"'.H1' !i]]fl.|!l-LC}-t1E!])11l. ratio. r.1_."d. 1-111:1 the 1'1i1i-:1 111' 1u1ri2.:m-
given hf.‘ AC1 511'. 11.5.3.5 uutl 501:. 11.5.5111;
1111 1|:-11:»-ilc t'o1'00 11:1 v0r1i-ral fume. 1'v'....,-'1-"... am‘ 1111111011 to a 1'1'mxi||1111'1'| ‘M11111-<_I1l.lt|il_'1‘. T111.‘ I.11I1['1l]'1 1111' thr r;'I.1t'i.It-1 all Lilli-
.-1,. = .1, + .1.
uutsitiis ccigu u1' h<:z1ri11g 1m:11 11111111 not ht: 101111 than d,-‘L1. .\\t tht: their uf 1111:: :i\lp]‘.lIIJI'1-. 1-hr fDI‘L'l.‘fi uvting 011 t]1ct'ur1:r'1
arr! .1 1-111-1'11!‘l‘ furrrn. 1"". .-1 111411110111. I.-’,,r.1 + .'\',,,t:1'.I — r1'_]|]. 111111 :1 1|.-11>.-iir 1'u1v:r:. 1\',,,.. T1u_'-:11: ruqiiiw 1v:i1|1'|.r1'|_'1.-1111.-nl art-115 of .11.“-. .=1_.-. 111111 A... rmi|1c1c:ti\'0|}'. Thu 51111111‘ f1'it'tic1u III
0
nun-w.ppilpar|.:n|'n
T» 1%"! + .4. }11.1ujj {111 —
fu
IIEIIIFGIIGEII cflllcurri nilln-111
T111.‘ 1ui:|i11111111 rc!c|1|irc!d 1111111 of crlcxqtrrl tics rli1»‘trii111tt~tl
T111! t1:11:iir.1u rc!i11i':11'c1::111<.-11t
1'11.'r~|' .-1 clrepth |':i".!r.I'_."3 is-1 gi1.'1'e|1 hj.-' AC] SH‘. 11.3.-1 11.4
Elva. 115.15.-.l :15
1 :
.1. = +4“ A'-
H
1111111 is 1.';i\':r11 by AC1
:
""5
-LlIki]1:~1
[ma] (£111
.“|.C| Sm‘. 11.5.3.1 15i1'I.'::- H11: v1lll.lI.! uf I111‘ :.lr1.-1|gl.l1 rw.l||c-
tiun I'111'I:c1r 111-1 0 _ ILT5.
1-23
111'
= [L359 in?
Example 1 .12
T111: l'zu."Lu1'4.-11 111uu1c11L 1\cti1|1.', 4.111 the 1.'ur|1L'] i.-1'
T111: l"l.‘ill[L;Il'I.TL‘l.i. I.'|.|-|11;"1'4.-[1.- |.'4.»1'|1I.-l :<]1uw|1 in H11: l'u-lim-'i11g i]]1|1
111,, = \-"Ha + .'\',,, [J1 - rl}
= 111111 kipfijalid. i11]+{=Hl 1=11»=<](2 111) = lfifi i11-kips T111: 1111.21 1.1-F nl.‘X|.|.Iili. L'I;1ll1fi_|11r;‘1.'111r11l- 1'u[lLlrI.'1l [ur c.‘1=[l'.T5
I
as _<_',1vt'11 by .I"1C'I Sec. H 1] 15.11.] is
4 in
ii
V“ — IDIJ klps
jg, 2|n
1
40kip~s
-i—
11.aL5mr;'f_ 1 - |1'1 -
/_-—'3—Nu-?
i
_
_
—-I
M 111 ii“:
'1'.
.-1 I =
11.31211-,..1-;_.
ff‘
= 11.11.-'. 1111
""1
T111: [1ri|1u11'_'.' 11ci1|l'u1'I.'1.'1111-11! 1111-11 rcq11i11:1.l is givun |1_v
_
'1'!
3—No.3 {closed
I
slirrupsi
J"1C| Sun‘. l1.B.3.5e1.es
A, = .1; + Ah = 11.5-1r. an" + 11.11!-1111 iii = 1.-1:1-1 in’ T111111 nu. T |>11|H 1111- |m.wi|.IL'1|. 1-.f,i\']1'1g an Ul'l.'i\ uf
Suire-fixm
.=l"_ — 1.3-CI in:
1"1.~z...;1_1>._.1 — {u.2]1o.1's1
[ 15 1.1111720 my
'.'> 1--134 ill?
|:=n1i\=l'|1rtr11'_1"|
Alrin, Fr:11:11 AF] Sm". l1_H.li.."1-_ the 111-era of |1ri1111-1r_'.' rr!in-
— 123-5 kipu
I'u1r.‘r.-111¢.-11t- 111I.|HI nut he law-1 t-i111||
L“.-I 1--',,. H81] + [l.IZJSf’| _}|.-;'1i1,.r.i = {[I.T2]|ID.'F-5_H_l5 i11]lI_2[li11I|
+ .4" =
= 1|}? lI:i|r.~a
+ 11.:-ms: 111*
= 1.515 in‘-'
:> 1--',_.
'.'-‘H:
[l|1|:i:\I.i;-1|‘11.|'1|.1-.1}'|
1.13-:1b,.rI — {1.fi]il].T5§|[ 1:3 i11_II[‘2[J in] T111: 1111111 uf|.'lu1+ul.l 5lir1'up:s rL'q||imci i>.- 15i\'L'11 hf.’ ."|.(_'-I
_ I]-[ii] kip:-1
Sac. 11.5.-1 .115
3: 1--',_.
.-1
T1111 e=.I111.111' f1'icLir111 1'ni11l'c1rr!r!111u11T 1111111 is gi1'n|1 by .-91.(II 5:ir:c‘- 11-5.4 1'15 qf_
1'“ _
“’*'P" = 1.-59 in?
- [L53 in! 'l'i1|'r!n 11c1_ 2.1- -nlnunci 1-:Li1'r11|1s 1111* |1-1'c1\=iri1'»:l. |.{i'.'ing an
IUU k1]1:-1
¢11.?5'1(en
.\..;1
4 11,... — .-L, 1.1]-'1 111' — IL.-mi] 111 ' "" = 1 : 1
Hc111:1:. H11: 1.'u1'l1u] 1.1u11l'urm.~4 to AC-I Sec. 11.3.3.2.
=_1rc_e.1 r_|-I'
(1 .11
.1. = 1.1.611 1.1"-' .':- Cl.-53 1113
PPI
}=11ti.\>l'111'1|ur_1']
l v|u|uv.ppl2|:|nnl.:n1n
Cunc12r -1
1-24
$1'Ru1.‘:1l.II1n|. Euulusznlnu IE
FEREI¢E
Torfiuu
Illllll.
Ffgum 1.1.5 I11rs1-011 1-1 F.Is-.'1-gen‘ S-e~:*1|1J11
'I'111.*11*1'|111111:11L1-'_.5].' 1151311 in 11111111111 1111:-.=ig11 1:-1 i1111:1t1'11t111 in
'
Fig. 1.1-1 111111 Fig. 1.151. I11 :11:1:11r1111111:11 1.11111 AC1 51111:. 11.5.1. F111‘ :1 1-1111111-1-1113.‘ 11111111‘111i||1111* r11m11111-1 r_l1r; 1,-1]11i|1111'i1|111 1111*.-1i1'_>1|:1l 1,1-1‘f1_-1,-T:-1 111111’ 1111 11cg11-111-11. 111111 c111111.'11 :~=I!i1'1'1|]1s1\1111 1|.r1|11,i1I.11li11111 11.\r>i1111z11 1'1~i111'111'1rn111r!11t 111-1! 1111t r111|11i1'1'-11 '11'l11!11 11111 1'111'1111'1\r1 L111'1|un
""1""
....--
, '- -''
1.
area AM _
‘ ‘ "'1''' '3
_-—'closed stlrrups
111_1r!ri ]'|1_'11 1,‘-:~;1_‘1.'1'_'|1
H11“
.
:7 AL i
= 13.11.-.'|||'_|r'_
1'-1.-[1
parlm ate-1 1:1,, __
\1.'111-11 1111:-1 1'1-11111? i1-1 111-:1'1r1:111r11. 1'vin111r1:111111111l 111111-=1 1111 ]11'm.-1111_-11 111 11191-11.11 1111': E1111 H11:-1111-11. W111,-11 11-11111 1-1|I|'!1‘11‘ 111111 l1.1rsi1111 1'r:111[|.|-1'1.11:1111-1115 1111- r1'1|11ir1‘11. 1111‘ $11111 1.11 1111i1111i'.'i11u111 111111111 11111.-11 111! 11111111111-11. AC1 S11-1". 11.5'1.3.[i1-i|1111:ifi1!:-1 11111 1111111511111 11r1*11 1|-P111111 111.1 111' :_1_ 1:f'|1_|:-1'11 ri111'1'11]'| 5'1.-1
T111! 111i11i11111111 1'1i1~111111T111'. spr~r*i1'|1*11 iu A1171 511-11. 1151.11.11. is _ Tr 5 _ ‘I_J¢_;1___J"j_
—
T
1111 1'lllll|lJl':Q'i1l.H1 11111111111111» |1t_ -lE1"_
111. = 11.11-1‘1-'1 -Z nu. 3 11111"
"
1 .11».-1...;_.,.
1
Afifféf
-
T111! t111l11]11l1||1 r.'l.1t11|.I11'11'r1 1'1l'1.111 111' :
1e.1|1:11r 111111 t1.11'e111111 in g'11=1'11 11_1' AC1 S1:1:. 11.5.5.2 1111 T111.‘ 1rm'r1:1-1.]:-1111111111.; &1r1'1-1 111 111111;i1111111111] 1'1-i|11'u1'c1r11|1r11t
r11<|11i1'r~11 i:-1 1-aprvrrifinri in AC1
.-1. — T111‘ 1|1iui11111111
.
1].-5.71.? mi
.-'1 1, ,
“riiii”
11rc11 111' 11.1-1|11,i1u11i11a11
_ I.
rL'1111'111'cc11|1"|1l
1'cq11i1'1*11 1:1 >;p1"|:‘ifi1'11 in .-1C1 Sm‘. 11.5.5.3 11:1
J.
W, M5,,
Iv|
[A131 11-22]
I;
_.1|‘,:
-Q r'
F
_
'I'111_- 1111,11-;i111|111'| sp.-11_-i1"|g1_11'1;-l1|s1_-11 >1-l_ir1-1111.1 is gi\'1_1|| I:-_1' AC] 5:111". 11.5.6.1 11.-1
IACJ ;7.24|
Jw
.1 = E
i 2: lib,
S
.1 _ _|'_,|.
if. 12111
Figura 1.14 T1:r1=.1:-1'.‘ in F1a1:rar|g1.'.'ar .5‘-a:11'|:fl
closed stirrup: _
______._,.....__...,. /_:I-" ._:--:1" _
stirrup center lme area AU — D.BE1Au,,_
area Aw, ____
perlm later 1.1-_., ..__
____-{______.1___.!17'_
_ _ _ -1. u
q_____________;
____-____7_____4r|,
________ __
IIIFGIIGEII cflllcnrri niilnu
In Jl|lI![‘U1'{i.Flllfl.“ with .\'|.C‘I Scr. 11.5.2.2. wiicrii rc'clist1'ii>1:|tinn of i.l\H'T‘l1:ii fiurrma |II|l':1".lll‘5. in an imlr:r.r!r1ni1mTr- .~it.r11r-
1.5 in truvttr, tin: urea trlicririsrrl I1-_\' t-ht! |:!t!|1ti:'rlinr of t-hr fi.Ti|'l‘1l]1c'-I is E
turn \|]1r.m r_:r:|cking, a rnlfvmhc-r um}; he 1'1:-aaigaic-:1 fi:n' t.l|r_e l'm'1urc<] lursiun vnusing c1'm']-ci|:g. wl1i1:h is given by .—
T.. = 4.»...-’,1'j
1-25
.-'l,.1,: {ID in
3 in
(1.3?-5 in]
=-< [12 in — 1] in — |.I.3T5 in]
HE
= 115-‘LT? in"'
.1.
I-"mm ACI Hr|. ll-21. tlm |'r:q|_lir£:ri =-1|'na Hf |'_:-|1n arm of :1 l.'|IJb'l.‘l.i. sli1"ru|1 is j_£__i\-'L‘I|1 hf:
E|‘.\H=l.l'1‘l]I1i£! 1.13 .'\ siinply suppurtzrd rL-i|:i'urcr_*ci ouiicrctv i.H.‘£ll]] uf IlUl‘1Il]£li. weight fl'|1‘II!‘Tf*H‘! with nu raw-|'+1|l rlnptli nf IF! in, an r!ffi~:'tin‘ |.l|.'|i1Il uf IG ill. am! i1 wiilih ui l‘2 in is 1\¢:i|'L[|.>l'~.r|.ul with graulv lili liars mul has H lI'U-11Cl'L‘LE‘ cc1||1]1rcssii1.'t' strcengtli nf £5[1||(] lhf‘,-"in"'. D(!‘il?1.'lllilI|E! the nun1i>inc~(l slmar anri rr.'=|-aim: rr:i::f<:|I<'i_=1ii(*1it. 1'0q|_|i|'|t:r| \1.=h.m|
[ii] H111 f.1r.:lurr.n'i .-111:.-zlr fr>l'crc! is 5 I-zips zmrl I-he fact-|)|'cs.l
Q= .-1
'T.. l.Tefi.-1 ,,|,_f!_,r
[4 I't-kip:-.] (12 [1 .T] [1115]
[l>} tlic [awturvcl shear furcr: is 15 kips aml t-hi: Ek1L‘iIUl.'l.‘{i. Lursiun is -1 Ft-l-zips
(nu
I2 _ ft
tursiun is I.’ fl-liips = [].|i5(i- ill'3|,"'fT
m
||1|'|' arm]
Fruill AC1 E-{|. ll-‘Z3. l.h|j' i-;'1'_II.'Ij'l‘1'1il'|1;,Jilillitnlilu 1;'uI11|J-illul
Suirifime.
s]1i:n.r Fl[|.(i. tursiun ri:infcm:::1m:11t area is givim by
[ii] '['h1_' :1|'rv-a D!1‘|f.‘i1'JrHre|'| Ii}; tlm -m1t_\iir1t_' |'|f!I‘i1i1~l?'[.|':|' 1'»? the iiczun is .4,-J.={1!-)i11:|[1Qi11] = 228 in:
.- - E ."i.,-+ 211. = :.n1»_..: i-"M12 ‘mils E.) ="
1"gr
riu.u-110 Hi“
= 11.12 i11'*i_."[t
The l|."||gl|| u-l' llu: unlsi4.lI.- p-I:l'i||||.'lc1' uf Lhu huiuil is 1|," = [2][|9 in-+-1? ill] = G2 in
l|!',U-‘F1'fIlH]
Thu [II[!Ii]]1€!ilI'1' ni tin.‘ (!mm!rii1u'- nf tin! rlusnl stirrups is ,1.“ — I:2]'[_l[l i11+ 12 in — [2-:|(3.3'r'5 i|1]] - -1B.5D in
'I'r_ursi-mm! H.-i1ii'r_ri-nnninint is nu: 1-re¢_|1|i|'r:rl in ==n:'cr_:r:i=1||c:|': 1.\'iLh ."'|.(_'-I Sr.-1'. l1.5.l wh1:n Llu: i'm'lurn-cl Lurquu duos nulr.'xc'I.'ul
Tlir: g_uv|_-rniug llJiL\il[ll.lIIII| |JL'Hlli5a'iiJ]L‘ spacing ui Llu: ctlnsml sl:irrI.||Js is 511-mrifiwl in .-\f.'I Sec. 11.-"1-.fi.1 as _
.- .~\'.-T.
11,-.
-15-.5[J in
. _
5,“... _F_T_{J111
Ts = I1“1'A 1,‘,-"_||T
i"¢,i.-
C‘-lrx=nivrl HI.il‘1'll[‘.|5 mnsi:-iriiig uf H1.-'0 i\I‘li1H uf 110. 3 |'|»<"|.I:< at. G in spacing; |:ru\'i-cits am arr.-u of
: iU.?5ilIl.t]_ivI"3UU[J |ll'
i = £1.44 E
(225 in"? is-2 i1.](12 (1000
>~:
= 2.5? [I-Rips
."-1 2.1]
|Clusc~d stimips an: not l'L‘lI|_llil'l.‘ti..|
Thar 511:-ar .m~ce||g'lh |:n'0\'i 2 |r'.,
:Sh='u.r -“1il'l'I.l]15i <'mr' nut rwiuirr-1|-]
[|a} H1'!4"':I11:-H" g-"1'|.-",._,>'2 < |.",_ <2 rt: \-"_._ mi||im1m| 2'-iii]l.'!?‘ll‘ minI'u1u~1||o||L is l‘I;'I;]‘l1il‘L1i. ilillii i.!'L‘€'il.ll>.-It T“ 3:» 2.5? fl.-kips. tricrmcl stirrup:-1 urn 11|:
s
ft
'.‘-=- U. 1'2
|>=|u:i.~=fiu'1m-_~.-]
The rr::quiru] J\1'(_‘Jl uf tilt‘ luligitiulilml ri:infc>rc:t'|nt!|:t is
give-11 by ACI Fq. 11-22 mi
<%>~(%)
_
. -
l|:i|i:=i
[I] i.
005:: ii <45 -50 in} ii ‘"2 ' ft ' ' _ lcipa
fill i . ,.2 ill
-E
UH
_ 11.21! in" PPI
l vru|ur.||pl2panl.:nn
Cuncr:-r
1-26
trnucrunnl. zlluuusinunu nersnsuce |1|l.11u.l.|.
BL'L'1111s1: U11: ru1[11irL'1l 1-'11l111.' uf .-1.,-'-'1 - 0.004513 i112,-'i|1 [:-1:1‘
,'|.-I|_,_
i111't011'r.l1:111| 111101110111 1111 11 c~11111pr1--'1~1ir.11|
arm is loss tlmn 25!; »1u| .|."f = iI.[]|L'1l1 i11"'|."i11. H10 minimum
['1-l1i|1s
11111111111:-1 1'11 tl11:-12111] 1'11 I.1'l'1i1-11 M. 111-11-.
].1<-1-|"11i.~11.1i1:11r.- 111':-1111-t'|o11giu11i111al 1'ci11i1:rcc11111;1111 in gi'-'01: I13.‘
-:|1|1- 111 i|11'1ri;-1 l|1111 c:111|:\u :11:111.pj|:1|'-1'|:i11'|1|11
."1.C'l E1]. 11-24 11s
1-:1ir.l1':1-.1.'11].'. 1:'11|1'I.1l1=11|:1l 11.-1i1u._: 11 f11st-<>1'dc~1'
11111.-1ir f1'111111"- 111111]_\'11':.1
...
IG
11‘|_1-11|||l
Jr’.
-._ 11 ,_,-1U‘ E
Jr":
I-'11
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111'
111111 111 11:11-11111 that 1'1111s-1'1 11pprc1:'i1'1|1l1‘
.1-1
='l1L~11iI.' Fr11r|1|.*11r|11]y1=i.-1
larger |'11.1:t1.11'1'1l cncl 11101110111 1111
ll-kl|11e
c:11t|1;|1|-11:1.-1|c1-11 11111111111-1'. 11|'11.'11}':-p1|:1i|i1.'e1 i=1c:l111‘<11| 0:111] 1111111111-111. 11:11 111-|:11|1:|'|e-z-i11|1
1"’
_ ([].iK]._1-H
fl-ki|1:¢
1111~1r|i1|.~r# 111 1111* #1111 111 v-'l1i1-11 .\-I. 11111-s. 11.i1l¢m1I.'113.'. 1:11|1::l|]1al1-1| IL‘-1i1|.g_ 11 fit:-cl-»::|1111.'1'
ri 1511:2211 111"} ,1':'1|11111 lb
i.=11:111|11-1| 1-111] |1|.1|1r|11'111 1111 1-11-|11|11'|w\i|1|1
Tl -ki.| 1:1
1I|l1"lll|JL"]' 111 the 1.1111 <11 v~'|1irl1 M1 art:-1.
1111.11 11.1 ]u1~11;L-1 that 1:111111x- 1111 11111111111-iz1h|.11
110
'1;
:\i1|¢'s\1.'11}', 1u1|c:|1i11l|\1| ||:
l:_~'13..'.1H 111] fin kip“
.1-1.,
1. .|.
11]‘
1'l11e-‘tic t'1'11111I:~111111i}'si1= i1'11't1:11'1'1l1_'11
11-111.11.
1111111111111" 11.1 l|'11' 1:111] 11.1 I.\'l1i1']: F112 111:1:-1.
— 1.0-'-il in!
H.242 i113
= D-T519 ill:
[;,11_1\'r11'11:=|
rim: 111 iunrl.-1 t|1:11 1u11|:
U.*1i11g1-iglit 11r1. 3'l1:1r1-1 111111111111 1l11=]111\1'i111r1r.nr 11f 1:110 r:lr11+r.~rl sl.ir1'11ps givvs 11 ]1'.1||g,il.\11]i111\] 111111] 1111-11 u-l'
P, 1",,
rrrifirzli iuml. rI:"'E[,-"[U..:|: 11|.1|:11i1|11| 11xi11| |c|1.11l st1'1.'|11;t|1 111 giv1'n n1:1;\11|1t1ic-i1}.'
kip: kips
P, .
|11|||:1|11|11| 111ci11| i1|111|. 5111-1111111 :11 v'.1"r11
ki||s
1'I."1:~1.'|1t1'ic‘i1}.'
.4. = 11.111-'1 111? 21- [Il.T"QD in!
:1111I:isl'11c11'.rI).']
F-.
f1'1trl1J111!1'l 11.321111 [11111] 1'11 {_j_'i\'l!l| 1!L“1:1!I|1ll'iII'iT}' E r,1F',,
Q
1-r~11>1|1i|it_'.' i1|dc~:<1 fur 11 1-r»10r_\'.
1'
111|.|.il111 11i'g_'.'l'11.li|.m 111' I::1‘
l-111111
ZR, .'J1,,_.-' 1-",,I,
G. CIDIIGIIETE G‘-DLUIIIIE V...
Nomenclat-um 11r\r'|1 I.Ii1~h1'1.' r1-i --1|.1ir1l||j.' rr'i|1ir.1IrI.'||
-'1 1 .1
1
.-1 _,
gr1.>1=s4111r'1\ ul'1'm|1'1'1'I1' -m'1i-I111 1111111] 1'11'1t~111.1t'l|:111;gi1111li1111| 1'|:'i11l'urc1:'1|11:~|11 1| P1111111 1'1'|-a1i1|g1w11111| 111111110111 1li1I1.1r11111
1-1 ..-
C...
Sy|nl14:1]s1
.lI‘l'-. -111 2
5-1.1...
|.n1|.111I Ll]
11-111111 ll 1lia1111!11:~r 1:l'tI11:~ 121111111111 5...
|11.u1|11l11s of 1-I111-1ti1'i1].' 1.11‘ 1'u11c1-1:-t1.'
ll1l',."i11:
1'1'11111|:-s |.1n\1:1:-r.l 111511111111 111111-1.-11'11_'.' 1:1
in
mfluc-t 11H1:11:111 11f11|.11|111'11:1 1:111\.'1'111|r11
‘.-
1't'f1"c“ti1'c 101111111 t'111:1or fur 1~1J111|1|‘1'se1i1111
L.
|r!|1g1i1 1_1F11 1-1_11||11r1-s11i1>|1 1||<'1|1h1"r in 11 l'1*:1111u. 1111:~11s1.1rc11i fIu111
i11:1|1\'1*111|1 urids 111' 111|r|||:1114!:1
r|1I'111|1r=r='
1“.
|1'11.-1:|1|11.'1|1-1
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.-1'1...
it ur i1|
.11,
.-l1|.11liI."|' f11c11.1rr-1| r-ml 1111111111111 1:111 :1 1:1|l11|'11.‘1.'5e1i.1ul| l]r1r1|:1i11'|'. ]Ju:1iii'1.'1'1 if
n11~111l1nr is I11~|1t in .~1i1||;|¢- rr|1r\'=1111|1.'. 11-:~g11.ti1.r1' iE'|111'11t i11 1[1.111h[1: 1:'1|I1.'11t1|1'1:
0
urn-w.ppilplsl.:nm
|!1|.11| ilm 11111-111] 1|1!|'|-111.:li1u|1 in-111.\I.'1~1!l1 l|11' l1:||11 11.|||i in:-l|1|:|1| u[1: 1-l.1|r].' clue! 111
I-".... 1'4.1|11pI11I:d 11e=i11|.1 11 first-urrlvr 12111-1ti1: I'n1111-:- a11.11l1.'1-i11
l'| -itllph
111' 1:11111|111'|:ssi|:1|1 1|1c~111h1:'1'
III
1.11 r1r1'|11vt l1111.'r11| 1i1'ii't r1-s1I.l1i111; Fr1_11|1 l11t1'1'11l 111111 |:_Iavi1_\.' 1:11-111s
1111:-111l1»:-1' i1u't||rwl 1111111111111 In in: 11111111 I-111" 111'.-
11101110111 11111g11ifi1:a1i1.111 li1c11:1r i-:11 f|::|.11'11:- 111.11 'i.11.'11.1:1.-11] :1;-_-,:1.i1|;-1| 1-1i1i.1r:1'11.':1_1.'
H 11r in
1:1'|1l|~1'-I11-1:1'11IL1'-1' u1il|11- }ul|1l:-1 in H111 I:r11:|m:
.11.
1111111111111 1||1|.g\||:i'11'1-1l'|-1111 f1u'l|1r |'|1:r
111.1111-11l l|1i1-11111":-11 uf1111'-111I1-:-1' 1111111111111! Iii i1|11'rli11. 11f H11‘ 1231111.-1 r1<:1|11rr
1..
1'111i1111|'s111111\i|1t\1i 1111111 11.1 111:1:1i11111111 t|1r- rntin uf r.l11~ rli1=1|\1|r.'1~ h1'r.w1_-r-11 1'r~1111'1.1i1i1= 1J['t|11' ]u|1_1:i11|1|i1u1| II:'i11fi.1r1'c'|111:11t 111-1i11'
to 1111 1!q11i1'11l1:11t 1111il'111'111 1111111111111
I0
l-111111
ll'l'
1ii1:|1r1|1||
11,. 1.
I111-11111011 l111ri;<1::11t11l =11|1c'111' i11 11 1-111111.’
-2
1:r1|11111'1‘111-111.111 1111:n1|Jc~r 111011111111.-cl to u||1:1i1i1.! ||i1u|1e!l1~:r 1.1-i.~1|1i1'11.i
in
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1'-*1
1'11tir1 111' \'I_1l111111' 11fs]:1i1'11l 1'<'i11f1|r1:1'1|1I:~|11
‘F
11t'11pi:11-1].~1:| 11f 1-1 spil-11l]j1' 1ui11iur1-mi 1_'r11|||1r1~e1_~=511r| r|11~111|1nr 1-11if1'111_'1111 I1-11i1:1 at H111 lI"lI|(i1Jf1‘1 1'ol|111111
£11 II1JlI:|.l '.'1;||.11]!1.u £1i1r1:1'1! [u-1llI-I131-1.1111
ill
IIIFIZIIIGEII <:n|H:n:'rE IJEBIIZIII
1-2'?
Reinforcement llequiremlemts
.5'rJI|.e!:0n
ACI Hr.-r1. ILHI limits the arr.-=1 uf I<.'|1'|;_\_:it11<|i||=\| r|':i:1i'<.m:1.-
I-'1'mn AC] S-rec. ?'.H].-L2. [.h|'ellli!fi1111|lll [2||'et'1'|1i.~t-li|'||t_'|'ii:1|||I.-la-1' uf n'|1i1'e\l rL'i|1furcL'11m1l is
]l|t‘||l- lu nu! 111! -rv than STE and 11: It |l'.-1:\'1|li'\l| 1'}? 1.r|' Llu: gruem Ell.'[‘l-‘l ui tlu: >.=ucllu1|. Fur r_'ulu1nn>i witla rtrcrtulzgull-11'
nr rrircrulnr tic‘:-s. :|. mini1n||1u of l'r:||r h:-11's is rw|11i1'r~cl. Fur n'|.=lLl||111:>' will: :>|.|-inn]:-'. a1 ulillimllm uf nix ]|_1t|.[=j_il..|Ir.iinn] In-mi is nrqllirul. Thu milnimnlu mtin of 1.'u]m1w uf r'.|&lm| rc!i11fi'|rfi\11w|1L Tn 1.'|':|l|Lmre nf I:-urn in pjwelx by .-!|.[II S!_'('. |U.§P.3 1!:-s
rh, = ILHTFJ in
Concr2:-r
.-lg, = nma of .~:piml lum= LLI1 in? .-'l_._. = |;l'Uh?i aura uf »:uln|111u
i_ 1 .-i -.
p, = l_1.41j,r'f_
|nc: 10-5_ .\'I
M24 in]! =.4. = -I52 in: .-l,,|_ = F|l'f!:-I r>F rum
In £l.[E[M]-I‘{|.i-lllfl.‘ with AC1 Herc. T.1l]. flu‘ =::]
I-|<_-1-.x-1_'ee|| .~:|1im1:< c=.1r\nnr. re.~=11ml]1*rel11<1 nu. ~l fur luugilucliluml 1.1411}: larger than uu. ll]. T110 11uuci1||ul|1 \'1:r1iu\| b[IIl-1Cil|.|£'_, of lime in-i
gix-‘mm hf."
_ n|_‘2] in)“ ' 4 — 3-lfi in? d, - lntrnu ~rli|-u1u*t1~r uf spiral
= 2l in — 11.37-5 in = 211.625 in
.q,,,_,x - llli :-c ln11git1|¢ll|ml hm‘ :1in111:m~1's I-'rmn AC1 Hr]. Hi-._|-_ Tlm :mini1n||m .-1]l|':|\1.':ah|0 5]1i1‘:i| minE -IS 1-C tiv hm‘ ill!-111|L*t0L':a
fUI'ClL'1llt‘Jll- ruliu is
E lrnst tlilncrnfiiull of Hit! m]111url
i_ 1 'I'in-:<.~4]1allIn.-]:r|'u\'irl:.-:|. i’|:\' .+lu_m'|: in Fipz. l.|[i. r.|.>.-m]'r|'|-m-t
p_ = ['|.-15].:
J’...-
L".-'l.'l‘].-' L'u-rm-r and kll|.l.‘|.']]élU.' bur. and nu hm shall hv ||:urI_ill:-111 Ii in rrlrmr Frmn n s11]1p-nrrwl In-xr.
452 in"
= [I].-l5](4.5
Figure 1.18 C."<:2\\\'.--r1n Ives
|"
==.Bin
"|
lcipu
|||*
_ I
[H] l-up.-i |n
— IJ.[J1l]3 1.'ululm' ul' lsjlifill bar 111-1" 111111 \'Ul\]1]]l:! (IF 1'U|l[§|'l:!1'l"' l:§Ul'l".' pplf |:111'll
.~h,]'lI|'I, .4. , _|_ H
}
i 6 In
[rm i113]||1:[2[].f_i2.T> in} (gm am].-, H _ 2 in
::i;\:i:.l'=u'-1u1).'|
Thv l'i|l~:‘1l|a1<'r1 piluh liL'-< bl'lwL'I.'11 1111' 1mI.xiI|11|1|| M3 ill and thv luini11111||1<:f 1 '111:i]1»:!c!Hiu] in ACI Sm‘. 'F.1lJ.-1.3.
Example 1.14 ."‘|. ‘Z4 ill1.lli\|||1.'|.1.'r fi].l'il'i'l||_'|' 1*.~i||[|.>L'u.-cl u.|]||lun with 2| I.-5 in 1201121" tn thv :;|1irn] is-:~ r1ri11ft>rt'wl witll grsulv till hnrei and ha.-a ;\ -:'cmc:rm:' rn111]n'r-.~i5i1.'n .~'.t.r::1:5!_L]1 <11” :|.-1:-[H] |hf_."i||"". Dt'lL'l'1Jlill1_‘ ll|I.' rL':]11i1'1.‘
Efllcflvl Lnnglh and Bl-nnllnrnlss Ratio 'l']w c'fl'r»r:ti1.-"n rrralllmn I1-ngtll nmy Ian rlnrc!rn|i|mrl fi'rm| flu: n]i1.§|nur.-ul. |_'ha|rt:s givn-11 in ACI SI.-r. R1[l.lD a1||1l slmwll in Fig. 1.1'F_ PPI
1 IIlI!.|I|I|I|I8I-l.GI|II
1-28
$1'RuI.‘:1un:|. Ellullueznlllu nsrsnsuci Illlllll.
Fiyurl 1.1? -'11-'fgvwr|cv1rIf-‘-‘ra-rls-'-::\' k‘ “A
*'
4'5
4-\
‘Pa
*
fl
501]
i1.|1
10.0 H
_
3-“
1un 5.0 O5
ZJD
MID
-—
2.0
“B r
‘I
' 1D|1.U “-0
mg
mu
151° Hm
-
3‘lII.€I
5“
Jun
10.0
In
FLU
ZG 'l|Il.D 5.l] 8.5 1|] fill '5.El
3|}
ill U H1 IIJB Il.I
ansUHE=.-J.~r=.5 QQU
OJ 11.6
\l.D
#0.?
0.5
in
-U]
F‘‘Q =I.I'\-I'FID"=O'F'."‘
0.4
|;|_l
"-3
:|.:
11-?
M
3.“
3|]
I‘.|J
In
'1
n.1'-“
O.1
*
1:
—o u
u
1.u
I
[|_1
D
L19
nonswav frame
0
swear frame
Min]:-14~
To 11:11‘! T|u'- :1lig'|1uu"-ut rlu-111.5. thr! :-itifi'm!:-'e-c ratio:-'. at »:!:1rrh
L-11:1 |.1fl;]II.' (:ul||||m |uu==1 he L:n|<:|.||u1e.-<|. am! this is gi1-"(fill
1-"U, is llu: story s-1|1:z1r. and Z Pu is the l-utnl \'r_-rliun] luml nu :1 star].-'_
11-_'|' {HUI Fig. |"UU.l(].1.] am
Exarnple 1 .115
EFL.
3., ET =W
Dr-tm'|ni11sr Llm ea-kr11|rlr\l'||ce!a.-2 rntiu crFc:c:lL1|||!1s I2 and 3-I nf
ET‘
T110 suhsrtripl: r' rr~Fr!r.~: tn Llm c:nlu|:nn!=. nu‘-|~ti|l|'.1 :-11 F1 jni11t_
the s\\'a1_\-' |'r:_1|n0 :
znui the .-mlx-x:L'i|11 J1 rr.-fv.~1>= to 1|u.'@ l:|:==\|'||.~i |:1r.-r.@linp; at a
_ I" 1
jui11L. For :1 11uns1.\':1_v Erzmw. the c!iT1*ct-ivc! lungtla fncrtcar I." nun}.-'
1511
_ '|" :3
151: "1 5
Iw -m|nu:!r\.':1t.iw-13' taknrn ma ||ulr._1.'. :-15 i11dicnt.nrl in .-5.(.5l
Set‘. lU.1(]. 1. Thus]I;'lu|L'r11I.‘:s.~s1'aliu is 1l1:l'Ln|:1l as kl.-_,-"r". ulul
'lDl"|£
flu: r1|.{liu:e- uf gg.'1'|-zficm in giv1:|1 I1)" _-'L(.'I Sui. l[].l(].l.2 mi 2
2' = [L25 >1: (|i:|1nc*101' nf r:irc:11]:1r rrn-l|||1m
— [I'.3[I H (HlI.l1.‘ll.a‘iLJ|II U1-kl. 1'u:ln1|1.g||lnr L'l.JlI.lIIllZ| in T|u'- I!|il'l"!l'!l'.i[3ll ritnhility is being fllllfilflflfflti ."'|. ||ul1:s\\'z'L3' L‘L|-lllluu is :|13r|lu.'~c] in ACI 5|.-L1. ll).l|].-;'r.l us um.-
in wlaiuh Lhr >ac~::u:ulnr_'.' ]Il]0[ll.{‘[llH (luv Lu P-dultn c:ifc»c:t>a dc: nut nxfilvri -7|-‘H. n-F Lhn |1rim=11'}-' n|r:mu>11T.~< rlun tn li-1T!'T:|.l lumhs. AC] SL1: 1lJ.l|].-5.2 apwifil.-:4 i1 nlury within an -:¢.1ru¢:iu1'L'u>.< llUllP.~'|.\'El}'. |.\ruvi1lL'1l llml l]1L' sluhililg.-' inLlL'x. Q. dII)Dti nut oxcrnwl H.[II.'1 1.\']1(!m the :-:|.:-:|1i]it_1,' indux is given I1].-'
£2 III
0
Z I-'..-1..
wurw.ppiIpar|.:n-In
|AC.l ra-m1
4
B
.';I-'n.|‘1.1.t.in.|iFur r_'ulu:nn 12_. Lhu stilTuc:sz~; mtiu of t]1r_' fixed hum: is |'_gi\.'m1 by ABC‘ Ctml:11:!:|1Tar_\' Sun. (T2 :-us
'41. = 1.0 Al. juilll. 1. I-I11." 1'|3|1'|l-ire at-'Lil'tl(:~¢:> 'l-'iI]l.l1.‘ uf l-III: |=L"4:|'|| in Z El.-[A = L I1.
15
IIIFGIIGEIII <:1.'11H:I1£'r£ uiilnnl
.111 j11i11L 1. 1:111: r1:111ti1.'1' 1-1ti1l'111"11s 1111111‘ :11 t111:: 111111111111 is
1-29
F111111 1-1111 11lig111111~11t 1:!11:11't. F111" 11 :111'11_1' Fr111111!. 1111: 1:11:11!fiwl 1111115111 1'a1'*Tn1' 1111" 111111111111 34 is-1
Z E.-Ir
E
L
1.-
111
.1.-_1,| = 1.8-5
T1111 111111111‘:-re 1111.111 :11. j11i11t I is
‘-1-’
1
Concrc-1
T111.‘ :111'11:11:r11c:1s 1111111 <11 11111111111 34 is
an E7?
5
H“
2-E111.
1[)
1-
11
_... . , 111' 11.11.1111] t1_|{11 H) 11.4 in —. 3T.I]
=1.5
F1'1.1111 t-111' z|l1g|1|111!11l $112111-. fur 21 :<1\'z1j.' f1'11111L'. 1111.! 1!1i'1-<'tivr: |t'11|!,t|1 f111'11.11' 11.111111111111111 12 is
m=1m T111: 1'11c|i111-1 111 1-:L\'1'11liu11 111 t111: 111111111111. in 1-11:1::1:11'd11|11:t' W111! RC1
Short Gulmnn will-1 Axial Load I11 1-1-r~r1111|:1111'11 11'it|1 AC1 111.111.], :1 1'1111111111 i11 :1 1111113.-' 1'1'111111: 1:1 L'111:1§11'11.-11 11:1 11 5111.111 1.\u11111111. 111111 :="11.~11111.-1'11».-11.-1 11111111111 111113: 1111 ig111.11'111l. 1111011 1111: 1-11111111111111:-Q1 r11ti11 is 1:15.11 1111111
111.111.1.2. i:-1
& = 2'3
r _ 11.31111
|111:1 111-1.-1|
T
— [1].3|)]Ii1S111]
Fur 11 111111111-'.'1\_1' 1'r111111.'. 11 1'11-11111111 is I.'l11s.~'ifi1:11 1111 11 1s11url. 111111111111. in 1-11:c:11rd:111c:u wit.|1 .~'L(.iI 501'. l[Il.1U.1. 1.I.'111.~11 1111‘
- 5.-=1 i11
1111111111‘-1'11n11.-1 1~111i11 is 11111 1111111- r11:1|1 T1111 1111111-:11~1'110_\11=. r11fi11 11f1:!11l1111111 12
% = :11 -
,-,._ lll &=ummmflufi)
1'
5.-I 111 = 21.6
|.1c1 1.1-1|
'1'11c1 1111111 [I14 — 11!11f]_."1'1-1-_.:| 5 411 1111-rl .1-1|_,-".1111 1:-1 pm-1iti\.'n 11' 1111- 1;1u11111111 1.~.- 111.-111 i|1 :1i11g11.- ('|11'\'1:1I.11'1:. I11 111111111011. 110111111111; i11 11 1-11111"); 111111." 11:‘ r1.11111i1lr'r11c1 11111111111 1.1'11»::11 1111*
F111’ 111111111111 15-'1; 1:111: 1111111111:-111 1'1-11111 1:11 1-111' pi11111:11 111-1111* is
11r;11:i11g 1*1r11111'111:'-1 i11 1111* .\11111}' 11:11-11 :1 mt:-1| .\1ti1'l'111*r1=1111'1-11
5511117111 1131' AISC’ (f1.'11111111:111.11111’ S1.'¢. C2 1111
1L'11:~'II 1'2 l-1:111:11 l-111: grows 1~'l-11'1'11I.'1e:~s <11 1111' ('r.1l1|111111~' \1'iI11i11 1111: 511.1111".
‘F; — 1|] .*11tj11i11T I1. 11111 1111111 1'11 T1111 1'1*1.11ti1'n 111111111111.-1 \-'1-1111115 of 11111
Fur 11 11111.11"! 11111111111 wilh -11.111111 ]‘1.‘1l|1Ul'l1'1llL‘ll1. 511.31 Sr.-1'. 1'l].3.G.1 g11.'1.-.1 1111- 111:-.~'ig,11 11111111 11.11111 1'a1p11cil._1' 11:1
1'-1'11 hc1'1111.~1 1.-1 Z.P“'i1!— 1'.-1 1_. 11, 1-J 1-J
11!-".. = 11.&5c1(U"5Yf'i _ ‘ "'
2|)In = 11.111]
.1
[AC1 10- 1]
‘.2
_ 15 1111 j1.1i11t 11. L111: 1'L'111ti1'1: st11T11|.'-res 1.111111.‘ 111 L111: 1.~1.111111111 is
mL_i 2TT_w
Fur =1 .~111ur1 c1.1l1111111 wi1..l1 1=.1t.r:1a1l 111': 1111111'1'.11'1t111|1117:111. .-RC1 51:0. 111.11.13.11 gi1."1::1 1-111' 1l1:=1i|z_,11 11111111 101111 1'11p11cil}' 11:1
.9."
ZEL 1,.
T
_ 21'} _ 11.?-5
'
|ACJ 111-2|
T111: 5111111111111 1'11ti11s1t j:1i11r. I1 is
“"1 =
.4 -
¢m=ummFHfgJ§AM) b~uM
l"}1ca111|'11e 1.16 15111 IR 111 11q11r1r11. 111111111111 i.=.1'1‘-i11t'111"r:c!1'| with I2 1111. !1 g1'11.1|1'1 (141 11111‘.-1 211111 11115 11 1'u|1-1'l'ul|.' 1'ul|||111'.\'.<11'|.' :1-In-11g111 1.11-'111[1l1 1111'_."i11'3. T111: 111111111111. \1.'11ic11 in 1>1'111.'1:1:1 1111111111-it 211111!-
:=.1\'11_1.=. 11111-1 1111 1111s111]1|1r11'1.1‘1r| 1111111111. 11151 11. 1-11111 1-.11p|1111't:-1 11.111111 11.11111 1.1111}: 1'-'i1l1u11L 1.-1111 111u-11111111. D1-1r.~1'111i111: 1111.lntvral t-its 1'r'q11i1'1!:l 111111 1-111' 110.~1ig11 axial 11.11111 :'11p111!it_\'. PPI
l 1n1n11|v.ppl2|:1.nnl.:n1n
1-Bfl
ITRUGTIIIIL Euulueznluu IlEFEREll¢E Illlllll.
S0-|'ni:-rm
Short Column with End Moments
Tim mini|n11111 Lit! size! 1-i[JlI![Ti.fiII!d i:_\' _-9L|l_.?I S-:!|::. T.1(J.-"|-.1
Thu nxia] lmul r.nr|"_@'iu|:{ c=1pm~ir.y n-F a ccmlunnn dw11~aea-e-:-c rm 1-lul [ll-Ll'l|lUll[-ii i'll‘l." up-|>iiu1.l Lu 1|u'=¢:.|||l1'11||. i_'-'+.=-iigliu1'1lui=
nu. 3 1k.n- iull|§_£iI-llriilliii liars uf size nu. '9. ACI Sim. T. l[>.5 io :s[>u('ilil.'-4 :1 lir: -=];|z1[:im_=_£ llul gm-(nah.-1' Limii
vulutnn 111413" thcrn he ulltiiilmci by uu:m1s uf 4| vumpiiitcr
]1rngrruu. 2-illftil rue Si.!'1H‘il.ll'£! Point?-c .1p|l"-'r1I1.mm, iwmwl nu
Ir = 18 in
1i|1_- ‘2[H]S :'&'[_iI r_'|_a_lo_e." A|Trv|'m1r.i1.-'niy. :-z]1|&|'|':|xi|1|:n1=- Ii-r-Higll
\'uIu1.'.~' mu_',' |Jl' u|>luilu.'1l [rum I111‘ i111c1'i1('1iu11 :1ie1grn1u:~' of
~1SrI, = i_4S]lf[).3T-5 in]
App. A ihruugh .\!|.p|1. F.
= 1-5 in Example 1.11’
1Li-ii.-. = i_1[i][l.l2S in]
A 2-i in {iil\1l|i.‘i1."l' i-iul culunul wiill :1 1.5 in uuvrsr to llu:
= 18 in
ii,-".~. in {i.ik|[[lL‘lL'f Liure is 11:iuFI.u'L'L'1l wil-in 1-1 nu. 9 graulu
From AC1 S41‘. 1l].1[I.l. 1110 r.'iT1.'|.'ti1.-'I.' lciigiii [nclur [ur em |r_'|::|lu|1n1 |mu'|.'(i ugnilu-it SIi(it3?.i'|\"4\}' is
-ii]EJ[|' Ii'»i'_.*i|'|'“’. Tlm witil facrtnrni um] 11‘lUIlI|1II!111Ei nf 11-1| = M-_-,=~iii(] Ft-l-cipa. ]'Jv1r~r:ni1m the m:1xin||m|| axial
it : l.(.|
The 1':-ulilui of g_\'1'niiu11.
[HI imam and hm-i r1 ctnlicrc-Lt! (f(IIlll]I|1‘l‘1-i!ii‘|-‘II! :-atrungtil of
iu ncr_'ur:izm::c- w'|t]1
.-'LC'I
Film‘. ]I].H|.i.'.!. i:-i
lund limi Uni: L'uiumn UH]! E'FllT}r'. .5'rJI|:!wn
Il is clear t-lint 1111: 0311111111 mm" bu 1.'iJ\.'a5i.i_1lL‘lIi aw 21 5]lUIl'l-
1' = [].I{ii
lilflillltlll ami eaism:im'|m5.-; (!iTPl‘i!i (in not ill-HT! tn lm cun-
= {(1..'i}{li'§- in]
r~i
= -"'1.-I in
1111* r:n-llimn is
'['h:_\ !ii|I_'l'lI:|1_"1't|.|"..'i!-i. mtiu i:'-:
F‘
. ., - _ in ||1.il][.-lIfi._]|(12
H“ r'
24 i|| — {2)[1.-5 in)-|[2}{i1_3?-5 in} - 1.125 in
' —
24 in
_ 11.511
5.-I in
Thu l'ni|:1'11rcm11m1L 1':-11in is
— Sill) In m_'c:u1'1la:m: witi| ACI Eq. 1|]-T. Lin: 1."-u1un1|i. nm_\' hr triassififll as :1 :='l1urt- CU]‘l1111ll ]}1'LH'iIIiC1Z] that
5534-%:"' T‘ . ' '_
.--1..
. _- , in i_-mu ff-i:1]1r\.}(ll H]
My
20 -ii 34
14 in’
‘HI? :u.u:s1 -M _
ma m1"{*2~1 my
= [).-14 ki]1_."i11'3
'Wiuf!l'II!.
Fllllll f\|Ir[1. B. will] 1 = U.'i'5. iili.‘ I.|l.':>igI| amiul :
iii] = [I Jui = -H:|n|||
Hr~||n|=-: Lin" -:'nlu|nn is :-1 .~i]1urT nnimml. anri tlw Ilmiigti
axial lumi |_'n|mc'ii;.' is givn-u |.I;\' AC1 Er} Ii)-2 a.-.4
r,-,P_,, = [].H£)r,1[il.Z-i5)']'_(.-i.‘. - .4,,] + .4,,j_q]
P . .. -—“ = 1.2 1-u|1:=_,-'n1‘ "iv Frum App. C. with q _ii.13li. thv sic:-=ii.,'11 iucin] zitrnui is P" . ._ -. — All = I."" ki I 1.",-‘111’ “.
{£1.85} (4 Ill.‘
={i_1.E'i[|'][U.'[i5}
.1-=1 [32-'1 ill! — 12 inz]
~ [12 n-*1 (nu = 926 kilns
lll'
I3}: i1li{‘F]IIUi.l-‘liiflll. fur 7 : [LEI]. the dcrsig.-,:|1 nxial ':i|'.Il'L‘%L*i is
IP,,_ 1.2_ iiifhi = I .3? ki]1s,-"111",
. F kip
5 (E)
Iuroncen concnrrz uialnu
1-31
The 11mxi|1i11111 fmriurul axial imul that the eululmi earl
."lI| = M3:-lli(] it-kips. De'i1:1':ni1ie W]1i3'i-il.{‘l' the 0311111111
earl}; Ls
e:-111 ea|'rj.' a in-r:h'>|'r:|'i .-axial In-:a:| nf NH] kips.
1",, = 1.314“
Hrlltatirm
-1.3T"1't[12i|:|}|'
fi:= LU and 1"= [HI in. 'T'he slemierime-as" ratin is
_ BED hips
-.- _ . , 111 [1.l_|_|i12 f11(1l H)
H1 Long Column Without Sway
Concres
1"
[Li] in - 24
Fer :1 |:r.:||.~w='=\_'.' r.:r.>l1|11|||. AC-I Sec. lU.lI!.!i 111.-mlits .~¢em11cl2l|.'_\' el'EL'I.'ls in the L'Uilllllll Lu he vuillpcllsnictl fur h-_'; multi]1i_\'ing the eurl mmnenfs. cletermineci in ii First-m'1'ier liilefll'-r.'|:.1sl.i|Ir iLlil'li_'|'!\-iii. i.r_'|' 1'1 1m||_:;||il'|1I1a1Ii|.>|| iiitlur 1_|:;i\'|?tl hf.‘ AC1 See. 1|].1l]'.G as
@ :_LH_12.1.1,
._c
*
In u['eur(h-mce with .I'\C'| Eq. Iii-T. the eulullin is (‘hissi-
fiecl as a lniig mhimu if
T"
."|!-_>
_
0.1"‘-3F,.
3 Ln
[12]I|:=i[]|lFt.-kips}
2‘ -" “*4
|Ac: we-r2|
:1-'2‘2 P,_. Ls the i':-1.eTm'r~r| mzi:-1] lrmri, i-lll(i. The Euler r:ritie:1l lumi
is giwll i.|-3'
Ilernee. lhe euimun is ll. imig ru]11111n. and seemulm'1.'
|r.@l‘l'o<~.r..+ rnnst. he rnnsirierm-ri-
.|.__
P, = The
fiexiirnl
rigidity’,
|_AC|' 10-1a|
i11
iwnirrlniice
with
'l'he tl:l|':-|'ill|l]:-'. r:i'4'-|:\stir:it.}-' is ,|.{iv|'en ii}; ACI Se-:'. 5.5.1 as
1~.',. = 5?,r1||c1,,_.-T
.-'LC.'I
See. ]iHi.iH.(i.i. lmiy he i:li-{fill as
0.45.-I
E! = —”
I.
= 57.000 ,~'4nuu ‘P
|.-1.0: ro-151
Fur siiiiplifientiuu. il- lung." he zuesumull [hill -'_1‘,,,,,— (LG. Then. as 1.,"i\'[!]] ii}-' .\5|.('.'I S-nr. R.1|l.1lI.fi.2.
The [!;l'n¢-s iumnenr. :11’ inertia is given hjr
E‘! = t1.:!5P.‘,.i'v
11112 iuii .i,= f
The faurlur C-‘,,, »;‘|.:~rr|.~4:l4~' Ru‘ El u¢_|111111ii'¢.|rm |1|.'mli|||g1uu:n|.-ul on >1 mlulnn and is \‘.ii!‘fi‘l‘Il.‘(i |:_\' .~‘L(TI Sm". 1ll.1llI.li.-I as
(I... — 0.13 +
0.4
|AGJ I-D-I6]
'
= ll] For c~n]11|uu_s with 1L'mui\=m'se iuml-< l.1L'I\\'L'|_'!l :~_-|l|)[:||_rl'[h
'I'l'|=.- :-|.:~l|.u|m is r|<.'|w Ilr.-signr.-Ii for The |||ag||i1i1*<| iumm-|'|r.. giimu by AC] See. ]lJ.1i].Li zue ."|I.. _ 5.\f-3
iii"
=11-.h'1 H 10"‘ lhf_.-‘in?
1 + :!|l'I|>
= 15.2543 in" The 1."m'_'i.'li\'L'
l'|L'surzil
1'i1:,i:iil_\'
is
giveli
by
AC1
See. FI]i].[i.2 as
El‘ = il.'.3!i':E_-I‘,
—[[|.25](2i-.61:-r1[Ii
[l£3.'.?SS i|l')
I 14.63 is ll!“ in"'-1>:i|:s [AC1 H7-ff|
The c'ritie:1l iflflfi. is given i)}" AFI Eq. lll-lli as Exaniple 1.18 ."i. 24 in iliuuwl-I.'r Liui cuiuilm wil|| an 1.5 in c|.1\'r.~1' lu lhu ii.-‘I-\ ill r.i]zll||I.'1e1' Iimi is rei11li.r|'-£1'~=l wiih l-I nu. 9 grade [ill imrs nml 11-as £1 lI'DllC‘l'1.‘lI[‘ eulup|'t::sii1.'1: strength
nf 1[)I|lI] l|»F_."i|12. '[‘l1~|= r:n-Inlim. 1-\'ili-|"il is hmeeri ngiiiiisr si1.l1_:<1»'a|;y. 11:1.-.~ am nu:-."~1||.~pu1'l~_-1| height u-i' 12 it illl'l.i. is hent in :-iingie run-'niI.1re with fnetcireci end mciniellts iii
pr = W.-i‘
r|:'5'{1-1.65 ».- 10“ i|13-hips] {[1.u](12 nj|(12 _ nun kipei PPI
l v|uuv.ppl2|:.nnl.:nn
1-32
srnuerunat Euulueznluu IlEFEREll¢E Illlllll.
The :nt>tut'ttt {'\l}1'l'{‘l"i.iU[l fnettir is tieiiiieti hf.‘ .-'|.C.'I Hrl. Ii]-il'_'> as
The meutinulm fnettareti axis] lend that the etilutnn enu e:-1|-r].-' is
_ U.-iii.-f] M C... — 11. Ll t Z ’ _ U 6 + [l|..1}|'J.nl| ft-itipsi)
' = 1.0
P ._- - ll.iJ'T.*'i:-r
= (u.r;?)s|[1'.= in)"-' = 1.1113 kips
mu n-I-.i;..
=: tun kn»:
The uttnueut ltmgttifieattitill F:-ietnr is given hf," .-9|.(_II Eq. iU*-ii HH
Lung Column with Sway
. =A C ,»_.m 1
PH
The |||2t|;nifii:nl-iun l'm:l-ut for eutl utumellls prutliteetl hy the ltmtls that emise sway is _i.§i\'e11 h_\' AC] Set". l[il.1U.?-4 uh"
— ll.TfiP,-
1n
1_
Heiife. the euilllutt ('€l.l]HLll 1'm'l'y.' the uxin] luzui ul Tflilitijm.
mu ml... |j_ll.T5}[l3El?3T itips}
ii. = i
=i..ii._I
Incl In-2:]
1-L P"
41152 11,.
1.0
The Jlletgttifieti end 1uun1t'11l is gi\'I.'|| hf." HUI E4]. 1|]-11 as J1r.f,- = I!‘||,,.1\]rg
The HllI1ll1Ii\lir.|l|s (Lt-:|.(!t|.|.l ul-'(!r all the l'|)|l.ltnlls ill at :~'l.|.rl‘__!.'.
= r_1.1s;|l.1:1t>r:-1-.t;..~:1
The st-.'u_v 1JlUIlJl.'1]iH-El.I1;‘ lIIl\1]ii[Ii.il."l.i by the 1uzig,l|il':I.'a|lil.|-it felettir. mid t-he Il1II)lll5'|\'ll}-‘ me-lnents are ntltietl. iu nectar-
= 451 H-hips
tinnee with AC]
l[Il.l(].t. t.|'|- give the fins] t]esi_t.{11 emi
111u|||I.'||1:~= in lhe t"uhl|||n oi F'rm11 Ex. 1.11’. "_.- = l|.til|', ,rJ = l|.l]Il1. lmtl . _ . _- _ in &: |_-ll:-1 i't-it1]1ts]-£12
AMI
ll-ll = .\I,,,, + 1:, ill],
pact to-:s|
Ii‘!-_+ = .\li'_I|., + liq"-3,
|AC|' ID-79]
rt{l2 11.1124 in] Exalnple 1 .19
= £1.51 I-:ip_."i|11
A 2-i. in tli.-tmet.er, ti.r-ti t:e|l1|||||t with >1 i..'_| in eu'|.'e1' tn the _
"-
Fru1|| ."'t[1p. B. with 7 — [).r=J. l-he tlwiglt £l3tii‘li ts|.l'L':~fts' is
3."; in tlizuneler lie-i is t|.'ittf|.=-t'01.'¢i with 1-l nu. 9 _g._£I"eule [i-U lliirs imti im:<. at t"I..1tu.'rel.e t"uttt|:|l't':<.:-.-'i'.'I.' :
~"llJ[JlJ ihf,-“ittiz. The enhmm is not hmteti anti hns an uus11|1pm-tetl Iteigiit nf 12 fr- an t'll7eeti\'e length Fsetm nf L3. atml l'm.'lul'e
% = :1.-1 1ti]1_-"in"' - u Fm-||| fillap. (.7. with 1-" = (1-EH]. t]1t~|.lt-sigll iutiail sltl.-:s~' is
r.:+:»I11|'|||'| :3-I-itit-sl ili_li'lliI\' is 54",. = 2El.lJlJ[l kips. mul the sum
Q = 1.2 |
of the htelurtsi 4.u]\||:m iuutis is EP1, — 'l!?[)lJ kips. Determine 1.\'i|eti1er the etillmm eau eat'rj.' :1 Enetnreti axis] ltmtl tr-l'9[K] I-£i]Jr~".
ill
.'i'riI|.e!z0r: B3.‘ i[lU_'l']lU]El|ZIiUl|._ for "r — lJ.BU. t]1e i1llu1.\'elhit' tie-sig|:| nxiztl sttes-c is
fi_ [H IE1 (US z l _..
in’ = [LET ltip_-"i||?
m-
1;-
The s1entie1"||r:-is mtin with 1' = [i in is
H"
.-P111 [1..s,ti1z.- t1_|{1H)
T"
6|'l| = 312
IIIFGIIGEII <:t.'|||t‘.:It£'r£ nillnu
Ill ntretlrtlnttee witil .~\CI See. 1ll.lU.1. the etllulnll is
7. DEVELOPMENT IND SPLICE LENGTH OF IIEIIIFDHCEH EMT
elnssiiietl as >1 lung eeittlllll if e H F
1-33
Nomencietltm
Wu‘. _ IQ PG
31.2 .'> 22
|'l'ht' e<.llnn||l is lt:1|l;=:.|
.-it
il1'l'jl. t1l' an i||tli'.'icllu1.i imr
-4..
l1.|l::l |.'|1.m.s-stltrtltlllrll ant-:|. uf all [|'ml:w11.!t:~1.:
1'r@i|1F1_1r1.'r!r|11*|lt that is 1'-'i1hi|1 the .-‘|l1t1."i|u: anntl that ('l'tIH-£':i the pntetttis] |:1hmetli'
The nlrllnent tltngllifimtitlll Ili'\|I?U]l‘ ftlr the sw:=l_\_' nltlnlellts is given l'1-_t' AC! I-{:|. ll]-El as
vs
]_ Z:-1. 111.1.-:1 Z P.: 1 1_
1f(].T3'l]['.3!‘.].[il|[] kipsi
ill‘ in’
:-]lliilil1;.; l|:1r0|l|.',h lhe t|'lt|l'-:2-1l::1*l||et|| |1eiu;_', ti|_"1.'1'l,n[l('1t| I"
spacing er cert-1' tlilnetn-.it1ll
ill
-l§|,
1.listenct- freul t-miter 1.11’ hat tu mrsrt-st
in
(I-llf|(Tl"l" E\'|1FFil|T!
Ft-
'_1 1;1tte-]uI.ll' the tetlter-tn-cetlter s]lnti|t,t.t 1.1i'
115.
1u|l||1in.=|i -:lin.l|1|~lt:t' 11F lmr
in
.lli'|
n1.'er|1.|.',e splitting tensilet'u1|1]ll'¢-ssiw
itips_."i.t|“
hats
ti-‘lIE‘lI||.',ll| tli'liglltw1:-igilt nggrtgtlte
= 1.1-'1
C1l[ll§l'(!ll'
The llletg_ttifier.i elltl .lllUl]1L'].ll is giwll lJ]." fill.‘-I E11. ll}-19 us
It
rn.'¢'r11.|| tiliel-tlt-1.-ss nl l1H.‘ll|l1l."l'
Kt
‘ll’:-\ll.t-1-‘r'l!ItiI.‘ it-itllultt-uletlt iutiex.
ill
.-l,-,fv_.|1' l-"l1l)l.l.1:|:
7..
Air} = 11-fr“... + I,l_.,.fi'I'_|,
= 5:1 Ft-mp». + (1 .ll)[:ttlt1 ft.-itips}
-.1rl1|it'm||ai r.'11li1-erlllwltt Ietttttil -:11 1=1tp1aurt 1.1r
[.1
1.l1!\'1;!i.u|lI|t1et11 |t'll;:__1h. |',¢,-,1|.|t]Jlit'l1.ltlD
= 3'92 it-itips
in
|lH)|l'irI'il1-IIH riH'Ll|I.'$
Frtnu Ex. 1.17. 1.-=l1.l-ill. p~,=il.l1il1. l-111\'l
in
intsie 1:lt'\'c~|t>]lt|1e|ll letlttth
in
-he
ll.1!\'l.!l.|ZJ|]]llI.!lll l['l'l;;lh uf slattthiltl lttlul-t i.l'l
in
iultsiutt. |u1.!:|:tlllt~ti ftuttl t'1'iti1:n1 serlittlt. In
t:-lthiiill‘ r'1|rl11i'||r1r1-it lI1=~1t1tht|11 1*|n|1r11h||='t|t
-. - -_ in I [5512 ll.--it|]_1e<_i[l' Z E) riuié
in
-lll |.1t1it|t hi" infl1.‘t'ti1;1n
lII‘l]|!,lll hot ween etitit-nl settitm and sutrt t:-Th-uuit |:||u.|t|l til [:|.l|gu|tt:jrI1 |||i|r~ t':uli1i:t u-i
(452 i|lii]l2-I ill]
l1ml1| ttnrl um.‘ hut 1|i:11||t-t1."lI1.
_ tl.-:15 kip_»'ilF
1',-,¢. x £'l])|)lilI'£'lliIll."'|I|.1illli|-l'lIi'Tl.i1Jll iitctuts In
iussit: L'l.t!\.'I."lI;>]Jll'lI."|1l it-|l|:,ti| uf !i[il.llI.ltil'1l Ilueit
Front Pupil. B. with 1 =1]/T5. 1lu:1.it-sigll exist] stress is fi - ..'- ‘-' Au _ — 1.13- klps,-lll
l. e
l1tp.split'e It-u;=.-;th
-4
lnuxinlunl telller-ttl-tr~|lter =-.r|lneiltg 131E lIz'|]l:i'v'L"Il-ll? |‘ei|lieIti't|lell1 within l'_|
in
]ll|]ll.llt"|'UfblL|'."1- t:1l' Wi.l'!!:l built-,; 2-1]1lit:1!ll ur tint-¢'lnl||ts| ;|hm|.|, the |2|lillI|l‘ ni' splitl i1||p_
l-"'1'-e-in App. C. with 1-=ll.lJ[l. the ti-r-si|l;|l axial strrss is
gt; = 1.1 l.a1..~.-,-'1.-F
ili
in to-q|.
Symbols
.-'1.
lntle nt'lul1'n 1Ji' reit1l'tlreelut'1|t r.'11tul‘:|'t1.1 tutlll
.5.
ii_|.',||1wt!ig|ll ;|g3l'|tgll|e tl1::-||trl'ete in-:tltl|' = IIi.T.f| Fnr nil light 'n'nigl1t_ Flfi§{‘l'l'!){1l.[1l' t-t1r|t-11-l|~
I'l.lII'll. ui 11.‘-|lsi.ut1 |ei|litn'tet|lt-ill st :iI."1ttlIi.t.1l'|
Hy i||t.et]l
L_ -
= f_._.,-'(i.T\.-‘T 5 1.Ll wllell 1. is 1tp11'eii'letl
' . E i
.=l...— 1'5 in‘ + (“'4 illijlil-3)
= .l.l'| hr! |lt|t'l:l|t-ll 'e.'t.:lglll. |.1:J|l|.'l1t:[e
‘P.
= 1.43 kip:-t_.'°it|"'
= 1.5 let I1'[lII>X_‘|'-II1!Z1tllE’(l Imls with t:et'et' <2 liir.i',-.01" clean s]:1:u'lt|g <2 [itlt = 1.2 ht-r ill] ttlhet |'||||:c_1.'-|'ut|l|.'~:] llill.':i
The lllztxillnlln l'nelt.1l'etl nltinl ltlntl [halt the eululnll \‘_'il[l entr_1,' Ls
1-U fer 1l|1t'1.1nt1.*tl hatr-1 ‘F.
lt-iltt'et'et-meltt size lmrtur = l|.H iirr lZ|ll_ H il1Hl :<|mtl|ur lsn-:1
P" = 1.431..
].l_l lt1l'n1.1 F nlnl |<1rgel" |k‘lTE-
= [l.=l3](45E lllgl
= G-<1-S I-tips DEN] hips
ritlttiitllt inrrtt:-r
‘P.
IC'ilthl|.'tt1."lllnrl|.[ lutrlilisllt im:tul' = .l.i§ iu-I l'lL|t'i.'AL|!ltlnl llfll‘ Willi l|JlJl.'l' limit 1'! ill 1|‘i -:'t1Il-:'ret|~ itnin-w
[Tile ttlllllttll is llll.-fillliil-€i:llt'1LI1':l.'.:
= ].l] let all ether Inns
PPI
l 1ItlIr.|I|IlI|III-l.GfiII
Concrete
1-34
srnuetunnn. EIIIZIIIIEEIIIIICI nsrsnsuez Illll.I.lL
Development Lérlgfll cl Slrflighi Iii’! in
I
'I'Q|'|5i|||'|
Using it l1|i11im1nll elenr spneilly, oi 2rl'_.,. 1| utitlilllllln elt-:-11' t:m't11' tr: ilexttr:1l tei1li'm'rs'-||tent tlf rl'_.,. ntnl ill the
:1i"1se-llee ei' :-1til1'1l[ls, The
1“
—=
11.11?.:~;,.~F,-\l=..\r_.
re
tit.
It
MCI F2-1|
,v,1'_|'i.{,-A _|. [{“'|
'
is
q]_[]4J|'U'|I|\|',
—" = i tit.
_}h~|,1"_?:
:l'1:>r .-It |lr.1. Ii 1_|1' .-.'llu1.l|e1'|
[ll
ll.[]ii_,l'L,'-l'|‘l",
_
— = i?
til.
lit
litril r.l'1, lltl. T |.|I l:|];_[_1.'l.'|
J\\_-"_||'_T
is T3 12 ill I -L],
Using :1 minilnltm elenr s11.-millg e-l' |.l,t. :1 millinnim t_-it-;_'||' t_'t|'\"t_'!|‘ In H1"-_\{|_tt1:_1] 11ei||['nrr-e|||e||t e-l' rI_.,_ :_||||i |ni_||§.
“ii
llll.ll[l .‘i[i1'l'I.|.[Jl-l~ stlqxihwl ill ."\Ci E11. 11-13.
1~'1~.. 1|- AL?! s-.1.-. 12.2.1.
1.. "-“4f.1‘*‘1"'»
— = i? nit, .]\'\,-" JV:
.‘int
.
r.l't 111.). (:1 1|: :-tm:|.li1:!t'|
‘Pill’, '3: 1.? illir Q =
Fl'l}11l AFI See. 12.1.2.
ii‘-P
1"—
F
-I
|"|' '|",
»7\11"'Tf
Ifrtr tit |1r1. T 111' Inrgt-r |
Ftlr nll t:1ther ens1.'.s.
1||_.'_|'_i 5 lflii li1i_."ltt'
in Tile tierivntitlll tlf the irs1tts1.'et:-:1? l'eittEtltet'ln<'llt itttlex is iiilll-t|II:lIi'ti ill Fig. L15.
._ 13.2.3 ... ttlsu _ ."'t(.l. bu.
_- ,_ llntlutlts
1h1._
l].[JLi,|'L,‘|'."l'. _
i
_- :~un]1ill1e1.l. _- -i'u]]u11||lg,
V '
H: 11.111.-' ~t—',.~P.
etmsen':1ti\'e \'Jll11II!5.
_ _ _ .i'-‘T "'1 |"‘- 5 '-‘T ellllliil li
r.i|_.
,\
It-Ur ‘M nu. 7 Ul, lmwlll '
Flgmi 1.18 t':i:,!!.'|.-I![.\f?1't [If KI, 1:, -'-I C
ab
C -=2 ca
11',
ct.
c
d___ No. 2 stirrup at spacing at ___
"
F1. — 60,|JDU psi Y
horizontal 2;‘
c~i_.,
T
crack
I Ti
iibmi.
ii-iii
A‘, — o.111n=,.1=.,, — e.221n=, n — :1 A. Krr_iuJyr_£ 1500.sn 5
0
J‘
'|'EfTlCFBl
|
=1 L
IIII
2;-
cl
wI:w.|:|IiIpl$I.:\'|-I11
Cfifiilii
' Au — 1:1.111n=,A,, - t1.11|n=,n— 1 AF. Kn_i"ii ‘l5DlJsr1 ‘E 8
i‘
it
IIIFGIIGEII <:t.'l||t‘.:Ii£'r£ llilllilll
For llillltlletl ili1l's. AC] See. 12.-1.1 stleeifitrs t-lint the
1-35
The tlilvtir tlilllellsiull it: the fieslitill l't'itlltlret!inellt- is
t]e1.'e1|':|1|lie|it leii|_{t.h shsll lie that i'ni' an int|i\'i<|il:=l| hi-1i'
i1i<'1‘e:Lse<'l |>_l' '2lJ‘J{- fer s tlirer:-ll.-it i:1lLIl|‘iiE_' niitl 315% f't.'1l- :1 i'i.11ii'-inlr hiiiitlle. Nu iliei'1.-lise is 1'L‘l[lli.l'l.'l.l for ii lwt.1-hut" hillltlle. Tile tiqilivtlletlt tiitliilettir tit tli :1 iiiiiitiie is spee-
ilierl in AC1
.== 1.-5 m+11.:n'-:1 is +i' '1; “‘ = 2.:_i?t. in
12.4.2 :1.-1 thttt 1111' :1 lint with =.'1|l an-:1
L't]lIill lu tiitll ul' l-he ilulitlie.
Ctincrt-1 The spiieinp, tiinleiisitili to the lieitlirlii reinfllrceineilt is
AC] 5121:. 12.2.5 s]'i-i:eifii.~s thilt when excess i'ein1'ul'eeil1ei1t. is |'li'tl1;irlerl ill fl illelnh-ei'. the tiel.-'ele»|1ltiellt leilglli 111:1}-' he i-rslliersl h_1' ii|i1.lti]1-l_1'ing I1}; t.he iilettjir A,,-,,.q,,;m|_|,1" .-'l,u-,,.,.-,.|.,1_,. This l'ell1.|etiu|l li1e1ul' IlIkl}' IlU|.- he iippllell whell tlevelllpillellt is rtiqilimti itlr the j.'ieltl streligtil tif
the reiiifureeiiit-lit. as is the ease for H~|‘|l‘illi-ii‘l_[[II.' i'lil'[l leillpei'ill.lll‘e l'ei|lit.1ret'illt'1ll- speeiliul ill .'\C'-I 511.'t.'. T12.
illlegrit-3' l'eilii't.1reelllell1- s|let'i!ieti ill .~‘iC‘-I Se-1:. 7.13 illill See. lfl-.li.i'i. ]'1tlsiti'.'e iilnilleilt l'eii1i'ti1l'eetiie|lt speeifieti itl
e_ _ 12.1] ill — [2ii1.5 iii] — {?')[0.-3?-5 iii} — 1.4] in .,. -
4
= 1.-iii ltt
[liti-i'iii.t1lila‘ll l:Iiit'kl|l;.j, l.';lJ\'lI'l'l'lE~:|
ts. =1.2-i1 iii Tile alrell ui l]'£l1Il.\.i'|1't‘_"]'!iL' Il'_'iIl].[lJI'\.‘l.‘1lll.‘lll; erussilig Lhe |lt:1l'i-
zulltill erilel-t is
PLCI Set‘. 11'-1|. iillil l-Efllfiitlll lil]) i>|'1-lites slltieiliell itl AC1
.l,.= {'2}-11.1.11 in"-'11 = 11.22 in’
See. 12.15.
The iiillnher oi‘ list:-i ii-eiiip; {leer-lnpeti nlnng the ersekillg
Exaitiple 1.24]
plzliie is
Tile simply: siippnrtetl reiilfnrted etnierete iieilln til’ ner-
1'1 = J
lliztl weigllt eull1:rr1:1tt- sliowli iii t.lleilliisl.rt1liull i:1i1e.-ii'|i'u-l“t:t1ll witli grtltle Bil halts niltl iiils n t-i.iiii:i'i:t.e etltil|m.ssit'tstrength tlf H-illill il‘ll'|."ill2. Tile IlZii"l.\Iilll.llIl1] nltlinellt ii1 the heilnl ri1ee1ii's at. it p-nint 1! it Fmnl the enti nftlie lusts. siltl
lU'i"E ttiul'e fle:tlil'.'1i l1eiil[ul"eettletil is pruvillell lllilil is ]‘L‘f|l]iI‘{‘{l. Deterlliille wiletilet the
The ti-tlilseeise leiliEurt:1:1in1:-iii iiltles is
_ H -it fr —
1‘-'l'|l"Hlli'l.l'lill"! is s:ltisi'nete1'_t.'.
, 11.1 __[t1.22...'_i[t'.li.t11lu
_4|___,.¥ (lam iLf].t..
—
ili-
(lain iiijis il1]1[3,'1 ill-
= [i|.36T iii 121111
1?.t+ -Fl} = 1.31 i.[l + (].I.ii3'|' lll ah. 1.ll iii =!.Ii"i
sf 2.5
No. 3 stirrup: at
[sstisiilettltjfl
B in spacing
Fmin ACI I-.".q. 12-],
19 in 1% l|'| ctwer all around
2 _[l-|:i'i’i:1fp"l";\|'. "l",E,,
d-'1 _
3'-\,-"T,ri_=?.1. + Kr--Ii -iii.
3—l'1.lo. B bars
=
t_u.t:i5}(u11.u1i1i g]l1][1){l][Ei.1]1]
Salli iieii
lti .
t 1 1,“;'3'uliii i“._,_t 2. 1-5) H M U
F1'i.n1l ACI See. 12.2.-l. = Ii-ill i-|-"_- =il",-= \|’,.= A =1.ii
Tile 1.-.~;e1:ss rei||i't.1l'ceiiieiil. [lielur is
A »i_pru1'r:l1\1j= 11.11"
Tile llL'\'elu]llilellt- lellgl-ll l'L‘{|_llll'L'Il is i.¢= 3131.1,-.
A-1_......1...1;. inn is" £..=i=i. iii.“
E
= (;it.:ij:1|jl.l,1 in] = 34.3 ill
3"» '24 ill The {l|I“l.'C'l(J]}‘lTll."l1lC. llillgt-ii lHr'Flill\l1itI! is tilii-=iltisisit'tury. PPI
l v|1u1ur.||pl2panl.:nn
1-BB
srttuitrunltt Entilnszllllul IlEFEREll¢E Illll.IlL
Development Length of Strainht Inns In
For n [‘lJllC‘1't"[lI' strellgth ill eltclrlei llf -"1-I-l-‘I iili-_1'.i113. AC1
Compression
Eitle. 12.3.2 :-‘ll'|l'l See. 12.3.2}. l.ri1.'e the i'er||lire|'i tlr-\'t1itlp-
lllt.-llt It.-llgtll as The llllfill.‘ tlL"l'l.“lt.l]}1llI.‘lll length lei" |Ilil.l'."'l ill t'1.iiii|lr1.'ssitlll is spneilietl i.ll. .-!l.(.'-l S-er. 12.3.2 as
I
1.1“ 1.25.-.-C,ri.rr
_ lj1.2l(u.si'j|ltl.l.5llll.tl1111:l].i..,F,
ll.t]2.-hf”
= [ l .2lt1l.slj1 tftl.l-'.'.]1i1l.tlr1tl:lI| (1 .13 ll.) [t.1l.tlr1-ll
.»\\'."T:f_
_ '3 ll.Il[)ll.lrl.1,_f,_,
‘W l1'Il
_
'
ill-
= l.T1.l'i ill
ttuvt-l'lls fut llutllml weight t-llillrtete i Jr, __ 44“ H H _, 1 _, Ill
Dllilloprnnnt of I-In-akctl Bars In Tension T|'|el1.I1l1it1i1ie\.'t1|1.1-[1-tiltilil Ieliglii. I... is r.1l11l1.ill1.'rl I1-_'l' liitt|li|l-l_','ii'|g In-,. 1.1-_'.' the l
elteess
l1eillf1Jtt'et|leill
iilelur
sp-eeiliell
ill
Tile |.lil...'iIlL' ll1.'1'elu]liiieilL l1.'ti|a'_.l-ll fut l|1.:-1.1]-tell halts ill leilsiu-ll
is !i]'ldT12!ifi.l‘1ll ill l\I1"| See. l2.:'l.2 as
AC1
i
See. 12.Ii.Ii[i-1]
11.112\it..l..j, i'|l'i _ T
WT
E -'i>1il\|l|l|.\l_l .‘_‘_ _ L 142l:|ll'\l\'iflI1li'
1'
‘tit-'|lei'e the li[.{|lt.1I."ei[.{|it. rl|:;1.{l'e;|!_i1t.e t:niiei'ete fsettlr s]leei-
iieti iii l"'lC] Set". 12.5.2 is
etlilfilietlietit Fzietur s|let'iiieti ill AC1 See. 12.li.Iilh]
/it = i].Tl'l = 1.[l
11;. = 111.".
ilill." nil lltllel -trnsl-s]
aiirl t_.lie 1"|l1i'|i{_\r'-(_‘t_'l:-1l.i'i|'l, i'ei|litllt_'t-lllellt Fsett_'lr ii]'lIl"{_‘iiifs'i iii
'l'lle t.:r>1|fillt-lllellt. i'llet.c1l' is alllplietlllle wltell s]lil':ll rt.-ill-
."'l(.'-I Set". l2.5.2 is
i'l.1n.'eliieiiL is pttavillell willl ll llliliiiiililll l.llkll[ll.‘LL'I' 1.1-l' £1.25 ill ililti s illasilllillll piteil tlf -1 ill. lillt.el'llati1.'e]}.'.
"1". = I2
l'|t.1- 4 lies 1.>i' iit]‘l.§l'.'I' illt1;1' 1.1-=.~ |:1lt_.\'i1.lt-1i ==1l. at |ll:ll
= II]
s[lneillg.', u1' =1 ill. Tile tiiiilillllilll il.|ll.iI'11."lll}l(.‘ vnhie ltlr 1,. is ti ill.
Tilt llll Di l.ll‘l' ni:-1.-_-1|
'I'llt.-.-1t.'t1.i1lI 1'l1'1'1'e|c1]'1lllellt. i't‘l'l.l§Ti'l- l.,._-,. is1:1-l1t.==1i||e1'l 1'13.‘ lt|.lll-
Tile retlllireillellls let ilillltiletl ll-itrs ill t'ulllprt'ssii.lii ill'L'
li]J'l}'ill_l!, 1'.-, 1, il_l' the felt't0ts giveii ill .".CI See. 12.5.3.
itielltiei-ll ttl tllm-in applieallle ttl llillltiieti i:1al's iii ti‘-iisitlll.
I
the E!(I1\"l"l' fsettlr itlr ilars lltlt ecceeetlillg slice lltl. ll.
with .-ti1i1.- t:1'.1'.'el~.-t |i1.1t. It-ss than 2.5 ill i'1l'l1.l eilil 1111.1-vets
Exanlple 1 .21
litll less lhilll 2.1] ill
."'|. spinllljr r1.'illiul't'etl t'r_lltl|llli t.1l 1lLlI'1Jl£li weiglll 1.'uliel'ele
witli n li.2i'l ill tlii~lllll.~tei' s]l-ital at ll lliteli ilf 1|. ill is n_>iili'1'.>|'r.:erl with lie. 9 grnrle [ll] hats ill i‘i1‘|l'i1'lli".'-l tlf thi'ee zillti hits ll euilerele l:t.1lll]l-l'essi1.'1.' slrellgtil l.1i'~l.5l](I il.Il.-|l"il.li. The et.llll]ll'essitl|l l'eiill'ul't'ettlelll |)FU\'iti1.‘1tl is 15155 lllDl'L' tlisll is i'et|llireti. Deteriliiile the Iil1q'l2li]‘t‘~tl tleveltlplllellt
(-1. - l].l'
= 1-ii
I
[Fur 1"-ilI|t|i.t_it:-lls N|1l‘\t'i.Fl('fl niliivrii
[Fer nil rl1h1.~l' l‘I'l]|.lli‘lilll|=\i|
5'.l-ill il'rll.1
tile tie fntrlllr itlt illir.-i lltlt exeet-llillg size iiil. I1. with tics p|'r_1-1.'i the l'i=_'ll' lleillpt lll_-ee]L1[JL't| t.1v1.-t l-he [till tll."\'L'iL‘I[JllZ|l.'Il]i. iengtll ill ll .~:]lel1.'illg. llllt l'!JCl"1lTiKilll.l'.',' I'ld.,: ill" fill" a Elli" lltlilit witil ties |ll'tleitieti, |lai'allel in the liar ileillg tlr-'.'eltl|letl. altlng the
l"‘l'nlli .5.('l See. 12.-1. the rlevelnpiiieiit lellgtli tlia hill ltl at l-ll.l'I.'l.‘-iJi'll' ll-I.ltll|i1: is l[ll.'l'L'iliil.'1l 'Z[i'.5’i-.
exteelliilg 31:5,,
iel'l3;li'i 1.:-fail illrli'-'i1il.li:i 1.11.11‘-
lilii eltlelil-til_ltl 1_lflill'1 ]l1_1|.lit [llllh |ll'1tl1.l ill it stl1.1{'.i|li.*, llUlT; — 11.3
Froill AC1 Sets. 12.3.3. the excl.-1~s l1.-illl'1'l|'t1t'1i1it1llt l'=:el
I
the elteess I'L"i11[Ul'L1‘llll3lll f:ii.'tul'
E4! : i.
i |-'1
= [l.5? lillltl the rtlllfillellietlt iilettlt is C; = i].T!]
Er.
_
'4I|llIpllll11:
-"‘|~i|:0:rli1lr1i.}
For htlulttrti illirs ilt t-he tlistrtltitilllltllls elltl uf ii lnellliler
witll etl1.=ei' rli' less than 2.5 ill. ties shill] he |1I|‘(1\-‘i.ill"!i'l, rl'.'el' the hill tievt-iuplllt-ill it-llglii. zit i1 s|.1.'lt'illg l|.'Ul t-ltt'1.-e1.lilll=; 1'1-cl... The lliutiiFit'nt-itlil filtrttlr ltlt this etltitlititlll is 1.1].
REIIIFGIIGEII collclirrz nillnu
I11 :1r\n:1r1l1-111csr11'iii1 .~\C'I SPF. 12.5.1. I:]1c111i11iuu11|1 :-1lluw-
1-3'?
Ffgurl 1.15 Cmaflwflunr I:-1' Ha-Wurwmunr
:1i1]n \':1|11n F|'1r H11": :1|:t1111] 1'lrew~l11]111l-mlt. I-r1|1g1|l Lu. ie-1
i.r1.-
rheoreiical GLIIOH point lur 2 hats \\|
34.1
If 4 bar: Iully :11 :1 5 =1: 1;|
_ flu2 ——~.\\|I
| maximum
r|'|0|'rmnt-
'3 Ii in
mumanl - M,
|
Example 1.22
f 2-11¢. s
.*71.H1il1I1|et.ilr‘1t. t.l1r_e rni111i_'|1c11c] |:~r_111|".rntr_- I11;-11111 i'r1|' I-11:. 1.2[J i:-1
/*1-N119
1'1:il1fu1'|:I:1l vrilll l1uu]-curl I1-11111. DL‘il.‘l'll1i]lL‘ wl1L'L|1I.'r l-hi:
cim-'c!]c1p|11:!|1i l1~11gli1 mu-\'i1i1rv:1 fur the 11111111121] imrei is :'
&
I
|
rpquirnql extanslon
1, - em -i i~
$r.rIr.1fmr1-
.;-0'
131111111111‘ t-I11: iIlFll'.\i |LlI!I'lllillF|i-i.‘1I.l t]11:di.s1:\1111t-i11||-1111:; rmi uf
1-1211], .7 :-1,
tlm |1c!a111 1111:] the f11'|‘1-‘HI prm-'i1'lnrl is iv:=.~'1 Th:-111 2.5 in. the
I
111ur.|]l'l1;'111iu11 l'a1r;'1ur is LU 11ml l-its must hr." ]111u1'i1lI;'d u1.'I.'r H11‘ full 1]1:\'1:]|:1p111c:11t- 1c:11gt11 at 11 111:-1:ci11111|11 :1|1a1:'i11g of
I11 1uiciiLiuu In 1111* 11ix.w1.' rr_-q11ir1:|111:11t>.;. AC1 54.11:. I2. 111.5
1'L‘(]11i1'1.‘ti 111111-um: u[ 1111* Eullu-wing 1.‘U]1IZ]ii-i.Ull:i be 11111-isfiul
.1= = 3111,
at the |1i1j."sic:al cniinff [1-ni11l.
= [3][l ill]
= 3 in
1'
T1111 fs11:'tt1r1‘1l 1-ihrnr iurcrc at L111! c11t-uff puint. ciurs uui-
c-xnnml 1.11m-tliirrls 11F rim si1n:=.|' 1-=-1|1:1r:it._\-'. gin I.-"H. T1111 01-cw-.~1.*1 1'r!i|1fi11'1‘11'1111*11t. F11.rTn1' :11'ri\'1'-:1 in Ex. ].‘2[] i:-1
I
.\1u"l|'|i1i:_'111al
:1t.i|'n_1|1:=1
with
11
111i11i111|_||r1
111-11111 (if
GDi1,.-g."f,,, 1111- |.11'r,~vi<|1=~(l =1|
E_.,. = OBI
fur :1 1lL-1le1|1I;'L' ui' (1.?-511 11! 11 11111xi|111111| spricilig uf
All ¢_11|1¢_*1' 11'|=?n'|ifi1.‘:11i<_'|11 f-_1rrLr_:|-11 11111 nquzil to 1111i1_._1'. T111.‘ l‘(!II]lIiIl'l?1!] cim-'c!]<1p111u|1t luligth i5 ,1:;i1':!11 by AC1 3111:. 12.5.1 R-111-Ii. S1111. 12.-"1.1.? as
rI_.~'H;'i,,. I
Fur 11:1. 1] 11.1115 :111c| .\111111l|nr, the m11ti1111i11g min-
|'1.|11'1H'|1(-lll- 111-m-1:11->1 1'-'.'i('1~ 1111- fluxurzil ¢1'1p11('_il__\' r1.1q11ir1:1l. 111111 L111: f111:'lL11'1:1l slwnr furcc 1-1t H11: 1'I.1t(1[f
1.11 = E11-31.1
p<1i11i ricimi nut 1r'x|:!t!utl t|1111er-it1111't-E121 uf t-hr‘ :1'hr'11.r
-
: (_:1.111_1[1211n
||>l'
11,1111,
91 ‘GT
Exzunple 1 .23
{_:1.s111(12m1 %)[1 111111.11] £1.11] ."':11mu 11'
cnpiwit-5'. r.'1‘l-",,.
111*
= 2|} i11
at 2=l i11 "I'l11~ rlrwnln-]1111r111t lr!11|;r.i1 prrivirlwl is 1-1:-11i:-ii.r1rr£c1r];_
Ourtallment of Beinlorcemant ACI Sec. l2.1U.3 amrl 5131:. l'2.1El.4 1-|111cit'}' H1211 1'r:i11IiJ11111l'|'|<*|'|l. :i]'|11|i II1>{l.II!|1r.l £1 I.ii=<[.iil|{11- I;-Cvynlliri Lilli! E111-|.1l‘II'lir;'i'1l [rill-
Tl1r.- .~
J-5rI1.. '1"t1|t: fa1:t.r1rr:rl sl'|<.~m iialw is |1'=*=:i 1||=111 two-tl1i|'|;l.1@t||+:1 >:~]|1:11r cz1p111:il-1." 1.1-H111: s1_11:l.iu1| 1:\'1:r_1'wl11:1'L' 11|u11g U10 spnu.
D1:t1:1'|11i111: Llic 11i1-1t11111_'L' from 111i1h-1111111 111 whi1'h t-wu uf 1111* 11:1. 1] |111111 1111-15' he h‘!l'Ii1i1‘|J'|.li'ti. .F1'11.|'11.!.i11:1
c1l'i'p1.1i|1L nut. less than H11: clTL'1'tiw 1l1:]1th1.1ft.11u 111c111l11:1' c1r1w1'elw- l:i111i!.~1 |:]1s' I11-11' rlin111nI:nr 11ml 1111.11-111111111111-1| Imp.-'n-1111 the 511.:-int all wl|i1‘-I1 it is f1|ll_1' 1-"t11:s~'L!1l 1'1ul |¢.'1>'~i H1111] I-I11.‘ 1i1"1'c!]c1[1|11c!11i- |t'|1gt-I1. This is i|iu:1tr11tu1 i11 Fig. 1.19. 11-111-1\1=t|1nfn111'11n. E} 'lmr.~1 are :1.~e"-111111111] 111 l>nfi1llg.' 1-1t.1c!.~1-1n:l
l~'1\om AC] S110. 12.1113 uucl Soc. 1210.4. the [1t1_\=.-iicul ur111=_|fl' ]1<.|im 111111 111- l¢:w.'-aw;-|.I 11 t11il1i]'1'|l.ll11 :1i:sl.1'|1u;:|:1 i'r|:1|11
at l-|1L' 11-|1l-L'r u-1' H11; :-.-‘imply.’ :illp|Jur111i i1r.'i1t11_ Timu-
I 12111 -:11; i11= [12'1|j1.121-: in'1+:u1 in
11.~q||i11.-111I.'11ls are 11ul- 1|1.1r.'ca~'|11"_1' at 1-111]1|1<.|1'L~1 uI simpll: 1-;p1-111:1 :11" at H111 frat! ands :1Fc!1111Li]:!v01's.
111id:1p1u1 giwli l1_1' H11: ]z11'g1::il; u[
= iii} i11
PPI
l vru1ur.|1|1l2|1anl.1:nn
Cuncer -1
1-38 I
ITRUGTIIIIIL E111:|||1E£1I|lI121 IIEFE
11+ 311 111 = 10 i|1 + 311111
IIIIJIL
1"1lt1'r11s1ti1.-'r'l].'. 111 11 1111111111! 511p[)U1'L .'11['.'l S-H". 12.11.11 511-1'~c'i111':=1 1.11:-11. I110 r1'i||1'1'11'::n111n11T 111113: 1111111111:-11.r! i|1 1-1
= 52111 I‘
REICE
1-'.1=111
1,.-= 5-5111.
Example 1.24
=1-3!]I|[l.l'3B1i1'|I| = ['12 in
111:1-<1111|¢_' 111111 1111.‘ 1'¢.'i||l'1_1-11111.1 1'-u11r.'11_'l1_- 1_11_-11111 fur E11. 1.2-‘.1. 1'-'11i1:'11 :~'11uw|:1 in Fig l.l‘J. 1111511 l'111'1u1101l 011:1 rL'1u'l-iuu
'|.',11v='1'1|-1]
111' II-11 kipei and 111111 t111r 11911111 11111111111 iutu ('1111c1'111.r' gir-
riii-1:-1 :11 1_':u':11 1_'111|. l1‘11_'tr1|'111i111' 11.-'11r1r111_'1' 1111' r1.1'r1 110- SJ I1.-11:-1
Duvnlopment ul Positive lilument
111 l.111'1111]1]11.1rl 11111111131" ll1I.' l'L'l|_Ll1.l'l.'IlI|]I.'1l1-11 l'I.11' 1ur.'1|1 111111111.
Reinforcement 511111111111 'l'I_1 11111111‘ 1'u-1' 1';1l'iuli1.:1ll-.-' 111 1111' 11].1p1i<'1=1 11111111:-1. .'\(_'1
51:11:. 12.11.l r1*q11i1':'11 11 111i11i11111111 111' 111111-thin] 111' t-hr ]11:111iTi1'1' 11r1i11E1'1r1:r1111:-111 i|| :1 :1i111|1]}.' e111|1|1m'r.n1'1 111-r1111 111'
'l']11' 1"lr11.'0|11]11111'||t. l1'||g1l| 1111' 111-r'. 11:1. 11 11:-11's W11:-1 1.511-‘r'.11 in E-.\;. 1.23 11:1
1'_111r1-1'r1|||'1|1 1111' 111111 |11'_x-1i1i\.'1_- 1'1_':i1|f11r1_:r111'|1_-111 111 .11 r_-1'_1|11i1'||_1-r1-1|:-1
11011111 lu 1:':clL'111:1 nut luss t112u1 5 in 11111.1 1111' .\:1|ppurI:. T111:-1
1,|'= 5-511;.
i:-1 511111.111 i11 Fig. 1.211.
= [12 ill.
Flgmi 1.20 P0511‘-M1 I-1'1:H'r-115-1'11 Ra-11-furcsmmr T111! 11c1111i1111l 11111111111] 1-;tr1!11gl:]1 111 1111- 111111111111 is p;i1.'1'u 11]." P1121 .‘H_'1'_-(_:. |U.2 11:-1
_..1'_,i.._ | A‘
5- 111.3341,
in’
5: 11254,.
Fr CI.33A_I
.1-1 n — 4-1,; v 11('1 - i—]'5"]"'i"'-“ blrtflli
-
— 1:1 111'-’1(1s11 %)1;111mj1
I
I
.
,.,fl.1., "'1'-1
and qirdaf
,,‘-fim
'
"
"-1
'
inierlor column
Bfld Gfllumfl
Tu 1'11-1111'1' 111111 111]I.>'\I.'111.1lr.'1.1<.111¢1 :slr1.':>.'w'I.=~' 11111-1101 I.'11111.~1'1l1.~1l. AC1 S1315. 12.11.11 1'1:q11ir1'1i 11 1111r diz1111:'t1'1' H1 1111' t'huear'11 :-1111111 that it:-1 111'1'1'1'|11|11111'11t. |1'11,L{T||. in 1111' 1:11:-1n 111' :1 111111111 l'l'11l11il1g 11111.1 11 girt1L'1'. 1:-.~ gi\'1'1| 11_1'
1.. 5.
11' '
111.r111]|j21n"'1(1i|1 k_L1")'
.}(
I11‘ 1 - -------------?-----f-
{12111'|11ni11'1(s ' '
in“
= 163-1 i|1-1111111
F111 .'<1 1111:1111 1'1":-11111111; 1111.11 11 1:1'111r:1'c!t1! 1.{ir111"r. I110 r1]:1|11"11-
]11'i11T1' f=1r:rc1|'11 |';i1'1'-11 113' AC1 Bren. 12.11.11 111'r1
.
- 1,.
1101 12-5
'\
h
M" is 1:111: 1111111i1111] sirr-11gt11 11111111111111; all 1'r'i11111n:1!1111:11t 11-1 :<[.rr_111.-1011 l_1'1T||1'1:-q11*.<7:i11r1r| _vi1'1l1'l 11111111-1. IV, 11",, is tl1r_1 1':'1-r_:1_1'_1-|'r11l 5111-111‘ l'1.11'I.'1' 111- I111: .~:1.~cl-11.111. 111111 1,, is 1-111' 1'111|11.'1111|1.'|1l
_ 113-S-1 i|1-1-111111
1--',, +1“ _
:1n 1:111:-i
.
+6 m
= 62.1 111
.> 1.1
1I;'11;;l11 111.'].'u1111l 1111' c1_"111L'r 111' 1111: >.=uppu1'l.
F111‘ 1111' 1::-1:-11' 111' :1 11011111 1'1'111|1i11|2; i11111 11 111111111111. .-“'11 -‘_iI.'r.'- 1'1 12-1 I
1'1.'1'|llil'I."-1 11 |1i’1l' 11111lI1I'Il.'1' lu 1|-1' 1Ir111.m1."t1 :~'l.lIIr11
Lu11:11] 11u1u11 l'L‘{|_ll1l'L'l!1L'1]'1:i 1111' S<'|.1II1>.i['ll'I.1._
111111 its 111:'1'c11u|11111_'11i 11_'11g_',U1 is gi1'1.'|1 113' L1
1.3
1,,
At. 11 |11'1i1u: 1'1-1' i11f1c!1:ti1111, 1'~‘|. AC1 51111". 12.11.11 rnq11i11'.~1 :1
1.1111" 1.l1i|||u.'11.'r lu |>1' L'111.1H1't1 11111.11 111111 11:1 1.lL'1'1'1r_1]111|1'||l 1c:11gt11 i:-1 gi'.'1'11 11)"
1,; 51
.11 ., . . I‘ + 111.~111|11111111 r1-1' r1 111' 12111,
Davulupmunt 0|‘ llngaflwa Ilolnant
Reinforcement Tu 11111111‘ 11.11" \'111"iz1l 11.111 in l-|1I.' 1151|11i1.'1.1 11111111. ."1(_1l S1112. 12.12 1'0r||1i1'r'.'i 1-1 111'111i11111u1 111 1.11111‘-thirtl 111' t]11.' 11c'g11tivre 1'1"-11|1':1|'r:r!111n11t :11 :1 .~1L1|1]1c1r1 1.11111-:tr!111'1 1111.111 1.1111 11-111111 111' i||111'11"l11_111 ||1_11 111221 1111111 1111' 1'111'L'[i'.'l' 1l1.'pl]| 111' 1111:
111-11111. 12 I!i1111's 1111' 11111‘ 11iz1111I.'tL'1'. 1.11‘ 1.1111'-:-=i111I.~1_'11t11 111' 11111 1!lr':-11' :-1[11111. T1111-i is 111111-wu i11 Fig. 1.21.
IIIFGIIGEIII cflllcnrri uiilnnl
1-39
Splines of Bars In Tension
Flynn: 1.21 Hagar.-we hfume.':-.'He.\n~.forcen1enr
1.:-1p :'-i|]11t!|I!!i- {hr 1um-; in I.-l'!ll.H1III|ll, in aH'ur(1n1:::n with AC1
Sun". 12.14. luny nu! I:-u ll-H111 l_‘11||1.'l' iur 1>eu‘:s 1i:1"gL'1' 1-1li'l1l nu. 11 u-1' 1'u-1' 1.||||u.ll~_-1.1 1I\iIlH- 1|| f1n~x1u"a1 IIllL'Il]1.lk'Il?\'. 1111: 11'u11:i\.'c1'ei:: :-Tamzrillg 111251-WL‘i!‘11 lnp !i]II11IZ!II!1-.'~ shall not crxrvul
-12¢, .== % .== 0' "i'| 3'3
= u.ssa;~\_
Ar-§__\
mire-1'|t'1|| 01' Tlw I:-1|) lm1p;I.h, ur (1 in. '\\"iT||in :1 1111111110.
i11<1i\'i:1uu] 1.m1' h'|II11lL‘L'5 rihull uul U'|'!.'I|'1il]}. and l-hu lup ]:!|:|gLh fur r'm:11 1mr mu:-;t bu i|1r1'0a:-:11 1|_'»' 21151 fur fl
T|lI'f!fi—|Nll‘ lmnclle mu] 33';-'{= 1h|':1f:_n\r-lmr |rlllI.|'|1\‘:. I
1,,
T11r_-lcuglll u1'n lap :spliu_- :|m§_~' uul hl: ll.-ass llmu 12 in nu-1' luss Hum 1110 VH1ll1.“:i giwli |J_\' AC1 Sec. 12.15. whit]: nu:
clear span
l‘1i‘l1'.i.‘i .-'1 splicr 1L'|1gl]1= 1.I]1,,cleues 13 :=.]11icr: ]|.'ngt11— 1.31,,-
Exanrple 1.25 Thu r:!infm'rc!d <:m1~:!re!t:! m111i1111c:l|:i hm-1111 :-c11m\:n in the
A r.:|=\:-¢ 9|. :<].1li{x~ r|m_',~' hr! 11.~a.'=¢l only.’ “'11:-11 I111‘: r0infurr.-L--
fn1lnwin|:_ i11u51r.n|:irm, with an 0F1'nr:ti\'c! rlnpth 01' 115 in. i.~i
111t'111 Hl'L'l‘| pru-\'i-[11:11 is H1- lumil l'W1Il‘-L‘ 11u|1 l'L'l|llil'\1‘(1 mill
11‘i|:fi.1l'l;111 with gl"a:|.1|1' {111 lmrs 211111 has II (1:11-(1|'('1¢ u|)11'|])11.'s-
wlmn. in uziditirm. mar. umrv tlum nun-lmlf uf thr Lnml TE'11‘lF1'r1'l'?i"|ll-|"ll|1 is 511-lirvrl witlmin tlm 1:1]: lullgth. UTl1m'1'-‘inn. us :<1|I.>wlL in Tz1h1|.'- 1.31 an ("lam 13 LI.'||:si<.|11 |il[ifi[11.1l.N.! is rtrqllimcl.
H1\'[‘ :it.r:'u,g111 u1'l1i11lH] l|1l'||"i112. D:'r.I:!rm'|m' 1111* ll]1[L1[[lLl[[l
1nnp;Tl1, 2'. at wlnilrrh 1.1111 11:-1|'5 ilulimtnl ||m_\' tm'mi1|atc!. EflDi|‘|
1|:-|
Tabi! 1.5 Tension Lap S,u|';::es
2-No. a _\\
1w|xi|1\I|1|| |1r'rr'+.-1|.uu.:1~ Hf .-1, 1-qmliurrl witl'|in L-1|: 1c~n|.1tl|
" .-l . "1 I i’ W“ 1‘ E1 .~1._._ Il'L'I:]ll1t'1‘IL1.
2 01' nut-H‘ lmiei Hum 2
:,,—2-mum
|
an
luu
1.'l|l.-H .-\ rlmiei B
1'11:-*4 [1 cln.-<- I3
In rlnmrnninlng thn 1':-lvwuat :1e".'nIr:|m:c:||1 ]nngL11, all u[:pli1'u1=11.' JllUl|111(.‘l'5 illl‘ ll:sr.'t1 witll l]1r.' l::<»;‘|_'].|1iu11 u-1' 1.11111.
Iur ['X{\l.‘:i.'i rci11furu.~11u:|1t. Thv-r11"nr1<:|J1111r11t lcugt-ll. 1,1. is ri\"T¢\1'|nl|mr| 11}; using him \':1.1‘lIl|Z':i- fur tt1\'!F||' :-:|m-r*.i|||1, r:__. i1u|i<'=1lo:1 in }'i|:5. 1.22 mul Fig. 1.23.
Saint:-rm T110 L'utuF1'pu1nt u1'l11c1Jnr:i lllH_\' 1H."1LPL'1lU."I1 n |ni11i11|um dieatauu: lnrgruml the puint 01 1u1'1L:c:tiu|| giwrl by .-'LC'I 51:111. 12.12 as tlm grmtnr n-1'
Ffgurl 1.22 1"er-R-'4: tn‘ cf, Iur Lap S1;-vI'I'c:['::»' h-mam
cuiumn
'1-1'13.-."';|
ll ,1,“ 112111 13b |u
_ 111.5 in (1 = 1|] in
L: {'24 M12 my Hi
I6
- 18 in
|gm1'I11==]
T111: mi11i||u1:n nlluwnlnlc la-nglh fur J1 L1 gin-|: h):
I _ 5 n. -+ 1.5 ft -: L1
'
"'
L?-1
1.1.1
3
PPI
l v|u|uv.ppl2|:|anl.:nn
Concr:-He
1-4Q
$1'RuI.‘:1un1u. Euulueznluu IlEFEREll¢E |1|11|1un|.
Fiylnrl 1.23 1'51»; 1:.\' 1:, 1'1 S1'a11'.1s a-'10’ l11"a-I-Q; nun-slag gered
cs
1=Exalnple 1.26
51a-ggered
5* Exan1|1|11.=.- 1.27
A :r1r111Fn1'1'1\11 1'1>111'r1!11r 111111111 i:-1 1'1.~i11E'111'111\11 with 19:11 1111. 1'1
gmrlrv [111 11.111’:-1 111111 1111.11 11 1111111-|'ntn c:c111111r1!1=.~1i1.'r' 1111'1~11g111
T11t' r1'111fu1'c:'t1 t'u111'r1'11r1'1111111:1111 1111111111 111 1111' 111111J1.\'i11g i1l|1s11'ati1"111 is 1'1"-i11F1"1rr'r111 with _1.fr111ir: 1,1-11 11.'1r.~: 1.11111 111111 F1111}-'
1.11 311111] 1|.11',1"111"'. B11111 1.1a'11‘:\ u1'1j' 11111 :¢|.r|i1"I.'11 all 1111' Hi'1t1|1.'
r.-l.|u1.~'L'1.1 111111 111:.'~.- 21 u.111(':|'1.'1L' L'Ulll[iIl'l.‘d!11.'l‘ 11111.-111-41.11 01'
1111'nti1.111. 111111 L111: 111:\'1:11Jp|n1'11t l1'11|;tl1 1:11 1111' 1111. S 111-mi 111.113." 1:-1* 111111111 as F1»1lr1_1,. D|'!|1f!I|'1‘|11ll1"! 1111'! 1‘1N'|1‘l1l‘1'e1'1 splirrn 1L'11gl11.
41111111 111111113. Thr 1:-1111111111 is 1-=11h_'1:'c't1'11 11.1 1:11111prr's11i1=1= sT11r:~1=1 r111|_','. l]1*T1=-1'|11i|11= T1111 1'1'1r|111111'11 lap Ei]‘1111':1'! 1111' 1.1111 nu. S 11111.1 111.1 11 1111111.
12m :1.-12in
51111111-1111 T112 1lL'1=1'11.1p1111.'11l l1.'11|:,L1| 1:1 1.',i1.'1.'|1 111-1
ip——_
III ' "“°"“ I
1.1 = 511111. = 1-5101111 111] = -3|] 111 1'1nr:1-11150 1111-111 1111111 arr! s]11i1'1'11 at 1111* 1-1111110 11'>r::-1111111, r1
No.3-1§12in 0-.c.
‘
c'1a1.<> 13 :s1:1iL'u is 111.|1|i1"1.~|.l 111111 1111' 111111110 1L'11g[11 is
1, = 1.3!.-,1 =(l.3_|-{.3-111111 = I35 i|1 8|llI1:-as u'I Bars In -Complusslnn [11 um;-1.>1'1.l11111>1:: \'-'i1|1 .-‘H31 S-1-1*. ll‘. 113.1. 1111- 11'-11111.11 1.>f :1 1111: :='[1111~L* 11.11" 1111111 in L'1.11|1[1r1'1es11.111 5111111 11111 111: 11_'.~.;-1 t-112111 112 111 111111 i:-1 1.,ri1.'r!!1 11_\'
1, = 11.111111.’-1,151-1'1,
_'* 1|-No. El
[ [:1 5 |11'|.1'||'11| l1.i_-"11.“]
1. = [l1.11111l51_|'___ - 211111
|f\_ ;-4111.111:-11 111r_,-'...-'|
11111 i111'1'1'-a.'-11' in 1.111". 1.1111 11'~11g111 111' I13'.3'1= is 1'1'~q||11'_r11'l 111111‘-11 1111: 111.1111J'1~1.'1u :~11'1J'1|1_=_£l.|| 1:1 11,-:15 1.111111 31101] l1.1-l',."it1":- '11.'111't1 1111r.\= uf c11Ff1'rc111 1-11:11:; 11r1* I111: splicird. AC1 5111:. 12.11.12 s|1»1'11~il'i11_'1 111111 1|11'- 1:111 ]n|1g|;11 5111111 1111 1111' lnrg-1"-1' -rn° 11111.
1-"1|11ir11~ lnngtli 111 1111- 11111:-1|l1'1|' I1».-11' 111' 1111' 1'l1w1~|1'1|11111'-111 1I;'11gl11 1.11 l||I.' 1111'1;I.'r 11111‘.
I11 111:c1.1rc1z111c1' 1111111 .1‘kC-I SL'|.'. l'.?.lT.'.?. 1111: lL'1|,1.',111.-1 1111' 1111111111111-1 111113.’ ho 1111111111211 by 1751 w11.1~11 tire:-1 1<1r1~ p1'1>\'11101l
.';1-'r1.I't.'.U1"I.Ii'
T1111 11111::-111p111r~11L 1c111|:gL11 111' 1a 11:1. 11 1111r is. gi'1.'1~11 115' AC1 S1.-1:1. 12.3.2 111111 Sect-. 12.3.3 11:1
I _11.11'.1.1.,,ru . iv?
wiTl1 1111 r:i11.1(-.t1\'1' 1111*.-1 1.11’ lJ.[J[l|5.'1~. 111111 11mg.-' 111- 1'01'l|.11:cn:l 11-_'1" 25% in 21 1e]1i1'1'111_\' 1'1'111f1_11'1'1.'1l 1.'u1I.1|n11. 1.‘\"h1.'n 1011:1111.:>'1r1'1a.~= 1'xt1.'v:'111111; 11.-5,1‘. ut'1'111'1; 111 11 11111111111. 11 {'1HRi 13 11~|1s1i1'1|1 111|1 11111111‘ 1'.'1n 1:111 1151111. A 1'111_'i.~'. .51. 11111:-111111 111p 5111111‘ in 1'1:11'<|1|1111' [:11'Ln'i111.'1.l 111111 1111' lL'11:-.1i11.' :~.~11'L'_e=:s l.|LJl1'~' 11111 r'.\:1‘1.11r1:1 [.'I..'1f_,,. 11111 111011: 1;|1s111 11111:-111111‘ 111' 1111: 1111r1-.= 5111'
1-1|1l1r11'\r| :11 T110 1111111-r'. I1-112111.51->11. 111111 :I11I"l'll1-‘111’! .~1|11i1:1111 11111 1:51.-il1.§[=f,l.‘l'L'l.1. 1.1-3' -1": u[11I;'1'w1:v.'. 21 L'1a1:.~'>1 13 I1I.'11:>'1-:.I11 111]) -I~I])11('L‘ i:-'
1'1x111i1'1~11.
{1'1.112](1.1:1s 11.1 (1311111111 1111) =
1]]-
1|
= 21.-1 in
I1-111[111
lll."‘
nslurunczu collcnsrz nsuluu -1-." Tu qlu-1]if1.' fur t-hr‘ l1'§-1r1:!1|11ct-iu11 in lap splint! lr'|1|:_tl1 nf
I,
I:-ngfll ui 14111111 in r.liIc~1'tirJ11 111111 :11u111<'1|1.~:
tlm ma. 8 i111|'5, ACI SH‘. l2.l r.2.-1 |'nq||irm¢ tlm twn .-1r|1|:'-1
.
= 0.22 11;-',-'11
tl 111' 111
111112 being 1iII!(1!t‘l:|'|it|!!1'i. 11|.1ea:+11|~:-1| 1:1'-11t1:1'-
uf t.l1c- 110- 3 t.i(:=1 [.11 ]1:1'm :1 111i||i1n11111 nffk>ct.i1'e 11r 11111 of
i:1‘ = 0.1111151 = 1u.u01s_1[12mj1[12
1-41
In-112111111"11|':1||]1p-c1|'l:1 -|i_|
iI.!l|5:_1]|. Iii :1]:|iu| |l1lJl:i\'l'l'hl' In I1. 11:11:11.-11111-1]
H“
4.'lI‘l1ll."I'-|3f>-4.'lI‘I]Il.‘T vi-=I1]1[1<1r111 mm] iel<'t11r1'rl _-'t1|rirr r|1|||r|r'r1T
fl ut i.l|
Ft-Rim
1;"
|'m'l1|r1-:|. I-mul ||1:|' ||1|i| 11.11-:1
ici.|1e\_,"f13
1-
1-l1nrI:1>1 uv1:r:1ll di1110|11ii111| <1i'1'
i11
||;1r1 u-ii 1'r|m.~1 :i4‘(T|iH.1l.
Twu .11r111:i nf tlw 1111. 3 time prcwicln an 1-11111-1 of A
'
y
iI.11||;|-1'u'.'1!l'::li 1ii!1|1!l|ni|1t| ul' r1-1:l11|1|.;11l.111-
i|:|
[1-rlrt rri 1.'rI.Iw= -=1.‘r.'tiu11
. .
—' = (1.22 1:13,-'11 H
Symbols r|_,-
Hmm, Tho 1?"}E n'r|||ct.ir1-1| applies.
rs1H|| Hf II-|"x1:|r|1| :~1'iFEl|:':u4 11" |1|'.=||1| :-2'1-Him in
—
H:-.1411r1\| -=tiii|11.*=-M11‘-.1 shill wiiillu 11nu111|r'|l
The I."ump|'1-m=iu|1 lap -:=.p]icr.~ II.-ng,Ll| ul' Lhu nu-. B I11111< is given 111' AC] S1111. l2.1l1i.1 and Sun. 12.17.11.-1 1-1:-1
lat:-1'11ll1.' I11.’ c1~1111:'r liur-:1 uE11clj11cc-|1t [NllIl']H 1{il'1:|1_','] ||||.1';1|.ti| r-.i||¢: 111' li:1|~
hr-11r|1— E.-|J1,_." E,_J.
1.. _ r1.u¢1115furM_[1.s'.1j| = [(I.Ul](]5:|(|3[II.l](][) %)[1.CI i|1_i[{l.S3:| = 1'5 in
Igc>1"1:n1s|
n_,
q'||||:~ar;111l; ||.-z-1] [-::1_'n1||]1|1l:- 1"].
—
r11-I
n_1i1|| ||in1'I.i-:1-1| (1-|' 1|
—
I'lj'_:-
1|‘: in ||i.||.'1:\‘.i-::|| u-ii 1!-_.
—
;I_.
mliu 11-i'l11-I11; eliiiu Lu H|l¢.Il'i .~1i|.|.11 I.>f1:u|l|1||.l1
-
;i_.
1'miu u-I"tun-.iu1111lhtifi'1u!:1-1 uf»:e1'|gie I1-1::-1111
—
1-a1:|;'Iju|1 [41 fl1::111r:1l.-1|iIIm-511 01-11.-1l:1'i1
I:- 21.4 in
wixifll |\:||1:1i l|| :<]11|.r| |r!|1g1]1 HF 111-11111.
cc-11101-tn»-cc|1:|:r c1l'1~=11]1pcm11 = L-.', 1,11-'_-"
The |"1'q11i11:d 12151 s|1]i1'I.' lwsuglll is 1'5 in.
1'5. J.
B. TWO-HIV SL1!-B SYSTEMS
Dirac: Design Ilflhnd
Nnmemrlat um
)"1(_'.| Sec. 13.6.1 ].\<:1'111ils tiu: <]i1'|.'L't 1l|.':si[=;11 |:|1L'l11ut| lu bu
(1,,
|11"1'i1111':c*r ufcritivul 1-1'c*tio|1
in
r|
sin‘ 1::-I'111'1“T<'111|.:11|aI or 1't|11i\'11||:-111
i|1
rL‘¢'u111r.:11ln1' ¢'olu11u1. 1:-11|1iu|.|. 01' |1m|."l»;1'i
111-wed p1'm'ici1!d 1111* fnllcawillg 1:muliti¢1111-1 taxi.-11.
I A mi||i1111|n1 of t_l111-=:- 1;-unli|1|.1ou.~1 111.1111: 1.-1
l:|.||.":u-¢|Im.'11| in tho I:|i.l.1mI'liul|. u-1' flu: .-1|'m11 Eur
1]i1"1:1:tiul1.
wili-;'h |n||1||nm1i Elrr! |mi11|.; rl1‘1|1n1|i111‘r| 1-3
I
si:-11~ c:-|'1-1-1-|:111|.||11I:11 :1-r u||11iv:1|:!l|l
mc't1|11;:11|nr <'ulu1n11. r41|.1iuI.l. or lmnur-I-:11 |:11f-:11-alllflul 1ra1|.-\.'1:1':m tu H10 qlirur-tiu11 ul'
P11111:l:i 1111* 1'r\t't.:~1ng_'|1l11r with 1111 11:-ap1~|:'L rs1l;i»:1 11:11:-1ccm<'li|1g 2.
I 5':'11m:-es-.1i\-'-:1 11111111 lc11g1.luu:l0 not. Iiilfer hy 111urr.1 M11111
tim :1p1:||1 Tm’ wiiirii :|r|-::-|1u*1|.|:\.' 1111' iwilllg
0110-l-llird of L111: luugur >:~]m11.
r|<'r.1".|'|r|i||1.'ri C-'
|':|'||:1.~1-:1|-c:|i-:m:||. 1-m1:1l1|.n1 In 111-l'im~ lc:-n¢i||:|;1|
p1'r.>]11"|1i|:1-1 [EH — L1.l'.51§.1'_-"_I1'II.1"'g,I)_.'2i1 ir_|r T- 111' L-m:1i<1|15. it i.-= |1c-1'|1|ittm] In I»:|"\'Jli1IllH‘I'l i:-_'1' rii\'irli|1g 1111‘ :\n|'li.11r| inn:
1
Culululls arr: nut ul'[.-11'! by 111011: 1111111 1(]'§F'i: u[ l-lu: 1-1111111.
I
[.11mli11g |Iffil12ii!iT!i nf 1111iFr1r|111_v -rlL*;T1'ih1m~:l g1'11\'it.y
|=;11'11.|>< with 1110 :s1:=rvi1:1:= livc: lcmd lu_rl- (mu;-ec1i|1g Lw-i|:=1:=
1u.-11111'11t1- 1'1-c't11|1|;11|nr|1111't.~: and 11111111115111;
1-hi: >1*r\.'i1:1: dczul luml.
.|':.3, L
tlw 1.1111101; oi [?l'1.11' c-11:-h 11:-111. 111011111115 of 1:11-111ti1'it_1' oi 11111111 4:-1111:1011‘
ll.1f_."i1|'i
E, _
||1ur.lu]u-1 ut" 1~]nsti<-it_'r ui slnh 1'u1u'r1~tc-
l|.If_."i1|'i
I1.
1111111111111 of i11I.‘rfi11 ;1im|_|1 1.-1_'11t|'<>ir|11l |1.1:i~= Hi
in"
|!,l'1J9i1i sec-tiu11 uf 11011111 I,
11101110111 11i' i11|:~rtin 11111.1-1.11 1w.'11t11>i1l1\l axis: of
lutlgfll uf 1:14:11: eip.||.|'| in ||i:rt~¢:[iul'1 1.]|.:|.|;
For i1-eram 1;|1pp0rtc1(l I-iilibfi. 1-111: 1":-11i<1 of the E:-1111111 stiff-
11o:i.-1&'1a in Tum prrl'[1m1¢|ic'11'|111' 1"li1'(1c-Ti11|1:-",1, 11_qIi::_."1"1-Hliji. i:-1
l1¢.~m'1t+1:=|| 1.1.2 aml 51] w|1e11_- the 1'|11.1r11-11111.11 1:»I' i|1<.~1't.ia1 1:1|' lllc Lq11iv11Ir_'|1l i1I.'11111 11111:] !i~]EliJ £l.l'L' 1141.-11:11 un tl1I.'s1:1_'liu|ls
in‘
|.1r1J:|.-1 1-1u|.‘1§ul:| I.>i' n]1il:1= |'11',|'12 liIu1'_-1 wiihli. |1f: 1ir!Fi11H| in :-'_*.'r|1|:>t1|:< I‘: 11:11] ff, in
I
ft ur in
:-:l111w|:1 in Fig. 1.2--1..
T111: slab is <]i-.'i:lul iutu dc!sig11 strip:-1, 11:1 1-i|1t1'-v11 in Fig. 1.2.]. with :1 c:n|||m|1 .~1r.ri]1 mm-11
:|1rr1|1<'|||:\ am! |ITIl'illfl_ -:]1!|1!|'|11i||mi,
[i.25I| ur D2513; un 1::1t'|1 .
:11|:'1u-=|1rc1cl fan‘-to-|h:'I:\ 11f
111i1I1ll1: sl-rip 1.1.1111-'is1:~' uf 1111: r1-11111i|1dr.'1' uf the .~'|a||.1 1111111171211 1:!t1lum|1 sitripei.
nllpp-ul'|:»= l'1 — 1'| I= lIll.Ei5l'|
PPI
l vruur.||pl!panl.:on
Eluncr -1 2
1-42
ITRUIFTUIIIL E1|1:|||1££1I|lI121 II
EFEREICE
IIIIJIL
F1g|.r1'-11 1.24 Eq1.11i.1a.\an.'Ba»am and 5'ab £h'r1:\s-1151011.;
-1'
1"
U
’
I
U
1:
"1 I
:1:
1'
1'
I1
I" "I
s 1 -1"
"ff
Dqslgn for Flalura
Figure 1.26 1'Jem1'1's 01' Us-s-.=g11 5‘r.r.*p.<:
T111: 1:111:11 f11c1ur1.\11 static: 1110111111111: 1.111 11 11111101 is 11'11l1'1|-
1',
F
1-1w>:411,
'1 3
11111111 111.’ AITI 51:11:. 115111.? 11s
pi?-I
| column _ mlclcl strip
.
.11.. =
strip
.1-.1?
1.101 13-41
T111: 11.11111 1'111:l1.u11:11 ||11.11111‘1|l- is 111.1-w 11i:slri1111l1.'11 in 111‘('ur-
:1
11111111" wi111 .-91'-TI S-1'1. lZ1.1i.I1- 11111.1 |111si1i1'1: 111111 111:1.111tiv1~
11111111111111-1 :11'1':111\1 11111 11111 M11111 111' 11111 111111111. 111.~111~11111111:r,
1111 1.1111 1<1_111|11_1r1 1:111:-rli1i1_1|1:-'1, 1111 .~1l11.1w1| in Fig. 1.25.
24-ftllln:
11 T
T11L'1>1.~c1i:1tri11l1U.':l 1111.11111.'111s 1111: 111.111‘ 1'111'11|1:1' s111111i'~'i1l1\11 111:11w1*1!11 1:111! 121111111111 1-11111 |:11ic111|1r strips 11.11 sp111!1fi1!c1 i11
P1(T|
13-I3-#1 1|1rr>u.1_._:|1 5011- 13-6-F 'l'|1=\1 111.1-1'li1.1l1 1.111111?
1111::11|1L'|11 111.11 11t.lri|:11|l1.'11 11:1 11 11111111111 1111111 is 11s‘-1ig11L'11 tu
_
__
____
1'1 — 24 ft III in typlcalapan
__
_.1 31I
Tabia 1.4 Pe1c1e1'1.'a_g's- D.‘s1‘r1£:|ur.bn 1:11‘ .'.n1an'ur.Nsgan'1-we 1'1-:lc1'1'1er|r 1:1 If.‘c1'1'..1'11I'I .S‘r.=.'1:|
20in >1 20in
column typlca
28110111
1';-2Bfl0in
- 11|t- - -;1E-- - -.41
11.1 pical span
1111* 1:111'r1::-11111111111111, 111111 11111111111 s1.ri11.-1. T1111 111'-1.111111-'11 111111110111 111. 1111 11111‘-1'i1'11' 111111111111 is 111.-11.1111-111.1-11-l 1.11 :1 1-11]1111||1 strip 11-1 :~'11u11.'11 111 T211111: 1.4.
1._._.*1.
-_ .1-_.- _-.1,-_ -Q1Ii} I"
1».1
11111;,-"11
11.5 l_l
1
2
| 1-
1|_r| li_>|>'1| Z 1.11
‘I1
I ‘JF‘ U‘>2?‘
1;.L1
'l']111 11:1-g:<11i'1'1~ 1111111111111. :11 1111 clxtelrinr .~111|1111"1r1 is 1'|is11'i1'1-
1111.111 iu 11 11111111111 slrip as s11u\1'11 in T1111-11* 1.-5. Example 1 .28 A 1] in 1l11r:11 F1111 pl;-11.11 1111111 I111:-1 1111111 1li111r111si11|11-"1 1>1"'1.W1'1Pll 1"I.1111l1111 1'1.'1|.l1-111 1112-1 11 111111 E5 fl 1'1-*1 H11u\1'11 111 F115. 1.2-:1.
C11l1'I.1|11t-1' t111r wi1lL11s 1.111111: 111111111111 strip 111111 t111r11|i111llr strip 1111' 1111" 11i1't11'tiu11 p111'1-111111 111 1:111: 211 11. siclc! of 111:1
11.-1111:-1.
Tabla 1.5 Parcenaage D.'srr1£1ur.1:n 1:11 Ex.‘e.r.\1J' N15-gar11-"9 f11‘or1:1e1".'I 111 1?-o.k:.1'r111 51.1.11:
1,11,
.._..11_.-'1-=11 1
11..1_..-1.r_-1.1.1
P511111 11'm1 F1'1.1-111 AC1 S111". 13.3. 1111: \\'i11L11 1111111: r."u111||111 .~:11'i1:| i:.1 1r.'..—- (].5I,.,,;,, -— [[I.51['E4 1'1]
.'1=11 I‘
11.5
1
2
mu
11111
11111
.-1,132.5
1:.
.“-r1
1.1
.-1.11 .-1.31.5
11.1.1 911
11111 .'-1'.
11111 1.5
T111: |10.\1iti\'1: 1111111111111 111. 111111:-11111111 is 11is1ri111111:11 11.1 11
1:r1|||11111 1"-1t1'ip ma s'l1111.1'11 i11 ']'1=1|1l1* 1.11.
— 12 [1 Tabla 1.6 Percxemage D.'s1‘r1'b|.1r11:1'| 1:11 R1:|51'r.'1-‘B J‘.-1‘1:11'I'.\e.'1.' to C1.11\'..'r11r.\
'I'l'11_- wi1lt.]1 1.11’ 1.111: 11111|1||1? 1111-i1: in the 111111-r.-Ti1.111 1.111111: 111111.51-1‘ 11111111 is 111... = 1...;_, — I).-51...“. = 2-1 11. — 12 11= 12 11
Sn-in
1.11.
11..-1
1
-.1
.1..1._.-'1.-11 .....1_._.-'1.:;1.r1
1111 1111
nu 1.’.
1:11 in
lurunceu collcnrrz nielnu
1-43
Figuns 1.25 M. D.~sr.'.'bur.\on Facrors
-%-
-%U
o.es.u_,|
°-35"-"0
é"
E
U
LI
,7
T-..
Cuncr:-r
oes-M,,
U.?5M|_, lbl and pancl simply supported
lal inlcriur panel any supp-url
-%o.5nM.,
T».
U
0.1::-M,
0.57-ML,
Ll
u.us-\-1,,
0.10m, | ,7
ii,
naur.-1,,
Fl‘I;rtn
11101110111 is
Edge Seem
|| :3 1.u IJ
B5
T-. |u.s5»w_._,
(fl end canal fully restrained end
Beu|u:< nl. |':=.\|u?l wlgni-.~: :-hall 11:.-=.1.~e»ig||c--_| the ]1<~1~(-.<.-|'|t.=.1_|';r.- of Table 1.? Percawraga D.\sr.r.iJ:|ur|‘0n |:||' CcIl'u.'?1r| S.'rI}e- Moments to
u.:asM,,
o.a5m, | ,7
cululnn strip mu-uwut. ns ehuwn in Tnhli: 1.T.
‘if ma!=ig11r~41 tn Iacnm
J 0.2m,
M
19} end penal beam supported all round
u,l|'3,-' 2,
E|.52MP
ldi flat plate, and panel wuthout edge beam
[cl Hal pleie, end penal wrth edge beam
Li
%
Li
0.20M, F
mean-1.,
ACI
§':i-lift:
,1-r.. =
13.6.2,
Hui!
tulai
fa!<'l.|.:-l‘L'r|
:
I--F
((1.241
(2: Fr.)[2£3.3.'i £11’
=a
Example 1.29
= -1115 E1-kip:-i
:\:~ie11l1w [lull llu: flat plnlu fluc-r fur Ex. 1.25. whirl: is
slmwn in Fig. 1.2-}. s|Lppm'ts a tntaal F:1rtn1'nl [iii-'~Tl'ii'fllH'91’i
l~'1u111M.?|S¢
]I.1i|<.| uf EUU ]bl'_-"['L‘. Till? ('u|\l1'J]|'| :e=i'|-tr in EU ill U3‘ 21] itl.
1Il]UlllL'll‘i an-rues the pnucl is
]IN.'lI."rmim: I111: Faust-uL'I.'Ll uu.um*1|l-ze in lhu L‘l.Ji|.lllI|]J .-drip and lniddlzr strip in the clirurtiun uf the lcmgarr H[JHl1.
.“n‘m _ U.E|-5."|i',.
Sr)-inflame
I [[I.35]{4l[i ft-ki|1s]
Fru-||| AC1 SI.'|.:- [3-5.2.5. (hr: :'lI.'a'Il' -‘*]m|| in H11:
_ 1-"H5 ft»ki]1>;
rn=:l_¢-, =2:»-I1-E 12$ it = 215.1115 H L‘-1' |i.|Ii-:1-1|
|Z"Hl'l.iih.fi-'llI[i.l|.'_$':
Frnm .-!|.(TI Sort. 13.6.4 and 'l'nl1]r! Hi, nrl-‘Q,-"i| =l].[J aml Hm I.1|.|-lumn -—=h'i1: |>u:sil-ivfl JllU]]lL‘lJl- ill |||i11:spi11| in .'|I...,. — U.I34IIM... = [(l.Gl')](_l-I6 [I-Ripe! = ST Fl--kipe
PPI
e vru|ur.||pl2|:|anl.:nn
1-44
$‘rRuI.‘:Iunal. Ellullleilllllu n£|=£nE||<:£ Illlllll.
P111111 AC1 Sec. 13.11.11. thtr111iilr11r' s11'i|1 ]1<1si1-ivir 1111111111111
Design for Shear
at mi1'ls|i1:i11 is The dtrsigii iiur 1-i111‘1\]'111I trululnii 1-.?11[J[JU1'l1:i 1111151 1::(1nsic1i:r
1111111 fl:-ic111'1-11 111' n11¢~w11_\' slimr anti pi111c'hi|1gr1|' r.\'.'1">—wa].' :=i|¢:z1.r. as :<11uwt1 in Fig. 1-‘ET. The 1'11.-.~;11rz1l b1|l.‘4l.I' :.‘z1[1au;"iL_v (111110 puiicl. in 11 ciiructiuii parnilcrl 1:1 11111: sirlv I3. is given 11}; AC‘-I 11.2.1.1 as
1\1'..,... — H... — .'1f,_.,_. = 1413- 1'1-l~:i[1-1 — ST 1'1-I-1111: = 59 11-]-ii|11s
'_
1.-11’. = ‘A1,:-.-111.11?-",1'f_
|1\c1 11-3|
1-"'1'-n-111 AC1 501:. 1i_i.[1.I_1 an-:| Fig. l.2['1[:-1]. the 1:11:11 1101;11-
livc |11utt1L'|11 mL'1'+.11~11~' l-I11: 11111101 is
Thu rriiicztl [IIL'1'111l(.‘101' fur 1111110111111; siiuiir is s]1cr.'i1'i1:11 iu AC1 S-H‘. 11.11.12 mi huiiig 11 r1i_s111|1t:n frrml thr! [am of
the mhiiim II!I.’|1IlF11 1:1 1111:!-111111111 the 1~1'1'nr:ti'.'n clr-1111.11. The
11-f,- = 11.11511-1\'.,
11;-|1gt.11 1.11‘ 1111:: ¢riLi1;ra'1| ]:1r.~1-i|1ut:l..1::r is gist-11 115-"
2 [11.£i5:|[=1lEi El-hips] 11,. _ (2]('r'| + c-_1] + -1r.1
_ 2111 1'1-1-:ips
From 1'11.‘-I Set". 13.5.4 111111 T211111: 1.-1. u;,1§_1_-"1| =Cl.U anti the 11111111111 strip iiirgiitiw tnmumit at an i11t1~ric1r :~1|_lp|1r_1|'t is
()|'1n11i|1gs in 1-1 |1m1re| within T1111 111111‘!-1 thc! riiirkiir-:=.~+ nfilin ]1au:|I.'| 111.1111 1111- 1.11.1140 1.11 E1 L"U1lll11[1 1’L‘11l1Ct‘ 1111- (l'1'1l11.'111 ]1c11'i11u~t0r. 111-1 1-:1u.1w11 in Fig. 1.2!].
1'-f,-,- - 11.15111. I {1].T5]lI'2T"11 1'1-1»1i|:vs] = 3113 1'1-1-tipzs
1-"ram
.-'-11:.‘-1
1Z3.G.[i-- tlm 11111111111 strip imgzitivn
1l1UI111L'I|11- at 1111 i11l1:riur su|1]1ur‘1 is
For =1 mrunr crilumii ifllffi-‘li.fil'1 less than r.!'_-"2 1‘1Tr11‘l the ncign 1.:-1 11 1111111-l. 1111: 1:ri1i-ml |11-I.-1'i||||.‘1t‘1' is 11-\‘u 1s11.l011- Fur 11 1%-‘i11111lI1'1}' siiiuitul crrige 1.-011111111. it Ls tlm.-1: sidtrri. 1111 simwn in 1-"i|:r_. 1.211.
In f1DC‘i]1'(11~lJ1¢!£? with AC1 H1111. 111.-1. npmiiligzi of 1111).’ size =11-r: |3-l_’:|'|ll1Tt1_"1'1 in tlm :_1r0=_1 ¢_-1_11n|111_111 tr; 1\\'<_1 i11rc_-11-1171011115; 111i1:]1l1I: s1-ri]1.s. I11 the 1l]'l.‘11 111111111011 tu iwu inI.L'1'.sL'4:ling lI![l111111I! :-ctripi-1. the liuuciiiiiiin wirlth nfnpmiilig is limifnil
1:1 1.1111-0111.111-11 111' the culiimin >111-ip \\'1¢|l|1- I11 1.110 arr.-1.1 L'U11l|Il1U[1 tu um: L'D1L1lllI|1 sLrip and one ll]1(1111t‘ strip. 111.11.
111c1rc! than 0110-fuiirtli uf the rci11l'1.11'c1:11wu1 in rithcr strip
1'11“... = 11-1‘, — M”
= 2111 11.—ki]'1c-i - 211:1 11-11111..-
shall 11¢‘ i11tn1'r11]irnr1 113' npn11i|1p.<1. 111 1111 (:1-1.~:-1':-1. tiw nrmi 01'
11‘i1|1i.rru1.'11u.'l1l 111lL'l'1'l.1[J|L'f.1 1.1}.-" u|1I.'|1i11g,1e 5112111 111* 1'I.'p12|£1'4.l hf; an |:'r|_uiv1-1112111 muuiiut :-1rlr1t'r1 cm 1111? fi1(1[‘1i 1:11 1.111‘
= 1.i'r' ft-kips
npmiiiig.
Figure 1.2? C.‘.'.'.h'1:a|' Ss1:r.'ms for Shear punching shear
flexural shear 1
|
tributary area
erltln-el perlmaler tributary IFEB
_ B |r|bu|an_,r area
?///// iniq-iqilb
III
0
wurw.ppiIpar|.:n|'n
C.-:1
Iuroncen cottcrtrrz uieln-111 Figure 1.28 Comer and Edge 1?1:|1‘i.u'1'.1'rs
1-45
Exurnple 1.31.1 Thu 11111. ]1-l11lt~ 1'l11-111' 111' 11u1"|1l111 '-1'1-igiil 1ru|1(r1'1'11' 1'11-1' E-11. 1.25 111111 Ex. 1.29 1111:-.4 an 1-l1'1-1'1i-:1- 111-plh 111' 7.5 iu 111111 11 t:t1n1:rt:tt.~ t:t1t1||1rwtsi*.'v strt-t1|'__c1-11 111 11111111 ll11'_-"1113. I11-1111-1111110 W'll1“!l.l1£'T‘ 1111- sl1r111|' 1,-111111-r.‘i1_._1r 111' 11111 |1|ntr1 is 11111-11111-111: fur 1111 i11I.1-tiut 1-1111111111. .';17r1I11.1iu11
1ril:|u1ar1r ama
critical
/ perimeter
'l'l1t_- 1_:ri1i-1-111 s1?t_:1i1_1|1 1111- 11r1111_1|':1I sl1r::11' is In-c:_1tr;i"l =1 {lis-
iain;-1: l'r1.1tn 1.l1r.- 01.-111.111 olllic 1111111:-l 1_ti\'t.-11 113.-'
critical _
perimeter H‘ .|-.=%— {11-1-%}
_ ES F1 _ '1
—-t .5 in _|_
12 in -
-
Cr;
Czld
1'1
211 iii
2 . [12 in -
1 '
11)
= 1'3-54 11. Thu 1':u.'tut'1-11 11]1|1liu1 s111.'i-11' 111 tht: rriliicatl :11-rtiutt 11.11“
Flgtrra 1.29 Re-:.'1.\:11'r1n.i-1 G-"1-‘ca1'Perfi'r>e-tar
flt-xiii":-11 shtutt is
radial pru]-Eclion
lrom column 1.-enter ‘xx’
l-"I, = quf-3.:
Opening I
|l‘lBTIBC1ll1'H length xi‘ fl
1
;
,1
I-'
.1
.1
- (5.2
,
- 131] 1-tips
-.=. 1011
1," -ll 1.1
,1 xx‘
in-', = 21.11.11-_..1i_.-TI
critical /K pnrimnlnt
/I3" 1'
_.
{2'1[l1.TF1]1T..'1 11111211 11.}
2 .1 1" / ‘,1 upening
1
Thu fluixilriil sl1ni11' t!i'q'11-11:i1j1' at the 11111111111 s|:!1:r1i1:111 is
1_1;i1'¢.~|| 113.‘ .-‘\'1.Yl 1-jq. ll-3 ris-
H Jr,-column
A.»
{Z24 1'1-_1[I2.5-1 1'11
- |1'- -1111 1-: (1.1_1t1E)|_1.u_1\, 1111111 11.11111
I
\‘{"__ It ineffeiriive length
1111
= TU-5 1-11[:1s Ir’ l-7.,
fs111i.s1'|11'1t1I}.']
T111: 11.-t|.it__111 ul um: sitlc 111' 1111- cril-11-111 111'ti1111:11-1' 11.11" 1111111-hing 9%-l11".l1Il' is T111: 1111111-111111"; sliuiir t:z1p1-11:11}; 1:11 the pi-111111 is 111.1: s111t1111::-it 1111:1111 II1]1'!1(! 11111110.-1 |'.§i\'t111 11}; .-915.71 5-111:. l1.11.'.!.1. which titn
11 = 1: - 11 = 211 in + T.F1 in
ti = 4¢:1i1l1..)i\_.-T.
sci rr-as]
5 111111.12 +1\\,.-T
|Aci 11-31]
= IZT.F1 in
'l'l1t_- li1r:I1_'1tt_-11 :1|1]"1|it_-<1 sliiieair :11 1111- t_:tit.i1j::1| 11-e_-1'i1111':tr_-r 1'11-1'
1111111-.111115; sin-111 is I
.-
5 ._:,i11,,(-2 + _"J*‘).1._1'j_T J-1
rt, _ -I11 for 1-111 i1111"ri11r 11111111111 = I111 1'01" 1-111 trdgv 11111111111 = 211 1111' 11 trtirtttir 111111111111
|.-11:1 11412
1"" = 11.1111-1 — 1'31
— (11.2
. ]-11]}
“
12511112-111]
_- . -3 [Q1'.;11l1|
(11
= 1213 1-tips
PPI
e \I1lI1.|I|I|I|llI-l.GfiII
E
Concrt-1
1-46
$1'Ru1.‘:1un1u. 51111111551111“: IlEFEREll¢E 1||1111un|.
T]11r]:!11gt]1 c1Et111r|:!1'itic'|-1] ]1:hr'm' is (1,, = -H1
1=_11Ac'r|c_£ 11-111::-|11.:|\|_s
_
_
_
‘I. Tim Fnll111.\'i11_|; i.ii.ll5Tl'i-'lii.[ll|. 1-ihr:-w'1i 11 rc!i11Fnrn1:l 11:111-
irn.-11~ I.»-041111 :.-unti1'|||u11>- 1.|W.!I |'u1i|'.~11:|=.'|11:@:||1|! iI'|l-(u_._£1'11] 1-1'11 ||
= H]i2'r'.5 in]
lI'UilllIlll!5 at U11: L'11d>.=. Tlw clear llifiifillil‘ ]1c1\1.'u*|1 sup-
= Ill] in
]1c1r1:-i is 15 it nml the ha:-1111 .~iu|1]1<1rt:-1 .~1 I":-1:11-1111'-:1 inml of
HI l\'i|15_,-"FT. The pu|1r.'|1i11g sllcnr cz1|1zu.'it-3.‘ ul' H11: plnli: AC] E11. 11-H-Z! as
0 1-", = --lodlli-,.A .5?‘ . . . iu_][1Hl . ||.iji[II.T-"1_][T_:'1 —
1[HJ[J
gu\'L'r111.~1l by I.3r!.¥i[1r1 r1.-1.1=.'1i'rl1'1H|m.\1
I .-EC] -‘$18
I
i11][].l]]||'|1'-l[]l|{]
— Integral columns
1111 1
1 kip
I‘
= 1-5? kipea 2* V"
[aesitieifi-1:-tu|'_\'|
is z1])|'>Ii¢.'4\1'r|1~.
iz 15 H
'—|-'
is '15 ‘HI
'-I-*
in 15 H
*|-'
is '15 1'!
'-I
i_:l] Tim
1e.11[1pu1't is 111u1~=L nl.-n1'l_\' II.-'1] TF1 kipee
FIIFIIIIIIGIS 1. .-\|11reri1:!a|1 Cu-111-1'r~tn Iu5Tit11tc!. .B'm'iri1'r1_r) Cridc Rcq~|.e1'r'cJltfiiillr rand [T-'rm1111r:1.I|!r1r'jr,vf¢11' _*?h"|:r:H1r'm! (“'rrr1r'1'r.-1'1‘.
1.1»:-'1 .1111-11:1]. 200$. [.-1 E.‘-‘I ."§H'\'-Js‘."|‘]. 1955.
Ii. ‘Willi:-111111. 151.. Dr.-.-11'_1}r1 of Rr!1'1'|_i|'0-rr.-r.-1'1 ff-'r111crc!r' 5'.F1'r1c-
I-1111'-5. 5l|11:1l. EH11. Er.'urr|-1. 1- H-"u1,r Slum". Er'a:'krf1". Fr1r1I111_q-1. Pale If-‘up-1. '_-’- il"r1;r,| $'i'11b.s mad .*?r:1'.-slnic Dc-.-11'_|]111. ZIHIFI.
K. .-111:1 |.'ln-|m~|. .-91.. W. D'1':.-11]]-rt r1f('r1»r1r:1'|'--fer
Berilriirrg-5 fur Er:T'1'.7r-‘111!-erirr um! Wiriri Fr.rr'1'1'-1. P1_I1'l.|i|111.l
Cuuu:11l- ."Ls.~;1.|1'i21tiu11. 1955.
T. .~’|.l||I.'Ii:"z'1l| ||1r
-vfrurr-'-ir.rr1 1'11'1-m.11-mi. 13111 1:11. 2i][iG. .-if?-il.'>'1|‘1'—|")|'l'.]
[A] T5 kilns
-'pC7u!1mrr1
[(_.‘-} B2 kipw [D] 511 kip»
{=71 Tl1r.- =l<.'+i'l i.-1 11'|<.'m1.. 11r_'z1r]}' II.-*1] 14[J fl:-kipee
G. l"'u1'l]a1|1d f_‘4:uu:nt 1'15:-.v|.|cia1I.iu11. .-\"1.1l4-"-s rm .--LCI-3'18-|‘?1S’." Euilrliizg C-'0rir.' Rr'r,uu'rn1nc11t.1jm' 5'f1‘11r.'f11rr1i If?-'1'.|1.I¢".1"c!.tr'. ‘ZLHJ-‘S.
Pui11l..
U1] T111! almiigil 1i]1zr11r furnv 111 the Enter of L111! <111t1r1' s11|1|1m't is ||u-mt rim-11'|_1'
[B] F9 i{i])s
4. .~\1|1|:-ri:-1111 C|.=n1:r|.-11~ l||:
Sl1"I.u.'ll1L'I.'
[C] H2 kipei [D] i'ii['i kips
‘I. .-‘|.||||.-ri1‘a1|| Cu|1L'n-10 limit-LLlr_'. Crrrrurirrrr-!r1r'y rm E-'1i!rIany C-'r1dr' Rrr,r|u'r<".rI:r.'r|i.u for .l'?r.'1'11_|'rJrr'e".d CrJr|r.'rr.'tc
-Tr. Ghneih.
[B] TU kip:-a
1r.
.~§.!.TU.
[S1|p[1ur1:~'
[B] 1['iriJft-ki|1:-;
[(_.'] E'lI]F1ft-ki]111' [D] 2111] ft-I.-cipee. (d] T111: t|t!sig|1 [ll.UlIll."[ll at the first intt!1'iur 11111111-11rt. is 11111.41 11c!:1r]].-' [A] 1-H] Ft-kips
[H] [GD ft-ki|1:< [C] W151]-ki])H [D] 2311] fl-i.-1i[1:1 (:1,-] The :|q=:
I].-'1] Hill]-l-;i[12e [B] IIIHJ H-]t1|1>s [C] Eli]-5 ft-kipei [D] 230 ft-kips
IIEIIIFGIIGEII <:1.'111\1‘.:I1£'r£ nillnu
[F] T111: 1l1~e1ig11 111111111.*111- i11 1111* first 11111111 is 11111111 1111111131" [111] 1~l1Jl'1-1111111
1-4'?
1!1|11i1.111|1r111- 1li111111:11"r. T111‘ 1'1_1q11i1'111l 1l1~1'1r]11]11111:11t- lc'11g.11l1 1'1i'1111 i111]i1.'i1]11.~1l 111-11' i1-1 1111'1.~'11. 11-1‘-.-11'l_1'
[.31] -ill i11
[I]-] IGD IL-1111111
[T1] GU i11
[C] 2115 ft--kipa
C1112ncr1-1
[C] 115111
[D] 211-U E1-ki|111
[ D] TH i11
11-1 T1113 1.11-nigli l111_11'111~1|l. 11] l-1111' 11:.-1"ut1r.1 11111111 1:1 1111.1111-
111:11r]y [J11] 1-I1] 1'1-I-111111 [D] [GD 1'1-1-11111-1
[C] 2115 1'1-l1i|.1e1 [D] 211-1] 1'1-1-ci|11;
2- 1'1 1'1:i11f1>1'1!1'1l 1'u111:1'1:l;1- 111-11111 uf 111.1-1111111 11.'1:ig]11. 11111-
11111111 wi1.|1 1111 nFf1=1‘1i1'1* 1lr-|1|:_i1 111' 211 i11 111111 11 11'i11111 111' I2 in i11 r0i11f1'111111_'1| 111i1.l1 3 in: 111' |;r1'1-11lr1 [ii] rni111°1'1r1‘1'1111-111. 111111 1111.111 cu111'r1'11~ 11.111111-1"1.'.~'11i\'1' slr1'11gll1 ul' Z1001] ]i1l'_1'i113. T111: 1111"u1i11111111 1-11111111111 1111111111111 1111111111111. 1111-11. 1111* 111111111
131.111 1-11111111111. is 1111,1111 111,-111'|].' [A] 211] 1'1-1-111111
5- 1'1 1'1'111]'u1'1:1:11 1'11111'r1'l1- F1111 5111111: [I11-u1' 1.\'11i1u11l. |11:11111:1
1111.11 11-1 i11.11q11:11'11 111111111111.-1 111 21] F1 12111111111‘:-1 111n111*11i1'11r1.1r1-11
111111 24 ft 1-1:11111.~1:-1 _ _ in 1.111.-0111111 1li11.-1-1i-£111, ., . -1 11111.1 i1 111.1|1[11:11't.1111 i'111:lur1.‘11 11111-l1'||11111'1l 11.11111 111' 2110 11.1-L111‘. D1!.~'1g11. 11-'\.1.=!I1'rljJl'i(JI1'-'5
I‘
."'1(_'-I S111". 13.5 is 11p|1]i1'1111|1-.
I
1'1_r| = 1'1]; = _1"1_1 = U
' mm‘ -11 F1
I
(711111-1i1|r-1' 11111-1111'-111.11 in 1l11'1 1|i|'r1r:1i1111 11F 1110 11111111111 11111111 111111’.
[11] The 11111111111 1.111111 111111111-111 111 l-111: 1.1111 1111]" >.1[11-111 is 11111111 11112111}.-'
[B] 2-‘$0 fl.-ki]11-1
[A] I15 [1-1:11:11
[C] 2111111.-111|111
[B] -ll] [1-kip111
[I1] 2111] f1—ki|111
3. 'l'l11'.1 1‘1_'1i11f1_1r1:1j11"| 1_-111111311111? 111111111 11.11 l’11.'11'1. 2 .<111p]1-1_1r1_11 1,1 l'111'1urc1i 5110211 [1>1'1'1' 1119 kips 111 l-|11' cril-i1'11l fiI.'ll‘11Ul!. I11 1-11111111‘ 1'1?i111‘111'1r1'~1111\11t 111q11i1'1?1]';"
[A]
i1. i1-1 1'1‘-1'|11i1'r11l [211.I1 111111-1 > 2 l’,,].
[C] [15 fl-l-zips [D] 111] ft-l-111111
[11] T111? 111111111111 1111111 1111111111111 111 11111 i1111.*1'i111' 1-11111|111rt 111' the r_!11r1 i'11_1_j]' is m1'_1_-11 1117-1_11'l;1.-'
[A] 35 IT.-k1)i111
[B] Y1111, it is 1'11.q11i1-1-11 [IFILT kip.-1 <1 ‘.11-",,].
[1-1]
=11] ft—i£i]11=i
[Cf] 3'11. it i1-1 11111 1'1:-q11i1'01l [l‘.'I.T 1:i|11; 221- 2112'].
[C] U-'3 F1-kips
[D] N11, it is 11111. 1'111[11i11111 [2[i.l! I-:i]'111 <3 ‘.11-",,].
[D] 111] 1'1-kips
[11] T111: 111111111111 1-11111.1 1111111111111 in 1111 i111.-111'ir.11' l.111_1' 11|11111 i1-.1 I. A 1-1111111: 111i11f111'c1.111 111111111110111111111111, 211 i11 111|11111'11. is
11.1i11fr.>1'1::111il wi1h 11111 111.1. E1 5_:1'1.11:|c1 Lil] l1=.1r11 111111 111111 1.1 1:11.1111_'1'1c1-1" 1111'1c1|,1',1l1 111' -H7111] l111',~"i11"'. W|111l- 111 [11] 1110 1.112!-111111 11111111] 11.11111 1'1-1]1111:11j1' 111111 [11] 1-111: 1'1:1§11irc11 1~1|1s11:i11g 111 1-111'
1111111111 1.ir111':'
[.11] T1111 11-1|»-1; 211 111 111} 1111.111 111111; 11.1 111
1j("-j1 111211 111,111 111 111 [D] 141.11) kip“-:. 211111
1110111 111-11113.-' [11] 35 l'1-1111111 [B] -111 ft-kip111 [C] [i-5 [I-1-111111 [D] 11!] ['1-hips
[1]] T|11' 111i1i1ll1' 1111111 1111.11111'111 111 1-111' 1-1111 11-11}; 11111111 is 11111111 11111111].-' [A] fill 1'1-1-11111-1 [11] 35 fr.-ki]11=1
5. A .~1i111p|y .\111|1|1m'1.11rl 11=i11Fn1'1*r-1lr111111'r11111. hm-1111 i.~1 111111-
l'u111*1-11 with 111.1. 9 g,1'11111' I34] 1111111 111 1111111111"-.< 1.1-1' l-i11‘1'1' 111111 111111-11 1'u111:r1't.1' 1'1.1111[1r1:1;11i'1.'1: :1I:1'1:11g1l1 111'-Llllilll ]i1f_1"111'3. T111‘
[(_.‘] -I1] Ft-kip11 [D] 111] 1'1-11111111
1'1'-i111'r11'rrr111|r1111 |11'1'1'ri1l1=1| is 1f1‘.!1-I. i11 11111:1'-11:1 111 1.11111 1'111|11i1'n1l 111111 1111.1. 11 1'11-111' 1'u1'1~1'1-1111111 11.1 l|11- 1-1111111111-111 111111111.-l»1-1' 111' 1111* 1111111111211 111111-1 111111 11 11111111" 11|1111'i11|; 111' 1-1111111‘ 1-111! PPI
l 1I1lIr.|I|IlI|III-l.GIII
]_-.e[..B
tfnucrunnn. EIIIZIIIIEEIIIIIU
nsrsnsucs In-llU.n|.
[P] Thv 1111111111! st rip 111c1n1:'111 111 1111* i11tc'rir11' 2-:~11]1p111't u-F
SOLUTIONS
1|11'- 1-ml h:1_1.' 11-. 11111111 m\:1rlj,'
1.11] 31111-1ii]'11-1
1 . [11] T110 1111:1111" at rhn 111110 ¢1t'tl11~ final i11t:1ric1r 511111101-1 11-. [{i\'e~1'1 113' ACI 5111:. .‘§.If1.I$ 1'1:-1
111'!-'1' 3:‘; 1'1-l-zips
1, = 1.15 .1.-,,1,, 2
|:(_.':| .l(| ft-klps
111]] 1111 ft-ki|11-1
11.1.-11(11_1%)11=1r1_|
If} 'I'|1:- 111i1|¢|ln .-i11'i|: 1nnmr1111 in 1111 i1111~1'ir1|' |m_\' .~1|1:111 i1-1 1111111 111~11r]).'
1111 1111111.-11,11 1111 1'1-1111» 101 11111-111111 1131 111111-1=1|1»
_
I] .-
— 56.13 1-:1]1.~=
[H3 klprefl
The answer is (D). H1] Tlw slwur at H11! F1111? 11f11]] 11tl11"1' :111]111<11'1s 1:1
= 1r'..
‘I
(111 k;:"‘)1_1s 111
= .
.
2
‘.2
= 1.-'1 111111 The answer is (A). {:'] T111‘ I11.-111111111, 11101111-111 L.-" 1_;_i1'1-11 bf."
111,, = 1-:11-1|":
kip:-1' , F = 1'(-1lIT)1|1.1I1j' = '3'.!5[JT Ft-lcipui
\"11]111'>.< I.1[ H11‘ I1-1*1|1ll11|:, 111111110111 1'1:-v[fi~:'11-111.-'_ T. nml llw
hc111<1i1111;111111110111:-1. :'|I,,. 11111 L
eiI.l|1p-111']
sip-1111
.~iI.l.||pu|'l
11111111
.’1f,.
1
12
'3
‘iii
ri\|.|1].|u|.'l Ii
1'
1,1111
1_.-'1.1
1_-"111
1_.»'11i
1|.-'11
1'| 1,, [fl—k1[>=~II
1-II
H5]
‘.1255
I-ll
Llffi
F111111 lh1'ta1hl1'. L111.‘ <]1".~ii1_f|1 |11u1111~1|t 111 t]11r<1l11c:1' :1|1]1]1<1r|
1.~= 1.11 [T-ki|11~1 11.11111-11111.-'1. The answer is (A).
{1]] F111111 tho mlmlcr. 1l11'- rlvsign 1111111111111 1-11 thcr |'11'1-11 i111<-|'iu-|- :-;|1;1]1|1r1 is 22.5 |'[-ki|x-: [2311 1'1-l~;i|x-1}.
The answer is (D). {_v] F|'u1|1 |.l11'l:1l:-I1-.
‘H119 answer is (C). FPI
0
IlItIr.pplIjIBI.:fl-I11
|u|=|:1I¢1=.u <:n|H:n:'rE IJEBIIZIII
[F11 FT11111 t11:.*t11h]1!. the 1lr'_\1ig11 1111.11111~|1t in thr first 11115111 11-1 ][iI fr-l1i1:111 1j:1[i[] Fr-l-;i|1111].
The answer 1; (B).
1-49
3. T111" 1l1~:1ig|1 1~'l11~ar 1:!s1[1111:it-_\' of 1:111! t'u111'r1~tr' .~11~rtin11 is. 1|11~|1. r_'.I 1", = 2115 '1". LU. \.-"ff:
[11,] F1'u|11 H11‘ t:1h|1'_ tl1tr dt::='i1.',11 1111111111111 i11 ll1t' -11u1'u11{l 1'1|1:~111 is 1-H FL-kipei [HI] F1.-ki|1.<1:|.
_ .. . . . . . :1111111 1111 121111_1r111_1-111111211111111_111\|.'
The answer is (A).
1h| kip
HIUH i
'
2- T11? 111.1-11111111] 1111111111111 of l'L‘Sifill-1ll11" is
111,, = .4_1'u11(1 -
= |9.T 111115 SP '21-'_.,
11.n11.=1_J_
S]11:11r r1"111furc1r111c11t is 111.11 1'c\1111i1'1\1l.
The answer is (C).
13 111E1(1111
1211 1111
Q1, 1:11} '|'|1(! c|:_'e-1i11,1] :1)11i;|] lmul {:1!]'1.'|.[:i[_\' i.-1
"'1 '-"_)(GH _ 2) (:I1.:1.]1[IE'1i11
112 11111_2u 1111 _
1,111“. = 11.1_1111.1(11.115ff.(_.4__, - .~1,_.'1 - .:,,1'r_} - {(].&]][[|.l'i5]
111*
ci 1:1
111.-s.11(1 '%)1411-u 111* - 111111"-*1
in
1? F X
+1111 111"1(1111
= 255.11 ft-kip.-1
|.Il'
Thi? r1!i11l'11r1"1~1111~11I: 1'11Li11 of L111! 11011111 i1-1
p_ .-1,. _ flrrl
= 11102 kip:-1
[1UII]||']-:i|11-1]
{l1] The mi11i111u1111 11l|1_-11.1-1111111 1.111 11-i-11,11 111
3 1111 [P2 lll,"{_2U ill]
r1‘, = 1111. 3 hm‘
= [i.'|]l25
T1111! 111:-1_\ci11111m tic! .~1p11ni11g 1111111] 11111 11-1? |'_§1'0:-1101' than
T110 1111111-111g rL'i11l'1.11u*111c11l mliu Fur 11 11'||1>i1.111-1'1.I-11l-r1.2ll1.~1l 1-1111111111 is
111-
. 11.:1111.-"1,,<' f jg
. .. . - 111111.; 111.319 [l.1:i!'| 3 Z.
-
"
H
M
fr = H1 in
-I-8111 = 1_=lE'~][[II.3T5 in]
’"( 111-‘) k1p11 i113
" 18 in liidh — {1[i:|[1.12Hi11:|
= H.II]]Ii[i TI» p
= 13 ill
'['|11* 11r1¢:r.i1'1|1 is t1~||.=1i1'111 r:r1|1rml|1'11'l, 111111! T||1‘1 .\111're|1p_'Ih
11:~1l11I.'liu11 l'11clu1' is Q = [LE1
'I'l1=.- 11111.\1i11|11111 11lI1_111'11l1l1': 11|ti111:111- r111_1|m.~.|11 1.1. 1.111-11.
.11., = 11.111-11 = 1111131125.-.'1.s 11-1111111-_1 — 2311.2 11-1111» 121111 11-1111111
:1»:rw1'rI|=~']
1'1'1a answer is (B11. 5- "I111-1 cl:-1'1-1111111111111 ]n|1gr.h of 11 'h=1r in =1 1|1rr1n-I11-11' 1.111111ll1_- 1:11 i1111'11:1\.w1l LII)?’-1. T110 +.'xccu-1' 1'1.'i11l1_1rL'L'|11L'11l l'111'1ur is
E"
_ 1l]l] _ -
T]
U.‘.)1
The answer is 1'8).
PPI
1 IIlI!.|I|I|I|I1lI-l.GI|II
Conc2rc-1
]_-5D
STRUCTURAL EIIIZIIIIEEIIIIIG
IlEFEREI¢£ II1lllJ1l|_
T111! r1!q11ir11cl d1r1'<']c1[1111c'|11 ]1!11gtl1 111 1;i\'1:11 l1_1.'
T111! 111111] 1-11111i1! 1111111111111 is di1~'tril111t1*1l 11:1 1111111111 111 1l11* li11l]1':11\-‘i111; 1;1l1l1'.
[)ll1"l-"-I"
11 _ 1.-zE.,.11_.,
1j1'1.11sj1(1111.111111
=11.21111.111'1|j1.1:11111 am . 1 1111 11.111 1-1111111 , l1 F = 1'11] 111
1111111
1.|'|uI||.|1;'|.|1
r'1|rl i1|lr'1'ir11' i1111~1-i11r 1111-11111-11111111111 11111111
l1.1l.l 1\'l
1li:1I1l'll1I.ll 11111 11n1ff.
11.52
11.711
||11|11|r'1|1 [l1-I-ii]-111']
I117
I -I -l
?2
1-1111111111 1-:11'i|1
1li1111'il111I i-;111 1"-11-:-11'
111i=i1l|r- ~11|'i11
1li11r.1'i|1I1l i-111 rm-ll"
[1_Li|J 11.1 11.-111 -1:1
[L7-'1 11111‘ 11.25 :16
0.131] 1:1 11.-111 E11
1_'1"1r'lll<'i1'rl|_,-'
171
1111111111111 l:l'l-l1l|1r1']
11111111»:-111 [l1-l:i1111_|
11.35
{lill 111]
1119 answer is (B). {111 F111111 I110 l11l1l1*. 1111' cr.1l1|11111 :1l1'i|1 1|1u1111'11l i11 1110 (‘ml
l1:1_1.' 1-1111111 11-1 (i--l f1-ki|11-1 [115 I1-l1i111~1‘1.
51 T111! 1.'l1.-111" -~p1'111 1*
The answer is (0). 11
_1' l
r." l _E[]fl
1.l'1f1
_ 13.71 l1 1- ll.(i51'|
].-.+'11i11f1-11-I111-_1'|
H1] l-"|'1'1111 H111 1r1l1l1~. tl11' 111111111111 1-'111'l|1 1111111111111 111 1l1r1 i111rr1"i111'1<11|.11.11.1r1 1_1l'l.l111-1'11r.l 1.11131‘ in ll]l3~ l'l-l1i]1:- ll ll] ['1-l1i].11-1].
‘five answer is (D). T111: lutnl l'|11;'lu1111l 1.1111111" 111~:11111'11l is
{_1:_']
|"l'1_1-I11
[l11;' l1l.|1l[', ll'|1.' 1_'ulI1111111 :-1[Ii]'1 |111_|1111~l|l_
lll 1'|l|
11111:1'lu1' l1-11)." 11111111 la =13 ll-lii]1:-1 I:-LU lt-l'1l[1:-1].
M = 11.1l1lf_ 1. H
(11.2
‘I711! answer is (B).
l'L-
1'24 1'11|j1.11..j1 '
The answer is (C).
-H
{PI
_ '.?.'11.:'1 ft -l-zips
l||¢.*1|l. 1111*
1:=1l1l1‘-, 1ll1'1 1'||l1l|'ll1"
.~111'i11 ||11'11'1|1'|1l_ :11 1||1"1
‘me answer is (B). l_l'_l F1'I.1|11 1l|1.' li1l1lI.', ll11- 111i1:l1ll1' :~l1'i|.I 111111110111 i|1 1111
-1111
1"|Jr~_1
51!,
Ll‘
LI-'= 11 l1
0
l"I'|'1-111 1l11
l]111_'|'lu|'1
‘Tlw r1!]1!\-'11111. :'c11'1fl'11-11111111. 111-1 git-1111 111 tlw |1n1l1]c1111 51:111--
FII
{1]] F111111 1111: tnl>l1*. 1.111: 111l1l1l]1: 1-111-111 1111111111111 111 1111:
1111:-w.ppiI||as|.:u-|n
11111~1'i11r lm]: 11111111 i.~1 2!} ft-111111-1 [Ill] ft-M1111].
The answar is (111).
Foundations and Retaining Structures . F5-lri|ll-"ul'lril1g....................._.
E-1
I-‘il.P|i\1<‘1!i (_'nll:1llll 1'-'i1ll -‘:ir||llll1' Fl.>llIilll_1_ - - . . . 2-5 j.;l.:-- l:il)|i\1II‘\I] (.'»:1lli11111 1.l"11|l H<'|:!1ll11§_5l|1l1l' l"l'1-l'lTilll.f . _ . . . . . . . _ . . . . . . . . . . . . . . . . . . . . _-
-,._
(_'1.l1ll|>illl'l.lFuulillll,
..
..
..
..
I-C4‘:
- _.>- Ii:
Pllssullo Distribution Tn 1i1.'|.l.'l‘JIlil|1‘ wllil ]P|'l.'-“i-“=ll|'l.' |l||.I|.l'l El l'n-lllillll. 1ll1.- r~"l.-If\'-'l.'il;ll[ uli I!]1:- ]'<_ll.lli11g is iullll-ll ll.‘I lI1l.- ll|>[:lil.'ll ll.w.r.i ]'l'ulll tilr wllll. T1111‘ f»;1ll1ill|!, II]i]ili“llz-iiI.>l.L.*i NIT‘ l1<|_'111l-cl wl Ill l.‘[l.5-I~1il't‘
that tlul :-mil pr:-:-e-l|l1c' i'|H <-llllrulllrreli frmll Tlu'- l11'li':'l<-1
5t1"ll]lFl>ulilll_§_........... .. .. . .. .. ii. (‘:a1l|ill~vl~l' F{l*l:-lillilll; \'l'.ll]] _ . . . . . . . . . _ . . . ..
-
]l.1i'l(iH 1ll_ll':~< ll
T. [_i.‘il'llll||'!l'ii‘.|‘|'i H:-l:'lil|illll_ \'\.';l'|i . . . . . . . . . . . . ._
-
1111112‘ fill‘ IiiIIITIZ!II!5 lllltillg, on ll folllillg. t]1l! 11l:*1 [IIl'II'H-illI|‘II! is
Q,-1
nL‘EI.'l'l1'1lIi'I.'.\.\..................
III't|1]'il‘1"<| rl:i l|rlr|'-rn'|i||l'-ll |'l'l>lll Tlm ;lp]'|lil-ll \\.':'l|l Illml r>lll_'l'.
.
Prllcrlillcl T’l'llil|l~lll>l . . . . . . . . . . . . . . . . . . . . . . .
-
J \:‘l|-J1.:-Jl':.'J H-lllllrirllls _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. QF-'I-CI |'-JRD —=P-'-';5-I “-'1 1'-I :
|-int’ :1 .-¢1l‘i[:l flllrlitlpfl 1l1' |1-ll_u_1|l H|ml':'l||I.'|I-:l1|ll'\‘I.'z1||,1|lll
11r.'1 [)1'(‘R'ilI1‘(‘ lli'| ill_l:__ ll-ll iilt‘ full-li|l|-._',. aloe r4ill.iI'v'.'[l ill Fig. 2.1.
is-1 p;i\'<'ll h_\.'
_ E l” r|l-
1. STBIF FOOTIIIIG N|:l:lll.1:|||:i:|l.ll.ru1
.-1 -
lu.-lliul :-'lIl.":| lll |m:-4" uf (‘<.l|11lll1|.
T1:
ill'\t'i! llf |]l.l" |l:ml- -:1-I‘ I ill‘ [ZI_'|'l'£ll|Ji.1]. 'l'l'lt|:l _-li-:il-
I1:
_ Ii] |r- -
P[i11 ".'=
.-ill:-|1l*:~ of If}. [0l'l1l¢'ll w:ll|l1l:l lill‘ Iillllillp, il_'l'
ll
=
thr- I-'\ll
l»- ll
I’.
fl" Ii‘
[ll-1 i1lll.'[4'!' uf |.'|'i1il-.-li .~lv<'til.:-I1 flu ]lll|ll'|1illg .-]al'l-|1 |l'||g1il HE t¢1i'i[l int:-I i:l_l'_ p.=ll';l|il~i 1|l 1.‘\|'£l|i. l-l':lll.'_l |l
l.'
lI.'ll;_j_1]l. llf :liliI.' llfI.‘ull11l.ll:|
ill
]ullr.i.-'. (il‘ll.'l'1]1illl1‘
I} rl ..
<]l'll<1 lllllll <'l'('4~l|||'ir'i1j,' vril I1 11'?€|1l‘~C'f rll r'c'r||r'|' l|Ff|l|l1i||j;
1-lip:-l i||
E-Ji-€!.lfl[I1(‘ 2.1
-l-:1:-l'llll"i-c-ilj.' ll-'i|l1 1::-|:ll~<-t l-.l 1111.9.--<;-|' [iJuti.l|:2__.
ill
ill {1
H1‘:-li|:_'l| llf :'l 1'-:'|l':-liligq ii-l |l-:i:~A*<] utl l|il" |ll'!i i':'ll'til'l-|‘1'!ll :i]'l]'||i1'll|
ut'sll-:>l-l :~il:ll' ui 4| l'l'IT'|
|:1__."2 — l'|
1‘. H l' L
ill
|¢'I1I"l'4l| |f‘I|'¢'4" rilllv 1-» IZ'Jll'| h ]1l'l'l=l=l.lrr'
1-lip:-'
<]i.~»|llll|;1l' i)1'i'I'|'l.'l'Il. l'l.I-lllllill 1'1-l'lIIl']5 il'|l:;:1il llf :<1l.'i|l fix:-I i:ll_L'_ [1-c'l'|l-vllrli-:'L||:|1' Ill
1'1 ‘H
Wllll. lc'l1|:1h llf lflllfl -\li|:ll' 0| ll. l‘l‘II'|-il|'l|.!'ll|-HF [1JU[i|l'r'|. |.1'!lll.';l |l l.ZIrhilll' I.:-I. it h||\lill'!' fl_lu1ill,=_{
1.
lirv |-nml
I-:ip.-z
[J
l-llllllllll axilll l=c~l'\'il-l~ Illa-:1
llip-'
15.. ,
1",.
lJI.lI[li]|.ll.i. |l|.':l.l'i1:|l.', :»II|.'1'1l.gl ll (:lll||1:l|1 :lxi.'|| :vl'l".'i-:tl' -:]l';l(] ]ll:1|l|
kip:-l Icipl‘-l
I’,
l'llll|1|||1 ;n;i;l| sr-|'l.'i-:'l~ |i\'|- Illiilild
I-;ip.~;
I‘. ‘I
l-ull|1lll1 Elxidli i:'llI'[<'Jl'i'I.i il.Hl\1]
1-lip:-
‘L
t‘l'|ILi\'lli'1'l|I |N"lll'i1]L', ]ll'l'1=l=lllv'rlllr'1ll>r'l"-'il'l~ i'i‘IJl4iF nvl l'lll":-lrwl ]‘I|‘I"‘€\illII.‘ lll'1illg r"-l1 I-"I"-li1l_l.£
']'.. r-". .l'
iIIl‘i'lIi.lI3 |l1'lE\b1|.l'1' |.|.l||.' ‘(I 2'il'|'\'iUl' ]lli1ll.‘i
'|\'1'il:§|Ill 0|‘ l1HJl‘]l'il.'
Thu 15 ill -lil"l"[) strip full-tillg llf llll-‘l'lI.lI-‘ll wl"ig]11 {'1II11II!!'l"H“ :'~|ll:'|\'|‘l'l ill HI!" fi'>||llwill_l{ i|lll.~lll';lTi-:'n'| .~ll|]1pm1.~l :1 12 ill l'L>|ll'l'l'I.l' Wi\ii £11111 is ul'f.w:~l l lil [rr..l|11 l]1l' {'t"llll'l' Lil. |ll4.‘ ii1.ll.iI|.il][=f,. Till.‘ alp|J]il'li :-:l'l'l'il'c' i.U€l.l.|h- i|l'l.' illl.i.il.'Hl1.‘\Ii. ill lll§.-
fig1111". lam] thv Jl.]][II\1|'Hii|i‘ sllil [3I|'II!:\‘-illfli! i:-i TAIIJII ll1F|.~‘t'1"'. I31-ll-l':llill=~1ll¢~ll=*<|1li|'l~l| ii»-l'|1illll;.
0
cu mrrata wall —
lllr,-'n* Jhl,-'|l'
PD.
]h-|_-‘II ’
1l.r,-'n-' {1
-q1__
::lrip 'l'u uti rlg _
RX
l-l_l]l_ll1ll| |-:l- l'l'il ir.-lll .~=r'r1iull (]:J.'|| i|.|ll.'!' f.lI.lIl:l 1'I.|.,l.{1' Hi |lIlllp:'t'[}' ]i.llI.' [11
- - 4.32 ki|'.l:I'T'l
I
T1
|
]l‘I
18in
_ _ _ _ _ _ 'J_
5:» lnh-ob-1 rllti-1+ <1-l' l\'Ill|;Z .-i-:ll' 1-.| F~]l.1.Il'[ ~=i
10 kI|'lsI‘ft
._’-U
l'l-lltrnid raf .-ee'r\'il'l' lcullls
.1
1ft
I‘ "I
i€
—
F-|
L
PPI
O
\lll\Il|ll.|I||l2|Ia1I.:nl1'|
Fnundatn s
2-2
§'|'lll.l¢Tl.llIll.
EPIGINEERIIIH
REFERENCE
ll-lllllll.
Fiyulrl 2.1 N-5'-! Pressure D-‘srr-‘bul-iclrl l:ll1 <3‘ FUU\'-'-"-§'] c-D
swig
sf’:
E
it P
F
P
lu
_ _]Q
I
SUD1E’!pLl"I
'
I
I
_
ll.
‘
I
¢-
L
I
l.
qrnu:
qrnux
T111: lllil1i111lllll suii |II1'l.".5“c1'lIl'l.‘ 1111licl' i-il.L' l'u¢.lli11l:, is
Snriliflxlrl.
The tntzll 4|.|J]}iiEhI] HF_‘]"~'iCII? lullld |J['f [nut rlln is
[in
P10 -1) + P-2
P. — 1",. I P. — 10.1100 % - -L11-EU
qllllll Z
= 14.320 lllf_,l'El
_ ll
P-_- — ..-,.l.L — {mi |T’DI1.s ll._>L
[1-1'1->1: IIIEIK1 -
"“
'
U fl
+ 1:1.-'.ll1hE
{1Ei][Eiir.]
Thu I|]l'_‘i [llciuwli i.U£l[| ull t]1l_' i'u0ti11g. ill lllxurcillllcc 1\'Iiiil
= 2'35], l|"lI'_-"Ii."
J5l('l Fitlll. 11.2. is
.‘\.:i511l|.|.i.[\g that 1' -C L.-"Lil. t-hv lllnxilillllll :iDii ]1l'I.‘£iI51l.l'\I.‘ is giv-l~ll il-_\'
_ ”'i';“
BL
_ I1flIlIl3fl.} = 22-5 l lr_.~"rl'=‘
T110 scllf-wrligilt rlF tiln Frlc1ti1l_l.1 prer EDHT Tllll i:-i .
B1‘.
Pu = 1.21"” + l.GF',-_ = [l.2II[ii] i.-lips) + I_i.Ei](_=i.3'2 kiwi-II = 15.911611:-.l
+
Tilt! llll1:\ti11llllll not fnzriomzi ]III|'t.‘?i‘i‘l1]'L‘ llci-illg llll iilli‘ font..
. '
'
_,
[l»l_.l1u llll)[1+[I’) _ 2.1512 1'. = .'Il[]|i(] iiliffiu
iii
l'. IIL1 ;;i1l'I.!tl]
.l'.. = Li Ii. Till: l11zl.\:illll|1n lluil ]’Il.'lI‘£-ihTlll'lI‘ ll.[I.{i.II‘l’ the foui-illlz, is Eil-
"i|'l.mlsc =
+
= .5IIH][) Il=[_-'I'l'*'
. .. l..p.._l(l _. _. +fi I_6](_1 fl] I_lr~..!IIl I1 Ft]([i En
'I'Ilc_- millillllllll t|.l'!I.’ I':lr:tl'll'rer| |111_':-mlrql m_':[.i|1g mi the I"nl'lrillg is
'i':l|_l1lill'I =
[l=l.3'2[I Ib['I(1 + E51“ '7’) + i [1 it-][Li fl]
-
P..(l - E)
P.
~ r.
=
pv(|-
"'""""°" = BL = = l-l.:ln 1.111..-_I'rl*
Fioivillg fur Till‘ i'l1<1ti11g llrllgtll givnl
mi‘ "' I)
lillfi I:-I
13-":|I1i1-ii
|
. . Iiiiiil ii-ii .' — (1 5.3'1 k 111'-j(1 Uni )
[1 fljlI.6 Eljl
[1 Ei][I3 it]
= 5'
F-uuuullrlnilut lulu nirnlllllln §'r|luI:'rI.lIRE$
Design for Flexural Shear
2-3
The |JI|'£!R'illIl'lI? 111- ILI11! rriticrsll :-i1‘C‘111lIill For 1+11r'11l' 1111 thlr 1:1115.11111" 111' 1.1111. 1'|'1-1'1Ti1l;._'_' 15
T1111.‘ lrriticrl-'11 :1l"t'I.iull fur fl1~x1ll'111 1111:2111‘ is II1(T'i1.IllI!(| i11 .~'L(.'I
5111'. 1-5.5.2 aml Sell‘. 11.1.3.1 mi iininp; Irlrramll :1 {iii-Iiillliil‘. nf f1r_'1111 the 1':=1c_~c_- 111-I‘ 1.111; r11;1|u::1-131.1": 1311- 1||:1:wi1111'_I_1' '||\'-i111. 1.111 slluwll in Fig. 2.2. T111: 5111-111" S1.-I.’L'l]gl1] 1.11 I111»: 11.1-:.lii1l,1:__ is
_ r,1,|{2.H.'1 ft]
1-
lI1£!‘1i"'l'l!ll1Il]€!(1 in 1-1l:1:cil't1:l|lc:n with .-511-11 5-l\l". 11.2.
_
Example 2.2
(6.311 L.’,“)12.:s:1 11) Et- _ G Fl
'1'|11_'- 1=T1'ip 1'l'_>(1Ii11g fur 1-Ix. 2.1 l1:a.~1 r_Itl 1_'~1'El?1'_:li1.'l'_- clnplli 1111'
= 1-15 kip:e._,-'11!
1-I i11 llllli 11 L"Ulll.'l'1.'l-L‘ 5l1‘t.‘l|_I.',iil 1.11 1111111!) 1111',-"1112. U.~1i11g 1110 iliilciwillg 1“lil.‘=T1l.':-1.L1IIIl[l._ l1lrTvl'||1i11cl ‘|‘L"1.|.DL1]1I!I‘ 1:111! 1111:1111"
r.-1lp1ll."it._1_1' is 1'1l:|c<|1.11m.*.
I-"cur :1 1 1'1 strip, Til-1'1 F.~1cI.r1l'r1l'1 :i.1lP:tI 1'r:ll'r:n :11. tho r1'i1.il:.~1|
at-(11011 is
Fuundauns
50111114111
1, _ 112.113 11.1111 11].; ll‘
T|l<.~ 111.-L fal1:l~.:-1'c1I. 11111-#1111111": ilI.‘11I'|1_L 1.111 I|l¢.- Ii:1<.l1i11g is .~ll1l.='-1'11 111 1111* 11111-.
2
, kip;-1 [2313 1'1-111 ll] go in 1:; j..= -.;.-' { _ , . _ . _ . _ _ h
iiun fur !-i1IlII!élt‘ 1.111 till: rigiit 51:11: of 1.11:: 11:11.11-illlg is
1.
. 1.1.5.01 l -1
= 2.11.51 iviipli
if = E
|;.',u'.11'i':1l_-1|
15 E:
(1-1:111
T111: 2-:11-tzlr L'1lp1l1L'i'l§|' L:-1' l.|](' fou-11111:, is §_;i1.'1.'l1 1:-_1.' .'\.(_'-I
15.11? 111
Eq. 11-:1 .11.
=E = 5.515 1
.11-', = :1.-111.111.‘,-“I
Fur ll 1 11- strip. L114: 1zll'turL'l1 5111.111‘ iul'L'1.' ELL 1111: l.'rilicz11
9411111111 is-1
12j11_11.1s11jl2 1.11114 1.._11_1.nj| \|1':1l111u = 11.1 1111111 i kip
|'___ _ 1j11.:1:1 11111 11.11.; 1- ¢,...'I
= l3i.t11I kipei
ll _
12> 1""
lj1l.;l-.1 11.111 [1](-5.1]-5
I 11.311
|:
Dusign for Fillllfl
2
'I'l1<.* 1.11-itir.-all .~1r.-rrTil:11l I'r.>l“ I'Ir.-1<1l1'ltl i.~l l:lr:fillli:li in AC1
= 2.112 I-lips
Sr.-c. 15.1.2 11.-1 Ill.-illg 11101111-r1 a'lI 1110 1111.10 111' 11. LfLl'ilL1\‘I.‘11? wall] 111111 11ll111\'11_1" 1101-wlllrii ‘iil.I.' 1:l:l1tcl' 1111111 the 1'1-1-2011121
Figure 2.2 C.r.~11'1:a1'.';'1‘s~1:r.\:11'.~s for Fraxurs and
1*;'1 masonry wall -
CEll'1Cl'E1.E wall -
fllalcura '~.
flaxura flan-aural shear
flsxural shear Q. -rib
1-
E-11._.1 1:1
“
11'
anchorage Iungth
PPI
l v|ulu1r.ppl2|:l.nnl.:nln
2-4
$‘IlIl.l¢Tl.|IlI|I. ennunesnlnu usrznsues Il.l.Nl.llI-
Hfiaatrafian for E1. 2.2 ‘I1’!
E
"I ‘P/-"
__ccm|:rele wall
‘Pu — 13.91 kip: lIl'|‘llD813BflllDI'IBf|III"'||BXLlFG
h-'§'|'"—-_
"1--_____
\ n'1.1?&|
'| '“‘~
_ crrtical section for shear
15in I anchorage length
i
factored load
____é_.
epunng SUO1
I
If/’
_ 2.33 n
-—III
F?
—
-0331?
|..i....i,_.1 I 1.c|n 1.sn ,
__;_
2.45
CI :r __cT
Q
l 3.68
4-73
fanmrcd pmssurn
5.95
s.au
, 2
"M"
l__
|-I
3.5 HI
critical section __ for shear acc-
£l'— 'l.'lTfl
I
I 2 02
2.85
TI'.EI'|
Shéflf
mus
‘F’ u-1 ca
l'l'lDl'l'lB|'l1
H-kip;
11m.~u'|-||rj.' wall. as shu\\'n in Fig. 2.2. 'l']w n~¢|||ir:':| rainl'4.|-rI."I.'||1unl z\rr:<'\ is d1:l|.'rmi|||.'d in 4\r.'L'ur»:h|1|1.1.- with :'\.CI 311*. 1[].2_ For :1 Footing. Thu mi11iluu111 ratio. p,,.;,__ uf 1'1,"-it|fi'|1'[:-|'e:|m11t :1|'re:1 m grue'\~e |':r;|||':n,~tn :1|'r_!:1 is H]11_-cifincl in :\(_'-I Sm‘. I(].5.=1 il[l.ll S11‘. 7.12.2. fur huill lnzlin rL'in-
i'u1':-:-:m:11t Flllll di:-atrilmticm r-sriufc1rr1~mc~n1. H:-i H.H(]1H fur grnriv [HI barre. Tlu" 11mxi111u|n :=i]m:!i11g of The umin 1"1'il|1'1J1'(M.=tnI.‘-111 -¢]'m]] nut u.'~¢1.‘w<.l 18 in <_|1' Lln'u.= l-iI'|11'=< ihv Euuti1|_g.', dcptll. Thv tliau11r:iL'r of bur |>rm'id:!t] uulst Iw 5-||r'l1 Thrll thv rlrwce]|;1|m11*u|: lnlugth c]uc!eA nut nxnnr-rl Ihl‘ i1\ca1]|z\hl1' zu1n'||u|'i1gI.' |l'11g1|l. Di.~t1 r|.-]||l'ur:-n-
Exzunplc: 2.3 D1.~Im'|nin»:: tlw rvi||fur<:c111sr11l rc:qI.|irc:d in the 51 rip {nuting For I-fix. 2.1 :‘1ll|'| I-Ix. 2.2. Snliielrurr
Ar: -4|:u\'-’t|. in the iI|||.~¢:1-a1iu1'| fur Ex. 2.2. on t.|:r- riglul :-i1l+.'= of H10 fuuiiug. ll|L' i'1\L'lur-2:] |}Fl'-55lll'L' ul H11: L'ritir_'2ll 521'iinn for [']11.>:1Ln!. whicln is at tlw right fact! uft]11> wall. i:-a |_{i\'¢.~|| 1.|_'|'
lncut 1|1n_\' hr s]mc:c::1 at. n mn.\;in|u|u uf 13 in car [imiirncrs flu" [ranting llrpill.
. fl‘_ '-'-{J-7' {T}
'
:3 r1
kipus 6.30 —.. :14.-' n FT-' J 0 1 _ .1T'i '_ K 13 n ' ' '
l-zip-Hit.’
"’
|=-uunulrlnut lllll Irirnlllllln §'r|luI:'rI.IRE$
2-E
For n 1 it strip. the t'ar't.urr'rl uu.m1c11t. at the rritirriil
Thu lniniluum rrtilflurccllimit I-U'L"J\ govrrlus and. for :1
>u'~c'1im1 is
fi'mr.i|:|g_ is ;|r,i1.-'r:|1 I:-jg ACI Elm. T121! as .4 < = lHJ[llSb.i!
M"=|:1M1:|*
= (:[Il.||(]1H:|[]‘l i.l.l:I|:]fi in]
[1
(1..-'>f1_1‘{1 h](-11::
[21(n.:m H
_ u.:!D in" I"r|.wi:liug uu. 4 |Jill'}‘.-' at G in un I{'L']l1(.‘l' lur bullr rrmiu iiml diz-abrilmtinu r1~ilifc:i':!r'r|m||t- give:-i
= 6..-'r-U It-ki]1+i
.-'1. = [:|.-11] in"_."fL
As slmw11 in tho i.|.ill:-i[I'fl.Li.flI|Il for Ex. 2.1!, can thc! Inf: side (if
LP! _ ‘Fl _ A _ 1 _ ' _ _
ilw 1'innl.iug the f:1r!r.rm\d ]1i'1=:+iui'c! :-11 1l|.r- rtrific:-ll :-er
11:.-xurv.-. '-\'|li1I‘]l is :11 ll1|i- lc-I1. lime |.:I' Llntv Willi. is given l.r_'r
‘|', = (1.3 r:"-iiri _ 2.5 4 I.
_ qr,‘ [Ii-.5 I1]
‘I W
AC]
(0.311
::r:|.[l.~
[s..a :11
|l1.1r nu. -l hnrs]
Fuundauns
|l"|nm .l\(‘[ SD27. 12.2.3:
12-1 for rlciimlupiiiolit longth l'[!(|.lIII!(!5 to .
E
0 r1 = 3.0.5 ki[:s_,-"[1?
[I |::|u'u;|l|:!|| h-call-::>m iliurer ] ||:| |:|||r|r|;|.| wr-ighl -::||m'n'lu
.
= |:[)_|]T5]|:U_$rttJ‘_] = U.l|lJ|'ll,([IU.[]lHl 11'
ll
Ii
2"r'A"*'T
:2.r1j|[ 1.11) '|"Ii£1lHJ H]
[ll
= 1'li.H-ch.
I-"':_'|r i;‘| 1 ft. strip, they EZ‘1|'?i_.l'_:-|'|':|'[ ||l1f|-l111?'1li_. at rho r:|'iric_':il :s|:cl.iu11 in
= 13.1‘ i1‘l
|iu-|' nu. -l imr.-r|
=1 15 in a11:~h»:1r.'1gr~ I:-rigrli 111'-rwirlvd
[>-.~1|i>d';|=:|m-_\-|
M = r:r.5 frag: [1 friq 2. ISULITED COLUIIII WITH SDUIFIE FOOTIIIG
I
r':r..=. {EH1 £n(:s.rm
Nomenclature ll;
[i
_ -r . . ft-l-zips "-‘I’
wi1]1|| HF llw r:|'i1i1';f| p|":'i||1|'rr!|' l'l1l"Jlt\-‘l!|l'H'l in H:||‘-
in
clirrvti-:>1: oi ."|!,,. r-| — if
:gu\'r-i'm»]
As-unirililig :1fntisirmn--m11tl'ral|P<| .~mr:r.ir|-I1. Th|'!1'fn'||li|.'\'!|'| min-
l'u1\L1*1||'L*ill- ruliu is givn-11 by
[13
\\.'i1]1h uf llu! l'l'i1iC:|] ]x!!|'il|1i'1ul' l|n'iL-ellrml pc:|.'||u|u.|.lc:|.|]:1:|' 1|| iq. rt: + rl
in
FI,. B
lr'r|g‘r]i |_rE 11w :'|'iTir<'|l 1n*1'ir||r't:-r. 2H1, -1- fi,] lnugth of flu: lb-c:tili\|._: l.l'llI'{|.:-l]I€1l|
in ft
F1
\\'i1i1iiut'li|1' (‘
purpurlrli-::l|iiu' ill L
. . - '1 -i", 1.; .-5 U b K (1 \|" [1-3S3[l!F,f:.)
in
rlirrv:-tiu-11 uf ."|!,, 4:-_.
” _ i.
\'|-'i.1]"L1Jt-"L1! i;n|1ll:|'|!|. |:|.|I.":u-rl]!|.'-d
in
[x!r||r!||r|i<:|||;1:' 1|| r'|
iu"vI=1g|:' +.~fiw:1i\"I:~ 'liII‘|11|l
i_|r.x.1j1£:r
.- . |ru]:1t‘ lr|I.:-rlwlil uf il|I.'l'|iF| carirlilitriil |'u'l'i1|u!I£i!] . I-. - ._.l|"y 2. [b,a|f|: ht + .'j-h_.') + n“'|_-"3 Hm’ n. I-::nri1\|.; with 1_'|~nl|'n|
11]‘
|;r.51 fl-I.-Lip:e](1'.'.’
in ill‘ in"
culumu as :~'pt1'iiic'r| by .-'H_‘[ fit-. EH I. l l.T.2] L
lmrgtli of flu: F;:-citing l.l'|II'-ll:-illllfiil in tl:r-
ft
rlirl-til iuu ui ."lf,,
>< (IDOL! ><|-1-L
(u.3.*3:1](12 in](1=l in)“
.1--L
m|.I|||r.'n1 -.1pp-liwl lu 1|u' (“l‘||1!|Il|1|.
it-Iiirm
\-',,
l'|u:rc|m"l siuear l'urct- ac-ting on tho critic-nl
kips
p(:l'i|:|u't|-1'. P1l:l — |'.I|[|_=-,I'.l'31'.'|
pr
... |[-sun-0
<1ie~'tui|r'4.' i1'r.»1|i tho l‘f'l11flJi4i HT tlu" r1'iti~:'u.l
in
p<'ri11u'rI:~r tn »:'r.lgr' uI:'1'itiI:-all ].1I:~r]|1|-:'t1'r. -';|_."2 [Fur fimlIi|]|.1 with 1t0l'|ll'al L'1.r]I|.lm|]
Ill“
Symbols Ill"
= +1.00-07
'1...
fuu-riu|1 r_>f't|1r~ |L[l‘|IIiiII‘l| mmrrlrnl 1ri\r|=-:Ii:'l'u-cl In}: .-il|I.‘||.l' :|..-i :ipc\r:il'u:cl hf." .-\.(‘I Sn;-. ll.11.T.] marl
-
5.... 1;a.r,.;r.2. 1 - l_-"[l + |1.i;'.',,,»'.'.Wg> PPI
l vru|ur.||pl2|:|anl.:nn
2-B
$‘I'll\|¢T|IlllI-.
EPIGIIIEERIIIH
REFERENCE
llelsign for Punching Shear
ll-llllllll
SI-l'E‘liHif‘l-I from lmtll II!Ult{l.iIlII)ll5 art! E'UllllJl.Il£f(| ml llptrtrililnll
- . tn giw: :|. lllaxilnlllll \'fl.ltll'l I'll‘ ill AC1 Sm"; l{ll.l 1.4.1
Tllv t'l'iiil'al| ]J'L‘l'l[lIll.'l1_‘l' [ur |IIlllH.'|llll[i', sllullt is l*.i[IlL‘lt'lfl'L‘ll
ill AC‘! Stltr. 15.-"'l-.2 and SPF. 11.1l.2.1 lmtl illlllltrnttltl in Fig. 2.3. Fur :l ljajtl'|<-l\l_':l_.n r_>l' l1'|:L-lt_'|lll'_l' l?rt_lll1lllll. the lj:l'itit_-:_ll ]lc1'iltll.'tI.'r is ll llilsllulcc l'l'ulll l.hI.' l'lu:l: LII llll: culllmll cqllell
_."|- nlrlliwl la, = I"-ll + T
Exa.lnp1t.- 2.4
in tllll'~l1.llll tllrl t.~ITt!t:l:i1.'t! tlnptll. Pm" :1 sttltll tttllllltlll witll it
epunng
lmstl 11-Iatv. tlltl tlritiral |>l~l'i|lltett!r I1-i min-Ilalf tlltl t'l't'ret:til'n
A li fl. :-ll'|_lIJl.I|‘(I l'nitlt't>l'nl'tI lI?flll("l'I£'T!‘ lt:n1illgnl1ltll'1m1I 1.\'t!i|'.1lll
rlt*]jrl.h l't1.Ill1 ll |1l-lzl.IlI.' l|.l|II'\'l'l'l_\' l.lt.*l'l1.'1.*<.~|l lIll.! I'ilt'L' l_Il' lhl?
l'u|lcl1_~lt~ wllh illl 1.!ITI.'trl..i\'l.' 1Il.!l}l-It l_=l' I2 Ill H'll|_l]_n_:l't:~ ll I2 ltl
[!IZIIl.I.llIl1Il1 El.[l[l tllt! tltlgl: til the lliltillf pllltv. Tltt‘ [llllltrlling H-llf":\T liTl'l"!tl.}'{l.Il nl Elli‘ til-rltillg Ll; -l'l~I"l'.l'lt‘1‘l‘|lll-WI l‘|f|‘ .-9lCl Soc. ll.ll.2.1zl.~l
I5-(]llEtt'l.‘ collllnn wltll at fllcturtrtl &l.3l.lill. IUt11I(.Il2l.H.I I-:ip.~i. TIH.‘ (5l'|llt“l‘£"lE' strlvllgtll in I1‘-llllll lht'_.-"ill?. l.l1‘T!'T||lllll* 1.l'llrltIlnl' llm jlllllclling t>'ll4.'ilI' ("-il.[1iI('ll_‘1' ul IllL' luutillg in £
'_
ti-1-j = -1§_i|'l‘.l|IJ|,)\.l\|III1';
SUO1
|Ac'r H-I.l3|
P.
‘ll.-'lu.'tl -'1” 21- 2.
cl 1...? = r_f|||‘”),,(2 +
J.-.;T
IIIII Q»
1.113: rt-alj Ml:
.3 = [175 'l'llt* (il'I‘|‘rTlI tll Ill!" liltltillg is IL'i11:'lll}-' ;.rtwl~l'llnrl I1}-' tlln |l-lllll.'lling_ ts'lll.'iil' L'il[Jtl('ll.}'. “I-'llL'tl lllc L‘Ullll|lll sll|:pul't.~:~ l.l1ll_'; Ill] llxilll IU£ll|. Pv. :lllL'lll' hil.t‘IZ‘l5l*i Ell; thl: tlriticlll putillltltcr is llnil'urllll_l.' LlI|5l.l'2ll.Hll.l.‘l.l. Ftt'(IIll.ll[i TIN" t'rit.it::=lI ]wl'iltlrltt!r. ‘I.'l'llrlll. in i-1tl1'll.lllUtt ttl tlln alxilsl llmtl. al lmllllitlg, lllullzll.-ill. I'll... in zl|:].llit'tl In l.hl.'IZ!EIIl.lllI|111. lltl t!t!t!t'|lt1'it' >=hl'nr Hll'II!liti i.\l i1lt.rtJtlllt!t't| itlttm
lb
un llll- Izltru |ll'iIl'l.'-SI Lllu lzlrt-;l.'.~ll |=-L'll1'illg [Jl'l'S.‘:illl'L'- 'lThL'tl lmtll :l..\:inl ltillti sltltl htwltling [tI[ill.H.‘llIL tl-ctlllr. tlltl filllfl-ll’
Figure 2.1 Cr.-J|'r:.=l|' Pl-:r|'me.'|-2-r" mr Pr.-m:1'l|'r1[: S1192:
critical i
Z
"-
__
I
aclctlcln .--:I3::"-ii'::il
5
“I I I ""I I I
r._ I I I I |_
|_ _ _ ;._ _ _ _
m
2
ha“ VIM“ l:I5"'
I .--:1
I
I
l_ I-nil-IQ
c-rl
critical perimeter
I
_2 | 2 . ._.
+| 2 +
old
I
1-Q
critical
2 4+-.
I1.=1-I _
m c
I
critical
I
we
steel column
sactlcln . I
I
I-
l'l‘lfl5OI’| ff Cfl|Lll'fll‘l
I HECIIDPI
I--l
l_ _ _"_ _ -
tllrl trriti-ml] .*il‘.l':I.i|I!llt with tlln lnlulitnuln Vi-]l'Il!" 1'»-."t'lll'l'in5!_
collcrete column
-|
. critical perimeter
Bl
c-m-0 critical perimeter
F-uuuunrlnut tutu BETIIIIIIIG rrrtutrrunct
2-‘?
51:1-ltlill-rm
Exmnple 2.5
Till‘ llul [El.l.![LJl‘L'l.i tart-s~'llrc l.rll llltl l't.lulillg in
Fur llt1.' l'l;litll't.lrt‘t'ti t'l_1||l.'t|.'lt‘ lllulillg ul E-it. 2.4. tll.!t|.'l"llli|ll.l \\‘l1(!ili1.“i' t-ht‘ Iit'.\cllrl'll->illl"n1' t!slpl1l"it.j.' is El{l.lZ‘[|_tl.I‘ll{‘.
P, = '2I]lllt' .... = H5
= mt. lnps,-' ll.P.
Tlltr lvngt I1 uf thv t!1'it.it'ni ]IlIi!I'lllH.“lIl.‘l' is l»,,= 4[t-+ tl]
I
Wu
l'JI1!'i
_l..
Fuunda
l'-lj|[l2'ill—'-1'.?i1ll
12 E it
=
D
in
It
Silt-tltl" all. I.lll."1L'l'i[il.'ill. _|.l¢.‘l'l.lIltl.f[I.'I its
1-". = P. — t.ti~+ tn”
B 1
_ Ellll kipls —
It‘
1., In
I
it
Lml
= I'i'i'.'F ltilat-< Silctlt L‘-ll|JilL'll._‘|' ul Lht: luulillg ill._l:__i1.'t'tl lay AI.‘-I En. 11-321 al:~l
...
TllL‘1.ll.-ii-ilIl1lt"f.' [rr_1l|1 l.llL' t‘tIi.I,l_- t_ll lllt: ln|_l-lillg uf l.i1l_' ('l'llicul
= -’l¢lr.l'li,.)t gf
letrtltitm fur Fltlxlmli tllltlnt it-a
(4'l{l1.tr.;[12 ltljlljllls llt'llj1.ll} ,~I:llllltl if
111“
I=£—i—rI=fi—L“—l ft 2 2 1J ZJ
= 1.5 fl.
llltlll II_’I
kip
Tilt: t'tlt:t.ul'l*.tl Hlllllili‘ l'l1l'tu:- all l..|li:\' wt.-t-li<_m ill
= 1t'i!).Il kins I» 'l-".,
Htliltilulr
[1-"-lltiltlnt-tut‘)-']
1...": .,_,lt.. = (.156
liluslgn for Flmtural Shoal
is f1][l.!] tl._l
= -5lJ.l.l kins
F't.l:l" t.‘ull|;r|‘t.*1t'tl.:lrl lllll.~t|lll'_\_t' t“t.||l|llll'lr~'. tilt: It.l|IrHl.it.lll ul IIII3 t_'ril.iL'lli lst_'t_'litJ11 Eur flcxlmll :i|I|L‘t1l' its ltI1.‘[lliL'k1I with lhllt
fur :1 strip l'nt1till_|.t lmtl is slltiwll ill Fig. 2.2. A:-; 5-i1t]\\‘1] in F'i,lt,. 2.4. Ill!‘ critical :-l.t't'tinll 'F1'lT tl Httlni t:rl-Illlnn with tl i.Hl.M.‘ |=llll.t.' is lt.lcall.|.'ll an t~li'I.'t'lil'l.' tI4:pl.Il ltuttl lht: |.l]il.llL' l1llilwllj.' lrlrtwolrrl till.‘ lllt'l" of tilt‘ trulttrlm l-llltl tltigt" til tilt‘ l'HL‘i-li‘ plntrl.
Tl]!!! lliltlnr trapnttity til tllt! i't>rl-ting it-l gil.-"ml by .*'t['Tl l:Jq. ll-3 an
l.=~ l".. — 2-:1l:r.Ul .,.-“If
.ttt}|_l.: lllll_l.lnvl_ulllll . .. llt |j_.t]{[l.l.1_l[.-.2 -. 1111' lllllll kip
Flgnlra 2.4 Cr.'n'|:al'.S‘a1:r.lcl'?s icv a F.-:lcl!l'rlg' with Stclarfiasa Plate - FLU i-ti]1>.= 'SlEHlCU|lJ|'l1l'l
?=- I-"..
d
E
Dasiqrl for FIUIIIFI
E
:I
:~
trace pllllbe -..,_\\
Ftir tltlllrrrnttl anti m.ll_=t:llr_1.' IIEt'IIl.tllII|1]H. tilt! it>r':ltit'ln til ill-fl I
I;
|fit'llitiiti('H)l'f|'|
cntlcal secllnn I ‘M "Mum "‘"-\l : I
I
:f':"I'II='I sncllnn : l'u-r slma I
l'l'ili('lli :~'l.~('l.iull Iut li1.'.'4'tlll'L" is llll."llliI!.‘-Ell willl lillll [Ll-l" at le.l.t'ip iutitillg F|ll(l. is I5-i1li)\\-'1] in
2.2. .-‘Lee. l-.=lluw11 ill
I-'itr_. 2.1. Tilt" t'r'il.it:nl 2-H'N'2l'i|‘bll t't:l' fl€'X‘|11'¢‘ lin-l' ll stml mllllnll tl-'itll al hillw ].llilIL' is all at ])lil.I|]l.' llili.l't‘.'i\]|' i.!'l.‘I.'l!t'L'L'lIl tllu l'alu_of tilt! Ct]i‘l1111ll anti tilt? ttlgtr til tilt! III-it-ll‘ pittttr. PPI
l v|tuuv.ppl2|:|anl.:ntn
2-B
§'|'lll.l¢Tl.llIll.
EPIGINEERIIIH
REFERENCE
Example 2.8
ll-llllllll.
Tilt‘ llllllcilllllnl l‘liiU‘I'l'tI.i1lt‘ l't!illitll't't'|llt!llt rlltitl ftlr El
l:l'4.fIII."i‘llllll1.‘ l.it1.' llt'it1f|.:1'l.'l.'l|l|.'lll l1.~t|llill.-ll lit lil1' -'4l|_|.lill‘lJ i'4.lt.llillg fur Elt. '2.-I. Till: llvplil of iilt‘ luulilll-.3, i:~' 15.5 ill. llllll iitl.‘ ]1?llti[il'['PtllPlli is grlltlo till. Sollllmrl
iIl"'tl.fi.l|'|=tI.-lIIi'!llllil't'|llf!|'i !lt!4".litlll i:-l ).{l't'-fill ilj,'
. . IT .1, — 1l.l1t1.-11,!-U —nmw
10;]
__ I
s1\ti~"l'lll'1url'. ‘iliE‘:6l!t'il(H]
i. Ir
I!- I-l!!ll_-tltlll-trllltllltllitlti
Pll
Tilt! l't!t|llirt!ti rtrilltil-l'tll~l11l!11t larllll is -D‘R:
.4, = pill-i
SUD1E’!pLl Fl-
_
__ _ _
I"
= {[l.ll(l23l[T‘2 in}[I'2 111] = 1.119111‘!
t-112 |
Pl'tl\'itiillr; ttlll lltl. -I liars gi1.'t!!l I-‘l l't!'illi‘tll't1~ll1t!llt ll1't-ll l'li' .-"I. = 2-U Ill:
El
:l=llti.~=i'lll'1tn'_'.']
'l'ilt! lllillilllllnl ?'tll1'l\\'fli]il'! rt!illl‘i'1l't‘t!llll>llt :=1l'r!:!l is gilmll ii}-' ACI St,-t,-. ?'.I2.'2 Ht-ti l
'4 -
L
'l'llt! liltrttlrtlti llltlllltlllt .'1t till! t!rit.it::-ll l-'1-I'\!‘il1'l1‘| till‘ ll-r-ltlll'r! wilicil its ill |.iJl.' iilfl.‘ 1.:-I I.-ill.‘ t't.l|ll11111. its givcll i1-_l'
ill,-,=
1.t(;—%) 2
“'
=
.)
q
= {ll.[H]il3.l[72 i|l)[l5.5 ill] = 2.1] ill:
lslltilalat-tlllwf
I-'llllll I-Llc. 2.3, tilt! l'l.|'!'l.-'1"!lt'l]‘|-ll|t'!|lL I-rlllgtll tlfll l‘|t_'l. 1 iii-'ll' is
1,, = l:l.2 in
= lllJ.3 It-ki|l:t
Awslllllillg :1 l1.‘!tl!¢iI.It|.-("Lillil'I.>llt'!I :
Tilt! I-‘I‘lll.'liU]'llf_§t‘ icllgtil pl-tlvitltrti lill illtriltrl-3] ill rt in = — — — — 1'-llti rtlvnr wr_ - 1!L. ._.=1.~a 12in .. 2 --T--Jln
Mn
‘an’
fl=
= 2? itl
;'- l._-
r -HE (11.1-t1_1(.l mg )
11114.3 ii-iti]1l*.=i( 12
:Fl'llililI'l\I.'lUI'_‘t'l
Transfer of Force It Base of Golumn ill rltlrlllrtll-lllt't! with .#t('l S-lll‘. 1.'1-.H, Itlllti I:r.!lll.~:i'r!r iM"1'|‘L't"\("ll
><(ll.HJlJ >< 1-
1-Em, ll.i.3EI>l3:IlT2 il1:ili2 ill]., 1. (.11lt1t1
._ iiipfi [ill mg
= [l.lIl(l23
ill
fl rteilllilrrtltl mllt'r‘l!tt! rln-llllllll anti tilt! ftlfliittfi 1tnl_',' llr! a1ll't~t"tctI i)_'l' I11.-ll1'i|lg, un t.lt.l11t‘ll:tt.- tlnti hf.’ l'L'ittiUl'('L'IllL']li. Tilt! iltrlltillg trtlpntrily tlf tilt! trtlilltnll t!tlt1t'tt!tt! ill: iitt‘ iIl'lli"i'fi'l.f2d" is givtlll i'|]|' AC! Eimr. ll_i.l-1.] ll:-l
l_j.P|_,,| = l1.ltrl¢1'_i.!l. = l1.55:1j|f.4. ell is till?‘ I-‘ll't"'l-‘l tlf tilt! ttlilllllll.
[r..1- .1 = 11.1‘.-'1]
|=-uuuusrluus lllll Itctnlltlltn srllucrunct
Rt:fcl' ttl Fig. 2.5. Tile iltrllrillg lI'l~‘l]'Nl(!ii}' tli tilt: ftltltillg
2-Q
E.\1't!s.-l ctlllllllll ltlnti in ht‘ trtltrilrti i1_\' titnvcls is
t!tltlr:rt!tt! at tilt! lllEt'!IfHI!‘fl is gilt-1'-ll ll}; .-IICII Silt‘. i[l.l4.l ll:-l r_"i.l"’__ = Pu — 1;,'.lF|\," I
¢.P._., = 1l.s5¢;;'_.-1,101‘?
= Hill] ltipt-i — 23!} I-ti|I1!=.
I |
= -"II kips
1: {ll.Ei!]l,-'1_|'_I.»i,}[2) Tilt: rL't|llirt:ti ill'L'l1 ui tiuwcis is gi1.'t:ll I1-_l'
1-is = i"l.i't'!t-‘L tlf tlln III:-1."-ll’! til‘ tilt! ]lj.'r.'l1lliti. lvitll silll: slurs.-.-1 u-i' 1:2. i't.lr11ll:ti l\'il.hi|l tilt: in-lltillg ll}; tilt! [TI-llililli illlst!
4
_ = till‘. =
' ""'"“"
11.1-15;,
-!
Ill llt'tll.ll'tillllct: wit-il .-‘t(.5I St!t!_ R1."l.t-i.1.2. l.lrilt!|l tilc ilc11rillg stl'r!ll|:tt.il at tllt- l'l1iL'i£" tll tllr! milllllll 1'l!'l' at tilt! ttlp til‘
~li I-lips
_
1t1.l3..}(ts1:1
ki ._. Iii
= 1.1115 111“
lilu It.lul.i|l1_-.'_,' is cltt"I."l:l|L'ti. l'L'i|llurt"t'll1t'11l. lllllsl ix: [lrt:ll'itil:li
ill t!1lrr].= tilt! tllcctrl-at in-llti. This rt~it1I'tltt:t!lllt!|ll. 1118}-' illl ]ll'n-'.'itit_!tI ll]: 1'lrll1rr!l:l t_lt E_"l(TE_"1‘|l'l1'21'l it,lllgit_.1|t|ill:li lltlt!-1. ?'lIiI|'l
Fuundauns
i1l'U‘1-'l'iii[lt; lullr llu. 5 1.iU\'l.'L‘i’:€ gilrvs llll lll'l.'ll uf
tilt! ctlp=lt*.it.y tlf tllis lt~illl'r.~|'tlt!lllt!tl1 is
,=l_.;w_.,,_.;, = 1.24 illu
til". = 0-*'IJ.,.
[=-=lltil=l'=lt'tt.ll'_l']
Tilt! nlillillllnll ritl-wtrl artlll tlilrl-wnti it-1 gil-"011 ll}: AC1
F1 lllillill1l.lnl art.-tl ul rt!illl<:lltrt-lllt~l'1l. is t'Il't']‘lIi]*.‘
Ht-1:-. l5.S.2.l :1.-1
illtl:1'i"1t.'I.'. 4 ltllti lilis is.. "ivl:t1 n i.l_\' ."'1Ci St.'t_'. 15.3.2.1 its .-'1_.,;,,,i,,| = I].[Ill5.!i, = (U.I)[|5}li~I-I il1::|' A=.ll=lm'| = (-I-UII5-’1|
— [L72 I113 -1: .-'i.;1,,,,._.§.
Example 2.7 illsslllllt‘ lillll tilt: t'I.l-iutnll itl Ex.
l1!l.s ll l.'Ultl.‘l'L'i.L' tolli-
lstltisfat-tu1'_v|
Alltlwlllg fur tilt: E')tlI?!l'!*l:i lt-illl'|i»l't:t!t1lt!1lt ]ll‘twitlt-ti, tilt!
]‘l-1'l"'fi5-i‘.-‘II! 1-ltttlllgtil tlf Illlllil il1E'.'Illl." anti t!:ltl'it!l-l ll El-‘l.1[‘I'.[i1'l'9l'i
[iL“.-'L'iLI![J[ltL'lItli lullgtil ui tilt: li|.lwt.'ls in tilt: L'U!ltll[ttl llllti ill tilt! ltltltillg is gilrtlll ll_\' ACI Butt. 12.3.2 as
i'lKli!l Itltlti uf ‘Z80 I-ti]):~l. licsigll lllr: tIt.'|'l-Pills l'£n’.|llit‘r:|.l all till? i]1iL‘l‘i2tL‘L‘.
I
Saint:-ml
Till.‘ Iwllrillg cll]Jzlt'it1l' ui I-il.L' t'uil1tn|l ct.lnL'rL'lc is givcll ll}.-
!4»ajll-~<|tI'l . KfyugmI) l_lJ.[)2rt;Jg] -l'r=
-'\‘t-‘T
AC] St!t:. 1l].1-I as
1.115111" , . . lb!’ _ H24 mu) [:[tl.lll}l_ll.tl.l m1(t1l1.l11ll1
._:-P... = 11..lrl:l;'_'.-I, . _ _ . _ i-tips . -Z : [Ll.::-5.i_l .3 fi [1-14111 I 1t l
11 .1 1).‘,'-1'.i[)0(l 1111 mu
I 231] icips
— 12 ill
Flgm 2.5 8c.~lr1'rlg.- ct! Futlrmg -Cutlwt-re C
I
|
.»
d
_,.= ..'
1
/’
‘__.-
l
[__ I“
\
-.\_
-..
-if
“--1.
.41
loaded area
If
c2
"~- --_____ -1.
ii
1:‘ I -Ila‘
at '-I \‘A, — base IJ1‘|J'|'l‘Bl‘l'|||Il is _ 40,]:
PPI
l vrullu.||pl2panl.:nn
2-]_fl
a1't\ul.‘:1t.|rt1nt. clttltltccnltull rlcrsnentcc Illlllll.
This ilrllgtil cxt!t!t!t|s till! lllillitnlllll ltrllgtil tlf l'l ill spl.!l:iiil!ri
Design for Flelture
ill .-\[Il F_ir!r:. l‘!.I_l-.l anti is .!lllt.isl':lt!ttlrj.'. ill tllr! Etllrltillg, lilfi
It-llgtll t_'1ft|ll_!l'1.'1_-lt_- r_>l' tilt! |ll.'r:1tllirl, witll !titl11!sl1‘_lpr:!l r_tl' l:'3. iul'1l1l:ll wil.hill tilt! iLll.ll.it1|z_'. I1]; till: ll.lz1t|l:t| ll1!l:1l is L_,.= rr+ -ill = I? itl — [=I]l:l2 ill]
Plllrt. tli' tilt! l't!i|lltlrt!t!lllt!llt flI!lIl‘l]i]'Hl itl tilt! t|':'1lls!l't!l'l-ll!
= (‘H1 ill cf. L
10;]
llill.!c1il:lll is (‘t.'Il1¢.‘I'.'llll‘l1l-Elli ill ll <.‘i.']lii'i1l ll.-llltl witltll f.'f|lllll
l5i!ll.
to tilt: icllgtil t.lI ‘iil'L‘ silurt sitit! ul iitL‘ Euulillg. as sill.1!.l.'ll ill
Fig. 2.11.
Tilt: I-‘ll't"l-‘I tlf t.ilt! Ilnl-at! tlf tilt! [1}"l't‘tilil.fi is
.4. = 1.;-j = 1,611 ml’ = 34][l[l ill‘-' 'i
‘Ii =
l.' .4.
SUD1E1pl.1
Btltltiillg lllullltrllts I-‘ll'[‘ t!l1it!l|irltr!ll 1-lt ‘ilItl‘lZ!1'iii['I-‘ll strtrtitllls
ill lltltll tilt! il'lIlj.'_‘iTllliiI]flI lllltl r.l:llls\'t!ll-lr! fiiI['[7li(]iIl-l. Tilt! rt_!il"|lljl-l!1jll_!.l|1ti!||t lll_!t'|llilllj!t'l ill tilt! l(l!l'l_l{i‘ll_ll'l_illi_'ll tIirt_!t_~tit_lll i.~1 llilfil.-fIil)lll.l.‘l.i lll1il'l.ll'tnlj.' 1lt:l'l.»m till: witltil t.ll' I-il.L' Iuulillg.
Tilt! lll'l'!ll tli' tt!illful'c1l!lllt!llt rtlqllirtlti ill ti1l!t!t!ntl'lli Ill-lllti is
|_;§il't_!ll I13! ACE Sntz. ll]-.4.-1.2 tlrl
-:-
lllitilllltl in" = 5
2.-1 .4 = i‘
I‘ 111 ill"-'
I'
list! 11 lllllxillllllll vllillt! llf 2. Tilt!ll, iIIt"l-il'l.lI.|'{ cll]'1ltt!il:_!.' tlf tilt! Etltlting t\lll1t!1't!tt- L!l gil=l'!t1 i'l-_‘.' .F'l(Ii Hlillir. ill-I-I ii-‘i
er... _ 2[ll..;lilll_l_ .111 _ (21|_11..!-112.111 (:1
i l!l
it + 1
Tilt! l.'t‘lI]Etl.tl.ti[!I' u-F tilt! 1'l.!itlItlrt:t'lllt!llt. I‘l.‘ll‘|‘l1ll.'l.‘(i llt tilt! tl'1!1ll.~l\!t!l!sn tlirtltetitln is
1 1.-1.1 ...-1
_.t,_ =
.-1,. 5- i 12 4- 1
_ -ITS I-:i|ls '1'-\ F,
This is tii:ltl'ii)lltt!ti ll11iFtl1'1lli_!.' tlll t!llt:i:l sitit! tli tilt! t!t!lltt!r
|::lll[l:-lllt:tut‘jl.':
ilfltlfi.
3. ISOLILTID OOLUHN WITH HIGTIQHGULAH FDOTIIIG
Exmnple 2.5
Nomunclat-um .l|.l1t!:~l til ll.!l1I1f|.lIl1.!l|1l!l]t itl t:l.!.lltt'll.i llalllll
ill
.-I_
It:-|;ll rr'4'|lli:rl!ti l'|!i1l.Fllrl'l!llll!'llt lif-|"i1
lrl
Tilt! 1'1:itlit.lrt'l:li CL‘IIll1‘t'L'ilL‘ I-UUillll.'. slluwll ill l.llL' iuiiuwillg ilillstrzltiun is Ill It il.ll1g_!, il.[l.[i T ll. ll.-'il.il.!. llats Etll t!llul:til.'l.! tlt!]ltil tll I2 ill llllti an twtlnlii tit!|ltll tll ill ill. llllti il.ll_!l rl
Ll!
lt!lle_.1ll uf sllllrt sitil: tll' ll. l'L‘1I'II-ltl]E__‘Il.i-Ill‘ i'l:»lltill1.!,
it
1-l.ll1t:1't:ll1! ('l.lIIl].l]t.'1<-li‘r'IIl slrl.-llglll l.ll' -Slllltl! llll,-"ill"'. Tilt! l't.ll.lt-
ll!ll;_j_1il ui :til.tll'l l'iill.I‘ oi ll. rl!t:l:lll;;ltl.'ll' trllitllllll
itl
illg sllpptltls El l2!Uill.IlZl1] llritil {iiI1I|E!I|Il5l(JIl15 12 itl ll_\' 18 ill
lrlllaiil llf llln1;.~=itll! tli ll Tl"1'illl|fi1!llJlI' lillilllllrl lr'll|:1il 1_1f IUII15 sitil! HF ll i|'l.‘i‘i|\l|2_‘l1illl' iillltilllr,
ill It
i-Illfi is rt!illI'rll"r:r!l'i witil gmtir! til] i'1lll's. DFIfit'1]]lllt‘ tilt!
.-it,
P-9
Symbols If
l1'll1ll
rellill nl tlll! Itllllg sillv lll tilt! silllrt .-litil: tl-l tilt! fl;-~.ltil'1|.!, LIB
Figure 2.5 Rscrawgula! F0c.l'l'n_gr." Fle.'vl.lclr1:el'nelnr Areas L
_
B
“Pl
U3
reinlclrcement —l- -r
areas FGIIIUIFSCI
l-I-r
-Milli ‘ll 2"; I 11
I-llr
EA,
|t 1 1
1- Ir-
A,,[|$
‘II
zip, I 1|
FDUIIIIITIUIQ
S0-|'u I:-rm
I-Ill! IIEIIIIIIIIG rrnuctunzi
2-11
T111‘ 11lnxi|n|l|:n nll0wM1l1~ rr'i11E01'r'r|mrut ratio fur :1
The fm'lurI_-d |11um|.-nl in l]|c ln\11;-:1'c|'m.- l.|.il'L'C1iILll] ul Lhl: critirn] eexmrticm. whicrla L4 at 1lwfm:c!nftl11* crululnn. L~i B
I|u'" =
11*rLsi|'|-n-r:n|:tml|n|'l sw".ri»:'n1 is j.{i\'-fill hf,‘
.
-m
1'
_. J’:
11,- '[|.J1Q,'i| E
'7"L[? " T'}
j
— [H1213
2
.k1]x=:.
.Tfr.
lit:
_:i
_ (1.5 fi){1l|fL:|[T—T)
m|l1e1l':u|'|c:-l'_'|'. |||u :1|1'l'un|
' F
i~=1I.*|1>=im:|-|.'rm\n.I]|1'm| {JI'l!'i
1! 'I'lu'_- minilnllm :1ll1_1w;1h]r_: rninfi_'|1-¢1_*1m=-|'|I :'1|'(!:a is gi1.'c|| lay
= Ell] fl-kip:-'
."'|.:=:sl||uing at lulsiuln-tu11lrull1.~:l>1-4.'l-iull. lhu l'L‘l[lli.I.'I.‘l.| ruinfun:sr1m.~nt mtiu is glx-0:1 by
1'l|l.(_1-I SUE. T.l}.'.2 as
.--1,;,,,,,,, _ u.uu1sa>n _ {u.u-u1s](12u m}¢j1ni1|] _ :1.-m mi
%
:1.H;1j_T (1 - UFI -
Thr: rI.':|uirL'd I't‘il|[LI'1'U.‘lll1.'lll iu1'a is
P=
J’, .-'1, — pll-rl — {(].[HJ2B)[l2[J ln}I{_1? in]
[11.::>.>_| (.1
- -1.113 iui ‘;-.-'l_|,,,i,,;
£2101":-km.-1[12 ><(1uu|| ><]—
l—
Thu !‘1_‘ill[IJl'l'L'|IllL'[il r+.~quirL'1l in lhl: L'l.'[l|I1'il] T Fl lmml
width i:-i
I-up
H1.:u~;:+'>{124| in)[]2 m"]‘
3-C -sumo [K
lm-uist':u-1cnj:|
1 _ 2.4, _c':!'h{-1.m-i 511"} ;'.| — 1
lll
r ff
= -Ii-36 in“
l-Lips
5'3 m--.
P|'m'i:li|||x ll rm-. 5 |>:l1'H giv.-'r:=i a rni11fi'|rfi*1111*|1r are-.1nf'
= []_[H]28
.-1.'.||.r..-,-_, — 3.-J] inu
Hflu.-sfr|1h'|:|n for
If-.| fl. + I
[a-=uti:e1'm't-.11')~']
2.6’ 0,. —1B|n
T“?
n‘-12in
I
h
‘lfiln
B—7ft L-‘lE||"l
PPI
l IIlI!.|I|I|I|l8I-l.GfiII
Fuunda
2-12
trnucrunan zuulusznluu nersneucz Illlllll.
The rcrllminillg rt'i||iur
Exmnple 2.9 |Jr-Tr!|'|ni1w the plan 1'limr:nsinns n'q11iw~:| fur tlm c'-;1|n-
'4| = '4: — '4Pr:||[w.-II
hiliuci fi.1|.|-lillia, >.-|lu1.\'u in l-hr llllluwillg illlislrelliun lu pm.viclu a unifurm soil i:-vnriug1111*:-asiirircaf-lillill 1i1f_."ft 1111:1121‘ tlw s:-1"\'i:'r- In».-iris imli-r.‘:1t|:':|.
= 4.1.15 in’ - 3.41 ii?
= 0.0? in’
.5-'rJI|:!w:'?
1-"'rc>\.'i1ling hi-‘(J 11:1. -l imni uu L'm."ii sidc LII the l.‘L‘lliIf£ll
lmnd |'.§i'.':'s n miufcmrrrmimnt nrrm of
105
.-i,,;;,,,.,\.;, = [4ii;u.2u My — (1.311 in:
SUD1E’!pLl
P\||:_n.\‘il'|g |7u1' [-hr s1-It‘-w0igl'|1_ |_>l'1||(e i|_>ulltu_-;. []'11.' ||u:Xinmiu zillu1|1.'ai1ic L-qui\.'u]i_'11L suil bL'nri|||!, ]n'i:ss111'i: is
B].-‘
ins]wctim:,
rfl. = if — ugh
[satisfm-tuL'\'|
tlm m1::imr.e1g1~ lungtli
|u'cr\'i-:ir-:l
_ ||.r
is
-mun
i'll.iE‘!l||.li\l-l.‘!-
[1-
I2 E
=
FL
4. OOIIBIIIED FUOTIIIG
1uu-u
Pressure Dlstrlhullnn
The cL'nir|.|-i
is z1rl_ii|su'.-I! |m1i| 1||(: |i.'n.=I:ing (‘lflll-l'I.Ii.l|| ouim:-icii.-s with Lim-
(list:-1|u‘1~ ;r,_, Fruln thr! ‘|H'1')]H"l'L_V iilw, which is c:h1.ui|::!d by
r_'L-1:|irui:l uf lhu .sL'r\'iL'L- luuds 011 lhl: t.1\'u 1_‘U]1‘l1|lll:i lu
hiking lnumvnis uh-mil Hie [:rupr@r1_\' liun utul is gin-11 h_\.-'
]11'n\'idu n imiiunn snil ]mss11n~. Thu Fnczting ‘|'L'i(|L]] is i1|.l_jI.|:~'I;l.'|i 10 L‘1ll:~ll1'|f! Llml. I111‘ :-¢.Ii] l||_-ul'i|lg [:l"I1'r~‘~'lll"I' |.lL:-1-.<
T _U.5.P1'i' |-5.5111‘;
nu! |.!.\u;'wv:I H11: allluwiiiilu [IlIL‘hh'|.lIL‘-
H
/fr line |
\
Pi - P2 {U 5 l'l,'|[2(]l] kips] + [1-5.5 1'! _)[3(]D kijm]
Figum 2.? Gamma-rec Focuing mm »'.p\-:|1-eua‘ Sen-ice Loadsproperty
l-up
= 3.13613 ]'ii].lfi,1'T|.-2
The L‘U1]1iJ'il|.l.‘1.|. foul-ing s]|u1.\'11 in Fig. 3.? [ms uuc uulumn nrlj.u::r~nt tn rim pruprarty line. Tim lwlgili of tiw firuting
I
_. ,
l-J4] ,—. ('2: mi
QUU liips —- Lilli] I-zips - centroid 0| service loads
= 9.5 fl. Thu lungl-h ui' ii.|uI!i1'|g l‘|.'L|tLin'r1 Iu |=r|.>|.ll|I.'v an u.||i1'<.|1'|u
service
ilcsirilzg |:rt'ssur1' <11] thc suil is
PI loads
L = 21,. = [2][E'i.5 fr; = 19 ft -F _1i
I
a
_ }_ _ _ _ _ _
Thu width uf Iuuti||g_tu [Jt‘0(i.llII'l‘ I-1 1m'|lun1| pr:-ssurr uu 1111? soil of -"!i|Uli ]i1F_-"I11 is
P-|
_ P‘, + P; _-s sunkip“ kips _- __ B-fl!‘ I-3|!.
r; - unifurm
nearing presaura
P, I P2
(.'1.ursc5
[In ft]
liin.-1i1'4zfim2f|'Jr Er. 2.9 |'—15f't
12m.»:12|n-
centroid of loads -
5”“
F1 — 200 k|pB -
P1‘ 2TinI
1
-
-r
-0
12 i" *1 13 i"
"x
F; — 300 hips -0
1
+
,
| [d[o' 23.5in
1 . x,
3L
I
-I:
1-
I.
FDUIIIIITIU
Design for Punching Shear
nun IIEIIINIIIG $'r|tI.I¢IulI£5
2-13
Thu lirligtli of tlw crrit-icn] p-irrillititcrr. ns shown in i-lw fiillriwiiig iiinsi.i:1tim|, is
T111: critical |‘.ilI!Il'illll."H‘f fur |11111|L'i1ing slicrar in n mliiiiilwrl ihnting is ii]:-mirual with that in rm isnlntr-d miilmn
i'a,,= [r'+ rI:l + 'Z(i!:
ii.'u'.1ii11g =.1|u'l is I|'.s:m.*=l :1 i'list.=u1c1.~ i'i'r.r||| the farm of t.l|r: L'Di.l.llI|l]1 L‘I1]lIii.i. Lu uiic-imlf U11: i:iT|.'I.'l.ivI.- li.L‘[Jl]l. The 111:!-
= [12 in + 23.5 in] - ij2](1;r in +
fHlI!‘ilZI|fE!IIi ]}1'i":-i51]Tl" can the furl-ting must lac! -i‘|.C!lIIZ!Il'l11ill-Oil
irmu the 1i|('lurL'¢i =\|>|iiie1i wlnmn ]i.:-siis. as .~i11uwn in
= H3 in
Fig. 2.3. lt will llU‘i nL1.1L‘ssairi]].-' ix: uuifuriii unless i-lit‘
ratios nf tiw facrtnmd lcmds tn sr~l'1.-"int! lmuls nu lm-ih crilnlims am irlrenticnl. Figunr 2.8 C-crnb.\-iea Focmng u.-.-in .-\\pD.l\Efl' Facrnred Loaas
If
9:!
I“i°“I
*1 2 |“'| 2 i*
P1,,
of factored ___\'
|u_.,d5
PM
fa'3t'3'Bd
loads
il-
critical
_ _ _ __i“"F perimeter
l-.
l_
i‘.
DDSir!
iH
critical |}BfIlTlB|IBl'
dL 5 5
|
.
ci
17;: d
centroid _
1“)
Fuund B
T2 ft
.-I
19ft
|____
'l']1ri pliiicliilig slwnr t'i'i-I'm at tiw criiiml |‘ml'iim!iv1' is
r‘ I
‘ "_1‘_T_'_‘i i1]1ri
qu
rm
1-',. — .P| , -- q,,[-c" iiji[r -|- g)
l'atl-bred
praasura on fooling
(5..-:~
{:iri.:i iiijiij 23.15 iii]
= SUD kipis — zero __-'/I
_ .,
(12
I
shear
*7.
>___
= 2{ii3 kips
l'l'1OI'l'1(lI\i
maximum ~ HE moment maximum
VB moment
The
pimcliing
slireiw
r:spa~r-it).-'
is givvli
by
AC]
E11. ll-33 as
Q‘; i-', = 4i.-iiiri,/\ 1,,-“I
i-li[lIl.T"-5-j|{‘23.5 iiiiiss i[l_i[|.Uj1|’,'|l5[H][)
Example 2.10 T111: ('utn|iiiii'.'-ii [l.KJ|iJl,l_!,' I.>[ |||.:-rliizil wuigiil lL?'l.l.iJ('J‘(.‘|.-1.‘ [u-1' Ex. 2.9 has Fl culicrcrtl: strcmgtli of 5l)ilU li1i,<"i|i2 and ii fmmzrmi luiuci un maul] mlmim tluai is [.5 iimr-s t-he s1=1'\'i-ff!‘ lrsiri. ])i:_'H.*1'mim'.: wli-r!r..|ir.!r I110 |il|iic-iiiiig slirsu' I‘.'il[ZI£H.'i|.-_\' is El-l.i|.'l|_l.lH|.1.‘.
lllilli
1-up
= --l1 -I. kips L3 ii“
ifiiilifii-il.l'|U|'_\'l
Fur {Tl-]1‘ll‘llll. ill}. 1!, tiw i.iirrtc1r:!d lmid is
Sri-I'r.g.li4m
Hnrralisr! Tim 1'H1iU+i of the! Efl{"i.[)l'{"(i lusuls to svl'1rifl~ 10:-iris
uli l:s.'|iI'| IL!l)il.ltI|.|lH imr irlriiiiirail. thiie 11:.-1 fac:t.|'.:mrl |)i'lI!HHl.il'lIi uh l.||C' fl)-uiiiiig is l|ili|i.|i'iu eulri lliis ii \'a]li<~ u-l'
P-3,, = 1.5-P3 = {1.-"i-]|j:l§[Iii kips) = 45-il kips T111: li:n|.',lh uf ‘i|l'L‘ critiiml pL'|'i11ici1:r is
Ir, _ -1|jr.' + rI:i _ I:-"l](Ii5.i'i in) _ 1-I2 in 4;" = I.-51:, = lll.-5:i(3.fi[i3
=
kips_.»'&"
Till‘ plum-iiiiig siicar [l.Il'I.!L'f ai I11» |.:riii<:z1l pc:ri:m-ier is
= P'."|| - i-..i<-+ iii"
Fuir L'Uilll|IlIl nu. 1. iilu l'i:I:'iui1~:i ]ui\»:i is P1,. = l.5P| = [].5}{2U|] Rips]
(5.5 ; -"1511 i:'ll[J!i
is.-3.5 mi’
‘s II]
(12 E1]
— SUD kips = 4|]? kip:
PPI
l vru|ur.||pl2|:|anl.:nn
2-14
Tlw
$1'Rur.‘:tunn|. EIIIZIIIIEEIIIIICI nsrsnsucz |||nuu.l|_
piniciling
|-:.-|. Ii-33 .». ~.-
slwnr
:'iipi1ritj.'
is
givvn
hf."
.-\(.'I
.'i'rJI|iIi0n
_
,
F
"414 ii‘
i142‘ i
"5-'1" -' — 'll.:"'”’nA'\.-"I-H —
1'31, = P1 1- _ qll-FF
= riis kip:-i
‘
_ , ii
L‘-' 1',"
_
fil lin- cc-1ii1.'i' uf |.'u-lnn|.|i nu-. 1. liw sin.-an" lun'r.~ IE
[Z"$iliihiIl(I[U|.':|':
'
_
(55-1
.
. n-.|'
— Ii-ill] lrips
10;] Daslgn for Floicural Shoal SUD].E’!|JI.l
H 25“ kip“
T111: r.'1"iiii'i1l swiiuii l'u-|' fli-xilml -ilirrair in n 1'un|l.rinu.l limtiiig is idcriiiiriil '>'.'it]1 that in an isulntcvci nulmnn
flit liw1::-iiiisr01':-ulnniii nu. ‘l. tin‘ .-=in'nr furccr is
iiu'1Li1'|;|.{ :-'|m'| is ]l'H"£Ii!‘\!i ll |;iislr'|ilH‘- ri Iil‘fl-I'll iiire f=ir:r: 1'il' ilm
1"-.=' — Vi — 132.51
ruiuinn. T111: siiL'a1' furur ill ilir L'l'iliL'4'l] svrliuli is r.l:~ln~i'lllillflti l'n_u|| llic siicnr iurrv :iizi[=;i'i11i1. am" -:~:]m\I.'n in FL_u,. '3.-5. The rinptli of iiw {ranting is ns1u\]]3.' _*.§m'
= '.-ZHU kilfii - (5.5
s||(::n'.
= -111-ll kins
Exilllll-J19 2-11
The siicrnr iurvv ilingrznn is sim'.1.'n in tin‘ Fullmi'ii1§_g illus-
D'l"if!l'Il]‘IiI1l" WiH"iill'!1' Tlw Flnxnml slicmr rsi|i:ac:ii_\' is :i:1<'qiizliv ii:-i‘ |.|ll' (1|inlrii|1.~4l Iiiuliiig 4.||' Es. 2-H]-
Hlusiraifnfl for
traiimi. s||1'l Tim c:riTir:al flcexuiriil shm1|' is :1 (list:-i|ir:re ._.} . -l_rI= rr,i-_) [mm [hr wnii-r ui i.'U|llI|llJl nu. 2.
3.1‘!
P1,, — anti lilpi
P,“ — -:50 iups
III‘
___'l
I
l
I
|
.1, 5.5 iupsnfi’ as-F
x-?.‘ll'l
I.-1;; -29.5
V1 - ZED kip
135 mpg
_ _ 5_Ԥ_
ah“.-
I
‘“‘-—- 20 kips
Va ' 217 lilfli
i V2 — :41-1 tips
178 we
mnmenl
sac ft-ldpa
IIII
i."-.2 i‘=ji[1.'. ii]
0
nun-w.ppiI||as|.:u-in
Flbuuunri-unis IND RETAINING $'r|tI.i¢IulI£5 T111.‘ crriticni flctxilrnl shmir iii this t-ii."£‘i-i.U-‘ll is
2-15
T111! n|i1:i1i11111n1 111"g11ti\'r! 111011112111 at t11is puiiit is
= 1-'._. - i,i_i:[.-1+5
l_|'"B(-I-' +
I’)
Jun '- -P1111‘
(5.5
ii_}i'2:-is 11.;
= 3]-.[ ]-rips, -
f
= [sun ki]is]iT.1 1'1-_I
_ 111 125
i-{iii-1 __ _ 1 _ 1f1' (5-!:1?)[|'-2i1:|(l-111} +7)
_
_ 21? kips
2
DDS
— 93-G 1'1-1-rips T1111 nl".'1Cll.l'i"l1.-t-iilf‘!H'1' cs]1»a1!it_\' 111 tin‘! 1:1rit.i1|g is giir-r-11 I1}; AC1 F111. ll-Il-:I1_s
Fur 1111: |11'ii1fI.1i‘ILrII!t|tiI!|lt iii Lilli! [.i_=|':i 1_1|' l.-ill} 11.1111-l.it1|g;. ii.-‘!~‘<|.llll'
iiig ii t-1'11si1111-inuiitruliui si.\i.'t-ii.i11. t11i: ri:i11i'u1'1~i:111i:11t ratio TE'(|1]1TN1 is
C15 1', — 2.91.112...-‘T1 '-_ ..-r"-.- 11 15 NH" ‘H-‘Z -3(1) ii) ii
Ii
11$". 1- 1'1-+11". dfi ii" 1i.3s:sii.1‘iT. ,i
f.,.
J4. [2:i..=. in]('1.li]\|.'|fiii[)l| I I.
|jii.s.=.'i (5
111-1111 M kip-
H1“
= 215 I-tips
fir-1",,
[use 1|.-ki|ie=_i(12
|ss1isl'|1r-t1i1'_I.']
s
Design fur Flexure
>< (111011 kip 1 — in ii1.:iii:i_iiss.i 11.1123»; iii}-
1—
'l'11i*t‘ni'1ri11g is 111-sig'|1i=~:l iii time 1rii1gii.1ir|i11:1| |'111'1"I!‘Ti(‘|1‘| .'i.s :1 1.K‘EllI] i.'u-11Li|i11ui:s um.-1' iwu s1|]ip<.i1'l-s- As siiu-w11 in Fig. '2.-3. l11L' ||i11xi11111||1 11L'g,i\1i\'1* ||iun|i.'nl u-L1.'1i1's 11l- l-111'
>< (51-01: M) i113
sm:ti.m1 111 rum slnrnr. T111: innxilniliii ]‘K]!-3i1i.'l."i" l.ll.i}]I1lI']1i
r.i|:<:1.1rsi1i.. the uutsiclite iiicitv <.1fr.:|t1l1.111111 Iii). 2. I11 1.111? i..r:1iisvi.-rsi: 11111-i.'Liu11. it is ussiiiiiui Lhnt 1111: iuuiiiig 1'111itili:\'r_-rs iibniii. the incur! of lsitli i'?IZIi111!1‘l11£-i. T1111 1'11i|1inrrm11ir11i
1511 L’? ‘I'll’ I U .[.'Il]-"13
11.s:|11i|~cs:l is r.-1.:111:1:=11i1-411:.-cl m1
1111. I Ls g'i\.'1111 i1_i.-' AC1
15.4.4.2 as
Tliu .lll£l.3'Lilll1i.l1l ii11uw11l.>li: 1'i;=i||1':.i|v;'1-1i11'i1l- rzitiu fur 1'1 tciisiuii-1311111111111211 scvirtiuli is _1.,'i1.'1:11 ill].-'
1'"
p_, _ 11.11-li!."i1 l
_.1,,_ I
I.-
111+ 1iiPi..+ P-2"]
= [I.D2l3
E-J(2|.lIII.J1i3 2.12
saiii.-11-111"!-1:-i'_'.'. liiu :\ui'1iu1:1 is triisiii||-1'11-|-|tn|]|i'i|
l]u':i.r1r111i11i* tho 1'w|11i|'r»il i1'|1‘1gii11(iitl.F11 nnri I'i‘:\1‘1:-i'1':"'i‘:'-if! graiiii: GU 1'1'i111urL'i.'|i11'1il- 1'01‘ 1-ill.‘ 11111112111111 [0-1.111111; u-1'
T111: ri:q1|ir1'ci ri:i|1ir.1rcci|1i.‘11l 1111-11 in I110 11.1]: uf l-111.‘ funi-
Ex. 2.11.
inir, is Srtitiiiiiii
F110-1'11 Ex. 2.11. ll11- |)-UiJi|.- 1.1-l".-21:12.1 H1lII'l'll‘ is :1 1lisl.:i||cv.- l'ri.>111 iliu C1‘-11101" ui 11011111111 110. 1 giwii 11,1‘ I_ L_
“*5
2Sl11i:i]is
(aw @)ir-111] "
ii‘-'
.4. = ,..1..i = |ju.un4siij1ifi.4 iiijiijzzis mi = 21.7-5 11.2‘ I"1'u\'i1li11i; I1-11 nu. 9 lsiis givi.-s nu 1111-11 of iii in‘: (slit-isl':11'tnr}-"J.
"
=T.1 F1
PPI
l vruiur.||pl2|:ianl.:nn
Fuunda
2-16
$1'Ru1.‘:1un1u. Elluliuezilillu nsrsnsuci Illlllll.
T111.‘ i11inim11111 pl‘l'IlI|11R‘iiiII1II! r1ri11l'1ii'1‘1~111r'11t J\1'(.‘J|. is givrii I1-3' AC1 501:. 7.12.2 sis
T111! ffl.l"lZUl'lI![1 lZt|Ulll.l"ll|l in thir triuis1'1rrsr' riirt1t'ti011 st t-111* 1:11:11 1'11 1111* crnliiinns is
.=i,,_,,,.,,, = 11.11111 111.1. = 1jr.i.1|1111_i',i ;1i1i..1 1111112? 1111 = 1.211111‘-‘ <: .4,
:1-1,, =
l.~ui.lisii|1'I|1I'].']
1.21%)‘
itipis 7.2 (5. fi){1Di'i.I|(? 11. E1 11) 2 2 = 5112 11.-11111.1 $1
'i'h1* nmxiiiiilni |nisiti1.'1" ttifilll.-l'il|.i. st tlm 1iutsi1ir! F.~11'1' 111'
11:13
t"ullt|11u nu. ‘Z is AI"
_ 1] .131: 1'. — 1- 1:]: .
Fur tht' [Ii'éLlI|5‘~'L'Ii‘a'L' 1'1.'i11furt'1'||iL'111 in I111‘ 1.11:1-tulii 01' liii: iiicilzing. .11.ss11|ni11g ii tc!|1si1Ji1-01111i;r1Jl1r'(i st'1'tiun. t.h1r ruin-
SUD1E’!pLl
11.2 11111111 1'1 - 15 11- 1 iii‘-’
iiirrc-1111'11t. 1'sti-n t'f!1'|lIiIII'l1 is
._ .
1-!
."
.11.
li.i!'.i-)_i'__(1 — H11 —
= ITS il—ki]is
.I'1= s D
l-"1311 Lill’! 11.*i11l'1'i1'-01'-111171111 in thr: h1.'1tt1.1111 of 1.111: i<11'.ii..ii1g.
ijossji (5
ussiiiiiilig ii 1i.‘llt~'i.L|'ll-i.'l.2Il|.lIl‘U1il.'l11 s1.'1.'li1.Iu. 1-ill.‘ 1'1'ii11'1.1rc1-uiciil
riitin l.'fliI|l.l.il'lZ!IIi is
111- _
1:-.112 11-1sp..~'i[12
115*." . 1- '1-2”". Mfli ii" 1i.:is:iJ11i*f{_
.K(111[]|.1
“=2,
x
l—
I
1:11.11.‘-'iIi-_i[22S i11}{'2ll-..'i in]?
111.1-1..'1i(ri
__ llif >1 (alltlll
iii‘
[1111 Fr.-ki|s](i2 1-111 LT
14111111: ><
1
1
111’
kn’ I |j1i.:1s;1iijii11.-1 i11]ij:-211.5 11.)‘ >< ($111111:
ill"
= li.(lUlli'i!-1
'l'l11.- 1ni11i111i.1ii1 pr:r111is-sililn r1?-i11t"1'11‘1‘i1'-111171111 111117‘.-1 Kt‘|\'|'1i‘1‘|s. nnil the 1'1-i1|iur1;1'1ii1:1ii- 1112.-11 1'i.~1111iri.-11 in 1)l.l'1.-ii 1111: lu-1: 111111 1101111111 cif tiin Friotiiig tr11ns\'1!isr~l}' is -
1.11.1 L1“
I2 - [L29 i113,-"11
= i].i][l(IIiE13 T111! ccmiliiiir-ii 1‘l‘lT'H 111 1'r1i11i1ir1!r!i1:11!i1t in tl11'~ trip 1-11111
l.11.1ii.1;m1 111' L111: l1.|1.11i11g 1.~s1:c1:i1ls 111:: 111i:1i1111.1111 1~1-1;|1.|i|'cs.l v11i11i: 1.11 l).l]lilSi2J'i. 111111 in sr.'1.'ur11z111t'L' with AC1 S1:1:. 1ll..":.'.l-. the r1.wr|11ir1:1i r1:ii1furc1:1111:i1t €ll'[‘l-1 in thc: hottnm iii the t'1'11'1ti11g Ls
.1, = 1.33..r..i = ij1.;11iii_1i.111.11is3}i§B1i.i i..ii'2:i.5 11.] = 2.2-l. in: Prnviiliiig t1r~|1 1111. F1 lmrs giv-r-s s11 r11'cs1 111' ll-.l[] i112 [Milli-<1-ilL'1I.1I”_'r':|.
III
0
1nurw.ppiIpar|.:11-In
-
J11 -_ ....
A :1i.11111siiii Z '-n'[mB1(l2 E)‘-3‘ "'1
1ll'
2
F*i'ri\'i1li_1ig 1111-. =l. 1)}lTH st. iii in II?f!Ii1Tl"i‘!i gii.-"rs 1-111 :'11'm1 1'11‘ [L31] i11‘!|."Fi. |:s:1Lisl'.s1:'t1'i1'_1'].
5. s1'i=|1i|=_- FOOTIIIG _ Ni:|||i1|!|||::1:|l.11rl:
.-11
is1.-1: sic-21 ut'p1i.1] ll:-.>tii1,1._( nu. 1
iii
.-i-_.
1:111.-11! i'il’l‘il 11|'p1zi.11 1'1:-cal iiig ii-:>. ‘Z
i1:i
Li'_-=
li.'i1i.:tl1 (51 sli-".111 siili" uf 1-tiriip
it
B1 E-_.
|i!ii.i.';l11 1.:-11-111111‘! 51110 uf ]J:1i1 Enilillg I111. i |i!i1_1.';[1] 11-1' 1-11111211 5i11L' uf ]1:1|1 |'u11[ini.'; lL1.i. 2
it ii
.|'1_._-
rlvpih lit .-drn]:
iii
In
rlilptli 01' 111-111 t'1.'1<_"11i111':_ 111.1. l
in
FDUIIIITIUIQ
nun IIEIIIIIIIIG $'r|tI.I¢Iu|l£5
2-1'?
f1-4
clvpth nf |mr.l fuu1il|g nu. '3
in
I’
l|.i:-1z‘|1iL'f' l:(![\\'L'\1'l| <:u|.ll!lll] I11!I|l.l!!t‘:i
Er
Thu mi] nrncrticmlis Jltfl at flu: n:|1tr'r of tlw pnil Eu-uiiugz;-i nnrl m-1- giw11 hf,‘
In
r|.i:~.l;n|||'|: h-eel w|\
Ft
[1'| = I]!-"11
L_-,-
llrmgth nf lung :-:~ir.l1' 01 .*-T!'z‘|]J
ft
LL
11'-]lgI1l| uf |.<.|ll;:__ :-il|.u LJ |1HI.|. fuuIIi.|'|;; nu. I
ft
-|'.-1 R,
'||"1|p,r|'| cal‘ |u||g :\i||1- n|' ||;1rl Funltinpg ml. 2 snlii r1*nr:tin1|. |.||1r|1'r ]:|u| f-:>c:|li'|1g ma. '|
Ft lcipn
‘li.l1IT.l|!1]'l]l'l nu. 2-H>1.|u\1 the lines uE=\cli1J11 r.>t' P; nml R-;
H,
Emil l'l!:-‘|lI'liUI||. I.unl1'r pml limting nu. 2
Ripe-3
urn: cuinr_'idr_'11i.
n'.',.
uuit v\.'u|g|1\ uf -::||m:r1r1|.-
|.||f_,"f1:l
H",
1.\'|:-igl-|1 r|-I.-:t1';|11 hvnlll
i€il|'»-
l1"|
wc-iglfl crf pad fouling 110. II
kip:-1
H";
v-'t!iy,||1 u-|' |mll fiullillp, IJII. Q
[wipe-
1+-. = 51.4-Pml foriring rm. 2 in l
B
L5 _ an _ H, Z H2 Fuundatb
F';q1|ati|1|.( wwticnl l'r|-|'r:r:-s givns
Preuure Dish-ibutiun
R3 _ ZP — R|
T]1c:atr.-1]} font-iu|:', slmwn in Fig. 2.9 hm-i the sitrap |1c:>1m. whi<*h r_:|'.m|u'r1?%t.e= t.h|:' t.w|'.r |'1a‘|(l fimtiligs, iimlilrlziizl ii}.-' :1
|u-c|uilih|'i1:m nq|1=1liun nu. 1:
'l':1ki||_q |||mm_*nt.*a :1|!1r:||Lr Tlln ¢_'u_*|1[.r!r uf p.-ni Fri-uti11,|._{ nu. 2 glx-cs
Iz1_\'+.'1|' 111' SL__vL'Lrt'cr:m'|'"" wu Ihm 1||(: mil |mw<\m- m1
H-"' - L - -|- E-
P,r+ H"',ly,-
si.il'f1L{*:i5 nFI:]1:! stm]1 lwalll, Lhc! :-itrap and pi-1I.'l lhritiligz-5
act :|..- in rigid bully ]>|'+J-clucing \mi|'u1-in mi] |>r|1-::~l|r|:
R =i I in |r.-quilihri1:||| {‘(|_ll:‘|fiI.Ill nu. 2:
umlur tlu: pm] f0Uli.ll.|Z,}i. Thu iuusx: -urcaui of 1-hi.‘ Lwu pzul fimtillgsi nmy ht! i-3I!|jll!-'~T-Ni To |1md11rc! nr|||:-11 soil Mme:-=|11'n rg ||m]m' |'|-r|T|1 fimr.in;q5.
Tn (Ir-r.m'mim* e-"~1|ir.:1l:lr- l!]il|.l.1"!ll.!-'>‘iIII|ll!-'\- that will giw :1 1-mil
'l'ln_* I(_1tr'll:-51'!l"\"i|'r1‘* Iuacl nr:r_.i:ng is
1.".-ari:1g |:n'~::+:>|.1i'c: I.‘i']'llEl| Lu l]'|<.~a':l|u\\'a1hl£e |'=r-:-:*:>-|.Lrc- -,1. :-|.Lit-
ZP= P, + P3 + H-'| + Ii"-3 + l-I-";.-
ulmll: 'ralll.lL's am: :>w:l<-flul fur |‘i|. Fr-3. I‘:-_-,-. El. B3. and .5'_-,-. Ilirllur. In and L_\_,- are (l1*t:'r111i11nl and
.= Z1‘
“ A, +
5' _ h'.',-
B5 Ill 5'
Figaro 2.9 Srrao F-:\:a'\"'|_g w-‘.'fi Aupliad Ssrwca Loads p|u-punlylirlu —--‘I
._
I
_|
I
I -I 5| [-.-
-I G: I1- column 2
column 1 -—-__\ ‘PH
I /'
purl Hlulillq
mll h|m|'n1r,| uruauuw
/’—'
wii
"
".1
a.
I
— ~_|
\~
I /
-"s
W3‘
_[
r.w.I fouling
.3’
Q 5-1\|'fDrOIl'|'l
L5
I
J P;
r‘/_ nlrin hnnm
+1. F iv.’
I15
R: 1
r--4
2,
2
8;L Q
I
~ PPI
l v|uuv.ppl2|:|nnl.:nn
2-18
ITRUGTIIIIIL Euulusznluu ne|=:n|su¢£ Illll.IlL
All initial crst-inmtr i:-i Illlldtf of R]. and i|t'|n:!t'
1"|.2-L‘ilI|111ill1.',' that R! _- IT] I-zips. t]1::11
,4,=£
Ii‘-1
"I
1T1 kiln
.'i-_v=T'=T|]_;‘=5'|i'|‘1
H-', _ 1,.-,.-1,e.,
’
=1
“"3 = 'I‘J!',-rig nrfg
.'\u initial lI!SiI-ilillilll.‘ i:-i |1ui»:ic: uf R3. and il['llII!l‘
= Eu.1_-1 %)[r1.“- h*J|j:1 M
.-1, = 5
105
_ '25.? kip:-i
‘T
_ 1!-‘, xiglll-_r
Zr: P, | P3 I W, | Ii-1, | n--'_,-
SUD1E’!pLl
Z1’: P, + P, + 11-’. + Ii-1, + H‘.-:1‘ = HH] kips+ 150 ki]'|H — ‘2i).l kips
Sulnsiil-uliug in [hr lwu L-q|:|i]jl_|-rinm C1;]1l-il.liUIl.\.- pru\'i
+ 2-3.? ki]1=< + 53 kip:-4
1'1_~|1-0.-m_\c| 1ml_.iI 1_*x_'|1:|\'rergr:|L|':r: i:-4 W-.'u':|n'!|'l.
= 304.-3 l~;i|m
Exaniple 2.13
I-"x|||aTi||g \-'re|'timl l'n|'ru-4 ,|.{i\'r:ei
]:N.'|.l.'l‘]Jlill1.‘ l|u' ].li£l.I] :|iuwt|.:eiun:+ l"L"([|.li.l'L‘l.i. I111" |.-|Z|I.' slralp fainting ialluwim in thv l':>lluwing iiillfilflliiilll tu pru1riclcr :1 1mil'r:-rm I:-r-.-uing |a|'ns.~,|1rr: c:fl_ifH1[] l'l1f_."fi‘2 nnrlnr I:-nth |m-rl
R2 = 2:’ - R, = Hill-1.?! ki|1.~',— 134 i\'i|3n'-i
l1|I_1li11gs fur l]1I;- .<1'n'it'l' luaulrs i||tiic'ulL'1|.
= 1?[].t§ kip:-1
|'-1Bl'lDin
-c
I: 1?] I-Iii]!-i
P-, |uu kps
P,
15:1 up;
,
Us:
H‘
.-,-1ar».ain
lg,--1nni=_.|_
wk’
r.,-121|-:ia-.
Qm|.ri.-;|':|.4'1||:|'§|.']
Taikilu; llli_IJlli_*|ll-‘i zlhulil iillf ('\1.'|llL'l' uf |.mr.i l'u<_|Ii|u_.; 1|r_I_ 2
gives |;.1.=L_.
R|—
_|_s,-sun".-,_|
[liifl] ki;1=\]|[1-5 n. 1| + (211.1 |
.5Tr1-IuUm.Frum 1110 (iil1ll"lltiiII)l.L!i in:Ii::aLr-:1 in tho iiillfitffliiilll.
,1].
:*,:+11-',e,,+i'“i 1+ *3
=
+, 16..-1 E1
= 133.3 iiijifi I-1",-; I |r',-L_uB_-,-.F:_-,% 134 i.'Li[II?E
= (0.15
lie:-i1i:=t'u.c-t-:>r_\'|
12 rut: n_>[2..s n] T110 itliliili t'5liIl]illL'.‘.\ \w.'rL' :~=||iTu'i1.'ul]_\' iiL't'u1"u.ir. ulul llu: rv::q11irh:l pad fuuiing arumi nrcr
= U |ii[_1:~ ."'|.ais1||uitig, limi R, - [3-I 1-zips. fl|1:|l
.4, = -1-us? Ii" A-3 = .1? 111
.4,_ —5—i—44e:'r1.'=' Q 3 . E1‘-' “"1 _ fl‘,-.-‘i.[|r\'|
= ([11.-. %)[--1-1.15? f:"j|[:+ in = 211.1 i'[i‘|‘lc-i
Design at Strap Beam for Shear Thu fiiciurul Furw.-re 4u'li1|g_', 0|: Llu: fouling nru :J1
Fig. 2_Hl. Tim mml facrtcmrrici lmici rm Tlm fimlzilig ifi
2:1,. = P|,, | 11,. | H-"|., | i "-_>,. » 1+-'_,..
Fbuulurrl-nus nun IIETIJIIING srnuctunzs
2-19
Ffguri 2.10 Fa11:r-av-I-\:1'F111'1:1:'.s cw Swap F1:1c1!1'rI_1;r
Flu
P212
1-1,, 1
I':||:1c1r-rd
W1‘, ‘
IGFCES
11111
3' 1:
DI=1 'l!'i
*
/ maximum shear on strap
Fnund
E
min
shear
moment [drawn on
l'I'lE.K1f'l'1Uf'l"l lTlDlTlBl"|‘1I D11 EIIBD
>-
_ _ _ _-
|:nrn prcssiun
M1111 M51:
'1':1.111:| 1'1‘:-1'|Til|p'_ 11-1'1. '2
givw
aid ei
1
_fi'rJIt.'.Ur;1.Ii
T111! Fs1c't111'1~rl fn1'c~1*:1 1111*
R 11-=
P, ,. = 1.51’, = 1."-111 111111.P3,. = 1.F1P-_, = '12.". 111,11 11-’, ,. = 1.2 H", = 24 kip:-1
-P11-1+ ""11111'1 +LIrj'n|: I B2] “ In
Eq1111ti11g \'f!t‘T1fli1 t'c11'1!r-:1 1.,"i1'11s
1-1-'. __ =
= Z1“, - 111..
1.1! H"; = 1.11 kip:-1
1'1" 511- = 1.2H"_1_,- = 11 kip:-1
ZR = -'1-ll
T111: 1e]11.~11r nt 1111' 11:11 01111 1:11 t111r 11-t1'1~1[> is 'l-"'_-.1,, = R," — P|,, - 11-"1,,
kiprsi
11-'1 'L-
P,_.1+ 11-',,,1,, + Rh‘
r
1.1.1
+ '
-
1'11
T110 .~:11c11r nl 1111' 1'i11__11l 01111 11f t]11' -21'1l'l'lj) is
111511 1<1,»-_11j 1111 1'11 + 124 1=1,_1~_11_111.5 111 ‘"1:-, = F11 — 1'1"‘-.111 — -11'-.-.1
1111-1i[1=*1l'1?i1+-‘J-1'I1 +1 111.5 1'1
E1111 rnple 2.14 _ 11111 1ii]}fi
T111r1-ctnip 11111111111111f11111'm11| w1*ig]1T <'1111::1':r11~ for Ex. 2.11! |'|;|_-i i‘1 1'51‘:-l|lfrl'|'1I(' 2-1I‘|‘1_‘l|'|,1;1|| :11 1111111] 1111"-"111? i‘1l||'1 :11 1':'|-[tI|'rl'|'1|'1
1111111 1.111 1.-111']: ¢.'nl1L|1'111 l.h='1l. in l-5 K1111:-=1 t|11- :~11.~|"-‘in: |<11'11L T11c strap I:-011111 111111 1111 1'l'1'11cli\'c 11111111 111' 2?.-5 i|1. D1‘tl'r-
H11 —
_ R1 11
— 2-15 111]»:
mi|11~ 1.\']wT|11'-1' H111 .~1|1c!:-11' 1‘.11j|1:1r-it}: i.~1 111'|1'1:;\|nt.r!.
PPI
n v|1nuu.ppl2panl.1:n1n
2-Zfl
ITRUGTIIIIIL Ellulllszlllllu IlEFEREll¢E |1|111||uA|.
T111: 11111r11r 111 1-111" 1'i1;11t- £31111 111' L111! 11t1'11p is
T1111 f1-11111111111 1111111112111 :11: 1111! l1~l't P1111 uf 1111* 1-=tr11;1 is
1"-11".. = P-:11 -1" 11'"-:11 - H11-
_111'h." = ,1=,__[5l _
_
= '32-'3 11111.-1 + 31 1-:i|11-1 — 2-11.4 ki|1:-
=
= 1; 111.1 1».1,;..~;1(1 11 -
kip:-1
[111-:1 111,111 - 2-1 11,1111-1 111
T1111 11111111! 111 1111'! loft 111111 1:11 1111- 1111':-1p is
1"'s11 = H111 - P111- ""111 _ 151-? 1'1-1-:i]11-1
= 193 ki]11< — 1511 I~:ip.~1 — 24 l1:i|111 O1E’!pLl10;]
= 11]
SL1
:|1_||1.'('[||:q]
[|;111.-'1'r111=']
1“'1>1s11111i|1,1.', 11 11:11.§iu-11-cr..1||11111111-11 111-1111111. 1l11.'11'1|11i11'1l 11-in111r1:1c!1111:111- 1111111 L11
T111‘ clveeign >=h1'11r t'11[11\1!1't_1' uf 1111* st1'11|1 111111111 is gi-:1.-11 111.-
1 11..~1.11f_ 1- 1'1 11' .
ACI E11. 1]-I1 11.11
111-’. _ 111111111 ,,-flif
. . 11.:_111:111.-11‘-1', 1|
111.5511 (:1
1{'2)[l1.Tr'1]-{2-I i11]1,'2T".:'1 in'I1[l.[J}\|,I'I1lK]lI
I-
- I111 l[I(]I.I1 kip
[1111 11.-111111.-j1(1'.1
I 5-I kijms 22- 21-"_-,-,,
><(1111'111
[Nu 1-11:-111' rt-i11furc1e:|1|1-111 L-1 1'1.1q|1ir1'd.|
>1
1-
1|:|.|'.liB3]l:'Q'-1 iI|:||:ET_5 111]”
>< ($111111
Design of Strap Beam for Flaxura
111'
F1'1.m1 Fig. 2.11]. 1111* fnc11.1r1:1l m1.11111:111; 111 1.111: 11:11 01111 111' 1|1-1'1 1-1111111 1.11
1.111 —"_i'_’f‘ 111'
,1, r____L, _ 1'1,“ (,13|_
= [1-111123
_
T1111 1:m1tm11i11g |11i11i111111n r11i111'11r1-11111-11111; r.11ti11 L11 gi1.'1~11 '['h1_1 i':1|':t1'_1r11|'1 1m'_1||1r:11l :11, 1111': 1'i1.{l11_. 1_111<| 1_1f 1111'; :1t1':1p is
111,‘ AC] f';I|_-:5. 111.111 511111 S1_'e(:. 11].-5.3 111:1: 1111.‘ 11?.-1:4.11_~‘|' 1_1['1_||1_‘!
1'1_11]1.1'11'11|.|_{_ 11~fi11l1:.~.
_@_ _..11>1 211-um
W211— Puuifiz .11..“1 = (R-2111 flllllll
I1 1111111111 lll“ = 11.111111:1 11m," = [j-D111.11r_12;1_1 = 11.111111 :|;111.-1-r11.-.-]
Exaniple 2.15 1IN.'11.'r111i111: 1-111' 1'1.'1[11ir1.'1i grz1111.' GU fl1.'x11rz11 r1.'i111'1.11'1‘1‘11|1*111 1111' 1111* 11111111 |>1*11111 1111' Ex. 2.1-1.
T111:1'1:i11[u1'1:1.'|||1.'|11 1'1:1|11ir1.'1.1 111 1111: 111.1]: 1.111.111: slrup 111-11111
511111111111-
15
'['l11_1 1':1|':11'_1rr1|'1 111111110111 :11 1||(1 right. 1,-ml uf [hm .~111':a]1» is : E"'iIl“|||ir.
-11%.-. = 1 1 W-.111 + P2» - 11211131
_ [31 111111111 1 225 1>:i|J1.-1 _
=21) 11-11:i|111
2
= 111 111112 :1 111j1111.1111".11_1 — 2.115 111!
Q43 ki[1eiII[5 11-}
Prri-\'i11i111; fm11' 1111. T 11:-1111 giver:-1 1111 1111111 :11 2.1 111-3
1':-1a1i.111':1c:t111'].-']1_
FDUIIIIITIUIQ
I-ND
G. OAIITILEVEI! RE'I'|lIlIlll\l'G WILL N|::nu|||':]a|l uru F
IIETIINIIIG
qr
r'|u't|1 ]Ju'+=:u1rc- unclvr H11‘ 'h|w'
rr.-
livo luau! 2-i'||.l'\i:i|u|‘gE'
l|,r_,-'n"
|I1"_“
we-':g||i <:-|' lm:-1:
icips
w1'L|.:||1 n|' l:|."_'.' wui.g,l|1 uI' 1-\-llI|I‘|'1Hl‘|.']l"
I-zip:-4
\'r1'i_u_hi <2-I. ||:n:tkl'i|| v.1-i}I_h1 of .-ih:'nl
icipe-a
l'1'i-c-tiulml l'm'c0 ut Lnllrlureiido of hm-i'
kips
F
m|1|.i\':l|-:!r|l ;u]||i||||||.'|.| |||'i5;ill llf fill. rJI_."'| ,
II
HQ, li'l";_
fr,-|
dr-|1th uf hm-£1
rifl-
l10i;.gJ|t uf Hllm-ll‘ kuy
I1 T1
[1"_._; H"'“-
J'|. _|-
lc:-l.=|| In-i|.|,l|| n|' r|~1:1ir|i:|p, wall. |':_|,-+ L||_-
H
1'? ||
str.-|11 1l1i-:'k:u-see lulu] :u::lil.1: I.-:|.l'l]1 ]J|.'\!!HH|.l]|.' |.m|.|iJu1 IA:|.||
T1 kl];-w
Syruubols
H.-\ ".1.
'§..,-
1-:~]n'c-ifir wrigllt of buurl-afill
Ir:-l.=|| ]1r1'e<:~'||rc' b-e'hi1\|| wnll dlw 1n |i|\'|" lrmti
I-ci]1~'
,1:
c-m'ffi|;-it-nl mi |'|'i:-timl
r.‘|
;||1p,i|' uf iIlll‘IILil| f|'it:| inn
s|m-|mr|.:»:-
1;,
lutnl ]J:l.-iii“! r-nrth ]IIl'U5:illTII' in from u1'v.'u|1
1-alps
I‘-'. |
Rillliiilll‘ 1'lll.'i-Flliilillli -:>|':|.|'1i\'|' 1'iII[ il
—
prr~.-c-\1|u~ 1 .|'\'|-
|hf_."H"'
Blip:-
|Ici|z~;
1m_.-'n*' |l1'|.|,r|~u
Frlrlsura Distribution
Fill -J,-"I - Hill 0
H;mki|n'-1:u-:-|'lic-it-ut u|' p:'n=4ei\'c- 1!:-‘|!'i|ll
—
Figure: 2.11 2-.=lu.w.':-i the fimnrm-1 artilng |::-|:| n ra11til1*v<:1'
it
L.-|
|<'ng1]1 I.-E haw‘
I-.'r L,-
lc'ng1]1 of lu.‘-rl |l.'l|;_j_1]l uf1u|."
11 n
L“
lwigln nf :<1|~|'n
{1
P1
m'tl'r1~ |a1-t-rnl ]:l'+.'mu1rc' -ilnr tn n fluicl |;-F
1r>|",m'-'
PI.
:i|||.\ri.l-I-:: 'v\'I.'ig|1IZ '_<'_1. .F\'_|‘|_< |:|1|.'r;|.| pl.-n-e-u||.|-1: lil|l.' lu ll-.1! ]||:a|l
ll:-T,-'1‘|'-'
=
1r>|",-11“
_ ]1|I‘l3'.\-i!i'l1I'lI' uxnrtenzl h_\' :1 fluicl
-*ilIIl.'|1l\I|.£l.‘. r-"H. |1:-m.-i'u'c lmc~|':|l ]umemm:' [Inn tn a fluid of
1]": walll is glvuu by l'iaLl||-cll|.I_-':e I]JIL‘tJI.'}' as 1 — ea-i11¢,:'| -
.-
]: lb‘,
-
h |-‘r.,-Ir€.-
H|='T= . 2 , 1
3|] hf.
r
=
-’“"-hf-
(1+ :~|||<_a) '5
"
2
|fu-r 1,. = nu 11,r,.-rr‘ nml rJ = :m-1
' .-=r' .-|.~.||.~m;.- -1l][] l|>t'_.-“Fr.”
.-i||uri.l'i-:1 \\'|.!ig|1l! 1.31» K]-15
Flynn! 2.11 {.‘.~s\.".~1|'|'ever H|er.9.'v:-.i'1g I,‘-'.'a|'|' w.'.'fl A,u_|:J1-ea’ Sew»?-9 Loads
L, F
n,,. 1-
-X
L" P-
wt
§|Q
| W
I
W»,
L,
l
W5
H 1
_
fly
HA I
hr
T hr
he
+ W, |
i
‘Iain. Pp hr
-. _ '4
F
ilr _. __. __._.
‘ _. _.
5
‘ Pl. -1
1
3 P.-1":
<-pi‘-|
i
i
qi
L fl I-|
“M mm 1 1 Milli PPI
dDDS
Fuund
rs-mi11i11,q wall. 'l'lm mml :-1t‘Ti\'1'i'nt‘i|1 |)t'f!H.'-illrf! hr-himl
|mw-||r1~ I + .-iin r,)_,"1 — MEI (J
Pr-
2-21
QTRUCTIIIIEF
l v|u|uv.ppl2|:|anl.:nn
2-22
$‘rRuI.‘:IunAl. Ellullleilllllu |l£|=£nE||<:£ Illlllll.
The tutal acrtivtt (‘I-11'i|I prc!:a1'I.|r<.* Flflifi at :1 lwigllt of h-,--_»"Il :1h|'>\'1- tlw inn-ara.
‘Flu? rr;t.:_1| s|_||-r:imrg-0 |'m_+:=n1T1_~ lmhi11c| Tim wall rimr ru :1 livu luzul :iunc]u\r_g.I,I.' uf w is
Srlllmon The lellcrail |}|.'L'h~".fll1‘l.'-1'5 f1'u-m l-hr: iiawkfill aml Lhu surc:]mrg.',c! nrv
, 1r-' _ is H,|__ — ;r-';__i'r;-- — 1:'h_;fir — g fa
105
_J‘1.
H.1
p'1,;J‘
_ (an 1i'Ti,_f)[21.s n.]*' i
'l'lw surclinrgn |m1_',' lm |'rv|m':-u*|1r.r!rl by rm r!r|||i1.-':-1|:-11r lirciglal ul' fill g,iv|_-11 by
5= 2 T3; SLIO1E’!pLl
= U934 ]l1l'
H;_ = pa Ml 1H,|__ = p__1J'r-,1-Ir
"l'lw mm] s|1|'r:lm1'g:' ‘|'|-1‘f"Ei!i1I1‘l‘: acts at a imiglit of 1‘:-,--3'2‘
_ (su .. mr , n._|[.z ._ ru. F)[z1.s
z|.l1I.>\'r: I111‘ |1a'|-*<|.'-
The tutal ]'Hlh§il.\'l.“ :!:1rt]1 ]111"s511r1: in lrmlt 0|‘ Lin: wnll is
'l + sin :55
= IEEHJ il1f'
-.
. r " JP"H I _ p,-iii _ I\,->-"_|-_._;h_';- _ (_] — emup "" I‘
'
2 =
-Muir“.
2
2 Qu-II‘
|li.:|- -_.-, = nu li'1l',-‘fix mull ».» = an-|
_ ]J1'ui:-:-1111' cxL'rl-ul l:|_\.' El flllid
_
_ of 1l|.'m-:~i1_\' =ll](] ll:|l'_."l'l:‘
ll
2 Fl live load :ur|:l1 urge
Tim Lu-1-aw] ]Ilil-'\hl\'1.' 1.'ilI'li|. |1I\'1\-film: MIIH iii il lwiglll 111' fii,-3'3 ahuvc the lruttuui of llzu key. Tlu: [1'lL'liulu-\] Furvu zlvtillg
on t-ht! llliliitffl-ililf‘ uf the lm:-in is givrn by
F‘ = ,-121$-' 20 1'1
Z H" is lhr: l-ulnl w1:ig]|l- uf Llu: Iuluiliillg wall plum hurl»:fill ]'1-lIl:'i li'|.'P- In:-ad 5111'r:lm1'gi*. PL l'uK'1u1' uf H€ll'u1_'|' ul' l.-5 iigflilml hlirliug in lwqliilfnl. ‘-'~'lll[?iI
giw:<
F _ H _ .:_ 1.5 Iinu-s Linc iurtiw |m.~e-m11.~ a'|£rLi||g I '- i'l1_|-I'll 111]) uf '-val] lu l1I.rl.tI.>tn1_IfR1113’
A Factnr nfsa-1fr!tj.' nF I.-"r is |'nq|1i1'ml For nu-urmr11iug almnlir. tlm Tun.
1.511
."“1 FL"
|
CH1
Example 2.16 Tim 1"r~Laiuing wall 2-almwu in the Fnlluwing illustraticm
Taking l!]()lti[!IliH almul: the Ln-1* fli'fl‘1-i
1\0t.=\in:< soil with :1 unit. weight. r.:-E l1[|' ll'|1',-"ft." and an r.-quivnl1:uL l'lui:l |.\r|.-easurl: uf 3U llzfl.-'l'l"']n:1' l'u-ul. The livl: luml iallrvlmrgi: lJL'l|m:i the '|"|"F|]l is 1.‘i]11l\'£l.ilZ'lli tn Ellil. eLtlditimml lmiglu. nl' L! FL r:l' fill. PH.‘-L‘ii1¢'l'! raarth |]T!'!\‘*iIIIlT* 111a}; he
z'u=.sl.ltru.r1l Ul|_|.ll\'il]L'Ili 1-u u llllill pn-:>--urv |.rl'=l5I[l 1111',-"11-2. ailul tlw c0t'ffi1:icr11t- of frit't.i
[1.1. n|‘!t(!I|'l1lillf! Llw fiirrtnn-1 nf Hafntp-' agnitist :-aliriing aml uv1_-rl||1'ni||[=',' uml Iln: l:u.-Ming, |:r|_-murl: »:ii:uI:iut1 m|1lI_-r ilw lmeeicr. III
0
an-w.ppilpar|.:n|'n
H411-1'
Mr. I i
3
Hg]: 1-
'
i
2
lzfifilll-l |lJi'][21.ci| ft] + f1'.7!‘fJ[i ll:F}[21.fi ft]
1! — 63.561 fl-lhf
2
Fbuuunrl-nus nun IIEIIIIIIIIG $'r|tI.I¢Iu|l£5 T111.‘ g1'm'ii-_1.' iuncis acrtiiig are
Tilt! prcssurc! Lllidcrr tlu: lmsx: is ,l.|"i\'lIElZ| by
ii"-|\' "l" l-‘iffy _ 11?.-Jl|.|'L1|,' "|' ill,-lllly; '" h1,1:|n'l|1' qt
_ [1511 M)|'I.5 1111-211 11.1 fl‘ '
‘I
r
-. -... .
in'
(_2r..i-lh ||1{)(l ;l:
W11 = 1'-'.ll11Lr1
= [1511 %)1|.-1r11112..1111 = 2s1:1 1111 1-1-',_ + 111,- = 1-5-l:|'JT _ 1111+ E11,, ,
,
-,
Fuunda
'l'l1:_' pa-issivn |)l'|':5:-'elll'|‘! ill F|'r_>11r 1'1-l‘Tl|1'e wall is
2 ii-" = -51i"5 |l:f+ ‘EH3 llaf + 19.36!) llpl'
H
= ‘2i'.3~1El ]l_1l'
ll PM-i_ (4511- T’__f)14.-5 111 2 ‘‘ 2 ' 2 = J5-‘iii llif
'l'lm dist.-mcrn r1FLl1n r:'s11lT.-mt 1.'re1'1ic11| lnml l'n"1||1 the tun is
-
—
-'
+111-',_ + 11-',{1[':.-,-+11" 1'--1 —
Z 11' 1.-111.". ll>t"ll:£.i'."1 111 +121-11:1 111111112.-'1 1'1] _ + 1'1n.:11s11 ]l»Ff|{1-1.!‘-1 11.1 " 21.2111-1 lht‘ _ 1.3? £1
'l'l1t! l-\l1E'Tfl] |i1'ns.-=.|11'ns |>r-llinri the 1.\':I1l| f1'n||1 tlw ll:-wkfill
mul s1|n."l1;11'gre .-110
H_., =
,-_-
l_ilI.Fl-'li1 EC-lili |:=;11isF::rlu|'_'r|
= 1111111 lhl
12 fr_.}{'2-1.5 +1.} = 11711 1111'
Thu f:I1r:Lm'-:1i 1=.11l'z!1_y 111.§r1i|1sl Hllillllfi is F —l- .”;I
The fzlrtur uf snii:l_\' zlguiiist r.JvI:rt111'|1ii1g is
-;= ‘I-‘ Z1-1-' 11.-.1? n'|121'.;1411 11111 =:{_2
=
, llif ., .. an —3 1_z=1.=1[1.1 -1
+11 = _,~1__|I1-1-1'1{231l]
H.-1 + U1.
_"2= Ll]
DDS
1"= 1121-1' = {11.4j|{2r.:1.1s 1111"] = 111.1131: 11-.1
-
= l£l'.36[l il1l'
1H,,
.5.
T111: l'ricliu1u11 l'L'E~i5t-H[lUL‘ 1111:l1:1' lhu lmsq: is
_ [1111 {@1111 F1 + .1 11111.11)
111-'11 + W1.-1. (1.-1 + 1
[Gilli-9 Tl-1'
'j1111<12..a11] 1,1,“. — 344.21 ||11_.-11? r,1|,,\| = 112:1 1111111?
= -511-11111
ilhf
E“ (1: L11)
'
1F
+(1.1|1m)1.sE:](1..1 r
2-23
lli.Ell3£'I ll_:f — 4556 ll1l'_ I 43
111111-1 1111+ 1-lTll 1111 _ ' R I
[_-1:|.lZl.~sl':|.1r1||:|'].']
Design for Shaar and Fluura To (itliifflllilltl t-hr! slwlir 1u1{l fl1~s|11"c' at l|I|II! crriticrnl sucrtirjms in the w:-1|l. they s11-il |‘|I!_'e-e'-ll|Il'l_* llnrlnr Llm lhqiliiig is
iv.-c:|l1"r11l=1t1:wl l'1}' using 1.11:: |':1=;-Tclml t'r.:1'r:c-s git-"can hf; AC] Tim 11.c:n1~11tri1::iT_'_1' (if 1-1]] nppliml l-lmcls fl.l)l}I1l the tue! Ls
_, _ 11211-’-.w.._ 17.111 &1[2r_:11s 1111} -113.5111 1111 "' _ 211“ 21:1-=|11 1111 = :':.lL"J [1
'l'h1_* 1_'H.‘1¢.‘\!.-11l_.|'i1_:it_\.' of all :1|1|1li-ml l1_1s1"ls :_1l1r_:-11: t.l1n 1"11ii11l_. r.1l' the lausl: is I-11 1 I2 5 l'L 1!=T—4-'='?—-5-[)5 Tl“ 1.‘Z[i it
:'U.'il]|.ll] lllldtlll! il1il'1'll
SE11‘. 11.2 as
11=1.2r1+1.1s1 + 1.1111
1,11.-:19-21
Shear is gr.'11I;*m]]_\' nul I{'I|'lllLii1l. Tlu: lU{'iI.liU[l ul U10 ("rit-
icrnl sc\rl.ic111 for i'l1rx11r1~ in l:]1»:! 5i{"[ll. is at H11: lmslr oi H10 sh"-111: fur l'|1?x1_1|'r: in T|11_=-1.1"»-1*, at flu‘: EI:_1n1_ l'11fi_~:_1ftl1n sfaml: 11ml fur l'lI.'.\1urI.' in l-lu: I100]. 11L l-|1I.' 11:11:" l'11c|.'4.|l'll1c sl|.'m. l'1xam|1ie 2.1T Dct1'1'|11i11»:: t-luv r~:ri11furn*l1u*11L areas rcq11ir1*(l in l-lit‘ st1:|11_
tun. anti lmnl 11!‘ []‘|lI' |'re:r1i11i|1g_ w:1l| Fm‘ I-‘Ix. 2.](i. 'l‘lm r.'u-1u.:1'~_-ll: sl 1'1.-1151-h is 30110 l|1f_1‘it1". uml 5111111‘ GU 1'ui:1fur1“L-11112111 is ]ir1_wid::ci. PPI
l v|u1uv.ppl2|:|nnl.:n1n
2-24
trnucrunan zuulussnluu nsrsnsucs Illlllll.
S0-1'11 11-r1I‘!
D1".1'i_qr1 rrf Tm:
T]|:.~ f111:11:-r1-11 1.1--'|_'|"1-1m|il|1; t|||.>t11u11t 11|.:-uI|l- 1111: luu is
T111: liu'lu11r¢i [1r|.'ssI.1r1' disI.rib11li1>11 l:11=l<~|' 1111- lmsrr is slmwn in thcr lulluwirlg i1]11st-rz1ti0|1. nml 1111' 11u\xi1n11111
.'1J,.1, = 1.[iM.1
filcrmrnri |!m|1:lin1.{ Lnrmi-r~|1L in 1.1m lnv is
= [I.1i'H:fiH-..'1l:i1 fi—lliE'} = 1111,11!-1-‘ii Ft-I111
vs
U
_ LiI'Bl"1TuF+ 2|?|1|_l|n'|
'l'|11* i':1r:[|':rr!rI mml 1.'r:rTir1\l In-1|'|
2L"l_i'
l:11‘1;|’{1 r1j|{:1s'1-1?
_ 13.1’.-'111111'1r_;1 111"
- [1.2)[51T5 1111' I I!-S13 1111' l 1T.li[l(]ll1ii
12]1'12.:1 11.} = 211.0511 11-1|-,1"
- [l.li}{]TLiU lhh = B211] 1111+ 3376 ll_|i+ 21.121] ll>1' + ‘ES-lfi lhf - 33.522 ll11'
an
The filrrtrirntl rrrst-nrillg llinmnlit is
l' [2](a11.-'1 11
Z W“ — 1.2{ li"11- -|- W1; -|- ii-"_q - lrifi-] -'r 1.11111",-_
SUD1E’!pLl"I
|.'2 |-lr"1;L€.-
[1
l‘
1.1-n: 'l' '1'
an '|
—'v—
M11“ = ([1210 ]11l'](ii-.?E1 [I] + {EIITG 1l.1l_I|[[i.25 [L1
‘*-._
+ [2l.1'2[II ll:-[}{S.-5 fl] + 12316 llafjf.-3.5 [ti
' 2 lfi lU'I'If
FF’.-2 in uuullr
— 247.8-H fl-111-1'
l 11.5 r1
T]11~1-c'1~|:11tricil-_\' of the f11ctu1'1:1l luauls 11110111 tlw 1111' is E, = M,q_.,
‘
j
3 In nnvnr —/'
—
11-L...
Z11-'.. : '2-1T.l'l-1-"I ft-ll1f— 1111.151}-H ft-1111
.|
1
3:5.-‘T22 |l>f
we 1: cu
= -1.311 1': 'l'l1l' i'r!t!fl11t1'ir:il:_v 111' tlw 1‘:-1-:'T-lirwl lmirls 11110111 1111'! miti-
puinl of 1-111' hilsu is r',, —
L”
'-‘-hiPQ
5I — 1'
:~:-1_.9-.-1
T
|
Z
335131
‘E
U
s I
1;
5 It _ .1_:11j I1.
1"'1s
2
furc:c:i11c:11t 1'1-iiiu is
= 1.141] ii
|_will|i:1 1|:|i:||l|u 1i1ir
'l'|1!* fnrztrarnrl pr:-ss1|.r1' |.||11iv1' Tho 11:1s1:- is g"i\'re|1 hi.-'
. 11¢. Z1-1-,,(1¢ TB)
118»5.l‘l(1- "l—i'lJ"
' '1 '11‘ 1r.sss1~F[’,. Fl 1'1(
‘Ill 1
|j11.s.a} :1
31'--11
\_
' 1" 133.522 11>r1(1_ = sill“ 12$T?. J) 11 111111511.)
Ill‘
l’ ><
rh,:1____._, = -'31 |-1 llJF||"l'-[2
r i
qru:|m,|:, - ‘Z-1'3 ||11_,- flu“
- ..
:
1K
124111511 11-11111(12 m H) _ li{11.:1s:1l(1'z 111111
>< (30011 1111 LY 111-
= 11.111113
1111'-
Fbuuulrl-nus I-ND IIEIIIIIIIIG rrnuctunii Tllr umxi111un1 :1l]c11.\'nhlr' l':!iul:11':!c!1111~ni rntin for :1
.4, I pbrl
trenmiranu-(‘£111trnllred ear-rzri-n|| is gi\"n11 1'|_5'
_ [llI.lJlIF:2}{12 i|1:|II1.'i..": in)
.
.
2-25
- 1'.-
= UH? in!
pl. = I]_.H.Fl|'1'l—
L
= [].|HHv{'i
D:'.s'iyn. o_i"$hYrr1 I} '0
[:i:|.|:is|';|.1'1||:|'}', |l|||- .-wrl inn is |!![l!\'iL|lIl-[T(l[l|l‘(JHl'\I]|
The mn_\ci||mm t'm:turul lrclulillg 1|Lu1m:11l in flu: slum is
.-*1, = phnf
={u.mr1+s]qj12 i11][1-1...": in} = u.:u-1 in‘:
L,‘._ .-‘l-I.. : 1.6
.*i_.,|,,,;,,:, = [].|H]]€7H.n'1 = [H.[]|HH-i|l::11! i11]|:1-H injl = [].35FF 111-3
I TL“ l __ . I
(:10 I
|p,|n':'rl|:<]
I3
L1 6|
D-n.uzgr1 of flew!
H
(30
The |1mxiuu.|:n ialrtcwvcl bvmling uLu111m1t in thv lunar] iea
+
Ln (1.2u-"'_~- + |.u|,1-'».. - ilg M")
Fuundanns
[an H1“ _l
[2 n}{2n- fr.}' 2
_ SILEIIJLI ft-[hf
J1‘
.11.. =
'
2
.-
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-!-"'.I;B(B'.\-ar * 2*?.|||||\||}
U 21.120 ]hl'+ 2-Elli lhf
pl = l].[?UTD <1 p_.
£8 fl?
[:i;ms 1hl){s fl.j| 12.5 it 2 {:4 £1j|’|'| r1){:a:m:s |12](2421
=
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+
li-
T. OOUIITERFUHT IIETLINIIIG HILL Numcnclahlm
= [i-ZLZIHS Ft-]'|1f
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u
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in
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H
T
l<'r|:-'i|u| Fllrlrr! in n".-4i:=IiII$'_1'|||||1]|‘
ki'|'l\'
Daslgn oi Stem and Base
II]
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H
l_l f.ip.||',-
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marl 1.0. the :-etcrrn t|l:.1_';' he cl:-=|' 4! \--n||.u*. <.11'Tl|1.". c-am]: [>l'II'-‘%fil.ll'I." an :1 1il:]]1.ll u-l' l'.H.ii,. '1'her ||1Ll]'i'i£-<.I]]1il] :-pun l]1ul|lr:ll1:-e:'|l'[!gi'='1P|| ll]; .-‘H11 Sr.'r.:. :|.-. qfjfll ut. r;-r.>u.nte!1'Fm'l: :i1:|])]1-urts am] r,II'j'|;"1{i hntwcmln cm1l1t0rI0n:i_ Thr-
lll“
Em klps in?
Thu :1'lr.'1u :e]mn.~.= l|uri;cuula1ll_\' ha-1“.-0;-11 |.'u-unu-rI'urls nml calltilnvvrs Fmm ilw hazan. For ratim-a uf I,“-"l'_. hc!t1.\'c:~:m 11.5
r.:=.1||t.ilr.!\--+.~.|' nnvmmn :|t- l|1:.- ha_-iz.' is U.U3-3p_1!i'. The |li:~t.ril_n|l.i1_r|| 1.1-l' '|.Il.'J1=|i|lg lll1_llll'I.'|ll- in f.|iI." :sl..II!t|| is H]]c_|\\'II ill
Fig. 2.12. zmcl ll!Ul'I.' prwiae-c! 1.'n11|cfi uf1110|m'1:t- nun}: hv
= ILUUEE
ralata-flnnrl frrml r.:1|mInt.re¢l £1114‘-Ffir!ir!1:ts_""
. C P‘
'l']w Imam 5|.-ah is :+i|ni1ar]_\' rlrlaiglmrlcl Fm‘ rhv nvt Fnrtmwl ]u1-:-a:<1m- us an b-'|.i1]_I :="|m11||iug luugilLuli11z\l|_v Iwvlwu-ll ctmmtcrrfurts.
[
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2-26
$1'Rul.‘:1unn|. EIIIZIIIIEEIIIIICI IIEFEREIIGE Ill-uu.l|_
Flilfli 2J2 L"-l1:'.'z1|'l's 01'-Dclurlrcr-'1:1'.' Rcrrel-WPILI‘ Wen‘-' H Rn
I \ unsu apur-tad edge
105
SUD].E’!|JLl
counterfort mom ant rEIin|'lJrcBl'I1Bl'll
I I
<:0ur|11:rl'ur[ 1.|EI
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reinforcement
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l
I
.11
ff? ilxed edges —____\\
T ____I‘_*;-.,:|_ E '1'
_
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/ mumsnl on Ei—B
1 B rm-Ir nlmrmion
side e|wa1I|:|n for B~B
rnurnem cm .b1—A
.§'rJI|:!1-011
Example 2.18
I-'11: 1,111": m1111I_nr1i_1rt. rnt=1i||i11g \I.'nll .~a]1u11.'11 in Hm fi"_>|lm1'-
TlJI.' l11l1'r<1| 1-1111]: 11-1'+.r~':=111'1' 11»;'li|11:_ on 1| I l1 ||u1'i;»:u|1l11l
ing :ill1|>=lre11lu|1. 1l1:l1'1'|11i11L~ ll11' |.|I.'>.'\ig_;11 JllUI|1lL‘1Jl:i in H11-
strip 111 .11
str-rn. Thu fill l1-1rl1i11rl L111! wall l!|.fl1-i 1-111 cq11i1.':1l4~11t fluiil ]'1-IT:-4:i1]|'(! uf -It] |l!If_,I'-fill ]'|-¢_-1' |i_'|uI.
q = lJ.fi]1_;l,- .ll:-F -, _. _ 111.11] (-111 fi)1;*..> E1]
1 if
- GUI] lhf,."l'I: At Tlm rrr11111tc'1'F1':1't _-1111111-1111.11, 1uu1||1'|11 is 1-_j_i\'r:1| l1_1' FUJI 51'1".
uuunlurlurls 1 P1 widu __ I1 I5 H D.E.
Ll]1" t'nrrr1'1|'r-|'l <|mlg|| ill|1.l. 311'. 5.2.1 41..-1
~ _ .75 _
"“-1. r|:1nIn-n:1:|11:-nl-_
_ l{i|]
.‘
_-3
1‘firH.T.l [111] £11.11 F)!-1 E11 .111: i = 1
-uh
1l
-I ., E
I1
= 5l.l.L?'F fl-lcijm -'7
,:|_"
l1r~t1.1't!n11 m1111rr~1'1'11rts. Lht! F11rrr11'wl :l11:-1i|':,11 1111111111111 is .
11!‘. _
-.1-I 1511
_l_
.
->
. 1 |_1.
= H-l.-"'>fi it-1:111;-1
FDUIIII-ITIUIQ
T1111 f111'I:111'1'1l 1lP1iig11 l_'1111ti11_"1'1!1' 1111111111111 at L111! 1111111" is
nun IIEIIIIIIIIG STRUGIIJIIEB
2-2'?
T111! fs11't111'r'11 1nt1*1'111 ]11'1~115111'1* f1'11111 1111' 111111]-zfill 1111 11 l It1111ri2|'1111:1l .~:t.:ri]1 at t.111- 1111:-H‘! 11f 1111' .=at1\111 1'1v1=-1' 111111 |1:1_\' L11
M, = 1.11¢'11.11:1s;1__,tj'1
Q, _ 1.t.ij1__|1,.I..
.
11'
.-
11.11j|(411
= [l.[1]lj[].|ll§.'1]([I.1|-1 %)[2.'1 1tj"
151.1 111124 11;: I11-i 1111111 H’
= :1."-1.1111 I1.-1111».
= 19.111 111;» Daslgn of Gn-untoriorts
'I'l11.- tire |\1.~.i||E1.1r1-rv111r-11t 111-1111 11.-11111111-1| 111. Lhr» luuw rr|'1l|1~.
T110 |>I:111.1111g |11u1n|.'nl [1ru111|1'1'11 113' lhu I.'111't]1 p1'I.'-s>111'1' all 11111 111-11-11* 111 11111 5111111 11-1 1'1":-iiee-tnl |1_\' t11r' 1'\1111p1.r- p1'n11111:1'~1l
11-y 1111* 1011:-111111 in t11r~ 1'1~i11t'11r1:1!|11re|1t 111 11111 111:1: of tlm
:111.4n 111 .'
1111* >=t1'|11 is r1r:-111111-11 11}; 1111: hu1'1zu|1tn| t-11:1; 111 1111'
1:11-11|1t1rr1'111't.
_ .
.-1, = & = E: 11.12 111?
"Jr"
1.-|.111|11<~1-t'1.>1't 111111 L111: 1-<.|111]:»|~1i=-11111111 in L111: :-tr.-111 |::|.»||1-|'1:r..1:. 111:1 1e]1m\'|1 111 F'ig.I,. 2.12. L111: 11-1.-'1-r-111-111 111' 1111: 1'u-11p|1- ncl:-1 :11 rlgltt :111glr:=i tn the 11~i1|F111'1!n111n|1t. T111! t|11'11:at 11111r1I.11'1¢1l 111' l-111' 1-:11-1|| ]1|'1-\'-1111\1- 111"-llllg 1.111 1111! 11:11!‘ E2101‘ 1.:-1'
(rt.H]([it1 111'
BEFEFIEIIC-E5 1. P11-111111111 (‘P11111111 .—\.1"+11"11'1i:11i1111. Hcc1r111_r1111r1r' C'r111r-1-1111". Tr1nJ.'.~<.
Exan|ple 2.19 F111"1111111~1|\11'11.ul'ir.|It 1‘0t.:1i||it1g W111] 111' E-:\'- '1 13. |||'Ir.'1"|11lt1|.‘-
‘Z. F11*_1'11u|1|:s. C.E.. -‘J'l1.~u11111111. -l.C.. T111'L'lfiI.11. -].(_'-- fi'r-'1t-'_forr.'r.'r.l' Ir-'0n1'1'r'Fr.' Dr.'>1r'_r;m"r'.=1 H'r1r1|'H1r.10-k.
1111.! l‘1.‘lll[l.1l'L'l.?llIl.'Ill ul'I.'1| It-11111110-1| in 1111' 11.~z1r LI-1' 1111' <'u|I11-
t1:1'F111't 111111 11111 tic 111-1111 r1!q11111:1l nt 1111: 11111111 111' H111'111111t1-1'Fm't. GI‘:-‘u'l1‘! G11 11~i1|F|'11'r:11111|'e11t is |1r11vi1'|n11, 1-11111 I111: 1'|.1111'rI.'l1~ I.'u-|||11r1'.~:.*si\'1* .sl1'1'11gl|1 is 3[1[I'1] 1~;i|:.~'_."i11¢$11111 Um.-
T111r F1-11211111111 111111110111. ]1r111111m1l hy 1111: 11111-111 pl't'5t-Illl't! 111 1111- 11.11.-11! 11Ft111- 1-1111111 m'11r 11110 1111].-' 11-i
L1
11.11] (-111
[25 111125 11'1"
M = 1.11-,~1__,.~.,tj=
H
1'' e''1(11u.111
11111-
= 1111? 11-11111 'I'l1=.~ rni1111.111.-1-n11.-111. =1|'r==1 |'1'er|11irm'| in 1111- 1'1-m-nl'rl1=.~ ¢1.111r|l1'l‘f|.1l'1 I11 I1‘:-1ir~1 1111-1 tt1u||11'!l1[ L-1
EL = 111.. Oaffl
_
dDIIS
1'u1111t1-1'1'u-rt tu 11'1=L~;1 l11i.~= 11111-1'11] 11r1-51-111rr: 1.11
41137 |'1-kiln
(U.U_||,12.£'1 E11 (1111 =U--1T ill!
PPI
1 IIlI!.|I|I|I|I8I-l.GI|II
Fuund
2-23
$1'Rur.‘:1unn|. EIIIZIIIIEEIIIIICI IlEFEREll¢£ IilllJlL
FHLCTIOE PROBLEMS
ll. Thr arm c1Fg,1'11d:! fill 1'cri11Fn1'n~llwl1t wtluircvd in Tlw 1111111-<*ti1'|11 uf tlw :1]1|1-liml |I1|':|lt|.|'el1T Fm‘ Tlw n':|':|::mg||l:=11'
‘I. \‘\‘]1u1 is rht! F>1{'tm'r-rl not ]1r1?:-L*i111'1* cm I]‘li? iT:1:1ti11g 1-;||n-w1'| in llw l':1l]|'_1'.1'i|||z; i1111e
‘Ht
an
_
>_1n__
an
fi1uli|1g :11 1"1'|.»|>. l i:~' 1||u.sl 1|1‘<'Lr]_1' [A] 1-EU in’ [B] l-5-5 i112
_
111;‘-1 111.1111" [D] 1.7Ii] lug
10;] q
PU
1|:-:11:-pa
A-E,
EIJH-!|ps
[‘5'"
SUD].E’!|JI.l
1511-1
5. Fm" the re>t|1i11i11g wall nF Ex. 2.1T_ vrlmt is-1 111051 11:m1']y Tlm 111i||iuu|111 >1|'r~:-1 nF 11<1ri2c1n111l |'rvinI\'1Ic!:!111:'11t 1rr¢]11i1'v¢l in H11: :~l1-|u'.’ U:~r~ |||.>. Li 1.5;1"eu|v [it'll |>-1:111
1111.1 11.3 111?,-'11 [B] I].-1 i||'“’_-"l'l [C-_I| l].T in’,-'[l
D
1» [1511
[J11] 2.55 l-ci[1.~i_." H2 11|4L:c.. 1112 I-ci[11a_,-"fill min.
(B) 5.11! 1:i|11s,-"ft: uu1x.. ‘I11-J ki]1>=_-"I12 min. [C] [i.2-"'1 ]1'.i]}H_<"]-Eu 111111-1.. [II.H‘.J kip.-1_."fL2 111111. [D] 1].[iF l-;ip5_,~"F1'3 11mx.. -2.531 ki[k!i_."fl2 mill.
2| Thv n-r11111gul=|r fI.>ul.it1|=f; all ||=.I1'||m] 1-.-1-iglll l'I_>l_u1rl'I.!l|' 1.1-l'
Pmh. 1 [ms 21 uc1m'rc'lc! :il1'0||1.',ih 0|‘ -lE]lHl lhf,-"i||'. Ia Hu]1|u1c'hin|!, 1-ihm-11' ct-¢'1[111::iT_\' .ault'(|_unH":"
[A] ‘|"1*:1'.
ll1f_-"111: 11- 1],.
(111 ‘-1111. 11111 I1=f,~'m“ ;> 1'“. |j(__?:| Nu. 1'13 l|:l‘_.I'iu2 -=1 flu.
(T11 N1». rm lt11',-"111" :> 1r,,_ 3- T111: flL'.‘1l|.|.'ill-N|I\l'ill' -;'z1puril_\' fur 1110 |1'c'Ie\|1gu|1|r [unling uf Prul1. 1 is mu:-at m-n1'l_\' [F1] BS kipea
[111 'Fll ki]1\~a [(1] H2 kipei
[D] 111 1:511:-=
IIII
0
wI:\v.|I|IiIpI$I.:\'|-I11
[D] 1.11111‘-‘m
FDUIIII-ITIUIS
SOLUTIONS
nun IIEIIIIIIIIG STRUGIIJIIEB
2-29
T111.‘ t'1'1-1cti1:11 of 1111* 1'1.1l1111111 1111111111111 Trs1|11;f1!1'1't'1l I11." s|1r::=11' i.-1
‘I . T1111 1'-1|11i\'.*1]m1T n1:r11'1|11ri1"i1_'1' 1:-1
‘
1+; . .U1 1 11.111
11-I -'_'1|'I| Fl-|\'i|1:i .'=i“=S= [LT h
P,
11111 111111
’
1:
_ _L _ 1 1.11? = 11.111
:\1'i1]1i|1 1u§11lc1]1- l||1r1|| I
T1111 1‘11|11l1i111\1'| s|11~.'1r 11t1'r'=111 1l11n 111 Hm :1|1]1|i1'11 axial I-:1:-11|
'['|'|:_* 111-I I';1r:1r_:|'1"e1i pl‘1":\'-1l|.t‘1_' 1'rI'| T||1_'1 |§:'11':I[i1‘|g i:-1
DIIS11:1
111111 l.h1-1-1111111111 111111111-111 is Fuund
P..(l 1
T1" =
'
"FT
.. _' {_-
_ 111111 1-1111~11(1 1 S-TIJFI U) _ "I||||||1|J1.| =
.1. L "J\f'!'I
0'11,-,
[HE I-1i|1."-1'j1(l[][l¢] ' k1|1
11511-11111111111}
[1 11111? 111 +
ki].H1'||'-[2
J,-
111.-111111111 i.ll-klp.'iII(l[.'l|JU
11 I .1
l:'1.T1J5 111"‘
r1“;,"i"| = ll]-"1 l1i]11~1|."FI:"'
= 1111 111111113 Thu answer is {B}.
Tl11' 111111: r.1[ 1l11' 1011,11, -.~:i1l1- lu 1h1'sl1url .si1l1' ufll11'1'ul1111111 i:~= ff‘. =
2. T1111 l1~111:',1l1111'tl11r1!riTi1'~.11] p1~ri11111T1"1'i11'
F1
E
bl-‘I _ HIE ' an _ |_=l][l'£ in
12 i11 = 1.(]D
If» in]
!.3 M
{'1
112
— D fl. T1111 11]]111'.'11|1l1~ Sll-Nil‘ 11111-_\11-1 I111 t11'11-1.\'11y :11'ti1>11 is gi'1.'1"11 h_1.' ,11('-| I-jq. ll-33 :_1.-1
S|'11*11.1- =11. 11111 1.*1'i1i1:=.1| 11-e.~1'i11|.111r.-1' is
<;1r.I,- _ ~l1__"'12\-1_.-"If: Fr = PM _ H'5{q11||||1|:1l _ qJ1I_r||i|||)
= 11111 111111 - 1j11.5_1(s.111
kip“
'11,. 3
2.111
-:1 " al1'1-1111,!-I1 1'1-111|cliu11 l'111'Iur ki]1c~1
— l'I.?-5 [r0111 AC-I S1-1'. 5.3
;
M
<_')1_1' = {-JH'H.T.'1'|[1.11115’ -IUIHI
-,1 12.-25 111'-!
llIl."
= 11111 111111111
= B2 l-1111:4-
‘.1--1.1.,
'l'h1* |111|:11' 111111111-111 11!‘ i|1nr1i11 111' thn 1-1'ir.ir:11l ]1111"i111-1'1r.1"1r '15
-I1 _ J-'1 rflhl + :1,"-'3] + rfl F 3
1111- 11 l‘11111111;_; s\'1l|:1 11 rv:'IIIr.=1| 11111111111
|‘_.~\:1|i:1!'1-|1'l111|.'§1'|
The answer is (B11 3- T111‘ 111:-11211111" 11f t|11' c1'1t11'11l 111111111111 E111 H1':111ra1| >1h1'11r
f1'u111 H11: 1!1ig1~ of 1111: E1101-111g is
'11:] -| =. |,1[l-5 111]-Iii? 111 + 13] [ET 111)] + [15 in)"
= 1.1.1111 111-‘
3
.-1=f'§-f;-11=T_—,"-'_—1P-12511 = l.'1'5 [I
PPI
1 IIlI!.|I|I|I|I1lI-l.GI|II
2-31)
ITRUGTIIIIIL E111:11111z|111||I11 11e1=:n1sn1¢£ |111111un1.
T111! 111:1 1111111111111 111'1:11.'-111'1~1111 11111 F11-1111111‘; 111 1111.11 111111111111 is
T111! f1"1c't111'1‘11 1111111111111 111 1111* 111111‘ 11ft]11r1'11l11111|1 1:1 -1
"{'1'11111_11: _ 111111111111]
Jun =
‘1'-._- = 11'11||11.1\| _ S
,.,
_ 5111 km“ _" 11.1 1115 01epu SL1
F
BU; -
('311..1..-.-1-1 "I" L1
1-11111-1
1-1 11111:: 11]*(1j-11 (1.111
111115
1|. ' 11.1 .1111 +— 2.114 Id J hi HF11
= 4.114 111]-1111'1'*'
+:1.111
Ii = -53.54 fl-1111111
11115111111111; 1110111111111-c11|1tru1]1:11 1111:11:t11111. 1111* r1*q11i1'1'11 111-111Ii:111'1'1111'11T 1":-1Ti11 '14
The 1'111'tu1'1'11 -5111-111" [1:1'1'1- 111 1111* 1'1'i1i1‘11| :~'1~1'liu-11 111'
. 11.11:" 1 J1 ( V : 1"1';1'(1'11m:".,L.(;_ + 11",) 1'
1 I1 11'
.1-1 11.111-11111111111)
p=
Z’
_ 11 11}-{1.1':. 11](.T1.|11
111.s.1_1(4
+ 1:11
'1'll'
-{_§~1._1.!]J 11:-11111.11 (1 2 H)
I
= .-::1.114 11111.-
=1: (111111 1'11) 1111]‘:-
><
T]11~ 1'11'r111r11l-s111'111' 1'1'1|1111'i1_1' 1.11 1111' 101.1-11:11-4 111 gi1'1‘11 |.1}."
1 -
1 -
11121.3-53,‘-1_-15 i1|](l5 111]"
AF] E11. 11-Z1-1111
.1. [-1111111 111]"
111-'.. _ 2._=;~1111,11,.1'f_’
:
1‘2}1_1II.T5][413 111_11|.-1 111111_1.11_1v~"4u11111 =
1 |'H111
I
= [].|lU1H
1111 i
4-'1, = [1811
11111
= {[].1l(]1SII[-I5 i11}[l-T1 in]
- Li-S 1-111121 .'-'=1"',,
kip:-1 111*
1'1] Z
= 1.311111"!
1-i1llis'1-1‘I1'lI11l'_1':
T111: 111111i|1111111 r1:i111'111'01:1111:111 11111111 1:1" g11'c1| 113.‘ J11.‘-I 51111:. 1122.2 1111
Th: IDSIIIF Is {A}.
1-1..;,,.,;,,;| = U.1)D1SB.71 = [[1.1]U1E}[1$ i|1_}{lE1' in]
4. T1111 11111 1.111:1:111'r1r| |11'1'.~a11|1'1~ 1111 1.111! t'111'1-11111.: at 1111' 1:11:11 1111111: 111111111111 is
= I-G-I 111':
11-('1-5 H12}
:1.',111'r-111*]
‘H111 answer is (C).
= 5.111 1-1
-1j".1..-:~1'1 - 11.-5111 5.111
- 2.111
S
= 11.111 1111-m;11‘1"
T11
5. I-‘111111 AC1
11.3.3. 11111 n_*q11i11'1r1 1'111i1_1 111' 11111121111-
111I 1-1111111.111.-1.-1'1'|=.~1'11 i11 1l|1.* 11111111 is
11,“ =11.1111211 .-1,1 = ,-1103,1111
= 111.1111'111'11'1z 11111111111] =11.-1:12 111'-‘,111 111.--1 111*,-'11] The answer is {B}.
Comprehensive Coverage of the to-l-tour Structural SE Exam Topics This book prepares you forthe NCEE5 15-hour Structural SE e=tatn.The Stnrctural‘ Engineering Reference Mnnuaiprovicias a comprehensive review of structural analysis and design methods related to vertical and lateral forces.lt also illustrates the most useful equations in the examedopmd codes and standards, and it provides guidelines flor selecting and applying these equati-ons.More than 225 example problems illustrate how to apply concepts and use equations,and more than 45 end-of-chapter problems let you practice yoursltilis. Each problem's complete solution allows you to chetlt your own approach.‘|'ou'il benefit from an increased proficiency in a broad range ofstructu rai engineering topics and improved
efficiency In solving related problems. Quick access to supportive information isjust as important as knowledge and el'iiciency.'l'his l:ro-olt's thorough index directs
you tothe codes and concepts you will need during the ertarn.Throughout the book. cross references to more than rotiequations, 136 tahies,14-Ofigu res, B appendices, and the following reietra nt codes point you to additional support material when you need it. - AASI-i'l'O LRFD Bridge Design (20101 - ACI 313 i2lJIIl$i
- NSC 13th edition l2005l + ASCE P [Z0051 - IBC l2Elfl‘9'i
- ND5 [2005] ~ PCI (2flEi4] - TMS 4iCI2i'J\C| 53D.i'A5EE 5 i2IJ(lE'i
- Prestressed Concrete ' Structural Steel + 'l'|mber
- Reinforced Masonry ' lateral Forces [Wind and Seismic] r Bridges
Structural Design Topics Coltrlrucl - Fteinforced Concrete ' Foundations and Fletairrirrg Structures Alsoutthn Author Alan Wiliiams,PhD,5E,FiCE,-E Eng,lsa registered professional engineer and structural engineer in Calfornia,a Fellow
and Lite Member ofthe institution of -Ei-all Engine-ers,a Chartered Engineer in the United ltirrgcionund a rnern berol the Structural Engineers Association otfiouthern Caii'ornia.He obtained his bachelor of science ciegree and doctorate from the University of Leeds in England. Dr.Wiliia ms has extensive experience heaching and practicing structural engineering, including designing and constructing bridges,schoois,and industrial and commercial structures He has umrited as a senior engineer with the California Department o'fTransporta'tion and asa Principal for Structural Safety with the California Division of the State Architect. Dr.Williams has published several tetctbooirsand papers on structural engineering design, structu rai analysis, seismic deslgn,and rel nlorced and prestressed concrete design.
Also Iurail-able for Structural SE Elllfl Canriiriotes Sinlcruroi Engineering Solved Problems Six-ll-linuie Solutions for 5tructr.rroli‘P'EErtom Problems
Concrete Design for the Gvliand Structural PE Exams Timber Design for the Cirriland Structural PE Exams
Bridge Design for the Crwi and Structural PE Exams Core Engineering Concepts for Students and Professionals
Don't miss all the Structural Engineering iSE) etram news,the latest exam a.duice,the exam Fi'iCis,and the unique community oithe Exam Fonim at t\"rnrr.ppl2plos.-com.
ISBN ‘=l'r‘E1-1|-5'=l1EE|-373!-“I
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