Vierendeel Beam

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Vierendeel structures Prof Schierle 1

ierendeel girder and frame

Vierendeel Bridge Grammene Belgium


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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 importantreference during more than half a

century. His first bridge was built 1902

in Avelgen, crossing the Scheldt river


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Berlin Pedestrian Bridge


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Berlin HBF: Vierendeel frame Vierendeel elevator shaft Vierendeel detai l


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1 Base girder

2 Global shear3 Global moment

4 Bending

5 Chord forces

6 Pin joints

7 Strong web8 Strong chord

9 Shear

10 Chord shear

1 1-bay girder

2 Gravity load3 Lateral load

4 Articulated

Inflection points

5 3-bay girder

6 Gravity load7 Lateral load

8 Articulated

Inflection points

One-way girders

1 Plain girder2 Prismatic girder

3 Prismatic girder

Space frames

4 2-way5 3-way

6 3-D

ierendeel girder and frame

Named after 19th century Belgian inventor, Vierendeel girders and frames are bending resistant


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Salk Institute, La Jolla

Architect: Louis Kahn

Engineer: Komendant and Dubin

Perspective section and photo, courtesy Salk Institute

Viernedeel girders of 65 span, provide adaptable

interstitial space for evolving research needs



Yale University Library

Architect/Engineer: SOM

1 Vierendeel facade2 Vierendeel elements

3 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 steelcrosses welded together at inflection points

The tapered crosses visualize inflection points



Commerzbank, Frankfurt

Architect: Norman Foster

Engineer: Ove Arup

Floors between sky gardens are

supported by eight-story high

Vierendeel frames which also

resist lateral load





Engineer: Ove Arup

Vierendeel elevation / plan

Vierendeel / floor girder

joint detail

Vierendeel / floor girder



Hong Kong Shanghai Bank


Engineer: Ove Arup

Gravity / lateral load support: Hanger / belt truss

Vierendeel towers



Vierendeel steel girder

Assume:

10 tubing, allowable bending stress Fb = 0.6x46 ksi Fb= 27.6 ksi

Girder depth d = 6, span 10 e = 10x10 L = 100

DL= 18 psfLL = 12 psf

= 30 psf

Uniform load w = 30 psf x 20 / 1000 w = 0.6 klf

Joint load P = 0.6 x 10 P= 6 kMax shear V = 9 P/2 = 9 x 6/2 V = 27 k

CHORD BARS

Shear (2 chords) Vc = V/2 = 27/2 Vc = 13.5 k

Chord bending (k) Mc = Vc e/2 = 13.5x5 Mc = 67.5 k

Chord bending (k) Mc = 67.5 k x12 Mc = 810 k

Moment of Inertia

I = Mc c/Fb = 810 k x 5/27.6 ksi I = 147 in4

2nd bay chord shear Vc = (VP)/2 = (27-6)/2 Vc = 10.5 k

2nd chord bending Mc = Vc e/2 = 10.5 x 5 Mc = 52.5 k2nd chord bending Mc = 52.5 k x 12 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=1,440 kMoment of Inertia

I = Mw c/Fb = 1440 k x 5/27.6 ksi I = 261 in4


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Load

Shear

Bending



Chord bars

Moment of Inertia required I= 147 in4

Use ST10x10x5/16 I= 183>147

Web bars


Use ST10x10x1/2 I= 271>261



Sport Center, University of California Davis

Architect: Perkins & Will

Engineer: Leon Riesemberg

Given the residential neighborhood, a major objective was to

minimize 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 chordsto articulates the faade and reduce bulk

Assume

Bar cross sections 16x16 tubing, 3/16 to 5/8 thick

Frame depth d = 14 (max. allowed for transport)Module size: 21 x 21 x 14 ft

Width/length: 252 x 315 ft

Structural tubing Fb = 0.6 Fy = 0.6x46 ksi Fb = 27.6 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 = 0.71

Uniform load per bayw = 0.71 x 34 psf x 21/1000 w = 0.5 klf



Design end chords

Joint load

P = w x 21 = 0.5klf x 21 P = 10.5 k

Max. shear

V = 11 P /2 = 11 x 10.5 / 2 V = 58 k

Chord shear (2 chords)

Vc = V/2 = 58 k / 2 Vc = 29 kChord bending

Mc = Vc e/2 = 29x 21x12/2 Mc= 3654 k

Moment of Inertia required

I = Mc c /Fb = 3654 x 8/27.6 ksi I = 1059 in4

Check mid-span compression

Global moment

M = 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



Chord bars


Use ST16x16x1/2 I= 1200

Check mid-span chord stress

Compression C = 313 k

Allowable compression Pall = 728 k313




Design edge girder

Assume:

Tributary area 60x20End bay width e = 20

Loads: 70 psf DL+ 30 psf LL =100 psf

Allowable stress Fb =0.6 x36 Fb = 21.6 ksi

Girder shear

V = 60x20x 100 psf/1000 V = 120 k

Bending moment

M = V e/2 = 120x20/2 M = 1200 kRequired section modulus

S = M/Fb = 1200 k x 12/ 21.6 ksi S = 667 in3

Use W40x192 S = 706 in3

Note: check also lateral load

Variable bay widths equalize bending stress

Load at corners increases stability


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20 6x10 = 60 20A B

Vierendeel with overhangs

MAL= (2x10/2)(5) = 50 k (Multiframe MAL = 61.3

MAR= (5x10/2)(5)-50 = 75 k (Multiframe MAR = 73.63Bars @ B are symmetrical



Scheepsdale Revolving Bridge Bruges, Belgium 1933


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Railroad Bridge


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Dallvazza Bridge Swiss, 1925


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Gellik Railroad Bridge Belgium


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Anderlecht Railroad Bridge Belgium


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Vierendeel Space Frame


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ierendeel girder and frame endure

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Vierendeel Beam