Lecture Lecture 1717Composite ConstructionComposite
ConstructionEffective Flange WidthNonencased Composite
SectionsShear TransferPartially Composite BeamsTimber and Steel
DesignTimber and Steel DesignMongkol JIRAVACHARADETS U R A N A R E
E INSTITUTE OF ENGINEERINGUNIVERSITY OF TECHNOLOGY SCHOOL OF CIVIL
ENGINEERINGShear connectorsReinforced concrete
slabSteelstringerShear connectorsReinforced concrete
slabSteelstringerPlasteron lathShear transfer made by bond and
friction along top of W section and by the shearingstrength of the
concrete along the dotted linesComposite sectionsComprise a steel
beam and a concrete slab,joined with shear connectors to achieve
composite action between the two elements.Composite sectionsUsing
formed steel deckRibsReinforcedconcrete slabFormed steel
deckRibsReinforcedconcrete slabFormed steel deckAdvantages of
Composite Construction- Increasing beams strength- Less steel
required- Greater stiffness- Smaller deflections- Greater overload
capacity- Smaller floor depth- Lower costDesign Issues1. Flexural
strength of section - Complete shear connectionFailure: Yielding of
steel beam in tensionorCrushing of concrete slab in compression2.
Flexural strength of section - Partial shear connectionFailure
occurs in shear connection3. Longitudinal shear failure within the
slabFailure plane develops within the slab4. Shear strength of
sectionDesign for shear as a plain steel beam (ignore the
concrete)5. Deflection must be computed in 2 stages5.1 Deflection
of steel beam due to dead load of wet concrete5.2 Deflection of
composite section due to live loadEffective Flange Widths, bet =
slab thicknessbe= effective width of flange1. 1/8 of beam span2.
1/2 of beam distance3. Beam centerline to edge of slabbeis the
minimum of:Nonencased Composite SectionsModular ratio: n = Es/EcEs=
2.1 x 106kg/cm2=1.54,270c c cE w fFor wc = 1.45-2.48 ton/m3
(usually wc = 2.4 ton/m3)Before concrete hardens, bending stress in
steel beam from deadload of wet concrete and self-weight of beam
must not exceed theallowable bending stress of beamDs bsMf FS=
where MD= Dead load moment and Ss= Section modulus of steel
beamFlexural Strength of Composite SectionAfter concrete
hardensTransformed section (concrete to steel)betbe / nt0.9D Ls ys
trbotM Mf FS S= + Stress in steel:0.45Lc ctrtopMf fnS= Stress in
concrete:o.aa++n +c-+ .n.e-v.e-urv.ru:auvu .:ra-ve .sc
|ee::.:r.e.au...ava.nna .e:'::rrv e::..uvrvr.e.e::ra:eevLLcc ..:...
v-v.vv-aac ..:..v-vnvrav.-v +c r:..+c ..:..fc .+c ..r:... fc c.+ fc
a+. ..r:... na. .-e .c3 @ 2.5 m= 7.5 m8 m10 cm concrete
slabW400x107 (A = 136.0 cm2, d = 390 mm,bf= 300 mm, Ix= 38,700 cm4,
Sx= 1,980 cm3).en+ rve|:.:v..v+nvou..nono.:n+oavoavo.oar+o. (. raer
.a v)nv(..)(.+c)ccc ...:.rv+c. ...:.:v-vr-:e.c. ...:.MD c..c.(a)..a
.cc .v.:.v+nvou..nono.:n+na+oavo.oar+o..vv-a(..)(ac).cc
...:.LL(..)(cc)+.c ...:.:v-vr-:e++c ...:.ML +.+(a)..a++.c
.v.:.o.+ro.++u.:aneoara+uo:b.(+.a)(acc).cc r:. (o.uor,b.(+..)(.c).c
r:.200/9 = 22.2 cmW400x107 (A = 136.0 cm2, Ix= 38,700 cm4, Sx=
1,980 cm3)10 cmNeutral axis39 cmyboaaruora+nv+o.u+u.:oau:A+.c -
(+c)(....).a r:..yb (+.c+a. - +c....++)..a .+.. r:.Itr
.a..cc-+.c(.+..+a.).-(+.+.)(....)(+c).-+c(....)(++.+..). a+.+..
r:.+Str bot a+.+....+....c.. r:..Str top a+.+...(+a.+..)c...c
r:..5.66(1,000)(100)286 ksc < [0.66 1,650 ksc] 1,980Ds ysMf FS=
= = =
OKo..+aaunv.aa.+n.orvuvnv+o:avrav..r.-erav..r.11.6(1,000)(100)2862,627728
ksc < [0.9 2,250 ksc] D Lss trbotyM MfS SF= + = += =
OK11.6(1,000)(100)9 6,37620.2 ksc < [0.45 94.5 ksc]
LctrtopcMfnSf= == = OKShear ConnectorsWeldStud
connectorsWeldChannel connectorsWeldSpiral connectorsHorizontal
Shear TransferCTCTAllowable Horizantal Shear LoadFor one connector
(q), tonCONNECTOR210 245 280fc, ksc12 x 50 mm hooked or hooked end
2.27 2.45 2.6316 x 62.5 mm hooked or hooked end 3.57 3.84 4.1119 x
75 mm hooked or hooked end 5.13 5.58 5.9422 x 87.5 mm hooked or
hooked end 6.96 7.5 8.04Channel C75 x 6.92 0.78w 0.85w 0.91wChannel
C100 x 9.36 0.83w 0.91w 0.96wChannel C125 x 13.4 0.90w 0.96w 1.02ww
= length of channel, cmDesign of Shear ConnectorsNeutral axis in
slabNeutral axis in beamTotal horizantal forcebelow plane between
beamand slab = As Fy0.85fcFyTotal horizantal forceabove plane
between beamand slab = 0.85 Ac fc0.85fcFyFy2 y shF AV =285 . 0c chA
fV=N1= Number of connectors = Vh/qq = Strength of one connector,
tono.aa++n +c-a .aa.uu-v.eee.e:|er.-e .c .e:ra-ve .sc e-urvvu
'::rrv rv':e..av:: .e:.uvrvr.e .n.e::.av..v-vurrr.e:v-vur.
rra:eev.LLcc ..:... v-v.nevc ..:..v-v.vv. ..:... v-vrav...+cc
..:..fc .+c ..r:... fc a+. ..r:... naAA9 m3 @ 3 m= 9 m10 cm
concrete slab2 cm plasterd ceilingon metal lathSection A-A.en+
rve|:.:v..e:...av.v+nvou..nora:oaa.++nv(c.+c)(..+cc)(..c) ..c
...:.e::.v-vrv(.+cccc) cc ...:.v-vr-:e.ac ...:.MD (c..ac)(a)..a..ac
.v.:.v+nvou..nona+oavo.oar+o..nev.(c)+c ...:..vv.(.)..
...:.LL.(cc)+cc ...:.v-vr-:e+a. ...:.ML (+.a.)(a)..a +a.aa
.v.:.|:.:v.:ree Mmax MD- ML..ac-+a.aa.c.a+ .v.:.aa+.aaounv+o w=oocc
(.= e=.+a zr.a, = =oo rr.,:== e rr., ::= +c rr., i.= ac,.oo zr.=,
s.= +,+oo zr.c,...av:ree Vmax(a..)(c..ac-+.a.)++.a.
.vo.+ro.++u.:aneoara+uv:b(+.+)(acc).. r:. (o.uor,b.cc
r:.raanv+onoa+o+.:Str e-u Mmax (.c.a+)(+cc).(c.cc ..)+.c..
r:..e::.:eevre-uuu.aeSs e-u MD (..ac)(+cc).(c.cc ..)+a.
r:..oaaruora+nv+o.aoar:Aa+.+. - (+c)(...a)..+ r:..yb (a+.+..c -
+c.+)...+.a.. r:.Itr ....cc-a+.+.(.a...c).-(+.+.)(.)(+c).-
+c(.)(+.a..). c.+.. r:.+Str bot c.+....a..+.ca. r:..Str top
c.+...(c.+..)..c. r:..W400x66225/9 = 25 cm10 cmyb= 38.7
cmna+oavo.oar+o.fs2 fs1- ML/Strbot cca - +a.aa(+.ccc)(+cc).+.ca.
+..a. ..r:.. c.aFy ...c ..r:..asfc ML/Strtop
+a.aa(+.ccc)(+cc).(a..c.) .c.c ..r:.. fc a+.
..r:..asoavoavo.oar+o.fs1 MD/Ss ..ac(+.ccc)(+cc).+.+ac cca ..r:..
c.ccFy +.cc ..r:..aso..+aaunv.aa.+n.orvuvnv+o:.ev.rveee.e:ree = 2.5
tf= 2.5(1.3)= 3.25 r:. > 1.9 r:. OK465 7.86 900384 (2.1 10
)(23,700)DL =465 18.75 900384 (2.1 10 )(65,122)LL =o+v.a.:a:aavo.:
avrav..r.= 1.35 r:. < [900/360 = 2.5 r:.] OK-erav..r.= 1.17 r:.
< [900/360 = 2.5 r:.] OKaueeu...ave-un;.:ee.e:..:r.aa+uaao.oaa.
+o rr. a+. ..u zr.uaao.oaa. +o rr. a+. ..u zr. =+ o. .++n++.n+_ov
ao o.vaoa:+v aa:nv+o.noa++u.+o+vnv+o w=oocc0.85 0.85(0.21)(225
10)201 ton2 2c chf AV= = =84.12 2.5105 ton2 2s yhA FV= =
=a.+.aavr+onavav.vav:Control..r +c+ r q.+. .v..e.a.vv.e.ar.a= N =
Vh/q = 105/5.13= 20.47 .v..e:evra.e|:.:v.u:ree20 studs 20
studsPartially Composite BeamsWhen allowable moment more then the
requirement no need for shear connectors of full composite action.
So we reduce the number of shear connectors to save the money.(
)heff s tr shVI I I IV= + Effective Moment of Inertia:2reqd sh htr
sS SV VS S = 0.25h hV qN V = Reduced Shear Force:Live load
deflection: partially composite fully composite trLL LLeffII =
o.aa++n+c-caa.uu.e.av.a+c.-:-:e.nnae-u|:.:v.:reer::r.e:rve::.av..v-vur.-:e.en+
Seff= Str r.a+.c.. r:.. ..ar +c.221633 1190105 84.8 ton1683
1190reqd sh htr sS SV VS S = = = 0.25 Vh= 0.25(105) = 26.3 .v <
84.8 .v OK.vv.e.ar.a = N = Vh/q = 84.8/5.13 = 16.53
.v..e:evra.e|:.:v.u:reeuaao.oaa. +o rr. a+. ..u zr. ++v.v c=
o.o+v.a.:a:aavo.:Vh= (5.13)(17) = 87.21 .v4( )87.2123700 (65122
23700)10561,450 cmheff s tr shVI I I IV= + = + =LL=
(65,122/61,450)(1.17) = 1.24 zr. < [900/360 = 2.5 r:.]
OKComposite Beams with Formed Steel Deck1. Rib height max. = 7.5
cm2. Avg. width of concrete rib min. = 5 cm3. Shear connector dia.
max. = 19 mm4. Concrete slab above steel deck min. = 5 cm5. ribs
perpendicular to beam neglect lower concrete ribslabribStud dia.
not greater then 19 mm 4 cm or more5 cm or more7.5 cm or
moreReduced factor for q0.851.0 1.0s rr rrH wh hN Parallel
ribs:Perpendicular ribs:0.6 1.0 1.0s rr rH wh h o.aa++n +c-= rr.ar
+c. |er.uu.-e..vr vu(ev..urv.-e) r:eraev.ru r:. .e:nvrav.-v r:.
e::. wr .ru c r:. e.eevuStud 19mm x 9cmt = 5 cmhr= 5 cm9 cm6 cm 9
cm6 cm15 cm rib spacing.en+ v+nvou..nora:oaa.++v-vnv.e:rv..ar
+c..ac ...:.e::.v-v.uu.-e.c(.)ac ...:.:v-vr-:ea.c ...:.MD
(c.a.c)(a)..aa.a. .v.:.v+nvou..nona+oavo.oar+o.ML +a.aa .v.:. ..ar
+c.|:.:v.:ree Mmax= MD+ ML a.a.-+a.aa....c .v.:....av:ree Vmax=
(a..)(c.a.c-+.a.)+...a .vr:u:ert.eranvb.. r:. .-:av.a
+c.raanv+onoa+o+.:Str e-u Mmax (....c)(+cc).(c.cc..)+.ca. r:..Ss
e-u MD (a.a.)(+cc).(c.cc ..).a r:..aa+.aaounv+o w=ooo=.c (.= +ao.+
zr.a, = cec rr.,:== o rr., ::= += rr., i.= cc,.oo zr.=, s.= +,.=o
zr.c,oaaruora+nv+o.aoar:A = 120.1 + (5)(225/9) = 245.1 r:..yb=
(120.1x19.3+5x25x41.1)/245.1 = 30.4 r:.Itr=
33,700+120.1(30.4-19.3)2+(1/12)(25)(5)3+ 5(25)(41.1-30.4)2= 63,069
r:.+Str bot= 63,069/30.4 = 2,075 r:..Str top= 63,069/(43.6-30.4) =
4,778 r:....eau-v..e:.av.nur'eauee...avree.e +a ::. a
r:..ev.rveee.e:ree = 2.5 tf= 2.5(1.3)= 3.25 r:. > 1.9 r:.
OK21682 1740105 3.15 ton < 0.25(105) 26.3 ton2075 1740hV = = =
...av:reev.vvav Vh= 105 .v ..ar +c...r +c+ r q = 5.13
.v..e.arve.reeeeee.e Nr= 1, Hs= 9 r:..e:- hr= 5 r:. wr= 6 r:.0.85 6
915 51 .reeer = = 0.816q reer.e = 0.816(5.13) = 4.19 .vNreqd=
105/4.19 = 25.1 (u 50 aao.oaa.,uaao.oaa. au
o.uvaoa:+vo+oa++o+vaa.uuee.ee-un;.:ee.e:uev.N = 26.3/4.24 = 6.2
uaao.oaa. c o.uvaoa:+vo+oa++o+v