9.composite construction

T.chhay

IX. eRKOgbgÁúMsmas
Composite Construction
9>1> esckþIepþIm Introduction
eRKOgbgÁúMsmasCaeRKOgbgÁúMsMNg;EdlGgát;rbs;vapÁúMeLIgedaysMPar³BIrRbePTKW EdkeRKag
nigebtugGarem:. niyayeGayxøIGgát;eRKOgbgÁúMsmaspSMeLIgedaysMPar³BIr b¤eRcInRbePT. eRKOgbgÁúM
smasRtUv)anerobrab;enAkñúg AISC Chapter I, “Composite Members.”.
Fñwmsmas (composite beam) GacmaneRcInTMrg;. FñwmsmasBIdMbUgRtUv)ancak;bgáb;kñúgeb
tug dUcbgðajenAkñúgrUbTI 9>1 a. vaCaCMerIsmYyenAeBlEdleKRtUvkarkarBareRKOgbgÁúMEdkBIePøIg
(fireproofing) ehIymUlehtumYyeTotKWeKGacKitBIkarcUlrYmrbs;ersIusþg;ebtugeTAkúñgersIusþg;rbs;

Fñwm. naeBlbc©úb,nñenH eKmanviFIkarBarePøIgEdlmanlkçN³esdækic© nigTMgn;Rsal dUcenHeKkMrcak;
bgáb;eRKOgbgÁúMEdkkñúgebtugeToteT. eKGacTTYl)an composite behavior edayP¢ab;FñwmEdkeTAnwg
kMralebtugEdlvaRTEdleFVIeGayEpñkTaMgBIreFVIkarCamYyKña. enAkñúgRbBn§½kMral b¤RbBn§½dMbUl Epñk
rbs;kMralxNÐeFVIGMeBICamYynwgFñwmEdkedIm,IbegáItCaFñwmsmasEdlman rolled steel shape EdlenABI
elIsøabxagelICasøabebtug ¬rUbTI 9>1 b¦.
kareFVIkarrYmKñaenHGacRbRBwtþeTA)anRbsinebIeKkarBarkarrGiltamTisedk (horizontal
slippage) rvageRKOgbgÁúMTaMgBIr. eKGaceFVIdUcenH)an RbsinebIkMlaMgkat;tamTisedkenARtg;épÞb:H

RtUv)ankarBaredayeRKOgsMrab;P¢ab;EdleKeGayeQμaHfa shear connectors. eKOgsMrab;P¢ab;enHGac
Ca headed studs, spiral reinforcing steel b¤CaEdkrag channel shape tUc²RbEvgxøIRtUv)anpSar
P¢ab;eTAnwgsøabxagelIrbs;EdkFñwmeTAtamKMlatkMNt;
edIm,Ipþl;nUvkarpSarP¢ab;CalkçN³emkanictamry³TMBk;enAkñúgebtugEdlrwgmaM ¬rUbTI 9>1 c¦. Stud
CaRbePT shear connector EdleKniymeRbICageK eKGaceRbIvaelIsBImYyedImenARtg;TItaMgEtmYy
RbsinebIsøabFñwmmanTMhMTUlayRKb;RKan; ¬vaGaRs½ynwgKMlatGnuBaØatEdlmanniyayenAkñúgEpñkTI
9>4¦. mUlehtumYyénPaBeBjniymrbs; shear stud KWPaBgayRsYlkñúgkartMeLIgrbs;va.
eKRtUvkarcMnYn shear connector RKb;RKan;edIm,IeFVIeGayFñwmeTACaFñwmsmaseBjelj (fully
composite beam). cMnYn shear conncter EdlticCagtMrUvkarnwgeFVIeGayekItmanPaBrGilxøHrvag

eRKOgbgÁúMEdk nigebtug/ FñwmEbbenHeKeGayeQμaHfa FñwmsmasedayEpñk (partially composite).

356 eRKOgbgÁúMsmas

T.chhay

Partially composite beam ¬EdlCak;EsþgmanT§iBlCag fully composite beam¦ RtUv)anbkRsay
enAkñúgEpñkTI 9>7.

eRKOgbgÁúMsmasenAkñúgGKarPaKeRcInRtUv)anbegáIteLIgedaykMralEdk (stell deck) EdleFVICa
Bum<sMRab;ebtugkMral ehIyRtUv)anminRtUv)anykecjeRkayeBlebtugrwgmaM. kMralEdkk¾cUlrYmenA
kñúgersIusþg;rbs;kMral EteyIgmin)anBicarNaBIkarKNnakMralEdkenATIenHeT. eKGaceRbIkMralEdk
pñt;EdlrnUtmanTisEkg b¤RsbnwgTisrbs;Fñwm. enAkñúgRbBn§½kMralFmμta rnUtEtgEtEkgeTAnwgFñwmkM
ral ehIyRsbeTAnwgrtEdlRTva. eKpSar Shear stud P¢ab;eTAnwgFñwmEdktamcenøaHrnUt dUcenHKMlat
rbs; stud tambeNþayFñwmRtUv)ankMNt;edaycMnYnpñt;rbs;rnUt. rUbTI 9>2 bgðajBIkMralxNÐEdl
begáIteLIgedaykMralEdkEdlrnUtEkgeTAnwgFñwm.
s<an highway PaKeRcInEdleRbIFñwmEdkCaFñwmsmas ehIyCaerOy²FñwmsmasCaCMerIsEdl
manlkçN³esdækic©sMrab;sMNg;GaKar. eTaHbICaeKGaceRbI rolled steel beam EdlmanrUbragtUcCag

T.chhay

manTMgn;RsalCagenAkñúgeRKOgbgÁúMsmask¾eday k¾ GtßRbeyaCn_rbs;vaRtUv)ankat;bnßyedaysar
tMélbEnßmén shear connector. eTaHbICay:agdUcenHk¾eday k¾GtßRbeyaCn_epSgeTotrbs;vaGaceFVI
eGayeRKOgbgÁúMsmasmankarTak;TajEdr. eKGaceRbI FñwmEdlrak;Cag ehIyPaBdabrbs;vanwgtUc
CageRKOgbgÁúMFmμta (conventional noncomposite construction).

kugRtaMgeGLasÞicenAkñúgFñwmsmas Elastic Stresses in Compostie Beams
eTaHbICa design strength rbs;FñwmsmasCaTUeTAQrelIlkçxNÐenAkar)ak;k¾eday k¾karyl;
dwgBIkareFVIkarCamYynwgbnÞúkeFVIkar (service load) mansar³sMxan;sMrab;mUlehtuCaeRcIn. eKEtgEteFVI
karGegátPaBdabrbs;eRKOgbgÁúMeRkamGMeBIrbs; service load ehIyenAkñúgkrNIxøH design strength KW
QrelIsßanPaBkMNt;én yield dMbUg.
eKGacKNnakugRtaMgrgkarBt; (flexural stress) nigkugRtaMgrgkarkat; (shearing stress) enA
kñúgFñwmrbs; homogeneous material BIrUbmnþ
fb =
Mc
I
nig f v = VQ It
b:uEnþ edaysarFñwmsmasminEMmnCa homogeneous material dUcenHrUbmnþTaMgenHKμann½y.
edIm,IGaceRbIrUbmnþTaMgenH)an eKRtUvbMElgmuxkat;rbs;ebtugeGayeTACamuxkat;Edk. viFisaRsþenH
tMrUveGay strain rbs;EdkEdl)anRbDiteLIgBIebtugmantMéldUcKñanwg strain rbs;EdkBitR)akd.
rUbTI 9>3 bgðajBIkMNat;rbs;FñwmsmasCamYynwgdüaRkam stress nig strain. RbsinebIkMralxNÐ
RtUv)anP¢ab;y:agl¥eTAnwg rolled steel shape enaH strain RtUvEtmanragdUcGVIEdl)anbgðaj EdlRsb
eTAnwg small displacement theory Edl)anniyayfa muxkat;EdlmanlkçN³erobesμImuneBlrgkar
Bt;enAEtrkSalkçN³erobesμIeRkayeBlrgkarBt;. b:uEnþ karBRgaykugRtaMgCalkçN³smamaRt
(linear stress distribution) Edl)anbgðajmann½yEtcMeBaHFñwmTaMgLayNaEdlRtUv)ansnμt;faCa


T.chhay

homogeneous material . dMbUg eKRtUvtMrUveGay strain enAkñúgebtugRtg;RKb;cMnucTaMgGs;esμInwg
strain enAkñúgEdkCMnYsenARKb;cMnucenaH

εc = εs b¤ Ec = Es
f f
c s

nig E
f s = s f c = nf c
Ec
¬(>!¦
Edl m:UDuleGLasÞicrbs;ebtug
Ec =

n = s = pleFobm:UDul
E
Ec
AISC I2.2 eGaym:UDuleGLasÞicebs;ebtug *

Ec = w1.5 f 'c (US)
c

c (
Ec = w1.5 1.3 ⋅10 − 3 ) f 'c (SI)

Edl wc = TMgn;maDrbs;ebtug
f 'c = ersIusþg;rgkarsgát;rbs;ebtugenA @*éf¶

TMgn; normal-weight concrete mantMélRbEhl 145lb / ft 3 = 2320kg / m3
eKGacbkRsaysmIkar (>! dUcxageRkam³ eKRtUvkarebtug n in.2 edIm,ITb;Tl;nwgkMlaMgdUcKña
EdlEdk 1in.2 GacTb;)an. edIm,IkMNt;RkLaépÞrbs;EdkEdlnwgTb;Tl;nwgkMlaMgdUcKñaEdlebtugGac
eFVI)an eKRtUvEckRkLaépÞebtugeday n . mann½yfaCMnYs Ac eday Ac / n . lT§plEdlTTYl)an
CaRkLaépÞbMElg (transformed area).

*
The ACI Building Code (ACI, 1995) eGaytMélrbs; E c = w1.5 (33) f ' c
c KitCa psi b¤ Ec = w1.5 (0.043)
c f 'c
KitCa N / mm 2


T.chhay

BicarNamuxkat;smasEdlbgðajenAkñúgrUbTI 9>4 a ¬karkMNt;TTwgsøabRbsiT§PaB b enA
eBlEdlFñwmCaEpñkrbs;RbBn§½kMralnwgENnaMenAxagmux¦. edIm,IbMElgRkLaépÞebtug Ac eGayeTACa
RkLaépÞEdk eyIgRtUvEckvanwg n . viFId¾gayRsYlKWeKRtUvEckTTwgeday n ehIyrkSakMras;eGayenA
dEdl. kareFVIdUcenHeKTTYl)an homogeneous steel section dUcbgðajkñúgrUbTI 9>4b. edIm,IKNna
kugRtaMg eyIgRtUvrkTItaMgG½kSNWtrbs;rUbragsmas ehIyKNnam:Um:g;niclPaBEdlRtUvKña. bnÞab;mk
eyIgGacKNna bending stresses CamYynwg flexural formula. enAEpñkxagelIbMputrbs;srésEdk
Myt
f st =
I tr
enAEpñkxageRkambMputrbs;Edk
Myb
f sb =
I tr
Edl M= m:Um:g;Bt;Gnuvtþn_
I st = m:Um:g;niclPaBeFobG½kSNWt ¬dUcKñanwgG½kSTIRbCMuTMgn;rbs; homogeneous section¦

yt = cMgayBIG½kSNWteTAEpñkxagelIbMputrbs;Edk

yb = cMgayBIG½kSNWteTAEpñkxageRkambMputrbs;Edk

eKGackMNt;kugRtaMgenAkñúgebtugtamviFIdUcKña b:uEnþedaysarsMPar³EdleyIgKitCaEdk enaHlT§pl
tUvEcknwg n ¬emIlsmIkar (>!¦ dUcenHeK)an
tMélGtibrmarbs; f c = nI yM
tr

Edl y CacMgayBIG½kSNWteTATItaMgx<s;bMputrbs;ebtug.
dMeNIrkarKNnaenHmann½ysMrab;Etm:Um:g;Bt;viC¢man EdlkMlaMgsgát;enAxagelIeRBaHeKmin
KitersIusþg;rgkarTajrbs;ebtug.


T.chhay

]TahrN_ 9>1³ FñwmsmasmYypSMeLIgedayEdk A36 manrag W16 × 36 CamYynwgkMralebtugkMras;
5in. nigTTwg 87in. enABIxagelIFñwm. ersIusþg;rbs;ebtugKW f 'c = 4000 psi . kMNt;kugRtaMgGtibrma
enAkñúgEdk nigebtugEdlekItBIm:Um:g;Bt;viC¢man 160 ft − klips .
dMeNaHRsay³ Ec = w1.5
c f 'c = 1451.5 4 = 3495ksi

n=
E s 29000
Ec
=
3495
= 8 .3 yk n = 8
edaysarEtm:UDuleGLasÞicrbs;ebtugCatMélRbhak;RbEhl dUcenHeyIgGacyktMél n CatMélKt;
ehIyvanwgpþl;nUvPaBsuRkitRKb;RKan;. dUcenH
b 87
= = 10.88in.
n 8
rUbTI 9>5 bgðajBI transformed section.

eKGackMNt;TItaMgrbs;G½kSNWtedayGnuvtþeKalkarN_m:Um:g;CamYynwgG½kSrbs;m:Um:g;enAEpñk
xagelIbMputrbs;kMral. karKNnaRtUv)ansegçbenAkñúgtarag 9>1 ehIycMgayBITItaMgx<s;bMputrbs;kM
raleTATIRbCMuTMgn;KW
∑ Ay 273.1
y= = = 4.202in.
∑ A 65.00
edayGnuvtþRTwsþIbTG½kSRsb nigedayerobCataragénkarKNnaenAkñúgtarag 9>2 eyIgTTYl)anm:Um:g;
niclPaBrbs; transformed section KW
I tr = 1526in.4
kugRtaMgenATItaMgx<s;bMputrbs;EdkKW
yt = y − t = 4.202 − 5.00 = −0.7980in.
Edl t CakMras;rbs;kMral


T.chhay

Myt (160 × 12 )(0.7980 )
f st =
Ltr
=
1526
= 1.00ksi ¬rgkarTaj¦
tarag 9>1
eRKOgbgÁúM A y Ay
ebtug 54.40 2.50 136.0

W 16 × 36 10.6 12.93 137.1

65.00 273.1

tarag 9>21
eRKOgbgÁúM A y I d I + Ad 2
ebtug 54.40 2.50 113.3 1.702 270.9

10.6 12.93 448 8.728 1255
W 16 × 36
1525.9

¬TItaMgx<s;bMputrbs;EdksßitenABIxageRkamG½kSNWt dUcenH f st CakugRtaMTaj¦
kugRtaMgenATItaMgeRkambMputrbs;Edk³
yb = t + d − y = 5 + 15.86 − 4.202 = 16.66in.
Myb (160 × 12 )(16.66 )
f sb =
I tr
=
1526
= 21.0ksi ¬rgkarTaj¦
kugRtaMgenATItaMgx<s;bMputrbs;rbs;ebtugKW
M y (160 × 12)(4.202)
fc = = = 0.661ksi
nI tr 8 × 1526
RbsinebIeKsnμt;ebtugminmanersIusþg;Tb;karTaj enaHebtuEdlsßitenABIeRkamG½kSNWtminRtUv)anyk
mkKiteT. enaHragFrNImaRtrbs; transformed section xusBIragFrNImaRtedImEdl)ansnμt;. edIm,I
TTYl)anlT§plsuRkit eKRtUveFVIkarKNnaTItaMgG½kSNWteLIgvijedayQrelIragFrNImaRtfμIenH.
eyagtamrUbTI 9>6 nigtarag 9>3 eyIgGacKNnaTItaMgfμIrbs;G½kSNWtdUcxageRkam³
2
∑ Ay 5.44 y + 137.1
y= =
∑A 10.88 y + 10.6

( ) 2
y 10.88 y + 10.6 = 5.44 y + 137.1

5.44 y + 10.6 y − 137.1 = 0

T.chhay

y = 4.140in.
m:Um:g;niclPaBrbs;RkLaépÞsmasEdleFVIeLIgvijenHKW
I tr =
1
(10.88)(4.140)3 + 448 + 10.6(12.93 − 4.140)2 = 1524in.4
3

tarag 9>3
eRKOgbgÁúM A y Ay
ebtug 10.88 y y/2 5.44 y
2

W 16 × 36 10.6 12.93 137.1

ehIykugRtaMgKW
f st =
(160 × 12)(5 − 4.140) = 1.08ksi ¬rgkarTaj¦
1524
f sb =
(160 ×12)(5 + 15.86 − 4.140) = 21.1ksi ¬rgkarTaj¦
1524
fc =
(160 × 12)(4.140) = 0.652ksi
8(1524)
PaBxusKñarvagkarviPaKTaMgBIrGacecal)an ehIykarKNnaTItaMgG½kSNWteLIgvijminmanRbeyaCn_eT.
cMeLIy³ kugRtaMgGtibrmaenAkñúgEdkKW kugRtaMgrgkarTaj 21.1ksi ehIykugRtaMgGtibrmaenAkñúgeb
tugKW kugRtaMgrgkarsgát; 0.652ksi .
ersIusþg;Tb;nwgkarBt; Flexural strength
enAkñugkrNICaeRcIn eKnwgTTYl)an nomial flecural strength enAeBlEdlmuxkat;Edk aMgmUl
yield ehIyebtugEbkedaysarkMlaMgsgát;. karEbgEckkugRtaMgEdlRtUvKñaenAelImuxkat;smasRtUv

aneKehAfa karEbgEcgkugRtaMg)aøsÞic (plastic stress distribution). AISC Specification eGaynUv
design strength sMrab;m:Um:g;Bt;viC¢manCa φb M n EdlRtUv)ankMNt;dUcxageRkam³


T.chhay

!> sMrab;rUbragEdlman compact web ( h / t w ≤ 640 / Fy sMrab; US b¤ h / t w ≤ 1680 / Fy
sMrab; SI) emKuNersIusþg; φb = 0.85 ehIy M n RtUv)anTTYlBI plastic stress distribution.
@> sMrab;rUbragEdlman noncompact web ( h / t w > 640 / Fy sMrab; US b¤
h / t w > 1680 / Fy sMrab; SI) φ b= 0.9 ehIy M n RtUv)anTTYlBI elastic stress distribution Edl

RtUvKñanwg yilding dMbUgrbs;Edk.
rUbragTaMgGs;EdlmanenAkñúgtaragrbs; Manual Ca compact web dUcenHeKRtUveRbIlkçxNÐ
TImYysMrab;karedaHRsayFñwmsmas elIkElgEt built-up steel shapes. enAkñúgCMBUkenHeyIgniyay
Et compact shape b:ueNÑaH.
enAeBlEdlFñwmsmaseTAdl;sßanPaBkMNt;)aøsc eKEbgEckkugRtaMgtamviFImYykñúgcMeNam
Þi
viFIbIEdlbgðajenAkñúgrUbTI 9>7. kugRtaMgebtugRtUv)anbgðajCakugRtaMgsgát;BRgayesμI 0.85 f 'c
EdlbnøayBITItaMgx<s;bMputrbs;kMraleTACMerAEdlGactUcCag b¤esμInwgkMras;kMralsrub. karEbgEck
enHKW Whitney equivalent stress distribution EdlkugRtaMgpÁÜbRtUvKñanwgkugRtaMgpÁÜbrbs;karEbgEck
kugRtaMgBitR)akd (ACI, 1995). rUbTI 9>7 a bgðajBIkarEbgEckEdlRtUvKñanwg full tensil yielding
rbs;Edk nigkugRtaMgsgát;edayEpñkrbs;ebtug CamYynwgG½kSNWt)aøsÞic (PNA) enAkñúgkMralxNÐ.
edayersIusþg;Tajrbs;ebtugmantMéltUc ehIyvamintUv)aneKKitkñúgkarKNnaeTenaH KμankugRtaMgNa
RtUv)anbgðajenAkEnøgEdlkugRtaMgTajmanGMeBIelI ebtug. lkçxNÐenHeKeRbICaTUeTAenAeBlEdlva
man shear connectors RKb;RKan;edIm,ITb;Tl;nwgkarrGil KWedIm,IFananUvkareFVIkarCaeRKOgbgÁúMsmas.
kñúgrUbTI 9>7 b bøúkkugRtaMgebtugRtUv)anbnøayeBj kMras;rbs;kMral ehIy PNA sßitenAkñúgsøabrbs;
FñwmEdk. dUcenHEpñkrbs;søabnwgrgkugRtaMgsgát; edIm,IbegáInkMlaMgsgát;enAkñúgkMralxNÐ. rUbTI 9>7
c bgðajBIlT§PaBTIbI Edl PNAsßitenAkñúgRTnug. cMNaMfa sMrab;krNITaMgbIenH eKmincaM)ac;bnøaybøúk

kugRtaMgebtugeBjkMras;kMraleT.
kñúgkrNInImYy²EdlbgðajenAkñúgrUbTI 9>7 eyIgGacrk nominal moment capacity eday
KNnam:Um:g; couple EdlekIteLIgedaykMlaMgTajpÁÜb nigkMlaMgsgát;pÁÜb. eyIgGacTTYlva)aneday
eFVIplbUkm:Um:g;rbs;kMlaMgpÁÜbeFobnwgcMnucgayRsYlNamYy. edaysarkartP¢ab;rbs;FñwmEdkeTAnwg
kMralebtug vaminmanbBaðCamYynwg lateral torsional buckling enAeBlEdlebtugrwgmaM ehIyeK
TTYl)an composite action.


T.chhay

edIm,IkMNt;faetIeKRtUvykkrNINamkeRbI eKRtUvKNnakMlaMgsgát;pÁÜbNaEdltUcCageKkñúgcM
eNam
!> As Fy
@> 0.85 f 'c Ac
#> ∑ Qn
Edl As = RkLaépÞmuxkat;rbs;EdkFñwm
Ac = RkLaépÞrbs;ebtug = tb ¬emIlrUbTI 9>7¦


T.chhay

ersIiusþg;kMlaMgkat;srubrbs; shear connector
∑ Qn =

lT§PaBnImYy²bgðajBIkMlaMgkat;tamTisedkenARtg;épÞb:HrvagEdk nigebtug. enAeBlEdllT§PaBTI
mYylub eKeRbIEdkTaMgmUl ehIyeKGnuvtþkarEbgEcgkugRtaMgrbs;rUbTI 9>7 a. lT§PaBTIBIrRtUvKñanwg
ebtugEdllub ehIy PNA sßitenAkñúgEdk ¬rUbTI 9>7 b b¤ c¦. krNITIbIlubEtenAeBlEdleKeRbI
shear connector ticCagtMrUvkarsMrab; full composite behavior EdleFVIeGayekItman partial

composite behavior. eTaHbICa partial composite action GacekItmanCamYynwgkMralxNÐtan; b¤kM

ralxNÐEdlekItBI steel deck k¾eday k¾vaRtUv)anykmkniyayenAkñúgEpñkTI 9>7/ “Composite
Beams with Formed Steel Deck”.

]TahrN_ 9>2³ KNna design strength rbs;Fñwmsmasrbs;]TahrN_ 9>1. snμt;faeKman shear
connector RKb;RKan;sMrab; full composite behavior.
dMeNaHRsay³ kMNt;kMlaMgsgát; C enAkñúgebtug ¬kMlaMgkat;tamTisedkenARtg;épÞb:Hrvagebtug
nigEdk¦. edaysarvaCa full composite action kMlaMgEdlmantMéltUcCagKW As Fy nig
0.85 f 'c Ac ³

As Fy = 10.6(36 ) = 381.6kips

0.85 f 'c Ac = 0.85(4)(5 × 87 ) = 1479kips
kMlaMgsgát;enAkñúgEdklub C = 381.6kips .
enHmann½yfaeKminRtUvkarkMras;TaMgmUlrbs;ebtugedIm,IbegáItkMlaMgsgát;EdlRtUvkareT. eKTTYl)an
karEbgEckkugRtaMgenAkñúgrUbTI 9>8.

eKk¾GacKNnakMlaMgsgát;rYmdUcxageRkam
C = 0.85 f 'c ab

T.chhay

enaHeyIg)an a = 0.85Cf ' b = 0.85(4.)(687) = 1.290in.
381
c

kMlaMg C nwgsßitenAelITIRbCMuTMgn;rbs;RkLaépÞrgkarsgát;enAkMBs; a / 2 BITItaMgx<s;bMput
rbs;kMralxNÐ. kMlaMgTajpÁÜb T ¬esμInwg C ¦ nwgsßitenATIRbCMuTMgn;rbs;RkLaépÞEdk. ékXñas;
rbs; couple RtUv)anbegáIteLIgeday C nig T KW
d a 15.86 1.290
y= +t − = +5− = 12.28in.
2 2 2 2
Nominal strength KWm:Um:g; couple b¤
M n = Cy = Ty = 381.6(12.28) = 4686in.kips = 390.5 ft − kips
ehIy design strength KW
φb M n = 0.85(390.5) = 332 ft − kips
cMeLIy³ design strength = 332 ft − kips

enAeBlEdlvaman full composite behavior ]TahrN_ 9>2 CaKMrUsMrab;lkçxNÐenH. karvi
PaKsMrab;krNI PNA EdlmanTItaMgsßitenAkñúgmuxkat;EdknwgRtUv)anrk enAeBlEdleKdwgfavaCa
partial composite action.

9>2> karsagsg;edaymankarTb; nigedayminmankarTb;
Shored Versus Unshored Construction
Tal;EtebtugrwgmaM nwgvaTTYl)annUv design strength rbs;va ¬y:agtic 75% énersIusþg;
sgát;enA 28 éf¶ f 'c ¦ enaHmanminmankareFVIkarCasmas (composite behavior) eT ehIyTMgn;rbs;kM
raldac;xatRtUv)anRTedaymeFüa)ayepSg². enAeBlEdlebtugrwgmaM vaGaceFVIkarCaeRKOgbgÁúM
smas ehIykMlaMgGnuvtþn_bnþbnÞab;RtUv)anTb;Tl;edayFñwmsmas. RbsinebIFñwmEdkRtUv)anRTeday
CnÞl;RKb;RKan;tambeNþayRbEvgrbs;vamunnwgebtugRtUv)ancak; TMgn;rbs;ebtugRss;nwgRtUvRTeday
CnÞl;beNþaHGasnñeRcInCagedayEdkFñwm. enAeBlEdlebtugrwgmaM CnÞl;beNþaHGasnñRtUv)anruHerI
ecj ehIyTMgn;rbs;kMralxNÐk¾dUcCabnÞúkbEnßmnwgRtUvRTedayFñwmsmas. b:uEnþRbsinebIeKmineRbI
CnÞl; rolled steel shape minRtwmEtRTTMgn;pÞal;rbs;vab:ueNÑaHeT b:uEnþvaRtUvRTTMgn;rbs;kMralxNÐ
nigBum<kñúgeBlebtugeFVIkarrwgmaM. enAeBlEdleKTTYl)an composite behavior bnÞúkbEnßm TaMg


T.chhay

bnÞúkefr nigbnÞúkGefrnwgRtUvRTedayFñwmsmas. eyIgnwgBicarNalkçxNÐxusKñaedaylMGitdUcxag
eRkam.
KμanCnÞl;³ muneBlebtugrwgmaM Unshored: Before Concrete cures
AISC I3.4 TamTarfa enAeBlEdleKmineRbICnÞl; EdkFñwmEtÉgdac;xatRtUvEtmanersIusþg;
RKb;edIm,I Tb;Tl;nwgbnÞúkGnuvtþn_TaMgGs;munnwgebtugTTYl)an 75% énersIusþg;rbs;va. ersIusþg;Tb;
karBt; (flexural strength) RtUv)anKNnaedayviFIFmμta edayQrelI Charpter F of the Specifica-
tion ¬CMBUk 5 enAkñúgesovePAenH¦. edayGaRs½yeTAelIkarKNnarbs;va Bum<sMrab;kMralebtugGac

pþl; b¤minGacpþl; lateral support sMrab;EdkFñwm. RbsinebIvaminpþl;Ca lateral support sMrab;EdkFñwm
eT eKRtUvyk unbraced length Lb mkKit ehIy lateral-torsional buckling GaclubelI flexural
strength. RbsinebIeKmineRbICnÞl;beNþaHGasnñeT EdkFñwmk¾GacRtUv)aneRbIedIm,ITb;Tl;nwgbnÞúksag

sg;bnÞab;bnSMEdr. edIm,IkarBarbnÞúkTaMgenH eKRtUvbEnßmbnÞúk 20lb / ft 2 = 1kN / m 2 (Hansell et al.,
1978).

KμanCnÞl;³ eRkayeBlebtugrwgmaM Unshored: After Concrete cures
eRkayeBleKTTYl)an composite behavior RKb;bnÞúkEdlGnuvtþCabnþbnÞab;TaMgGs;RtUv)an
RTedayFñwmsmas. b:uEnþ enAeBldac; RKb;bnÞúkTaMgGs;RtUv)anRTeday couple xagkñúg EdlRtUvKñanwg
karEbgEckkugRtaMgenAeBldac;. dUcenHmuxkat;smasRtUvEtmanersIusþg;RKb;RKan;edIm,IRTbnÞúkTaMgenH
EdlrYmbBa©ÚlTaMgbnÞúkEdlGnuvtþeTAelIFñwmEdkmunnwgebtugrwgmaM.
karsagsg;edayTl; Shored Construction
kñúgkarsagsg;edayeRbICnÞl; eKBicarNaEtFñwmsmas edaysareKminRtUvkareGayEdkFñwmRT
GVIepSgBIbnÞúkpÞal;rbs;vaeT.
ersIusþg;kMlaMgkat; Shear Strength
AISC I3.6 tMrUveGaykMlaMgkat;TaMgs;RtUvTb;Tl;edayRTnugrbs;EdkFñwm Edlpþl;eGayenA
kñúg Chapter F of the Specification.
]TahrN_ 9>3³ Edk W12 × 50 eFVIkarrYmKñaCamYynwgkMralxNÐebtugkMras; 4in. . TTwgkMralxNÐ
RbsiT§PaBKW 72in. . eKmineRbICnÞl; m:Um:g;Bt;EdlGnuvtþmkelIvamandUcteTA³ )anmkBITMgn;Fñwm


T.chhay

M beam = 13 ft − kips )anmkBITMgn;kMralxNÐ M slab = 77 ft − kips nigBIbnÞúkGefr
M L = 38 ft − kips . ¬enAkñúg]TahrN_enH eKminKitbnÞúksagsg;bEnßmeT¦. EdkEdleRbIKW A36

ehIy f 'c = 4000 psi . kMNt;faetI flexural rbs;FñwmenHRKb;RKan;b¤Gt;. snμt;favaCa full
composite action ehIyBum<pþl;Ca lateral suppoet dl;muxkat;EdkmuneBlebtugrwgmaM.

dMeNaHRsay³ muneBlebtugrwgmaM vamanEtbnÞúkGefrb:ueNÑaH ¬minmanbnÞúksagsg;enAkñúg]TahrN_
enHeT¦. dUcenHbnSMbnÞúk A4-1 lub ehIym:Um:g;emKuNKW
M u = 1.4(M D ) = 1.4(13 + 77 ) = 126 ft − kips
BI beam design chart enAkñúg Part 4 of the Manual sMrab;Edk A36
φb M n = 195 ft − kips > 126 ft − kips (OK)
eRkayeBlebtugrwgmaM FñwmsmasRtUvTb;Tl;nUvm:Um:g;emKuN
M u = 1.2M D + 1.6M L = 1.2(13 + 77 ) + 1.6(38) = 168.8 ft − kips
kMlaMgsgát; C CatMéltUcCageKén
As F y = 14.7(36 ) = 529.2kips

b¤ 0.85 f 'c Ac = 0.85(4)(4 × 72) = 979.2kips

PNA KWsßitenAkñúgebtug ehIy C = 529.2kips . BIrUbTI 9>8 kMBs;rbs;bøúgkugRtaMgsgát;KW
C 529.2
a= = = 2.162in.
0.85 f 'c b 0.85(4)(72)
édXñas;m:Um:g;KW
d a 12.19 2.162
y= +t − = +4− = 9.014in.
2 2 2 2
design moment KW
φb M n = φb C y = 0.85(529.2 )(9.014 ) = 4055in.kips = 338 ft − kips > 168.8 ft − kips (OK)

cemøIy³ FñwmmanersIusþg;Bt; (flexural strength) RKb;RKan; .

Cak;Esþg karsagsg;edayeRBICnÞl;manRbsiT§PaBCagkarsagsg;EdlmineRbICnÞl; edaysar
KmineRbImuxkat;EdkedIm,IRTGVIepSgeRkABIbnÞúkxøÜnva. kñúgsßanPaBxøH kareRbIR)as;CnÞl;GaceGayeKRbI
R)as;muxkat;FñwmEdktUcCag. b:uEnþ eRKOgbgÁúMsmasCaeRcInminmaneRbICnÞl;eT edaysartMélbEnßm
rbs;CnÞl; CaBiesséføBlkmμ cMNayGs;ticCagkarsnSMsMécelITMgn;Edk.


T.chhay

9>3> TTwgsøabRbsiT§PaB Effect Flange Width

Epñkrbs;kMralxNÐEdleFVIkarCaeRKOgbgÁúMsmasCamYynwgEdkFñwmCaGnuKmn_eTAnwgktþaCaeRcIn
EdlrYmmanRbEvgElVg nigKMlatFñwm. AISC I3.1 tMrUveGayTTwgRbsiT§PaBrbs;kMralxNÐenAelIEpñk
nImYy²rbs;G½kSFñwmKWtMélEdltUcCageKkñúgcMeNam³
!> mYyPaKR)aMbIénRbEvgElVg.
@> mYyPaKBIrénKMlatFñwmEdlKitBIG½kSeTAG½kS.
#> cMgayBIG½kSFñwmeTARCUgEKmrbs;kMral.
lkçxNÐTIbIRtUv)anGnuvtþcMeBaHEtFñwmxagb:ueNaÑaH dUcenHsMrab;Fñwmxagkñúg TTwgRbsiT§PaBTaMgmUlRtUv
mantMéltUcCageKénmYyPaKbYnénRbEvgElVg b¤KMlatrbs;FñwmEdlKitBIG½kSeTAG½kS ¬edaysnμt;fa
FñwmmanKMlatesμI¦.

]TahrN_ 9>4³ RbB½n§kMralEdlpSMeLIgedayEdkFñwm W 12 × 44 EdlmanKMlatBIKña 9 ft nigRTnUvkM
ralebtugGarem:kMras; 4.5in. . RbEvgElVgKW 30 ft . edaybEnßmBIelITMgn;rbs;kMral eKmanbnÞúk
CBa¢aMgxNÐ 20 psf nigbnÞúkGefr 125 psf . EdkCaRbePT A36 ehIyersIusþg;rbs;ebtugKW
f 'c = 4000 psi . cUreFVIkarGegátFñwmxagkñúgedayeKarBtam AISC Specificastion RbsinebIeKmineRbI

CnÞl;beNþaHGasnñ. snμt; full lateral support kñúgGMLúgeBlsagsg; ehIybnÞúksagsg;bEnßmKW
20 psf . eKpþl;nUv shear connector RKb;RKan;sMrab; full composite action.

dMeNaHRsay³ bnÞúkEdlGnuvtþmuneBlebtugrwgmaMrYmmanTMgn;rbs;kMralxNÐ
(4.5 / 12)(150) = 56.25 psf .¬eTaHbICa normal-weight concrete manTMgn; 145 psf / EtebtugGarem:
RtUv)ansnμt;famanTMgn; 150 psf ¦. sMrab;FñwmEdlmanKMlat 9 ft bnÞúkGefrKW
56.25 × 9t = 506lb / ft
+ TMgn;Fñwm = 44lb / ftt

550lb / ft
bnÞúksagsg;KW 20(9) = 180lb / ft EdlRtUv)anKitCabnÞúkGefr. bnÞúk nigm:Um:g;emKuNKW
wu = 1.2wD + 1.6wL = 1.2(550) + 1.6(180) = 948lb / ft

M u = (0.948)(30)2 = 106.6 ft − kips
1
8


T.chhay

BI load Factor Design Selection Table
φb M n = φb M p = 258 ft − kips > 106.6 ft − kips (OK)

eRkayeBlebtugrwgmaM bnÞúksagsg;minmaneFVIGMeBIeToteT EtbnÞúlCBa¢aMgxNÐeFVIGMeBIvijmþg ehIyva
RtUv)anKitCabnÞúkefr ¬emIl)TahrN_ 5>13¦³
w part = 20(9 ) = 180lb / ft

wD = 506 + 44 + 180 = 730lb / ft
bnÞúkGefrCa
wL = 125(9 ) = 1125lb / ft
bnÞúkGefr nigm:Um:g;GefrKW
wu = 1.2wD + 1.6wL = 1.2(730) + 1.6(1125) = 2676lb / ft

M u = (2.676)(30)2 = 301 ft − kips
1
8
TTwgRbsiT§PaBCatMélEdltUcCageKkñúgcMeNam
span 30(12 )
= = 90in.
4 4
KMlatFñwm = 9(12) = 108in.
edaysareRKOgbgÁúMEdlRtUvKNnaCaFñwmxagkñúg lkçxNÐTIbIminGacGnuvtþ)an. yk b = 90in. CaTTwg
søabRbsiT§PaB. enaH tamkarbgðajenAkñúgrUbTI 9>9 kMlaMgsgát;RtUvEtCatMélEdltUcCageKkñúg
cMeNam
As F y = 13(36 ) = 468kips

b¤ 0.85 f 'c Ac = 0.85(4)(4.5)(90) = 1377kips
yk C = 468kips . BIrUbTI 9>9
C 468
a= = = 1.529in.
0.85 f 'c b 0.85(4)(90)
d a 1.529
y = + t − = 10.33 + 4.5 − = 14.07in.
2 2 2
φb M n = φb Cy = 0.85(468)(14.07 ) = 5595in. − kips = 466 ft − kips > 301 ft − kips (OK)
RtYtBinitükMlaMgkat;
w L 2.676(30 )
Vu = u = = 40.1kips
2 2
BItaragbnÞúkBRgayesμIemKuN (facored uniform load tables)

T.chhay

φvVn = 141kips > 40.1kips
cemøIy³ FñwmBitCaeKarBtam AISC Specification.

9>4> Shear Connectors
dUcEdleyIg)aneXIjrYcmkehIy kMlaMgkat;tamTisedkEdlekIteLIgcenøaHebtug nigEdkesμI
nwgkMlaMgsgát;enAkñúgebtug C . eyIgsMKal;kMlaMgkat;tamTisedkenHeday Vh . dUcenH Vh CatMél
EdltUcCageKkúñgcMeNam As Fy / 0.85 f 'c Ac b¤ ∑ Qn . RbsinebI As Fy b¤ 0.85 f 'c Ac lub vanwg
man full composite action ehIyeKRtUvkarcMnYn shear connectors cenøaHm:Um:g;sUnü nigm:Um:g;Gtibrma
KW
V
N1 = h
Qn
¬(>@¦
Edl Qn Ca nominal shear strength rbs; connector mYy². Connectors cMnYn N1 KYrRtUv)andak;
edaymanKMlatesμI²KñaelIRbEvgEdlvatMrUv. AISC Specification eGaysmIkarsMrab;ersIusþg;TaMg
stud connector nig channel shear connector. dUcEdl)anbgðajBIdMbUg stud connector CaRbePT

EdleKniymeRbICageK ehIyeyIgBicarNaEtRbePTenH. sMrab; stud shear connector mYy
Qn = 0.5 Asc f 'c Ec ≤ Asc Fu (AISC Equation I5-1)

Edl Asc = RkLaépÞmuxkat;rbs; stud
f 'c = ersIusþg;rgkarsgát;enA 28 éf¶

Ec = m:UDuleGLasÞicrbs;ebtug

Fu = ersIusþg;rgkarTajrbs; stud

sMrab; stud EdleRbICa shear connector enAkñúgFñwmsmas ersIusþg;rgkarTaj Fu KW 60ksi . tMél
EdleGayeday AISC Equation I5-1 KWQrelIkarBiesaFn_ (Ollgaard, Stutter, and Fisher, 1971).

T.chhay

eKmineRbIemKuNersIusþg;sMrab; Qn eT flexural resistance factor φb )anKitsMrab;RKb;ersIusþg;Edl
manPaBminRbRktI.
smIkar (>@ eGaycMnYn shear connector EdlRtUvkarenAcenøaHcMnucm:Um:g;sUnü nigcMnucm:Um:g;
Gtibrma. dUcenH sMrab;FñwmTMrsamBaØEdlRTbnÞb;BRgayesμI eKRtUvkar connector cMnYn 2N1 ehIy
BYkvamanKMlatesμI²Kña. enAeBlmanbnÞúkcMcMnuc AISC I5-6 TamTareGaydak; connector cMnYn N1
enA cenøaHbnÞúkcMcMnuc nigcMnucm:Um:g;sUnüEdlenAEk,redIm,IbegáItm:Um:g;EdlTamTarenARtg;bnÞúk. EpñkenH
RtUv)aneKsMKal;eday N 2 ehIytMrUvkarenHRtUv)anbgðajenAkñúgrUbTI 9>10. cMNaMfacMnYn shear
connector srubminTTYlT§iBlBItMrUvkarenHeT.

tMrUvkarepSg²sMrab; Headed Struds (AISC I5)
Miscellaneous Requirements for Headed Studs (AISC I5)
Ggát;p©itGtibrma = 2.5 × kMras;rbs;EdkFñwm
RbEvgGb,brma = 4 × Ggát;p©it stud
KMlattambeNþayGb,brma ¬BIG½kSeTAG½kS¦ = 6 × Ggát;p©it stud
KMlattambeNþayGtibrma ¬BIG½kSeTAG½kS¦ = 8 × kMras;kMralxNÐ
KMlattamTTwgGb,brma ¬BIG½kSeTAG½kS¦ = 4 × Ggát;p©it stud
lateral cover Gb,brma = 1in. = 25mm ¬minmankarkMNt;sMrab; vertical cover

Gb,brma¦

AWS Structural Code (AWS 1996) rayCabBa¢InUvGgát;p©it stud sþg;darCa 1/ 2 / 5 / 8 /
3 / 4 / 7 / 8 / nig 1in. . edaypÁÚrpÁgGgát;p©itenHCamYynwgRbEvgGb,brmaEdltMrUveday AISC eyIg


T.chhay

TTYl)anTMhM stud FmμtaKW 1/ 2 × 2 / 5 / 8 × 2 12 / 3 / 4 × 3 / 7 / 8 × 3 12 nig 1× 4 ¬b:uEnþ eKk¾GaceRbI
stud EdlEvgCagenHEdr¦.

]TahrN_ 9>5³ KNna shear connectors sMrab;RbB½n§kMralenAkñúg]TahrN_ 9>4.
dMeNaHRsay³ segçbTinñn½yEdl)anTTYlBI]TahrN_ 9>4³
W 21× 44 / Edk A36
f 'c = 4000 psi
kMras;kMralxNÐ t = 4.5in.
RbEvgElVg = 30 ft
BI]TahrN_ 9>4 kMlaMgkat;tamTisedk Vh EdlRtUvKñanwg full composite action KW
Vh = C = 468kips
sakl,g stud 1/ 2 × 2 . Ggát;GnuBaØatGtibrmaKW
2.5t f = 2.5(0.450 ) = 1.125in. > 0.5in. (OK)

RkLaépÞmuxkat;rbs; shear connector mYyKW
π (0.5)2
Asc = = 0.1963in.2
4
RbsinebIeyIgsnμt;ebtugCaebtugTMgn;Fmμta (normal-weight concrete) m:UDuleGLasÞicrbs;ebtugKW
Ec = w1.5 f 'c = (145)1.5 4 = 3492ksi
c

BI AISC Equation I5-1 ersIusþg;rgkMlaMgkat;rbs; connector mYyKW
Qn = 0.5 Asc f 'c Ec ≤ Asc Fu

= 0.5(0.1963) 4(3492 ) = 11.60kips
Asc Fu = 0.1963(60) = 11.78kips > 11.60kips yk Qn = 11.60kips
ehIy KMlattambeNþayGb,brmaKW 6d = 6(0.5) = 3in.
KMlattamTTwgGb,brmaKW 4d = 4(0.5) = 2in.
KMlattambeNþayGtibrmaKW 8d = 8(4.5) = 36in.
cMnYn stud EdlRtUvkarenAcenøaHcugFñwm nigkNþalFñwmKW
V 468
N1 = h = = 40.3
Qn 11.60


T.chhay

ykcMnYnGb,brma 41 sMrab;Bak;kNþalFñwm b¤cMnYnsrub 82 . RbsinebIenARtg;muxkat;nImYy²eKeRbI
stud cMnYnmYy KMlatEdlcaM)ac;KW
30(12)
s=
82
= 4.4in. yk s = 4in.
sMrab;muxkat;mYyeRbI stud BIrRKab;
30(12)
s=
82 / 2
= 8.8in. yk s = 8.5in.
kartMerob stud mYyNak¾manlkçN³RKb;RKan; ehIyKMlatmYyNak¾sßitenAcenøaHEdnkMNt;TabbMput
nigEdnkMNt;x<s;bMput. kartMerob stud RtUv)anbgðajenAkñúgrUbTI 9>11. eTaHbICakartMerobenHRtUvkar
shear connector eRcInCagtMrUvkark¾eday EteKgayRsYlkñúgkarTTYl)anKMlattamtMrUvkar.

cemøIy³ eRbI stud cMnYn 86 edImEdlmanTMhM 1/ 2in.× 2in. tMerobdUcbgðajkñúgrUbTI 9>11.

9>5> karKNnamuxkat; Design
CMhandMbUgkñúgkarKNnamuxkat;rbs;RbB½n§kMralxNÐKWCakareRCIserIskMras;rbs;kMralxNÐ
eTaHbIvaCakMraltan; b¤kMralrnUt ¬Edl)anBI steel deck¦ k¾eday. kMras;CaGnuKmn_eTAnwgKMlatFñwm
nigbnSMCaeRcInénkMras;kMral nigKMlatFñwmEdlRtUvkarkarGegát dUcenHeKnwgGacrk)annUvRbB½n§kMral
EdlmanlkçN³esdækic©bMput. karKNnakMralxNÐminRtUv)anelIkykmkniyayenAkñúgesovePAenH
eT b:uEnþeyIgsnμt;faeyIgsÁal;kMras;kMralxNÐ nigKMlatFñwm. edaykareFVIsnμt;EbbenH eyIgGacGnuvtþ
nUvCMhanxageRkamedIm,IbMeBjnUvkarKNnaRbB½n§kMralxNÐEdlKμanCnÞl;.
!> kMNt;m:Um:g;emKuNEdleFVIGMeBImun nigeRkayebtugrwgmaM
@> eRCIserIsmuxkat;EdkFñwmsakl,g
#> KNna design strength rbs;EdkFñwm nwgeRbobeFobvaCamYynwgm:Um:g;emKuNEdleFVIGMeBI
muneBlebtugrwgmaM. eKRtUvyk unbraced length mkKit RbsinebIBum<min)anpþl;Ca lateral

T.chhay

support RKb;RKan;. RbsinebImuxkat;EdkFñwmenHminRKb;RKan; eKRtUvsakl,gmuxkat;
FMCagenH.
$> KNna design strength rbs;muxkat;smas nigeRbobeFobvaeTAnwgm:Um:g;emKuNsrub. Rb
sinebImuxkat;smasminRKb;RKan; eRCIserIsmuxkat;EdkFñwmepSgeTotsMrab;sakl,g.
%> RtYtBinitüersIusþg;rgkMlaMgkat; (shear strength) rbs;EdkFñwm.
^> KNna shear connectors³
a. KNna Vh / kMlaMgkat;tamTisedkenARtg;épÞb:Hrvagebtug nigEdk.

b. EckkMlaMgenHeday Qn ¬ersIusþg;rgkMlaMgkat;rbs; connector eTal¦ edIm,I

TTYl)ancMnYn chear connector srubEdlRtUvkar. cMnYn connector enHnwgpþl;nUv
full composite action. RbsinebIeKcg;)an partial composite behavior eKGac

kat;bnßycMnYn connectors enH ¬manbkRsayenAkñúgEpñkTI 9>7¦
&> RtYtBinitüPaBdab ¬RtUv)anbkRsayenAkñúgEpñkTI 9>6¦
kargard¾sMxan;enAkñúgdMeNIrkar trial-and-orror Edl)anerobrab;xagelIenHKWkareRCIserIsmux
kat;EdkFñwmsakl,g. rUbmnþEdlnwgeGaynUvRkLaépÞcaM)ac; ¬b¤Gacniyaymü:ageTotKWTMgn;EdlRtUv
karelIRbEvgÉktþa¦ GacekIteLIg)an RbsinebIeKsnμt;kMBs;Fñwm. edaysnμt;vaeFVIkarCaeRKOgbgÁúM
smasTaMgRsug (full composite action) ehIy PNA sßitenAkñúgkMralxNÐ ¬Edlmann½yfa EdkFñwm
lub ehIyvaCakrNIEdleKeRcInCYbRbTHCageK¦ eyIgGacsresr design strength ¬edayeyageTA
elIrUbTI 9>12¦ Ca
(
φb M n = φb (Ty ) = φb As Fy y )

edaydak;eGay design strength esμInwgm:Um:g;emKuN ehIyedaHRsayrk As eyIgTTYl)an


T.chhay

φb As Fy y = M u nig As =
Mu
φb F y y

b¤ As =
Mu
φb Fy (d / 2 + t − a / 2)
¬(>#¦
eKk¾GacsresrsmIkar (># vaCaTMgn;CagkarsresrCaRkLaépÞ. edaysarRbEvg 1 ft manmaD
As / 144 ft 3 ehIyEdkeRKOgbgÁúMmanTMgn;maD 490lb / ft 3

w = s (490 ) = 3.4 As lb / ft ¬sMrab; As KitCa in.2 ¦
A
144
BIsmIkar (># dUcenHTMgn;Edl)a:n;sμankñúgmYy ft KW
w=
3.4 M u
φ F (d / 2 + t − a / 2)
lb / ft ¬(>$¦
b y

Edl M u KitCa in. − kips / Fy KitCa ksi / ehIy d / t nig a KitCa in. . eKGaceRbIsmIkar (># b¤
(>$ edIm,IeRCiserIsmuxkat;sakl,g. smIkarTaMgBIrTamTarnUvkMBs;Edlsnμt; nigkar)a:n;sμan a / 2 .
dUcenH CaTUeTAbøúkkugRtaMgmankMBs;tUcNas; kMritlMeGogkñúgkarKNna a / 2 nwgmanT§iBltictYcelI
tMélEdl)anKNna As . eKsnμt; a / 2 = 1.0 .
RbsinebIeKeRbIsmIkar (>$ ehIyeKsnμt; nominal depth d enaHeKGaceFVIkareRCIserIsrUbrag
sakl,g)any:aggayRsYl. kareRbIsmIkarenHk¾pþl;nUvkarKNnaTMgn;FñwmedaypÞal;.

]TahrN_ 9>6³ RbEvgElVgrbs;RbB½n§kMralKW 30 ft ehIyKMlatFñwmKW 10 ft edayKitBIG½kSeTAG½kS.
eRCIserIs rolled steel shape nig shear connector EdlcaM)ac;edIm,ITTYl)ankareFVIkarCaeRKOgsmas
TaMgRsugCamYynwgkMralxNÐebtugGarem:kMras; 3.5in. . bnÞúkbEnßmEdlmanGMeBIelIkMralxNÐrYmman
bnÞúkCBa¢aMgxNÐ 10 psf nigbnÞúkGefr 55 psf . ersIusþg;ebtugKW f 'c = 4000 psi nigEdkEdleRbICa
RbePT A36 . snμt;faFñwmman full lateral support kñúgGMLúgeBlsagsg; ehIymanbnÞúksagsg;
20 psf .

dMeNaHRsay³ bnÞúkEdlRtUvRTmuneBlebtugrwgmaMKW
kMralxNÐ³ (3.5 /12)(150) = 43.75 psf
TMgn;kñúg 1 ft : 43.75(10) = 437.5lb / ft
bnÞúksagsg;³ 20(10) = 200lb / ft
¬TMgn;FñwmnwgRtUvKitenAeBleRkay¦

T.chhay

bnÞúkEdlRtUvRTeRkayeBlebtugrwgmaMKW
w part = 10(10 ) = 100lb / ft

wD = wslab + w part = 437.5 + 100 = 537.5lb / ft

wL = 55(10 ) = 550lb / ft

wu = 1.2wD + 1.6 wL = 1.2(0.5375) + 1.6(0.550) = 1.525kips / ft

M u = (1.525)(30)2 = 171.6 ft − kips
1
8
sakl,gkMBs; d = 16in. . BIsmIkar (>$ TMgn;FñwmEdl)anKNnaKW
3.4M u 3.4(171.6 × 12)
w= = = 21.8lb / ft
φb Fy (d / 2 + t − a / 2) 0.85(36)(16 / 2 + 3.5 − 1)
sakl,g W 16 × 26 . RtYtBinitüFñwmEdkedayminmanCnÞl;sMrab;bnÞúkEdlGnuvtþmuneBlebtugrwgmaM
¬TMgn;rbs;kMralxNÐ TMgn;rbs;Fñwm nigbnÞúksagsg;¦
wu = 1.2(0.4375 + 0.026) + 1.6(0.200 ) = 0.8762kips / ft

M u = (0.8762 )(30 )2 = 98.6 ft − kips
1
8
BI Load Factor Design Selection Table
φb M n = φb M p = 119 ft − kips > 98.6 ft − kips (OK)

eRkayeBlebtugrwgmaM nigeRkayeBlEdleKTTYl)an composite behavior
wD = wslab + w part + wbeam = 0.4375 + 0.100 + 0.016 = 0.5535kips / ft

wu = 1.2wD + 1.6 wL = 1.2(0.5535) + 1.6(0.550) = 1.544kips / ft

M u = (1.544)(30)2 = 174 ft − kips
1
8
muneBlKNna design strength rbs;muxkat;smas dMbUgeyIgRtUvkMNt;TTwgsøabRbsiT§PaB. sMrab;
Fñwmxagkñúg TTwgRbsiT§PaBCatMéltUcCageKkñúgcMeNam
span 30(12)
4
=
4
= 90in. b¤ KMlatFñwm = 10(12) = 120in.
yk b = 90in. . sMrab; full composite behavior kMlaMgsgát;enAkñúgebtugenA ultimate ¬esμInwgkMlaMg
kat;tamTisedkenARtg;épÞb:Hrvagebtug nigEdk¦ CatMélEdltUcCageKkñúgcMeNam
As F y = 7.68(36 ) = 276.5kips

b¤ 0.85 f 'c Ac = 0.85(4)(90)(3.5) = 1071kips


T.chhay

yk C = Vh = 276.5kips . kMBs;bøúkkugRtaMgsgát;enAkñúgkMralxNÐKw
C 276.5
a= = = 0.9036in.
0.85 f 'c b 0.85(4)(90)
ehIyédXñas;rbs; internal resisting couple KW
d a 15.69 0.9036
y= +t − = + 3.5 − = 10.89in.
2 2 2 2
design flexural strength KW
φb M n = φb (Cy ) = 0.85(276.5)(10.89) = 2550in.kips = 213 ft − kips > 174 ft − kips (OK)
w L 1544(30 )
Vu = u = = 23.2kips
2 2
BI factored uniform load tables
φvVn = 76.3kips > 23.2kips (OK)
cemøIy³ eRbI W 16 × 26
eKRtUvkarm:UDuleGLasÞicrbs;ebtugedIm,IKNna shear connector. BI]TahrN_ 9>5/
Ec = 3492ksi sMrab;ebtugFmμtaCamYynwg f 'c = 4000 psi . sakl,g stud 1 / 2 × 2in.

¬ Asc = 0.1963in.2 ¦
Ggát;p©itGtibrma = 2.5t f = 2.5(0.345) = 0.8625in. > 0.5in. (OK)
BI AISC Equation I5-1/ ersIusþg;rgkMlaMgkat;rbs; connector mYyKW

= 0.5(0.1963) 4(3492 )

= 11.60kips
Asc Fu = 0.1963(60) = 11.78kips > 11.60kips
dUcenHyk Qn = 11.60kips
cMnYn stud EdlRtUvkarenAcenøaHcugFñwm nigkNþalElVgKW
V
N1 = h =
276.5
Qn 11.60
= 23.8 eRbI 24 sMrab;Bak;kNþalFñwm b¤Casrub 48
nig KMlattambeNþayGb,brmaKW 6d = 6(0.5) = 3in.
KMlattamTTwgGb,brmaKW 4d = 4(0.5) = 2in.
KMlattambeNþayGtibrmaKW 8t = 8(3.5) = 28in.

T.chhay

RbsinebIeKeRbI stud mYysMrab;muxkat;nImYy² KMlatRbhak;RbEhlKW
30(12 )
s= = 7.5in.
48
KMlatenHsßitenAcenøaHEdnx<s;bMput nigEdnTabbMput dUcenHvabMeBjlkçxNÐ.
cemøIy³ ykkarKNnaEdlbgðajenAkñúgrUbTI 9>13.

9>6> PaBdab Deflections
edaysarm:Um:g;niclPaBrbs;muxkat;bMElg (transformed section) FM dUcenHPaBdabrbs;
FñwmsmasnwgtUcCagFñwmFmμta. b:uEnþ eKGacTTYl)anm:Um:g;niclPaBFMenHEteRkayeBlebtugrwgmaMEt
b:ueNÑaH. PaBdabEdlekIteLIgedaysarbnÞúkGnuvtþn_muneBlebtugrwgmaMRtUv)anKNnaCamYynwgm:Um:g;
niclPaBrbs;FñwmEdk. PaBdabbEnßmnwgekIteLIgenAeBlEdlFñwmrgnUvbnÞúkefrdUcCa TMgn;rbs;CBa¢aMg
xNÐ enAeRkayeBlebtugrwgmaM. tMbn;m:Um:g;viC¢man ebtugnwgrgkMlaMgsgát;Cab;rhUt ehIyrgnUv)atuPUt
EdleKsÁal;faCa creep. Creep CakMhUcRTg;RTayEdlekIteLIgeRkamGMeBIrbs;bnÞúksgát;. eRkay
eBlekItmankMhUcRTg;RTaydMbUg kMhUcRTg;RTaybEnßmnwgekItmaneLIgedayGRtayWtelIry³eBld¾
Evg. T§iBlenAelIFñwmsmasKWkarekIneLIgnUvkMeNag EdlbNþaleGayPaBdabtambBaÄrekIneLIg
Edr. eKGackMNt;EtPaBdabry³eBlyUr (long-term deflection) edayeRbIbec©keTsEdleKniym
eRbI. bec©keTsenHKWeRbImuxkat;ebtugEdl)ankat;bnßyenAkñúgmuxkat;bMElg dUcenHeKnwgTTYl)an
m:Um:g;niclPaBtUcCagmun ehIyeKnwgTTYl)anPaBdabFMCagmun. muxkat;Edl)ankat;bnßyRtUv)an
KNnaedayeRbI 2n b¤ 3n CMnYseGaypleFobm:UDulCak;Esþg n . enAkñúgesovePAenH eyIgeRbI 2n .
PaBdabEdlekIneLIgeday creep minRtUv)anENnaMeday AISC Specification eT.
sMrab;karsagsg;edayKμanCnÞl; eKmanm:Um:g;niclPaBbIxusKñasMrab;KNna long-term
deflection.


T.chhay

!> eRbI I s / m:Um:g;niclPaBrbs; rolled steel shape sMrab;PaBdabEdlekIteLIgedaysarbnÞúk
Gnuvtþn_muneBlebtugrwgmaM.
@> eRbI I tr / m:Um:g;niclPaBrbs; transfored section EdlKNnaCamYynwg b / n sMrab;PaBdab
EdlekIteLIgedaybnÞúkGefr nigsMrab;PaBdabdMbUg (initial deflection) EdlekIteday
bnÞúkefrEdlGnuvtþeRkayeBlebtugrwgmaM.
#> eRbI I tr EdlKNnaCamYynwg b / 2n sMrab; long-term deflection EdlekIteLIgedaysar
bnÞúkGefrEdlGnuvtþeRkayeBlebtugrwgmaM.

]TaheN_ 9>7³ KNnaPaBdabPøam² (immediate deflection) nig long-term deflection sMrab;Fñwm
enAkñúg]TahrN_ 9>4.
dMeNaHRsay³ segçbTinñn½yBI]TahrN_ 9>4³
W 21× 44 / Edk A36

kMras;kMralxNÐ t = 4.5in. ehIyTTwgRbsiT§PaBKW b = 90in.
f 'c = 4000 psi
bnÞúkGefrEdlGnuvtþmuneBlebtugrwgmaMKW wD = 550lb / ft ¬kMralxNÐbUknwgFñwm¦
bnÞúksagsg;KW wconst = 180lb / ft
bnÞúkGefrKW wL = 125(9) = 1125lb / ft
bnÞúkCBa¢aMgxNÐKW w part = 20(9) = 180lb / ft
PaBdabPøam²³
sMrab;FñwmbUknwgkMralxNÐ w = 550lb / ft
5wL4 5(0.55 / 12 )(30 × 12 )4
Δ1 = = = 0.41in.
384 EI s 384(29000)(843)
sMrab;bnÞúksagsg; w = 180lb / ft
5wL4 5(0.18 / 12 )(30 × 12 )4
Δ2 = = = 0.1342in.
384 EI s 384(29000 )(843)
PaBdabPøam²srubKW Δ1 + Δ 2 = 0.41 + 0.1342 = 0.544in.


T.chhay

sMrab;PaBdabEdlenAsl; eKRtUvkarm:Um:g;niclPaBrbs;muxkat;bMElgBIrKW I tr CamYynwgTTwg
kMralxNÐbMElg b / n nig I tr CamYynwgTTwgkMralxNÐbMElg b / 2n . sMrab;ebtugTMgn;FmμtaEdl
man f 'c = 4000 psi / Ec = 3492ksi nigpleFobm:UDulKW
E
n= s =
Ec
29000
3492
= 8 .3 yk n = 8
sMrab;PaBdabrbs;muxkat;smasEdlminTak;Tgnwg creep TTwgRbsiT§PaBKW
b 90
= = 11.25in.
n 8
rUbTI 9>14 bgðajBImuxkat;bMElgEdlRtUvKña. karKNnasMrab;TItaMgG½kSNWt nigm:Um:g;niclPaBRtUv)an
segçbenAkñúgtarag 9>4.
PaBdabdMbUgEdlbNþalBITMgn;CBa¢aMgxNÐKW
5w part L4 5(0.180 / 12)(30 × 12 )4
Δ3 = = = 0.0441in.
384 EI tr 384(29000)(2566)
PaBdabEdlbNþalBIbnÞúkGefrKW
5wL L4 5(1.125 / 12 )(30 × 12 )4
Δ4 = = = 0.2755in.
384 EI tr 384(29000 )(2566 )

tarag 9>4
eRKOgbgÁúM A y Ay I d I + Ad 2
ebtug 50.62 2.25 113.9 85.43 2.571 420

W 12 × 44 13.00 14.83 192.8 843 10.01 2146
63.62 306.7 2566in.4

∑ Ay 306.7
y= = = 4.821
∑ A 63.62


T.chhay

PaBdabry³eBlyUrEdlbNþalBI creep. eRbITTwgkMralxNÐbMElg
b 90
= = 5.625in.
2n 2(8)
muxkat;bMElgRtUv)anbgðajenAkñúgrUbTI 9>15. karKNnaTIRbCMuTMgn;nwg m:Um:g;niclPaBRtUv)ansegçb
enAkñúgtarag 9>5. edayehAm:Um:g;niclPaBenHCa I 'tr eyIgGacKNnaPaBdabry³eBlyUrEdlekIt
eLIgeday creep KW
5w part L45(0.180 / 12)(30 × 12)4
Δ5 = = = 0.0504in.
384 EI 'tr 384(29000)(2245)

tarag 9>5
ebtug 25.31 2.25 56.95 42.71 4.269 504

W 12 × 44 13.00 14.83 192.8 843 8.311 1741
38.31 249.8 2245in.4

∑ Ay 249.8
y= = = 6.519
∑ A 38.31

cemøIy³ xageRkamenHCakarsegçbrbs;PaBdab
PaBdabPøam²munTTYl)an composite behavior
Δ1 + Δ 2 = 0.4100 + 0.1342 = 0.544in.
PaBdabry³eBlxøICamYynwgCBa¢aMgxNÐedayKμanbnÞúkGefr
Δ1 + Δ 3 = 0.4100 + 0.0441 = 0.454in.


T.chhay

PaBdabry³eBlxøIedaybEnßmbnÞúkGefr
Δ1 + Δ 3 + Δ 4 = 0.4100 + 0.0441 + 0.2755 = 0.730in.
PaBdabry³eBlEvgedayKμanbnÞúkGefr
Δ1 + Δ 5 = 0.4100 + 0.0504 = 0.460in.
PaBdabry³eBlEvgedaymanbnÞúkGefr
Δ1 + Δ 4 + Δ 5 = 0.4100 + 0.2755 + 0.0504 = 0.736in.
edaysarbnÞúkefrEdlGnuvtþeRkayeBlebtugrwgmaMmantMéltUc PaBdabEdl)anBI creep
mantMéltUcenAkñúg]TahrN_enH.

9>7> FñwmsmasCamYynwgkMralBum<Edk Composite Beams with Formed Steel Deck
kMralxNÐenAkñúgsMNg;eRKagEdkRtUv)anpÁúMeLIgkñúgTMrg;kMralEdkrnUt (ribbed steel deck)
EdlRtUv)anTukenAnwgkEnøgedIm,IeGayvakøayeTACaEpñkrbs;eRKOgbgÁúM. eTaHbICamankrNIelIkElgk¾
eday k¾rnUtrbs;bnÞHEdkRtUv)andak;eGayEkgnwgFñwmkMral ehIyRsbeTAnwgrtEdlRTFñwmenaH. rUbTI
9>16 bgðajBIrnUtEdlmanTisEkgnwgFñwm. eKtMeLIg shear stud enAelIFñwmsmasEdlmankMralrnUt
tamviFIdUcKñanwgkartMeLIg shear srud enAelIFñwmsmasEdlKμankMralrnUt. eKcat;TukfakarP¢ab;Kña
rvag deck eTAnwgFñwmEdkpþl;nUvTMrxag (lateral support) sMrab;FñwmEdkmuneBlebtugrwgmaM. kar
KNna nigkarviPaKFñwmsmasCamYynwg formed steel deck mansar³sMxan;dUcKñanwgkrNIFñwmsmas
CamYynwgkMralEdlmankMralesμIEdr EtxageRkamCakrNIelIkElgmYycMnYn³
!> eKminKitebtugenAkñúgrnUt ¬EdlenABIeRkamEpñkxagelIrbs; deck¦ enAeBlrnUtTaMgenaH
EkgnwgFñwm (AISC I3.5b). enAeBlrnUtRsbnwgFñwm ebtugenAkñúgrnUtenaHRtUv)anKitbBa©Úl
eTAkñúgkarkMNt;lkçN³muxkat; ehIyRtUv)anbBa©ÚleTAkñúgkarKNna Ac .
@> lT§PaBrbs; shear connector GacRtUv)ankat;bnßy
#> CaTUeTA eKminGacTTYl)an full composite behavior eT. mUlehtuKWfa KMlatrbs; shear
connector RtUv)ankMNt;edayKMlatrbs;rnUt ehIyeKminGaceRbIRKb;cMnYn connector Edl

RtUvkar. eTaHbICaeKGaceRbI partial composite design edayKμan formed steel deck k¾
eday k¾vaRtUv)anelIkykmkniyayenATIenH BIeRBaHPaKeRcInvaRtUvkar formed steel deck.
tamBitvaminEmnCaKuNvibtþieT EtvaCaCMerIsxagEpñkesdækic©.

T.chhay

FñwmsmasPaKeRcInCamYynwg formed steel deck CakMralFñwmEdlmanrnUtEkgnwgFñwm ehIy
eyIgnwgniyayEtkñúgkrNIenH. tMrUvkarcaM)ac;EdlGnuvtþenAeBlrnUtmanTisRsbeTAnwgFñwmRtUv)an
bgðajenAkñúg AISC I3.5 c.
lT§PaBEdlkat;bnßyrbs; shear connectors
Reduced Capacity of Shear connector
edayBwgEp¥kelIkarBiesaF AISC I3.5b tMrUveGayKuN shear strength rbs; shear
connector Qn eTAnwgemKuNkat;bnßyenAeBlEdlrnUtEkgeTAnwgFñwm³
0.85 ⎛ wr ⎞ ⎡⎛ H s ⎞ ⎤
⎜
⎜h ⎟ ⎢⎜
⎟ ⎜h ⎟ − 1.0⎥ ≤ 1.0
⎟ (AISC Equation I3-1)
Nr ⎝ r ⎠ ⎣⎝ r ⎠ ⎦
Edl Nr = cMnYn stud kñúgmYyrnUtRtg;kEnøgEdlkat;KñaCamYynwgFñwm ¬EdlkMNt;RtwmbIenAkñúgkar
KNna¦
wr = TTwgmFümrbs;rnUt

hr = kMBs;rbs;rnUt

H s = RbEvgrbs; stud EdlkñúgkarKNnavaminRtUvFMCag (hr + 3) .

TMhMTaMgenHRtUv)anbgðajenAkñúgrUbTI 9>17.


T.chhay

Partial Composite Action
kareFVIkarCaeRKOgbgÁúMsmasedayEpñk (partial composite action) ekItmaneLIgenAeBlEdl
vaminman shear connector RKb;RKan;edIm,IkarBarPaBrGilrvagebtug nigEdkFñwm. TaMgebtug nigEdk
minGaceFVIkardl; strength rbs;vaeBjeljeT ehIykMlaMgsgát;RtUv)ankMNt;RtwmkMlaMgGtibrma
¬EdlCaersIusþg;rbs; shear connector ∑ Qn ¦ EdlGacbBa¢ÚnkMlaMgkat;tamépÞb:HrvagEdk nigebtug.
rMlwkfa C CatMélEdltUcCageKkñúgcMeNam As Fy / 0.85 f 'c Ac nig ∑ Qn .
CamYynwg partial composite action CaTUeTAG½kSNWt)aøsÞic (PNA) sßitenAñúgmuxkat;Edk. TI
taMgenHnwgeFVIeGaykarviPaKersIusþg;mankarBi)akCagTItaMgrbs; PNA EdlsßitenAkñúgkMralxNÐbnþic
EteKalkarN_cMbgKWdUcKña.
enAeBlEdleKeFVI elastic analysis k¾dUcCaenAeBlEdleKKNnaPaBdab eKRtUveFVIkar KNna
m:Um:g;niclPaBrbs; partially composite section. eKGaceRbIExSekag parabolic transition BI I s
¬sMrab;EtEdkFñwm¦ eTA I tr ¬sMrab; fully composite section¦ )an (Hansell et al., 1978). xageRkam
CasmIkarEdlnwgpþl;nUvlT§plRbhak;RbEhlsMrab;m:Um:g;niclPaBRbsiT§PaBEdlbgðajeday
Commentary to the AISC Specification³
I eff = I s + ∑ Qn / C f (I tr − I s ) (AISC Equation C-I3-6)

Edl C f CakMlaMgsgát;enAkñúgebtugsMrab; fully composite condition ¬tMélEdltUcCageKkñúg
cMeNam As Fy nig 0.85 f 'c Ac ¦. edaysarEt ∑ Qn CakMlaMgsgát;Cak;EsþgsMrab;krNI partially
composite enaHpleFob ∑ Qn / C f CacMENkrbs; compositeness Edlman. RbsinebIpleFobenH

tUcCag 0.25 enaHeKminKYreRbI AISC Equation C-I3-6 (Hansell et al., 1978).
eKminGacTTYl)anersIusþg;EdkeBjenAkñúg partially composite beam eT dUcenHvaTamTar
nUvmuxkat;EdkFñwmFMCag muxkat;EdkFñwmsMrab; fully composite behavior. b:uEnþ vaRtUvkar shear
connector ticCag ehIytMélrbs;EdkFñwm nig shear connectors ¬EdlrYbbBa©ÚlTaMgtMéltMeLIg¦

RtUv)anKitcUleTAkñúgkarviPaKEpñkesdækic©. enARKb;eBlEdl fully composite beam manlT§PaB
Tb;Tl;FM ¬EdleKEtgEtCYbRbTHkrNIEbbenH¦ eKGaceFVIkarkat;bnßycMnYn shear connector Edl
eFVIeGayFñwmkøayCa partially composite beam.


T.chhay

tMrUvkarepSg² Miscellaneous Requirements
xageRkamCatMrUvkarEdl)anBI AISC Section I3.5 a nig b. GVIEdlnwgerobrab;xageRkamCa
tMrUvkarbEnßmBIelIGVIEdl)anerobrab;BIcxagedIm³
- kMBs;rnUtGtibrma hr = 3in. = 75mm
- TTwgmFümGb,brmarbs;rnUt wr = 2in. = 50mm b:uEnþtMélrbs; wr EdleRbIenAkñúgkar
KNnaminKYrFMCag clear width rbs;EpñkxagelIbMputrbs; deck eT.
- kMras;kMralGb,brmaenABIelIEpñkx<s;bMputrbs; deck = 2in. = 50mm .
- Ggát;p©it stud Gtibrma = 3 / 4in. . karTamTarsMrab; formed steel deck enHCakarbEnßmBI
elIGgát;p©itGtibrma 2.5t f .
- kMBs;Gb,brmarbs; stud BIelIEpñkx<s;bMputKW 1 1 2 in.
- KMlattambeNþayGtibrmarbs; shear stud = 36in. = 915mm
- eKRtUvP¢ab; deck eTAnwgsøabFñwmedayKMlatmineGayFMCag 18in = 460mm eday stud b¤
eday spot weld. kareFVIEbbenHedIm,IkarBar uplift.
TMgn; deck nigTMgn;kMral Slab and Deck Weight
edIm,IsMrYldl;karKNnaTMgn;kMral eyIgeRbIkMras;rbs;kMralTaMgmUledayvas;BI)atrbs; deck
eTAépÞxagelIrbs;kMralxNÐ. eTaHbICaviFIenH)a:n;sμanmaDebtugelIsk¾eday EtvamansuvtßiPaB. sMrab;
TMgn;maDebtugGarem: eyIgeRbITMgn;ebtugmaDsuT§bUkbEnßm 5 pcf = 80kg / m3 . CaTUeTA edaysarkM
ralxNÐenAelI formed steel deck CaebtugEdlBRgwgedayEdktic ¬eBlxøHeRbI welded wire mesh
CMnYseGaykareRbI reinforcing bar¦ karbEnßm 5 pcf = 80kg / m3 sMrab;EdkBRgwgGacmantMélFM b:uEnþ
deck manTMgn;cenøaHBI 2 psf = 9.6kg / m 2 eTA 3 psf = 14.5kg / m 2 .

eKGaceRbIvFImü:ageTot edayKitplbUkrvagkMras;kMralEdlenABIelI deck Edlx<s;CageK
CamYynwgBak;kNþalkMBs;rbs;rnUtCakMras;ebtugkñúgkarKNnaTMgn;rbs;kMral. kñúgkarGnuvtþ CaTUeTA
eKGacrkplbUkrvagTMgn;kMral nig deck enAkñúgtaragEdlpþl;eGayedayeragcRkplit deck.

]TahrN_ 9>8³ kMralxNÐRTedayFñwmEdleRbI formed steel deck EdlbgðajenAkñúgrUbTI 9>18 Ca
mYynwgkMralebtugGarem:EdlkMras;srubKW 4.75in. . rnUt deck EkgnwgFñwm. RbEvgElVgKW 30 ft


T.chhay

ehIyFñwmmanKMlatBIKña 10 ft edayKitBIG½kSeTAG½kS. EdkeRKOgbgÁúMCaRbePTEdk A36 ehIyersIusþg;
rbs;ebtugKW f 'c = 3000 psi . TMgn;rbs;kMral nig deck KW 50 psf . TMgn;GefrKW 40 psf nigTMgn;
CBa¢aMgKW 10 psf . kñúgkarsagsg;enH eKminmaneRbICnÞl;beNþaHGasnñeT ehIyTMgn;sagsg;KW 20 psf .
!> eRCIserIs W shape
@> KNna shear connector
#> RtYtBinitüPaBdab. PaBdabry³eBlyUrsrubGnuBaØatGtibrmaKW 1/ 240 énRbEvgElVg.

dMeNaHRsay³ !> KNnaFñwm
eRCIserIsrUbragsakl,gedayQrelI full composite behavior
kMralxNÐ³ 50(10) = 500lb / ft
CBa¢aMgxNÐ³ 10(10) = 100lb / ft
bnÞúkGefr³ 40(10) = 400lb / ft
wu = 1.2wD + 1.6wL = 1.2(0.5 + 0.1) + 1.6(0.4) = 1.360kips / ft

M u = (1.36)(30)2 = 153 ft − kips
1
8
edaysnμt;fa d = 16in. / a / 2 = 1in. nigsnμt;TMgn;rbs;FñwmBIsmIkar (>$³
3.4M u 3.4(153 × 12)
w= = = 17.4lb / ft
φb Fy (d / 2 + t − a / 2) 0.85(36)(16 / 2 + 4.75 − 1)
sakl,g W 16 × 26 . RtYtBinitüersIusþg;rgkarBt;muneBlebtugrwgmaM
bnÞúksagsg;³ 20(10) = 200lb / ft
wu = 1.2wD + 1.6wL = 1.2(0.5 + 0.026) + 1.6(0.4) = 0.9512kips / ft

M u = (0.9512)(30)2 = 107 ft − kips
1
8
W 16 × 26 Ca compact section sMrab; A36 nigedaysar steel deck nwgpþl; lateral support

RKb;RKan; dUcenH nominal strength M n esμInwgersIusþg;m:Um:g;)aøsÞic M p .
BI Load Factor Design Selection Table

T.chhay

φb M p = 119 ft − kips > 107 ft − kips (OK)

eRkayeBlebtugrwgmaM bnÞúkemKuNsrubEdlRtUvRTedayFñwmsmas EdlRtUv)anEksMrYledaysarTMgn;
rbs;EdkFñwmKW
wu = 1.2(0.5 + 0.026 + 0.1) + 1.6(0.4) = 1.391kips / ft
ehIym:Um:g;emKuNKW
Mu =
1
(1.391)(30)2 = 156 ft − kips
8
TTwgkMralxNÐRbsiT§PaBrbs;muxkat;smasRtUvEtmantMéltUcCageKkñúgcMeNam
span 30(12)
4
=
4
= 90in. b¤ KMlatFñwm = 10(12) = 120in.
yk b = 90in. . sMrab; fully composite action kMlaMgsgát; C enAkñúgebtugKWCatMéltUcCageKkñúg
cMeNam
As Fy = 7.68(36 ) = 276.5kips

b¤ 0.85 f 'c Ac = 0.85(3)[90(4.75 − 1.5)] = 745.9kips

EdleKKitEtebtugenAelIEpñkx<s;bMputrbs; deck ¬dUcbgðajenAkñúgrUbTI 9>19¦ b:ueNÑaHsMrab;smIkarTI
BIrxagelI. CamYynwg C = 276.5kips kMBs;rbs;karBRgaykugRtaMgsgát;enAkñúgebtugKW
C 276.5
a= = = 1.205in.
0.85 f 'c b 0.85(3)(90)
édXñas;m:Um:g;rbs; internal resisting couple KW
d a 15.69 1.209
y= +t − = + 4.75 − = 11.99in.
2 2 2 2
0.85(276.5)(11.99)
φb M n = = 235 ft − kips > 156 ft − kips (OK)
12

T.chhay

w L 1.391(30 )
Vu = u = = 20.9kips
2 2
BI factored uniform load tables
φvVn = 76.3kips > 20.9kips (OK)
cemøIy³ !> eRbI W 16 × 26
@> Shear connectors
edaysarFñwmenHmanersIusþg;m:Um:g;FMKYrsm eKGaceGayvaeFVIkarCa patial composite behavior. dMbUg
eyIgRtUvrkcMnYn shear connector caM)ac;sMrab; full composite behavior nwgbnÞab;mkkat;bnßycMnYn
conntector. sMrab; fully composite beam/ C = Vh = 276.5kips .

sakl,g stud 3 4 × 3in. ¬ Asc = 0.4418in 2 ¦mYyenARtg;muxkat;mYy³
Ggát;p©itGtibrma = 2.5t f = 2.5(0.345) = 0.8625in.
b¤ 3 in. lub
4
Ggát;p©itCak;Esþg = 3 in. (OK)
4
KNnaemKuNkat;bnßyersIusþg;rbs; stud
Nr = 1
kMBs;rbs; stud BIelIEpñkx<s;bMputrbs; deck = 3 − 1.5 = 1.5in. = tMélGnuBaØat (OK)

BI AISC Equation I3-1,
emKuNkat;bnßy = 0.N ⎛ wr ⎞⎡⎛ H s ⎞ − 1.0⎤ ≤ 1.0
85
⎜
⎜ h ⎟ ⎢⎜ h ⎟
⎟ ⎜ ⎟ ⎥
r ⎝ r ⎠ ⎣⎝ r ⎠ ⎦
0.85 ⎛ 2.25 ⎞⎛ 3 ⎞
= ⎜ ⎟⎜ − 1.0 ⎟ = 1.275 > 1.0
1.0 ⎝ 1.5 ⎠⎝ 1.5 ⎠
eKminRtUvkarkat;bnßyersIusþg; stud eT. sMrab; f 'c = 3000 psi m:UDuleGLasÞicrbs;ebtugKW
Ec = w1.5 f 'c = 1451.5 3 = 3024ksi
c

BI AISC Equation I5-1, ersIusþg;rgkMlaMgkat;rbs; connector mYyKW

= 0.5(0.4418) 3(3024) = 21.04kips

Asc Fu = 0.4418(60) = 26.51kips > 21.04kips
dUcenHyk Qn = 21.04kips


T.chhay

cMnYnrbs; stud EdlRtUvkarenAcenøaHcugrbs;Fñwm nigkNþalElVgKW
V 276.5
N1 = h = = 13.1
Qn 21.04
yk 14 sMrab;Bak;kNþalFñwm dUcenHsrub 28 .
CamYy stud mYysMrab;rnUtmYy KMlatKW 6in. ehIycMnYnGtibrmaENnaMKW
30(12)
= 60 > 28 EdlTamTar
6
ebIeKeRbI stud mYysMrab;ral;BIrrnUt dUcenHeKRtUvkarva 30 edIm EdlenAEtCacMnYneRcIn. Rbsin
ebIeKeRbI stud mYysMrab;ral;bIrnUt enaHKMlatnwgkøayCa 3(6) = 18in. ehIycMnYnrbs; stud nwg
30(12) / 18 = 20 EdlvatUcCagtMrUvkarsMrab; full composite action. b:uEnþ vaman flexural strength FM

dUcenH partial composite action GacnwgRKb;RKan;.
sakl,g stud 20 edIm sMrab;FñwmmYy dUcenH N1 Edlpþl;eGay = 20 / 2 = 10
∑ Qn = 10(21.04)

= 210.4kips < 276.5kips
dUcenH C = Vh = 210.4kips
edaysar C tUcCag As Fy dUcenHEpñkxøHrbs;muxkat;EdkFñwmRtUvrgkMlaMgsgát; ehIyG½kSNWt)aøsÞic
KWsßitenAkñúgmuxkat;Edk.
edIm,IviPaKkrNIenH dMbUgeyIgRtUvkMNt;faetI PNA sßitenAelIsøabxagelI b¤sßitenAelIRTnug.
RbsinebI PNA sßitenA)atrbs;søabxagelI enaHtYsøabTaMgmUlnwgrgkMlaMgsgát; ehIykMlaMgsgát;pÁÜb
EdlbgðajenAkñúgrUbTI 9>20 KW
Pyf = b f t f F y = 5.5(0.345)(36 ) = 68.31kips


T.chhay

kMlaMgsuT§EdlRtUvepÞrenARtg;épÞb:HrvagEdk nigebtugKW
( )
T − C s = T − Pyf = As Fy − Pyf − Pyf = 276.5 − 2(68.31) = 139.9kips

EdlvatUcCagkMlaMgTajsuT§Cak;Esþg 210.4kips dUcenHsøabxagelIminRtUvkarrgkMlaMgsgát;eBj
kMras;søabrbs;vaeT. enHmann½yfa PNA sßitenAkñúgsøab. BIrUbTI 9>21 kMlaMgkat;tamTisedkEdl
RtUvepÞrKW
( )
T − C s = As Fy − b f t ' Fy − b f t ' Fy = Vh

276.5 − 2[5.5t ' (36)] = 210.4
edayKNnarkkMBs;énkMlaMgsgát;enAkñúgsøab eyIgTTYl)an
t ' = 0.1669in.

kMlaMgTajpÁÜbnwgeFVIGMeBIenAelITIRbCMuTMgn;rbs;RkLaépÞBIeRkam PNA. muneBleyIgKNna moment
strength eKRtUvkMNt;TItaMgTIRbCMuTMgn;sin. karKNnacMgayBITItaMgx<s;bMputrbs;EdkFñwm y RtUv)an

tarag 9>6
eRKOgbgÁúM A y Ay

W 16 × 36 7.68 15.69 / 2 = 7845 60.25

søab − 0.1669(5.50 ) = − 0.918 0.1669 / 2 = 0.0834 − 0.08

srub 6.762 60.17
∑ Ay 60.17
y= = = 8.898in.
∑ A 6.762


T.chhay

kMBs;rbs;bøúkkugRtaMgsgát;enAkñúgebtugKW
C 210.4
a= = = 0.9168in.
0.85 f 'c b 0.85(3)(90)
édXñas;sMrab;kMlaMgsgát;rbs;ebtugKW
a 0.9168
y+t − = 8.819 + 4.75 − = 13.11in.
2 2
édXñas;m:Um:g;sMrab;kMlaMgsgát;enAkñúgEdkKW
t' 0.1669
y− = 8.819 − = 8.736in.
2 2
Kitm:Um:g;eFobkMlaMgTaj nigedayeyagtamrUbTI 9>20 eyIgTTYl)an nominal strength³
M n = C (13.11) + C s (8.736)

= 210.4(13.11) + 0.1669(5.50)(36 )(8.736 ) = 3047in. − kips = 253.9 ft − kips
Design strength KW
φb M n = 0.85(253.9) = 216 ft − kips > 156 ft − kips (OK)
eKRtUvP¢ab; deck eTAnwgsøabFñwmedayKMlat 18in. dUcenHeKminRtUvkar spot weld edIm,IkarBar uplift
eT.
cemøIy³ @> eRbI shear connector dUcbgðajenAkñúgrUbTI 922.

#> PaBdab
muneBlebtugrwgmaM
wD = wslab + wbeam = 0.500 + 0.026 = 0.526kips / ft
5wD L4 5(0.526 / 12)(30 × 12 )4
Δ1 = = = 1.098in.
384 EI s 384(29000 )(301)
PaBdabEdlbNþalmkBIbnÞúksagsg;KW
5wconst L4 5(0.200 / 12)(30 × 12 )4
Δ2 = = = 0.418in.
384 EI s 384(29000 )(301)


T.chhay

PaBdabsrubmuneBlebtugrwgmaMKW
Δ1 + Δ 2 = 1.098 + 0.418 = 1.52in.
sMrab;PaBdabEdlekItmaneRkayeBlebtugrwgmaM eKRtUvkarm:Um:g;niclPaBrbs;muxkat;bMElg
BIrKW I tr CamYynwgTTwgkMralbMElg b / n nig I tr CamYy nwgTTWgkMlagbMElg b / 2n .
pleFobm:UDulKW
E
n= s =
Ec
29000
3024
= 9 .6 yk n = 10
sMrab;PaBdabrbs;muxkat;smasEdlBak;B½n§nwg creep TTwgRbsiT§PaBKW
b 90
= = 9in.
n 10
rUbTI 9>23 bgðajBImuxkat;bMElgEdlRtUvKña. karKNnaTItaMgG½kSNWt nigm:Um:g;niclPaB
RtUv)anbgðajenAkñúgtarag 9>7.
tarag 9>7
ebtug 29.25 1.625 47.53 25.75 2.282 178

W 16 × 26 7.68 12.60 96.77 301 8.693 881

srub 36.93 144.30 1059in.4

∑ Ay 144.3
y= = = 3.907in.
∑ A 36.93

edaysareKeRbI partial composite action dUcenHeKRtUvkareRbIm:Um:g;niclPaBbMElgEdlkat;
bnßy. BI AISC Equation C-I3-6 m:Um:g;niclPaBRbsiT§PaBKW
I eff = I s + ∑ Qn / C f (I tr − I s )

= 301 + 210.4 / 276.5 (1059 − 301) = 962.2in.4
PaBdabEdlekIteLIgedaysarbnÞúkGefrKW
5wL L4 5(0.400 / 12)(30 × 12)4
Δ3 = = = 0.2613in.
384 EI eff 384(29000)(962.2 )

PaBdabEdlbNþalmkBIbnÞúkefrEdlGnuvtþeRkayeBlebtugrwgmaMKYrQrelIm:Um:g;niclPaBbM
ElgEdlTTYlCamYynwg 2n RbesIrCagCamYynwg n . dUcenH eRbITTwgkMralbMElg

T.chhay

b 90
= = 4.5in.
2n 2(10)
BIrUbTI 9>24 nig tarag 9>8 m:Um:g;niclPaBbMElgKW
I 'tr = 920.4in.4

tarag 9>8
ebtug 14.62 1.625 23.76 12.87 3.780 221.8

W 16 × 26 7.68 12.60 96.77 301 7.195 698.6

srub 22.30 120.53 920.4in.4

∑ Ay 120.5
y= = = 5.405in.
∑ A 22.30

m:Um:g;niclPaBRbsiT§PaBEdleyIgnwgehAfa I 'eff KW
I 'tr = I s + ∑ Qn / C f (I 'tr − I s )

= 301 + 210.4 / 276.5 (920.4 − 301) = 841.3in.4
PaBdabry³eBlyUrEdlbNþalBIbnÞúkefrEdlGnuvtþeRkayeBlebtugrwgmaMKW
5(0.100 / 12)(30 × 12)4
Δ4 = = 0.0747in.
384(29000)(841.3)
PaBdabsrubKW
Δ1 + Δ 3 + Δ 4 = 1.098 + 0.2613 + 0.0747 = 1.43in.
30(12)
nig L
240
=
240
= 1.50in. > 1.43in. (OK)

cemøIy³ #> PaBdabGacTTYlyk)an.


T.chhay

9>8> taragsMrab;karviPaK nigkarKNnaFñwmsmas
Tables for Composite Beam Analysis and Design
enAeBlG½kSNWt)aøsÞicsßitenAkñúgmuxkat;Edk karKNna flexural strength Gacnwgmankar
lM)ak. eK)anbegáItrUbmnþedIm,IsMrYldl;karKNnaenH (Hansell et al., 1978) b:uEnþtaragEdlbgðaj
enAkñúg Part 5 of the manual manPaBgayRsYlCag. eKmantaragBIrKW³ design strengths rbs;bnSM
énrUbragepSg²CamYynwgkMralsMrab; Fy = 36ksi ≈ 250MPa nigsMrab; Fy = 50ksi ≈ 350MPa nig
taragénm:Um:g;niclPaB “lower bound” sMrab;bnSMdUcKña.
Design strength table EdlmaneQμaHfa “Composite Beam Selection Table,” GaceRbI)an

sMrab;EtrUbragEdlman compact web nigersIusþg; shear connector srub ∑ Qn ≥ 0.25 As Fy ¬Edn
kMNt;EdlENnaMTabCageKsMrab; partially composite beams¦
eKeGayersIusþg;KNna (design strength) φM n sMrab;TItaMgrbs; PNA 7 EnøgdUcbgðajenA
kñúgrUbTI 9>25³ Epñkx<s;bMputrbs;søabxagelI/ EpñkTabbMputrbs;søabxagelI/ bITItaMgEdlmanKMlat
esμI²KñaEdlsßitenAkñúgsøabxagelI/ nigBIrTItaMgenAkñúgRTnug*. TItaMg PNA TabCageK ¬nIv:U &¦ RtUvnwg
EdkkMNt;EdlENnaMTabCageK ∑ Qn = 0.25 As Fy . PNA TItaMg ^ RtUvnwg ∑ Qn EdlsßitenAcenøaH
TItaMg & nigTItaMg %.

edIm,IeRbItaragsMrab;viPaKFñwmsmas dMbUgrkEpñkrbs;taragEdlRtUvnwgrUbragEdk ehIyGnuvtþ
dUcxageRkam³

*
nimtþsBaØa φM RtUv)aneKeRbIenAkñúgtaragsMrab; design strength of composite shapes, nig φ M RtUv)aneRbIsMrab; design
i n b p

strength of steel shape alone. emKuNRtUv)ansMKal;edayviFIBIrepSgKñaBIeRBaHvamantMélBIrepSgKña.

T.chhay

!> eRCIserIs ∑ Qn . enHCakarkMNt;rbs; Manual sMrab;kMlaMgsgát; C EdlCatMéltUcCag
eKén As Fy / 0.85 f 'c Ac nigersIusþg;rbs; shear connector srub ¬EdleyIgehAfa
∑ Qn ¦.

@> eRCIserIs Y 2 cMgayBITItaMgx<s;bMputrbs;EdkFñwmeTAkMlaMgsgát;pÁÜbenAkñúgebtugEdl
KNnaCa
a
Y2 = t −
2
TMhMenHRtUv)anbgðajenAkñúgrUbTI 9>26.
#> Gan φM n RbsinebIcaM)ac;eKRtUveFVI interpolation

sMrab;karKNna eKGacbBa©Úl φM n EdlTamTareTAkñúgtarag ehIyeKGacGaceRCIserIsEdk
Fñwm nig ∑ Qn . eKGacRtUvkartMél Y 2 dUcenHeKRtUvsnμt;kMBs;rbs;karBRgaykugRtaMgsgát;rbs;
ebtug ehIyeKGaceFVIkarKNnaeLIgvijeRkayeBlEktMrUv. Manual eGaynUvsmIkarsMrab;)a:n;sμan
TMgn;Fñwm EtRbsinebIeKeRbItarag eKminRtUvkarsmIkarenaHeT.
taragk¾eGaypgEdrnUvtMél φb M p EdlGacRtUvkarsMrab;RtYtBinitüFñwmEdlKμanCnÞl;kñúg
GMLúgeBlebtugrwgmaM ehIy Y1 CacMgayBITItaMgx<s;bMputrbs;EdkFñwmeTA PNA.

]TahrN_ 9>9³ KNna design strength rbs;FñwmsmasenAkñúg]TahrN_ 9>1 nig 9>2 edayeRbI
taragenAkñúg Part 5 of the Manual.
dMeNaHRsay³ BI]TahrN_ 9>1 FñwmsmaspSMeLIgedayEdk W 16 × 36 CamYynwgkMralxNÐEdlman
kMras; t = 5in. nigTTwgRbsiT§PaB b = 87in. . ersIusþg;sgát;enA @* éf¶rbs;ebtugKW f 'c = 4000 psi .
kMlaMgsgát;enAkñúgebtugCatMéltUcCageKén
As Fy = 10.6(36) = 381.6kips


T.chhay

b¤ 0.85 f 'c Ac = 0.85(4 )(5 × 87 ) = 1487kips

yk C = 381.6kips . kMBs;rbs;bøúkkugRtaMgsgát;
C 381.6
a= = = 1.290in.
0.85 f 'c b 0.85(4)(87 )
cMgayBITItaMgx<s;bMputrbs;EdkeTAkMlaMgsgát; C KW
a 1.290
Y2 = t − = 5− = 4.36in.
2 2
bBa©ÚleTAkñúgtaragCamYynwg ∑ Qn = 382kips nig Y 2 = 4.36 . edayeFVI interpolation eyIg
TTYl)an
φM n = 332 ft − kips
edayepÞógpÞat;CamYynwglT§plenAkñúg]TahrN_ 9>2 eyIgeXIjfavamantMéldUcKña. karKNnatam
rUbmnþ nigedayeRbItaragTTYl)anlT§plRsedogKña enAeBlEdl PNA sßitenAkñúgmuxkat;EdkFñwm.
cemøIy³ Design strength = 332 ft − kips

taragsMrab;m:Um:g;niclPaB lower bound EdlsMKal;eday I LB pþl;nUvkar)a:n;sμanm:Um:g;nicl
PaBrbs;muxkat;bMElgmanlkçN³suvtßiPaBsMrab;FñwmdUcKñaEdlmanenAkñúg design strength table.
karsnμt;d¾cMbgkñúgkareFVItaragenHKWfamanEtRkLaépÞebtugEdlTb;Tl;nwgm:Um:g;eTEdlmanRbsiT§PaB
kñúgkarKNnam:Um:g;niclPaB. kMlaMgenAkñúgebtugKW C = ∑ Qn nig RkLaépÞénmuxkat;bMElgEdlRtUv
KñaKW
∑ Qn ∑ Qn
Ac = =
stress in transformed area Fy

edIm,ICakarsMrYlteTAeTotkñúgkarKNna eKecalm:Um:g;niclPaBrbs;ebtugeFobnwgG½kSTIRbCMuTMgn;.
edIm,IbgðajBIviFIsaRsþenH eKnwgyktMélmYyenAkñúgtaragmkbMEbkenAkñúg]TahrN_ 9>10.

]TahrN_ 9>10³ karKNnapþl;nUvlT§plCa W 16 × 31 CamYynwg ∑ Q n = 241kips ¬TItaMg PNA
3¦ Y 2 = 4in. nig Fy = 36ksi . KNnam:Um:g;niclPaB lower bound.
dMeNaHRsay³ RkLaépÞebtugEdlRtUv)aneRbIKW
∑ Qn 241
Ac = = = 6.694in.2
Fy 36


T.chhay

muxkat;bMElgEdlRtUvKñaRtUv)anbgðajenAkñúgrUbTI 9>27 ehIykarKNnaRtUv)ansegçbenAkñúgtarag
9>9. kMNt;TItaMgTIRbCMuTMgn; Kitm:Um:g;eFobG½kSenA)atrbs;muxkat;Edk.

tarag 9>9
ebtug 6.694 19.88 133.1 - 6.88 316.9

W 16 × 31 9.12 7.94 72.4 375 5.06 608.5
srub 15.81 205.5 925.4in.4
∑ Ay 205.5
y= = = 13.00in.
∑ A 15.81

m:Um:g;niclPaBBItaragm:Um:g;niclPaB lower bound KW I LB = 925in.4 edayepÞógpÞat;CmYynwg
lT§plEdl)anKNna.
cemøIy³ I LB = 925in.4

]TahrN_ 9>11³ eFVIkarKNna]TahrN_ 9>8 eLIgvijCamYynwgCMnYyrbs;taragenAkñúg Part 5 of the
Manual .
dMeNaHRsay³ !> KNnaFñwm
BI]TahrN_ 9>8 M u = 153 ft − kips ¬edayminKitbBa©ÚlTMgn;Fñwm¦.
edaysnμt;fa a = 2in. eyIgTTYl)an
a 2
Y2 = t − = 4.75 − = 3.75in.
2 2


T.chhay

BI Composite Beam Selection Table, ral;karbnSMénEdkFñwm/ ∑ Qn nig Y 2 Edlpþl;nUv
design strength FMCag 153 ft − kips KWCaFñwmsakl,gEdlGacTTYlyk)an. lT§PaBBIrnwgRtUv)an

tarag 9>10
φM n (ft-kips)
rUbrag TItaMg PNA ∑ Qn (kips)
¬edayeFVI interpolation¦
W 16 × 26 7 69.1 160

W 14 × 22 3 159 159

Edk W 14 × 22 CarUbragEdlRsalCag b:uEnþedaysar ∑ Qn FMCag vanwgRtUvkar shear
connector eRcInCag ¬GaceRcInCagBIrdg¦. sMrab;mUlehtuenH sakl,g W 16 × 26 . KNna Y 2

eLIgvij³
C ∑ Qn 69.1
a= = = = 0.3011in.
0.85 f 'c b 0.85 f 'c b 0.85(3)(90 )
a 0.3011
Y 2 = t − = 4.75 − = 4.60in.
2 2
¬Edl b = 90in. KW)anmkBI]TarhN_ 9>8¦
φM n = 164.4 ft − kips
BI]TahrN_ 9>8/ M u = 156 ft − kips CamYynwgkarKitbBa©ÚlTMgn;Fñwm . vanwgtUcCag design
strength 164.4 ft − kips dUcenHkareRCIserIsenHGacTTYlyk)an. dUcKñaBI]TahrN_ 9>8 TaMg

flexural strength kñúgeBlsagsg; nig shear strength KWRKb;RKan;sMrab; W 16 × 26 .

cemøIy³ !> eRbI W 16 × 26 .
@> Shear connector
dMbUg sakl,g stud 3 / 4 × 3in. . cMnYnrbs; strud EdlRtUvkarKW
∑ Qn
N1 =
Qn
=
69.1
21.04
= 3 .3 yk 4 sMrab;Bak;kNþalFñwm dUcenHsrubKW 8 edIm
Stud 8 edImRtUvnwgKMlat
30(12)
= 45in.
8


T.chhay

KMlatenHFMCagKMlatGnuBaØatGtibrma 36in. dUcenHeKRtUveRbI stud eRcInCagenH. RbsinebI
eKdak; stud ral; 6 rnUtmþg KMlatnwgesμInwg 36 ehIycMnYn stud srubKW
30(12)
= 10, N1 = 5
36
kMlaMgkat;EdlRtUvKñaEdlRtUvepÞrKW
∑ Qn = 5(21.04) = 105.2kips
edIm,IgayRsYlkñúgkareRbItarag eyIgnwgyktMél ∑ Qn = 104kips enaH
104
a= = 0.4532in.
0.85(3)(90)
0.4532
Y 2 = 4.75 − = 4.523in.
2
BI Composit Beam Selection Table, design strength KW
φM n = 182 ft − kips > 156 ft − kips (OK)
cemøIy³ @> eRbI stud 3 / 4 × 3in. cMnYn 10 edIm edayKMlatesμI²Kña. edIm,IkarBar uplift eFVI spot weld
ral;KMlat 18in. ¬sßitenAcenøaH stud¦.
#> PaBdab
BI]TahrN_ 9>8 PaBdabrbs;EdkFñwmmuneBlTTYl)an composite behavior KW
Δ1 = 1.098in. ¬edayminKitbnÞúksagsg;¦

sMrab;PaBdabEdlekIteLIgeRkayeBlebtugrwgmaM eKGaceRbIm:Um:g;niclPaB lower bound
Edl)anBItarag. eRbI W 16 × 26 CamYynwg ∑ Qn = 104kips ¬PNA TItaMg ^¦ nig Y 2 = 4.523in.
I LB = 623in.4
vaminmankarEbgEckm:Um:g;niclPaBsMrab;karKNnaPaBdabbEnßmEdlekIteLIgedaysar
creep. b:uEnþ m:Um:g;niclPaB lower bound mantMéltUcCagm:Um:g;niclPaBmuxkat;bMElgCak;Esþg

ehIyT§iBlTaMgmUlKWnwgpþl;nUvPaBdabFMCagkar)a:n;sμan. RbsinebIbnÞúkefrry³eBlyUrtUc
eKGaceRbIm:Um:g;niclPaB lower bound.
w = wD + wL = 0.100 + 0.400 = 0.500kips / ft
ehIyPaBdabEdlRtUvKñaKW
5wL4 5(0.500 / 12 )(30 × 12 )4
Δ2 = = = 0.5044in.
384 EI LB 384(29000 )(623)
PaBdabsrubKW

T.chhay

Δ1 + Δ 2 = 1.098 + 0.5044 = 1.602in.
PaBdabGnuBaØatGtibrmaKW
L 30(12)
= = 1.500in. < 1.602in. (N.G.)
240 240
kñúgkarKNna Rtg;cMnucenH eyIgmanCMerIsBIr³ ¬!¦ KNnaPaBdabEdlmanPaBsuRkitCageday
eRbImuxkat;bMElg b¤¬@¦ eRCIserIskarbnSMrvagEdkFñwm nig shear connector CamYynwgm:Um:g;niclPaB
lower bound. edaysareKalbMNgrbs;]TahrN_enHcg;bgðajBIkareRbItarag eyIgnwgeRCIserIsCM

erIsTI @.
KNnam:Um:g;niclPaB lower bound EdlRtUvkar. PaNdabEdlekItBIkMralxNÐ nigTMgn;Fñwm
nwgminpøas;bþÚr dUcenHPaBdabGnuBaØatGtibrmaEdlekIteLIgedaysarbnÞúkEdlGnuvtþeRkayeBlebtug
rwgmaMKW
Δ 2 Gtibrma = 1.50 − Δ1 = 1.50 − 1.098 = 0.4020in.
5wL4
BI Δ 2 = 384EI
LB

I LB EdlRtUvkarKW
5wL4 5(0.500 / 12 )(30 × 12 )4
I LB ≥ = = 782in.4
384 EΔ 2 384(29000 )(0.4020 )
sMrab; W 16 × 26 CamYynwg PNA # nig Y 2 = 4.5in. / m:Um:g;niclPaB lower bound KW
I LB = 804in.4 . BI Composite Design Selection Table, sMrab; PNA # kMlaMgkat;tamTisedkKW

∑ Qn = 208kips
edIm,ITTYltMélRtwmRtUv Y 2 nig I LB dMbUgKNnaTItaMgrbs;kMlaMgsgát;enAkñúgebtug
∑ Qn 208
a= = = 0.9063in.
0.85 f 'c Ac 0.85(3)(90 )
a 0.9063
Y 2 = t − = 4.75 − = 4.30in.
2 2
BItaragm:Um:g;niclPaB lower bound edayeFVI interpolation
I LB = 788in.4 > 782in.4 (OK)
cMnYnrbs; shear connector EdlRtUvkarKW
∑ Qn
N1 =
Q
=
208
21.04
= 9 .9 yk 10 sMrab;Bak;kNþalFñwm b¤srub 20 edIm
n


T.chhay

edaysarKMlatrbs;rnUt deck, stud mYysMrab;ral;rnUt 3 sMrab;KMlat 18in. nwgpþl;nUv stud
20 edIm.

cemøIy³ #> edIm,IbMeBjtMrUvkarPaBdab begáIncMnYn stud BI 10 eTA 20 dak;mYyenAkñúgral;rnUt 3 .

]TahrN_ 9>11 bgðajplRbeyaCn_rbs;tarag. CaBiess composite Beam Selection
Table sMrYlkarKNna partially composite beam Edl PNA sßitenAkñúgmuxkat;EdkFñwm.

9>9> FñwmCab; Continuous Beams

sMrab;FñwmTMrsmBaØ cMnucénm:Um:g;sUnüenARtg;TMr. cMnYn connector EdlRtUvkarenAcenøaHTMr nig
cMnucEdlmanm:Um:g;GtibrmaKWcMnYnBak;kNþaléncMnYnsrubRtUvkar. sMrab;FñwmCab; cMnucrbt;k¾CacMnucén
m:Um:g;sUnüEdr nigCaTUeTAeKRtUvkar connector 2N1 sMrab;ElVgnImYy². rUbTI 9>28 a bgðajBIRbePT
FñwmCab; nigtMbn;EdlRtUvkar shear connector. enAtMbn;m:Um:g;GviC¢man kMralebtugnwgrgkMlaMgTaj
dUcenHvanwgKμanRbsiT§PaB. enAkñúgtMbn;enH vanwgminman composite behavior EdleyIgRtUvBicarNa
enaHeT. RbePT composite behavior EtmYyKt;EdlGacmanKWenAcenøaHFñwmEdk nigEdkBRgwgtam
beNþayenAkñúgkMral. muxkat;FñwmsmasEdlRtUvKñaRtUv)anbgðajenAkñúgrUbTI 9>28 b. RbsinebIeK
eRbIKMnitenH eKRtUvpþl;nUvcMnYn shear connector RKb;RKan;edIm,ITTYlnUvdWeRkénPaBCab;rvagEdkFñwm
nigEdkBRgwg.
AISC Specification in Section I3.2 pþl;nUvCMerIsBIrsMrab;m:Um:g;GviC¢man.

!> edayQrEtelIersIusþg;rbs;EdkFñwmb:ueNÑaH.
@> edayrYmbBa©ÚlTaMgEdkBRgwgenAkñúgmuxkat;smasRtUvRbQmnwglkçxNÐxageRkam³
a. EdkFñwmRtUvEt compact nigman latereal support RKb;RKan;

b. eKRtUvEtdak; shear connector enAtMbn;mUm:g;GviC¢man ¬cenøaHcMnucm:Um:g;sUnü
:
nigcMnucm:Um:g;GviC¢manGtibrma¦
c. EdkBRgwgenAkñúgTTwgRbsiT§PaBRtUvEtmanRbEvgbgáb;RKb;RKan; ¬TMBk;¦

ersIusþg;rbs;muxkat;smasKYrEtQrelIkarBRgaykugRtaMg)aøsÞicCamYynwg φb = 0.85 .


T.chhay

RbsinebIeKKit composite behavior AISC I5.2 tMrUveGayykkMlaMgkat;tamTisedkEdl
RtUv)anepÞrrvagcMnucénm:Um:g;GviC¢manGtibrma nigcMnucm:Um:g;sUnümantMéltUcCageKkñúgcMeNam Ar Fyr
nig ∑ Qn Edl
Ar = RkLaépÞrbs;EdkBRgwgenAkñúgTTwgRbsiT§PaBrbs;kMral

Fyr = yield stress rbs;EdkBRgwg

ersIusþg;bEnßmEdlTTYlBIkarbBa©ÚlEdkBRgwgmantMélNas; b:uEnþeBlxøHeKeRbI cover plate enAkñúg
tMbn;m:Um:g;GviC¢man.

9>10> ssrsmas Composite Columns

ssrsmasRtUv)anEbgEckCaBIrTMrg;KW EdkbMBgTIbmUl b¤RCugEdlbMeBjedayebtug b¤
rolled steel shape dak;enAkñúgebtugCamYynwgEdkBRgwgbBaÄr nigEdkkgTTwgdUcenAkñúgssrebtug

BRgwgedayEdk. rUbTI 9>29 bgðajBITMrg;TaMgBIrenH.


T.chhay

karviPaKssrsmasRtUv)aneFVIeLIgkñúgviFIdcKñasMrab;Ggát;rgkarsgát;eRKOgbgÁúMEdkFmμtaEdr
U
edayeRbIsmIkardUcKñaBI AISC Charpter E b:uEnþCamYynwgtMél Fy / E nig r EdlRtUv)anEkERbedIm,I
TTYllT§plEdlTTYl)anBIkarBesaF nigkarKNnaRtUvKña. munBicarNasmIkar AISC sMrab;tMél
TaMgenH eyIgRtUvRtYtBinitüBIeKalkarN_rbs;smIkarsin. RbsinebIeKFananUvsßanPaBlMnwg eKKitfa
ersIusþg;rbs;Ggát;smasrgkarsgát;CaplbUkénersIsþg;tamG½kSrbs;EdkFñwm/ EdkBRgwg nigebtug.
u
vaRtUv)aneKehAfa squash load ehIyRtUv)aneGayeday
Pn = As Fy + Ar Fyr + 0.85 f 'c Ac ¬(>%¦
Edl As = RkLaépÞmuxkat; rolled steel shape
Ar = RkLaépÞmuxkat;srubrbs;EdkBRgwgbBaÄr

Fyr = yield stress rbs;EdkBRgwg

Ac = RkLaépÞmuxkat;rbs;ebtug

srésEdkBRgwgCaeBlbc©úb,nñCaRbePT deformed EdlépÞrbs;vamansac;lanecjEdlCYy
begáItPaBs¥itrvaEdk nigebtug)anl¥. RkLaépÞmuxkat; Ar EdlRtUv)aneRbIkñúgkarKNnaCa nominal
area EdlKitfaRkLaépÞrbs;EdkrelagEdlmanTMgn;kñúgmYyÉktþaRbEvgdUcKñanwg deformed bar.

tarag 9>11 bgðajBI nomial diameter nigRkLaépÞsMrab;TMhMEdksþg;darEdlkMNt;eday ASTM
(1996) nig ACI (1995).

edIm,ITTYl)ankugRtaMgsrub EckbnÞúkEdlTTYl)anBIsmIkar 9>5 edayRkLaépÞrbs;EdkFñwm³
Fyr
Pn
As
= Fmy = Fy + Ar
As
A
+ 0.85 f 'c c
As
¬(>^¦
tMélrbs; Fmy EdlTTYlBIsmIkar (>^ ¬enAeBlEdleRbICMnYseGaytMél Fy enAkñúgsmIkarGgát;rg
karsgát;¦ eGaylT§pll¥sMrab;EdkbMBg;TIbmUl b¤RCugEdlbMeBjedayebtugEdlebtugsßitenAkñúg
steel shape. ¬EdkBRgwgbBaÄrminRtUv)aneRbICamYynwgEdkbMBg;TIbmUl b¤RCug (concrete-filled pipe

or tube) eT dUcenH Ar Gacniwg mantMélsUnüsMrab;ssrsmasRbePTenH¦.


T.chhay

tarag 9>11
elxEdk Ggát;Edk RkLaépÞmuxkat;
in. mm in.2 mm2
3 0.375 9.50 0.11 71.00
4 0.500 12.70 0.20 129.00
5 0.625 15.87 0.31 200.00
6 0.750 19.05 0.44 283.87
7 0.875 22.23 0.60 387.10
8 1.000 25.40 0.79 509.70
9 1.128 28.65 1.00 645.16
10 1.270 32.26 1.27 819.35
11 1.410 35.81 1.56 1006.45
14 1.693 43.00 2.25 1451.61
18 2.257 57.33 4.00 2580.64

sMrab;eRKOgbgÁúMEdkEdkbgáb;kñúgebtug vaminmanEdkhMuB½T§vaeT ehIy structural stability
Reseach Council (SSRC, 1979) ENnaMfaemKuNkat;bnßyersIusþg; ACI code (ACI, 1995) Edl

mantMél 0.7 RtUv)anGnuvtþeTAelItYénEdkBRgwg nigebtugénsmIkar (>^ dUcxageRkam³
Fyr
Fmy = Fy + 0.7 Ar
A
A
+ 0.7(0.85) f 'c c
A
¬(>&¦
s s
Fyr Ac
= Fy + 0.7 Ar + 0.595 f 'c
As As
edIm,IkarBarT§iBl slenderness eKRtUvEktMrUvPaBrwgRkajkñúgkarBt;rbs;Ggát; EdlsmamaRt
eTAnwgbrimaN EI / L . karEktMrUvenHRtUv)aneFVIeLIgedayEkERbtMélrbs; E dUcxageRkam³
A
E m = E + constant × Ec c
As
¬(>*¦
Edl E = m:UDuleGLasÞicrbs;EdkeRKOgbgÁúM
Ec = m:UDuleGLasÞicrbs;ebtug

eTaHbICaPaBrwgRkaj (stiffeness) smamaRteTAnwgm:Um:g;niclPaB pleFobRkLaépÞsMrab;ssrsmas
pþl;lT§pll¥CagpleFobm:Um:g;niclPaB (SSRC, 1979). tMélefrenAkñúgsmIkar 9>8 KWesμInwg 0.4
sMrab;EdkTIbmUl b¤RCugEdlbMeBjedayebtugEdlbgðajBIPaBGnuBaØaténPaBrwgRkajrbs;ebtug
40% nig 0.2 sMrab;EdkeRKOgbgÁúMEdlbgáb;kñúgebtug (encased shape).


T.chhay

kaMniclPaBrbs;muxkat;smasKWFMCagkaMniclPaBrbs;muxkat;EdkeRKagbgÁúM nigrbs;ebtug.
viFIEdlsuvtßiPaBKWRtUveRbIkaMniclPaBEdlmantMélFMénkaMniclPaBrbs;muxkat;EdkeRKOgbgÁúM b¤kaM
niclPaBénmuxkat;ebtug EdleKGacykesμInwg 0.3 dgénvimaRtNamYyrbs;muxkat;enAkñúgbøg;
buckling. edaykMNt;kaMniclPaBrbs;muxkat;smasCa rm enaHeKTTYl)an

rm = r ≥ 0.3b
Edl r= kaMniclPaBrbs;muxkat;EdkeRKOgbgÁúMenAkñúgbøg; buckling
b = vimaRtrbs;muxkat;ebtuenAkñúgbøg; buckling

tMrUvkarrbs; Specification
sMrab;ssrsmasmansar³sMxan;dUcKñaeTAnwgGVIEdlerobrab;xagelI. eKeRbI
AISC provisions

Equation E2-1 nig E2-3 BI Chapter E of the specification edIm,IkMNt; design strength b:uEnþtMél

rbs; Fy / E nig r RtUv)anEksMrYl. eKRtUvBwgEp¥kelIsmIkar (>^ nig (>& edIm,IeFVIkarEksMrYltMél
TaMgenH. BI AISC Section I2.2, tMélEksMrYlrbs; Fy KW
Fmy = Fy + c1 Fyr ( Ar / As ) + c2 f 'c ( Ac / As ) (AISC Equation I2-1)

EdltMélefr c1 nig c2 RtUv)anKitsMrab;PaBxusKñarvag encased sectoon nig concrete-filled pipes
and tubes:
nig c2 = 0.85 sMrab; pipes and tubes
c1 = 1.0

c1 = 0.7 nig c2 = 0.6 sMrab; encased shapes

tMélEdlEksMrYl AISC E KWdUcKñaeTAnwgGVIEdleGayedaysmIkar (>* b¤
E m = E + c3 Ec ( Ac / As ) (AISC Equation I2-2)
Edl sMrab; pipes and tubes
c3 = 0.4

c4 = 0.2 sMrab; encased shapes

AISC I2.2 kMNt;tMél rm eGayesμIeTAnwgGVIEdleGayedaysmIkar (>(

rm = r ≥ 0.3b
edIm,IeGayssrsmasmanlkçN³RKb;RKan; eKRtUvBinitüemIlnUvkarkMNt;xageRkamEdleGayeday
AISC I2.1³

!> EdkeRKOgbgÁúMRtUvEtmany:agtic 4% énRkLaépÞmuxkat;srub b¤Ggát;rgkarsgát;eFVIkardUc
ssrebtugGarem:CaCageFVIkardUcssrsmas.

T.chhay

@> Encased sections RtUvEteKarBtamlkçxNÐlMGitxageRkam³
a. eKRtUvEteRbITaMgEdlbBaÄr nigEdkkg. KMlatrbs;EdkkgminRtUvFMCagBIrPaKbI én

vimaRttUcCageKrbs;ebtug. RkLaépÞmuxkat;rbs;Edkem nigEdkkgminRtUvtUcCag
0.007in.2 / in. b¤ 0.18mm 2 / mm énKMlatEdk.

b. vaRtUvEtmankMras;ebtugkarBarEdky:agtic 1.5in. ≈ 38mm sMrab;Edkkg nigEdkbBaÄr.

c. EdkbBaÄrEdlRTbnÞúk (load-carrying longitudinal reinforcement) RtUvEtCab;enA

framed level. EdkbBaÄrsMrab;Tb;ebtugGacpþac;enARtg; framed level.

#> ersIusþg;rbs;ebtug f 'c RtUvEtsßitenAcenøaH 3ksi ≈ 21MPa nig 8ksi ≈ 55MPa sMrab;eb
tugTMgn;Fmμta ¬minmanlT§plBiesaFn_sMrab; f 'c FMCag 55MPa eT¦ nigy:agticbMput
4ksi ≈ 28MPa sMrab;ebtugTMgn;Rsal.

$> kñúgkarKNna Yield stress rbs;EdkeRKOgbgÁúM nigEdkBRgwgbBaÄrminRtUvFMCag 55ksi
≈ 380 MPa eT. karkMNt;RtUv)anTTYlBIkarBicarNa local stability. enAeBlEdlEdk

eRKOgbgÁúMhMuB½T§edayebtug vanwgminman local stability eT. ebtugnwgGachMuB½T§Edk)an
RKb;RKan;ebIvaminmankarpÞúHépÞebtug (spall). RbsinebIeKsnμt;eGayebtugman spall enA
eBlebtugman strain 0.0018 enaHkugRtaMgEdkRtUvKñaenAkñúgEdkKW
Fmax = ε max E = 0.0018(29000) = 52.2ksi
EdlRtUv)anKitCatMélkMNt;Rtwm 55ksi .
%> edIm,IkarBar local buckling enAkñúg pipes b¤ tubes EdlbMeBjedayebtug kMras;rbs;
pipes b¤ tubes minRtUvtUcCag

t = b Fy / 3E sMrab;muxkat;ctuekaNEdlmanTTwgxageRkA b

b¤ t = D Fy / 8E sMrab;muxkat;rgVg;EdlmanGgát;p©itxageRkA D

]TahrN_ 9>12³ Ggát;rgkarsgát;smasEdlman W 12 ×136 RtUv)andak;enAkñúgssrebtugEdlman
TMhM 20 × 22in. dUcbgðajenAkñúgrUbTI 9>30. eKeRbIEdk #10 bYnedImCaEdkbBaÄr nigEdk #3 CaEdk
kgEdlmanKMlat 13in. edayKitBIG½kSeTAG½kS. Edkman yield stress Fy = 50MPa ehIyeKeRbI
EdkBRgwgRbePT Grade 60. ersIusþg;rbs;ebtugKW f 'c = 5ksi . KNna design strength sMrab;RbEvg
RbsiT§PaB 16 ft sMrab;G½kSTaMgBIr.

T.chhay

cemøIy³ eKkMNt;tMélEksMrYl F nig E Edl)anBI AISC Equation I2-1 nig I2-2. tMélEdl
my m

RtUvkarsMrab;smIkarTaMgenHKW³
Fyr = 55ksi tMélEdlkMNt;eday AISC I2.1
Ar = 4(1.27 ) = 5.08in.2
Ac = net area rbs;ebtug = 20(22) − As − Ar = 440 − 39.9 − 5.08
= 395.0in.2
sMrab; f 'c = 5ksi

Ec = w1.5 f 'c = (145)1.5 5 = 3904ksi
c

BI AISC Equation I2-1, yield stress EdlEksMrYlKW
⎛A ⎞ ⎛A ⎞
Fmy = Fy + c1 Fyr ⎜ r ⎟ + c2 f 'c ⎜ c ⎟
⎜A ⎟ ⎜A ⎟
⎝ s⎠ ⎝ s⎠
⎛ 5.08 ⎞ ⎛ 395 ⎞
= 50 + 0.7(55)⎜ ⎟ + 0.6(5)⎜ ⎟ = 84.60ksi
⎝ 39.9 ⎠ ⎝ 39.9 ⎠
BI AISC Equation I2-2, m:UDuleGLasÞicEdlEksMrYlKW
⎛A ⎞
⎟ = 29000 + 0.2(3904)⎛
395 ⎞
E m = E + c3 E c ⎜ c
⎜A ⎟ ⎜ ⎟ = 36730ksi
⎝ s ⎠ ⎝ 39.9 ⎠
kaMniclPaBEdlRtUv)aneRbIenAkñúgsmIkarGgát;rgkarsgát;én AISC Cahpter E GacCa r sMrab;Edk
eRKOgbgÁúM b¤ 0.3b edayykmYyNaEdlmantMélFMCag. enAkñúg]TahrN_enH buckling nwgekIteLIg
eFobnwgG½kS y rbs;Ggát; dUcenH r sMrab;muxkat;KW ry = 3.16in . enAkñúgbøg; buckling
0.3b = 0.3(20 ) = 6in. ¬lub¦

dUcenH rm = 6in. . eKGacKNna design strength dUcKñasMrab;Ggát;rgkarsgát;FmμtaedayeRbI
tMélEksMrYl Fmy / Em nig rm CMnYseGay Fy / E nig r


T.chhay

KL Fmy 16(12 ) 84.60
λc = = = 0.4888 < 1.5
rmπ Em 6π 36730

Fcr = (0.658)λc Fmy = (0.658)(0.4888 ) (84.60 ) = 76.55ksi
2 2

nominal strength KW
Pn = As Fcr = 39.9(76.55) = 3054kips
φc Pn = 0.85(3054) = 2600kips
cemøIy³ design compressive strength KW 2600kips

taragsMrab;viPaK nigKNna Tables for Analysis and Design
mantaragEdlsMrYly:agxøaMgdl;karviPaK nigkarKNnassrsmas.
Part 5 of the Manual

taragTaMgenHmanlkçN³RsedogKñanwg column strength table enAkñúg Part 3 of the Manual. eK
eGay axial compressive design strength CaGnuKmn_eTAnwgRbEvgRbsiT§PaBsMrab; concrete-filled
pipes and tubes nigsMrab; encased W-shapes. sMrab; encased column Edkem nigEdkkgEdlbM

eBjtMrUvkar AISC RtUv)anrab;bBa©Úl. eKeGaytMél rmx / rmy sMrab;krNITaMgenaHEdl K x L ≠ K y L .

]TahrN_ 9>13³ Ggát;rgkarsgát;EdlmanRbEvg 18 ft RtUvRTnUvbnÞúkeFVIkar (service load) srub
1000kips EdlpSMeLIgedaycMENkesμIKñaénbnÞúkefr nigbnÞúkGefr. Ggát;enHmanTMr pinned enAcug
TaMgsgçag CamYynwgTMrbEnßmenAkMBs;Bak;kNþaltamG½kSexSay. eRbItaragenAkñúg Part 5 of the
Manual edIm,IeRCIserIsEdk W EdlmanrUbragkaerEdlbgáb;kñúgebtug (square encased W-shape)

CamYynwgRkLaépÞebtugEdltUcCageKEdlGaceFVIeTA)an. eRbIEdk A36 Edksrés grade 60 nig
f 'c = 3.5ksi .

dMeNaHRsay³ bnÞúktamG½kSemKuNKW
Pu = 1.2(500 ) + 1.6(500 ) = 1400kips
tamkarGegátelItaragbgðajfa sMrab; f 'c = 3.5ksi nigtMélén rmx / rmy ERbRbYlBI 1.0 eTA 1.22
EdltMélPaKeRcInesμInwg 1.0 . edaysar


T.chhay

KxL
= 2 > 1.22
KyL

KxL nwglub. snμt;fa rmx / rmy = 1.0 rYcbBa©ÚleTAkñúgtaragCamYynwg
KxL 18
KL = = = 18 ft
rmx / rmy 1.0

taragxageRkambgðajBICMerIsEdlGaceFVI)an
TMhMmuxkat;ebtug EdkeRKOgbgÁúM rmx / rmy φc Pn
18×18 W10×112 1.0 1450kips
20×20 W12×87 1.0 14250kips

eTaHbICassr 20×20 RtUvkarEdkeRKOgbgÁúMtUcCagk¾eday EtlkçxNÐtMrUveGayykTMhMebtugGb,brma
dUcenHeyIgeRCIserIs 18×18.
cemøIy³ eRbIssrmukat; 18×18 CamYynwg W10×12 Edksrés #8 bYnedIm Edkkg #3 edayKMlat
12in.. KitBIG½kSeTAG½kS.


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