Vierendeel Bridge Grammene BelgiumVierendeel girder and frame Vierendeel structures Copyright Prof Schierle 2011 1 Arthur Vierendeel (1852–1940) born in Leuven, Belgium was a university professor and civil engineer. The Vierendeel structure he developed was named after him. His work, Cours de stabilité 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 Copyright Prof Schierle 2011 2 Berlin Pedestrian Bridge Vierendeel structures Copyright Prof Schierle 2011 3 . Berlin HBF: Vierendeel frame Vierendeel elevator shaft Vierendeel detail Vierendeel structures Copyright Prof Schierle 2011 4 . Vierendeel girder and frame Named after 19th century Belgian inventor. Vierendeel girders and frames are bending resistant 1 2 3 4 1-bay girder Gravity load Lateral load Articulated Inflection points 5 6 7 8 3-bay girder Gravity load Lateral load Articulated Inflection points 1 2 3 4 5 Base girder Global shear Global moment Bending Chord forces 6 7 8 9 10 Pin joints Strong web Strong chord Shear Chord shear One-way girders 1 Plain girder 2 Prismatic girder 3 Prismatic girder Space frames 4 2-way 5 3-way 6 3-D Vierendeel structures Copyright Prof Schierle 2011 5 . La Jolla Architect: Louis Kahn Engineer: Komendant and Dubin Viernedeel girders of 65’ span. provide adaptable interstitial space for evolving research needs Perspective section and photo.Salk Institute. courtesy Salk Institute Vierendeel structures Copyright Prof Schierle 2011 6 . Yale University Library Architect/Engineer: SOM 1 2 3 • • • • • • Vierendeel facade Vierendeel elements 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 Façades are assembled from prefab steel crosses welded together at inflection points The tapered crosses visualize inflection points Vierendeel structures Copyright Prof Schierle 2011 7 . Frankfurt Architect: Norman Foster Engineer: Ove Arup Floors between sky gardens are supported by eight-story high Vierendeel frames which also resist lateral load Vierendeel structures Copyright Prof Schierle 2011 8 .Commerzbank. Frankfurt Architect: Norman Foster Engineer: Ove Arup Vierendeel elevation / plan Vierendeel / floor girder Vierendeel / floor girder joint detail Vierendeel structures Copyright Prof Schierle 2011 9 .Commerzbank. Vierendeel structures Copyright Prof Schierle 2011 10 . 5 k’ x 12” WEB BAR (2nd web resists bending of 2 chords) Web bar bending Mw = Mc end bay + Mc 2nd bay Mw = 810 + 630 Moment of Inertia I = Mw c/Fb = 1440 k” x 5”/27.6 klf P= 6 k V = 27 k Vc = 13.5 x 5 2nd chord bending Mc = 52.5 k Mc = 52.440 k” I = 261 in4 11 .6 ksi 2nd bay chord shear Vc = (V–P)/2 = (27-6)/2 2nd chord bending Mc = Vc e/2 = 10.6 ksi L = 100’ w = 0.5 k’ Mc = 810 k” I = 147 in4 Vc = 10.5 k’ Mc = 630 k” Mw=1. allowable bending stress Fb = 0.Vierendeel steel girder Assume: 10” tubing.6x46 ksi Girder depth d = 6’.6 ksi Vierendeel structures Copyright Prof Schierle 2011 Fb= 27.5 k’ x12” Moment of Inertia I = Mc c/Fb = 810 k” x 5”/27.6 x 10’ Max shear V = 9 P/2 = 9 x 6/2 CHORD BARS Shear (2 chords) Vc = V/2 = 27/2 Chord bending (k’) Mc = Vc e/2 = 13.5x5 Chord bending (k”) Mc = 67. span 10 e = 10x10’ DL= 18 psf LL = 12 psf = 30 psf Uniform load w = 30 psf x 20’ / 1000 Joint load P = 0.5 k Mc = 67. . Load Shear Bending . Chord bars Moment of Inertia required Use ST10x10x5/16 I= 147 in4 I= 183>147 Web bars Moment of Inertia required Use ST10x10x1/2 I= 261 in4 I= 271>261 Vierendeel structures Copyright Prof Schierle 2011 14 . 71 x 34 psf x 21’/1000 w = 0.71 Uniform load per bay w = 0.6 Fy = 0. a major objective was to minimize the building height by several means: • The main level is 10’ below grade • Landscaped berms reduce the visual façade height • Along the edge the roof is attached to bottom chords to articulates the façade and reduce bulk Assume Bar cross sections 16”x16” tubing. allowed for transport) Module size: 21 x 21 x 14 ft Width/length: 252 x 315 ft Fb = 27. University of California Davis Architect: Perkins & Will Engineer: Leon Riesemberg Given the residential neighborhood.5 klf Vierendeel structures Copyright Prof Schierle 2011 15 .6x46 ksi DL = 22 psf LL = 12 psf (60% of 20 psf for tributary area > 600 ft2) = 34 psf Note: two-way frame carries load inverse to deflection ratio: r = L14/(L14+L24) = 3154/(3154+2524) r = 0.6 ksi Structural tubing Fb = 0.Sport Center. 3/16” to 5/8” thick Frame depth d = 14’ (max. 67 C = 313 k Vierendeel structures Copyright Prof Schierle 2011 16 .Modules: 21x21x14’ Design end chords Joint load P = w x 21’ = 0. shear V = 11 P /2 = 11 x 10.67’) C = M/d’= 3969 k’/ 12.5 k Max.5 / 2 V = 58 k Chord shear (2 chords) Vc = V/2 = 58 k / 2 Vc = 29 k Chord bending Mc = Vc e/2 = 29x 21’x12”/2 Mc= 3654 k” Moment of Inertia required I = Mc c /Fb = 3654 x 8”/27.5klf x 21’ P = 10.6 ksi I = 1059 in4 Check mid-span compression Global moment M = 3969 k’ M = w L2/8 = 0.5 x 2522/8 Compression (d’=14’–16”=12. Chord bars Moment of Inertia required Use ST16x16x1/2 Check mid-span chord stress Compression Allowable compression Note: End-bay bending governs I= 1059 in4 I= 1200 C = 313 k Pall = 728 k 313 <<728 Vierendeel structures Copyright Prof Schierle 2011 17 . 6 ksi V = 120 k M = 1200 k’ S = 667 in3 S = 706 in3 Vierendeel structures Copyright Prof Schierle 2011 18 .Commerzbank.6 x36 Girder shear V = 60’x20’x 100 psf/1000 Bending moment M = V e/2 = 120x20/2 Required section modulus S = M/Fb = 1200 k’ x 12”/ 21. Frankfurt Design edge girder Assume: Tributary area End bay width Loads: 70 psf DL+ 30 psf LL Allowable stress Fb =0.6 ksi Use W40x192 Note: check also lateral load Variable bay widths equalize bending stress Load at corners increases stability 60’x20’ e = 20’ ∑=100 psf Fb = 21. 6 x 10’ P= 6 k Max shear V = 9 P/2 = 9 x 6/2 V = 27 k CHORD BARS Vc = 13.6 ksi I = 147 in4 2nd bay chord shear Vc = (V–P)/2 = (27-6)/2 Vc = 10. span 10 e = 10x10’ DL= 18 psf LL = 12 psf = 30 psf Fb= 27.5 k Shear (2 chords) Vc = V/2 = 27/2 Chord bending Mc = Vc e/2 = 13.5 x (10’x12”)/ 2 Mc = 810 k” Moment of Inertia I = Mc c/Fb = 810 k” x 5”/27.5 x 120”/2 Mc = 630 k” WEB BAR (2nd web resists bending of 2 chords) Web bar bending Mw = Mc end bay + Mc 2nd bay Mw = 810 + 630 Mw=1. allowable bending stress Fb = 0.440 k” Moment of Inertia I = Mw c/Fb = 1440 k” x 5”/27.6 ksi I = 261 in4 Vierendeel structures Copyright Prof Schierle 2011 19 .6 klf Joint load P = 0.5 k 2nd chord bending Mc = Vc e/2 = 10.Vierendeel steel girder Assume: 10” tubing.6 ksi L = 100’ Uniform load w = 30 psf x 20’ / 1000 w = 0.6x46 ksi Girder depth d = 6’. Frankfurt Design edge girder Assume: Tributary area End bay width Loads: 70 psf DL+ 30 psf LL Allowable stress Fb =0.6 x36 Girder shear V = 60’x20’x 100 psf/1000 Bending moment M = V e/2 = 120x20/2 Required section modulus S = M/Fb = 1200 k’ x 12”/ 21.6 ksi Use W40x192 Note: check also lateral load Variable bay widths equalize bending stress Load at corners increases stability 60’x20’ e = 20’ ∑=100 psf Fb = 21.6 ksi V = 120 k M = 1200 k’ S = 667 in3 S = 706 in3 Vierendeel structures Copyright Prof Schierle 2011 20 .Commerzbank. Scheepsdale Revolving Bridge Bruges. Belgium 1933 Vierendeel structures Copyright Prof Schierle 2011 21 . Railroad Bridge Vierendeel structures Copyright Prof Schierle 2011 22 . Dallvazza Bridge Swiss. 1925 . Gellik Railroad Bridge Belgium . Anderlecht Railroad Bridge Belgium . 2002 . Spain. Zaragoza.Osera de Ebro Bridge. Pedestrian Bridge Vierendeel structures Copyright Prof Schierle 2011 27 . Vierendeel Space Frame Vierendeel structures Copyright Prof Schierle 2011 28 . Vierendeel girder and frame endure Vierendeel structures Copyright Prof Schierle 2011 29 .