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vierendeel presentation, structures
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Vierendeel structures Prof Schierle 1
Vierendeel girder and frame
Vierendeel Bridge Grammene Belgium
Vierendeel structures Prof Schierle 2
Arthur Vierendeel (18521940) born in Leuven, Belgium was a university professor and civil engineer. The Vierendeel structure he developed was named after him.His work, Cours de stabilit des constructions (1889) was an important reference during more than half a century. His first bridge was built 1902 in Avelgen, crossing the Scheldt river
Vierendeel structures Prof Schierle 3
Berlin Pedestrian Bridge
Vierendeel structures Prof Schierle 4
Berlin HBF: Vierendeel frame Vierendeel elevator shaft Vierendeel detail
Vierendeel structures Prof Schierle 5
1 Base girder2 Global shear 3 Global moment4 Bending 5 Chord forces
6 Pin joints7 Strong web 8 Strong chord9 Shear 10 Chord shear
1 1-bay girder2 Gravity load 3 Lateral load4 Articulated
Inflection points
5 3-bay girder6 Gravity load 7 Lateral load8 Articulated
Inflection points
One-way girders1 Plain girder2 Prismatic girder 3 Prismatic girder
Space frames4 2-way5 3-way6 3-D
Vierendeel girder and frameNamed after 19th century Belgian inventor, Vierendeel girders and frames are bending resistant
Vierendeel structures Prof Schierle 6
Salk Institute, La JollaArchitect: Louis KahnEngineer: Komendant and Dubin
Perspective section and photo, courtesy Salk Institute
Viernedeel girders of 65 span, provide adaptableinterstitial space for evolving research needs
Vierendeel structures Prof Schierle 7
Yale University LibraryArchitect/Engineer: SOM
1 Vierendeel facade2 Vierendeel elements3 Cross section
The library features five-story Vierndeel frames
Four concrete corner columns support the frames
Length direction span: 131 feet Width direction span: 80 feet
Faades are assembled from prefab steel crosses welded together at inflection points
The tapered crosses visualize inflection points
Vierendeel structures Prof Schierle 8
Commerzbank, FrankfurtArchitect: Norman FosterEngineer: Ove Arup
Floors between sky gardens aresupported by eight-story highVierendeel frames which also resist lateral load
Vierendeel structures Prof Schierle 9
Commerzbank, FrankfurtArchitect: Norman FosterEngineer: Ove Arup
Vierendeel elevation / plan
Vierendeel / floor girderjoint detail
Vierendeel / floor girder
Vierendeel structures Prof Schierle 10
Hong Kong Shanghai BankArchitect: Norman FosterEngineer: Ove ArupGravity / lateral load support: Hanger / belt truss Vierendeel towers
Vierendeel structures Prof Schierle 11
Vierendeel steel girderAssume: 10 tubing, allowable bending stress Fb = 0.6x46 ksi Fb= 27.6 ksiGirder depth d = 6, span 10 e = 10x10 L = 100DL= 18 psfLL = 12 psf = 30 psfUniform load w = 30 psf x 20 / 1000 w = 0.6 klfJoint load P = 0.6 x 10 P= 6 kMax shear V = 9 P/2 = 9 x 6/2 V = 27 kCHORD BARSShear (2 chords) Vc = V/2 = 27/2 Vc = 13.5 kChord bending (k) Mc = Vc e/2 = 13.5x5 Mc = 67.5 k Chord bending (k) Mc = 67.5 k x12 Mc = 810 kMoment of Inertia I = Mc c/Fb = 810 k x 5/27.6 ksi I = 147 in42nd bay chord shear Vc = (VP)/2 = (27-6)/2 Vc = 10.5 k2nd chord bending Mc = Vc e/2 = 10.5 x 5 Mc = 52.5 k2nd chord bending Mc = 52.5 k x 12 Mc = 630 kWEB BAR (2nd web resists bending of 2 chords)Web bar bending Mw = Mc end bay + Mc 2nd bay Mw = 810 + 630 Mw=1,440 kMoment of Inertia I = Mw c/Fb = 1440 k x 5/27.6 ksi I = 261 in4
Load
Shear
Bending
Vierendeel structures Prof Schierle 14
Chord barsMoment of Inertia required I= 147 in4
Use ST10x10x5/16 I= 183>147
Web barsMoment of Inertia required I= 261 in4
Use ST10x10x1/2 I= 271>261
Vierendeel structures Prof Schierle 15
Sport Center, University of California DavisArchitect: Perkins & Will Engineer: Leon Riesemberg
Given the residential neighborhood, a major objective was tominimize the building height by several means: The main level is 10 below grade Landscaped berms reduce the visual faade height Along the edge the roof is attached to bottom chords
to articulates the faade and reduce bulkAssumeBar cross sections 16x16 tubing, 3/16 to 5/8 thickFrame depth d = 14 (max. allowed for transport)Module size: 21 x 21 x 14 ftWidth/length: 252 x 315 ftStructural tubing Fb = 0.6 Fy = 0.6x46 ksi Fb = 27.6 ksiDL = 22 psfLL = 12 psf (60% of 20 psf for tributary area > 600 ft2) = 34 psfNote: two-way frame carries load inverse to deflection ratio:r = L14/(L14+L24) = 3154/(3154+2524) r = 0.71Uniform load per bayw = 0.71 x 34 psf x 21/1000 w = 0.5 klf
Vierendeel structures Prof Schierle 16
Design end chordsJoint loadP = w x 21 = 0.5klf x 21 P = 10.5 k Max. shearV = 11 P /2 = 11 x 10.5 / 2 V = 58 kChord shear (2 chords)Vc = V/2 = 58 k / 2 Vc = 29 kChord bendingMc = Vc e/2 = 29x 21x12/2 Mc= 3654 kMoment of Inertia required I = Mc c /Fb = 3654 x 8/27.6 ksi I = 1059 in4
Check mid-span compressionGlobal momentM = w L2/8 = 0.5 x 2522/8 M = 3969 kCompression (d=1416=12.67) C = M/d= 3969 k/ 12.67 C = 313 k
Modules:21x21x14
Vierendeel structures Prof Schierle 17
Chord barsMoment of Inertia required I= 1059 in4
Use ST16x16x1/2 I= 1200
Check mid-span chord stressCompression C = 313 kAllowable compression Pall = 728 k
313
Vierendeel structures Prof Schierle 18
Commerzbank, FrankfurtDesign edge girderAssume:Tributary area 60x20End bay width e = 20Loads: 70 psf DL+ 30 psf LL =100 psfAllowable stress Fb =0.6 x36 Fb = 21.6 ksi
Girder shearV = 60x20x 100 psf/1000 V = 120 kBending momentM = V e/2 = 120x20/2 M = 1200 kRequired section modulusS = M/Fb = 1200 k x 12/ 21.6 ksi S = 667 in3Use W40x192 S = 706 in3
Note: check also lateral loadVariable bay widths equalize bending stressLoad at corners increases stability
Vierendeel structures Prof Schierle 19
Vierendeel steel girderAssume: 10 tubing, allowable bending stress Fb = 0.6x46 ksi Fb= 27.6 ksiGirder depth d = 6, span 10 e = 10x10 L = 100DL= 18 psfLL = 12 psf = 30 psfUniform load w = 30 psf x 20 / 1000 w = 0.6 klfJoint load P = 0.6 x 10 P= 6 kMax shear V = 9 P/2 = 9 x 6/2 V = 27 kCHORD BARSShear (2 chords) Vc = V/2 = 27/2 Vc = 13.5 kChord bending Mc = Vc e/2 = 13.5 x (10x12)/ 2 Mc = 810 kMoment of Inertia I = Mc c/Fb = 810 k x 5/27.6 ksi I = 147 in42nd bay chord shear Vc = (VP)/2 = (27-6)/2 Vc = 10.5 k2nd chord bending Mc = Vc e/2 = 10.5 x 120/2 Mc = 630 kWEB BAR (2nd web resists bending of 2 chords)Web bar bending Mw = Mc end bay + Mc 2nd bay Mw = 810 + 630 Mw=1,440 kMoment of Inertia I = Mw c/Fb = 1440 k x 5/27.6 ksi I = 261 in4
Vierendeel structures Prof Schierle 20
Scheepsdale Revolving Bridge Bruges, Belgium 1933
Vierendeel structures Prof Schierle 21
Railroad Bridge
Dallvazza Bridge Swiss, 1925
Gellik Railroad Bridge Belgium
Anderlecht Railroad Bridge Belgium
Osera de Ebro Bridge, Zaragoza, Spain, 2002
Vierendeel structures Prof Schierle 26
Pedestrian Bridge
Vierendeel structures Prof Schierle 27
Vierendeel Space Frame
Vierendeel structures Prof Schierle 28
Vierendeel girder and frame endure