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