Framed tube Prof Schierle 1Framed TubeFramed tube Prof Schierle 2Framed tubeFramed tubes have narrowly spaced exterior columns that, combined with spandrel beams, form rigid frames to resist lateral load.1 Framed tube2 Framed tube with core3 Shear lag in framed tubeFramed tube Prof Schierle 3Large drift(unglued boards resist independently)Small drift (glued boards resist in synergyshear joins tension & compression)Gue-lam beam anlogyFramed tube Prof Schierle 4Framed tubeFramed tubes have narrowly spaced exterior columns that, combined with spandrel beams, form rigid frames to resist lateral load.1 Framed tube2 Framed tube with core3 Shear lag in framed tube4 Framed tube with outriggers5 Prefab framed tube6 Prefab framed tube elementA Shear lag at mid façadeB Shear peak at cross wallsC Joint at inflection point of zero bendingFramed tube Prof Schierle 5Column buckling K-factor review Pin support Flag pole Moment frame columnK = 1K = 2K = 1 (theoretic, assumes perfectly rigid joints)K’ ~ 1.2 (recommended,includes a safety factordue to semi-rigid joints)Framed tube Prof Schierle 6World Trade Center New YorkArchitect: Minoru Yamasaki Engineer: Skilling / RobertsonThe World Trade center had a Framed Tube structure,composed of closely spaced columns (~ 1 meter). Moment resisting beam / column joints formed a lattice wall to resist gravity and lateral loads.1 Axonometric view of one tower2Floor framing3 Prefab steel element4 Typical column cross sectionFramed tube Prof Schierle 7CBS Tower New YorkArchitect: Eero SaarinenThe 38-story CBS tower has a framed tube of concretecolumns that are triangular on the upper floors and diamondshaped on the ground floor.The columns have niches for mechanical ducts that decreasewith decreasing duct sizes from mechanical floor on top butnot from the second floor mechanical room. A Top floor columnsB 2nd floor columnsC Ground floor columnsConcrete floors span between core and framed tube:• One-way rib slabs face the core• Two-way waffle slabs at corners Size: 155’x125’x494’ high (47x38x151m) Typical story height: 12’ (3.66m)Floor-to-ceiling height: 8.75’ (2.67m)Height/width ratio 3.9Framed tube Prof Schierle 8First Interstate Bank Los AngelesArchitect: I M PeiEngineer: CBMFramed tube exteriorcombined with braced coreAMP Tower MelbourneArchitect/Engineer: SOMFramed tube tower, flanked by L-shaped low-rise wingFramed tube Prof Schierle 9Sears tower ChicagoArchitect/Engineer: SOMThe Sears tower is a bundled tube structureBundled tubes have interior walls to transfer shear from tension to compression side to avoid shear lag1 Bundled tubes reduce shear lag2 Large shear lag in single tube3 Framing plan (3x3x75’x75’)4 Architectural plan5 2-module top floors6 5-module floors7 7-module floors8 9-module floors9 AxonBundled tubeFramed tube Prof Schierle 10Fazlur Khan high-rise conceptshttp://en.wikipedia.org/wiki/Fazlur_KhanFramed tube Prof Schierle 11Mid-wall-columnsVc = L V/B=10x932/110 Vc = 85 kMc = Vc h/2= 85x10’x12” Mc = 10200 k”Axial load (gravity)P =30 floors x100x10x15/1000 P = 450 kPtot=P+MBx =450+10200x0.175 Ptot = 2235kUse W14x500 2490 > 2235Framed TubeAssume 30-story steel office building.Exterior columns resist gravityand lateral loadsDesign Ground floorColumn KL=1.2x20’ KL= 24’Wind pressure P = 30 psfDL = 80 psfLL = 25 psf (beams @ 50%)LL = 20 psf (columns @ 40%) = 105 psf (beams) = 100 psf (columns)Base shearV= 30psf x75’x 414/1000 V = 932 kOverturn momentsM0= 30psfx75’x4142/(2x1000) M0= 192,821 k’M1= 30psfx75’x3942/(2x1000) M1= 174,641 k’Vc =(L/2) V/B = 5’x932/110’ Vc = 42 kMc = Vc h/2 = 42x10’x12” Mc = 5040 k”Gravity loadP = 30 floors x252x100/(3x1000) P = 625 kLateral loadP=M0/ B = 192,821/110 P= 1753 k P = 625+1753 P = 2378 kPtot = P+MBx =2378+5040x0.17 Ptot = 3235 kUse W14x665 3372 > 3235HVAC floorHVAC floorLobby424-10 = 414’424-30 = 394’Framed tube Prof Schierle 12HVAC floorHVAC floorLobbySpandrel beamsV=(M0-M1)/B=(192821-174641)/110 V = 165 kM=V L/2 = 165 (5’x12”) M = 9,900 k”S = M/Fb = 9900/22ksi S = 450 in3Use W18x234 466 > 450Base shearV= 30psf x75’x 414/1000 V = 932 kOverturn momentsM0= 30psfx75’x4142/(2x1000) M0= 192,821 k’M1= 30psfx75’x3942/(2x1000) M1= 174,641 k’Vc =(L/2) V/B = 5’x932/110’ Vc = 42 kMc = Vc h/2 = 42x10’x12” Mc = 5040 k”Gravity loadP = 30 floors x252x100/(3x1000) P = 625 kLateral loadP=M0/ B = 192,821/110 P= 1753 k P = 625+1753 P = 2378 kPtot = P+MBx =2378+5040x0.17 Ptot = 3235 kUse W14x665 3372 > 3235Mid-wall-columnsVc = L V/B=10x932/110 Vc = 85 kMc = Vc h/2= 85x10’x12” Mc = 10200 k”Axial load (gravity)P =30 floors x100x10x15/1000 P = 450 kPtot=P+MBx =450+10200x0.175 Ptot = 2235kUse W14x500 2490 > 2235Framed TubeAssume 30-story steel office building.Exterior columns resist gravityand lateral loadsDesign Ground floorColumn KL=1.2x20’ KL= 24’Wind pressure P = 30 psfDL = 80 psfLL = 25 psf (beams @ 50%)LL = 20 psf (columns @ 40%) = 105 psf (beams) = 100 psf (columns)Framed tube Prof Schierle 13HVAC floorHVAC floorLobbyJoistsM=wL2/8=(105psf x10’/1000)x302/8 M = 118 k’S = M/Fb = 118k’x12”/22ksi S = 64 in3Use S18x54.7 89.4 > 64Spandrel beamsV=(M0-M1)/B=(192821-174641)/110 V = 165 kM=V L/2 = 165/(5’x12”) M = 9,900 k”S = M/Fb = 9900/22ksi S = 450 in3Use W18x234 466 > 450Base shearV= 30psf x75’x 414/1000 V = 932 kOverturn momentsM0= 30psfx75’x4142/(2x1000) M0= 192,821 k’M1= 30psfx75’x3942/(2x1000) M1= 174,641 k’Vc =(L/2) V/B = 5’x932/110’ Vc = 42 kMc = Vc h/2 = 42x10’x12” Mc = 5040 k”Gravity loadP = 30 floors x252x100/(3x1000) P = 625 kLateral loadP=M0/ B = 192,821/110 P= 1753 k P = 625+1753 P = 2378 kPtot = P+MBx =2378+5040x0.17 Ptot = 3235 kUse W14x665 3372 > 3235Mid-wall-columnsVc = L V/B=10x932/110 Vc = 85 kMc = Vc h/2= 85x10’x12” Mc = 10200 k”Axial load (gravity)P =30 floors x100x10x15/1000 P = 450 kPtot=P+MBx =450+10200x0.175 Ptot = 2235kUse W14x500