cable truss

Cable truss structures Prof Schierle 1


Johanneshovs Isstadion, Stockholm 1962Architect: Paul HedqvistEngineer: David Jawerth (inventor)


KLM Cargo Terminal 1966Haarlemmermeer, HollandArchitect: E. A. RiphagenEngineer: David Jawerth

Palaise des Sports, 1966 Bordeaux, France


1,2 Open air theater, Ötigheim, Germany 1962 Architect: E. HeidEngineer: David Jawerth

1 Ötigheim section

2 Ötigheim plan

3 Factory at Lesjöers, SwedenArchitect: Lennart BergströmEngineer: David Jawerth


1 Concave cable truss Top strand support gravity loadBottom stabilizing strands resist wind uplift Tensile web strands

2 Convex truss, bottom strand support gravity loadTop strands resist wind uplift Web compression struts

3 Concave/convex cable truss of reduced depth Concave strands support gravity load Convex strand support wind uplift Compression struts at mid-span Tension strands at both ends


1 Convex trusses with bottom support and topstabilizing cables and web compression struts

2 Concave trusses with top supporting and bottomstabilizing cables and web compression struts

3 Convex truss with diagonal compression struts4 Convex truss with vertical compression struts5 Concave truss with diagonal tension struts6 Concave truss with vertical tension struts 7 Inverted truss with diagonal compression struts8 Inverted truss with vertical compression struts9 Center compression strut and radial tension struts10 Center compression strut - vertical tension struts11 Outward radial tension struts12 Parallel cable truss - vertical compression struts


Auditorium Utica, USA 1958Architect: Gehron and SeltzerEngineer: Lev ZetlinDiameter/span: 240’A Circular concrete compression ringB Top stabilizing cable, 1 5/8” strandsC Steel compression strutsD Bottom cable, 2” strandsE Steel tension ring

Convex alternate (roof drainage requires pumps)A Twin concrete compression ring - costlyB Top support cableC Tension strutsD Bottom stabilizing cableE Steel tension ring


Cable truss UC BerkeleyProf. Schierle and studentsDesign modelErectionTop viewJoint detail


Parallel chord trussLoad bearing of parallel chord trusses:

• Loads P1 and P2 generate a vector polygon

• Load P3 adds a second vector polygon

• Wind uplift generates reversed polygons

1 Parallel chord cable truss with four bays

2 Load bearing polygon formed for two loads

3 Load bearing polygons for three loads

4 Externally stabilized truss with six bays

5 Internally stabilized truss with six bays


Pedestrian bridge StuttgartEngineer: Schlaich Bergermann

Assume:Allowable cable stress 70 ksi /0.145 Fa = 483 MPa(70 ksi/0.145 Mega Pascal = 1 million Pascal)DL = 1.6 kPa (33 psf) LL = 5.0 kPa (104 psf) = 6.6 kPa (137 psf)

The height for trains passing under the bridge and maximum slope for handicapped access required a shallow span/sag of about 20. Bridge deck of prefab concrete panels is supported by 2 55 mm strands, prestressed by a strand to reducedeflection under non-uniform load. Diagonal webs with strands form a prismatic truss.

Length sectionsand plan

Cross section

The small height difference between supports isignored, since it has no significant effect on forces.The code required 5 kPa live load was considered unlikely (it would imply 7 people per m2). Therefore, prestress was kept relatively low.


Uniform load per cablew= 6.6 kPa x 3.3m/2 w = 10.9 kN/mGlobal momentM= wL2/8 = 10.9 x28.872/8 M = 1136 kN-mHorizontal reactionH= M/f = 1136/1.45m H = 783 kNVertical reactionR= wL/2 =10.9 x28.87/2 R = 157 kNCable forceT= (H2+R2)1/2 = (7832 + 1572)1/2 T = 799 kNMetallic cable area (55mm, 70% metallic)Am= 0.7 (55/2)2 Am=1663 mm2

Cable stress (f =T/Am)f=799kN/(1663x10-6m2)= 480,457 kPa f = 481 MPa

Check allowable stress 481 < 483

US units equivalent481 MPa x 0.145 f = 69.7 ksi < 70 ksi

Length sectionsand plan

Cross section


Intramural Sports Center, UC BerkeleyArchitect: G G SchierleEngineer: T Y Lin

Existing Harmon gymNew entry hallOlympic pool4 multipurpose gyms, 120’x120’Lower level:Handball courtsSquash courtsGymnasticsWeight liftingCable truss: • Top and bottom chord strands• Twin diagonal strands• Vertical compression struts• Fixed-end supports cause negative global bending


AssumeSpan L = 120’, truss depth d = 10’, truss spacing e = 20’Allowable cable stress (210 ksi/3) Fa= 70 ksiDL = 18 psfLL = 12 psf = 30 psfUniform truss loadw = 30 psf x 20’/1000 w = 0.6 klfVertical reactionR= wL/2 = 0.6 x 120’/2 R = 36 kDiagonal cable force (10% residual prestress) T= 1.1 x 65k (from vector triangle) T = 72 kCross section area (70% metallic)A = T/(0.7 Fa) = 72/(0.7x70ksi) A =1.47 in2

Cable size (twin strands) = 2(A/)1/2/2 = (1.47/)1/2 = 0.68” Use 23/4”Global moment (fixed end)M = wL2/12 = 0.6 x 1202/12 M = 720 k’Chord force (10% residual prestress)T = 1.1 M/d = 1.1x720/10 T = 79 kCross section area (70% metallic)A = T/(0.7 Fa) = 79/(0.7x70ksi) A =1.61 in2

Cable size = 2(A/)1/2 = 2(1.61/)1/2 = 1.43” Use 1½”


Stadium Roof Oldenburg, GermanyKulla, Herr und Partner, Oldenburg Engineer: Schlaich BergermannThe roof consists of 14 anticlastic fabric panelssuspended from cable trusses

PVC fabric, Fa = 600 pli/4 Fa = 150 pliCable Fa = Fy/3 = 210 ksi/3 Fa = 70 ksiCantilever L = 17.8 m /0.3048 L ~ 58’Panel length 17.8+5.4 = 23.2/0.3048 L’ ~ 76’Panel width B = 9.25 m/0.3048 B ~ 30’Gravity load wind upliftDL = 1 psf -1 psfLL = 20 psf 20 psf = 21 psf 19 psf


Uniform gravity loadw = 21psfx30’/1000 w = 0.63 klfGlobal momentM = w L2/2 = 0.63x582/2 M = 1060 k’ Horizontal reactionH = M /d = 1060/15 H = 71 k

d=15’

Vertical reactionR = w L = 0.63x58’ R = 37 kCable tension (10% residual prestress)T = 1.1(H2+R2)1/2 = 1.1(712+372)1/2 T = 88 kCable cross section area (70% metallic)A = T /(0.7Fa) = 88/(0.7x70) A = 1.8 in2

Cable size = 2(A/)1/2 = 2(1.8/)1/2 = 1.5 Use 1½”Design fabric support ringWind uplift per panelP = 76’ x 30’ x 19psf = P = 43,320 #Ring length L = P/Fa = 43,320/(150pli x 12”) L = 24’Ring diameter= L/ = 7.6’Double fabric at 8’Use ring size = 4’

w (uniform load)

L/2

w L


Watts Towers Cultural CrescentArchitect: Joe Addo and G G SchierleEngineer: ASIA transparent membrane, suspended from radialcable trusses, is designed to provide sun protection for occasional performance at the Watts towersThe crescent-shaped roof follows the seating belowCable trusses minimize bulk for optimal view of thetowers and fast erection at annual eventsThe truss depth is designed to provide the requiredcurvature for the anticlastic membrane panels


Cable truss details1 Strut top2 Fabric corner

A Top chord strandB Diagonal strandC fabric attachment D Metal plate at fabric cornerE Edge cable F Edge webbing


Bardwell’s Ferry Bridge Conway, MA, 60 m span, 1882http://en.wikipedia.org/wiki/Bardwell's_Ferry_Bridge


Smithfield Street, Pittsburgh, 2 x 110 m spans,1883


Pushkin Museum MoscowEngineer: Vladimir Shukov, 1853-1939http://en.wikipedia.org/wiki/Vladimir_Shukhov


Bowstring truss bridges


Pratt cable truss bridge


Bottom chord tension strands


Pedestrian bridge Munich


Louvre Pyramide Paris, cable truss by I M Pei


Cable truss glass walls


Cable truss frameless glass walls with silicon joints


Cable supported glass walls with silicon joints


Cable trusses are fun

cable truss

Documents

concave cable truss

stabilized truss

cable truss uc berkeleyprof

allowable cable stress

support cablec tension

midspan tension strands

convex trusses

parallel chord trusses