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Suspension structures Copyright Prof Schierle 2012 1

SSuspension Structures

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Suspension Structures

Effect of:

Support Form

Stability

1. Circular support to balancelateral thrust

2. Bleachers to resist lateral thrust

3. Self weight: catenary funicular4. Uniform load: parabolic funicular

5. Point loads: polygonal funicular

6. Point load distortion7. Asymmetrical load distortion

8. Wind uplift distortion

9. Convex stabilizing cable10.Dead load to provide stability

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Sag/span vs. force

Considering force vectors at support;

H = horizontal reaction

V = vertical reaction

T = tension of cable at support

Reveal, for a given vertical reaction:

small sag = large force

Large sag = small force

Large sag requires costly tallsupport

Optimal span/sag is usually ~10

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Cable details

1 Strand (good stiffness, low flexibility)E=22,000 to 24,000 ksi, 70% metallic

2 Wire rope (good flexibility, low stiffness)E = 14,000 to 20,000 ksi, 60% matallic

3 Bridge Socket (adjustable)

4 Open Socket (non-adjustable)5 Wedged Socket (adjustable)

6 Anchor Stud (adjustable)

A Support elements

B Socket / studC Strand or wire rope

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Mast / cable details

The mast detail demonstrates typical use of

cable or strand sockets. Steel gusset platesusually provide the anchor for sockets.

Equal angles A and B result in equal forces

in strand and guy, respectively.A Mast / strand angle

B Mast / guy angle

C Strand

D Guy

E Sockets

F Gusset plates

G Bridge socket (to adjust prestress)H Foundation gusset (at strand and mast)

I Mast

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6/26Suspension structures Copyright Prof Schierle 2012 6

Loyola University Pavil ion

Architect: Kahn, Kappe, Lottery, Boccato

Engineer: Reiss and Brown

Consultant: Dr. Schierle

Roof spans the long way to provide open view for

outdoor seating for occasional large events

Lateral wind and seismic loads are resisted by:

Roof diaphragm

In width direction by concrete shear walls In length direction by guy cables and

Handball court walls

Guy cables resist lateral trust

Suspension cables resist gravityStabilizing cables:

resist wind uplift

resist non-uniform load

provide prestress

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Uniform loadw= 30 psf x 20 / 1000 w= 0.60 klf

Global momentM= wL2/8= 0.60x2402/8 M= 4320 k

Vertical reactionR= wL/2= 0.60x240/2 R= 72 k

Gross cross section (70% metallic)Ag=Am/0.70=3.99/0.7 0 Ag=5.70 in

2

Cable size=2(Ag/)1/2=2(5.70/)1/2=2.69 in use 2

Metallic cross section requiredAm=T/Fa=279/70 ksi Am=3.99 in

2Graphic method

Draw vector of vertical reaction Draw equilibrium vectors at support

Length of vectors give cable forceand horizontal reaction

Cable tension (max.)T=(H2+R2)1/2=(2702+722)1/2 T=279 k

Assume: Suspension cables spaced 20 ftAllowable cable stress Fa = Fy/3 Fa = 70 ksLL = 12 psf (60% of 20 psf for trib. area>600 ft2

DL = 18 psf = 30 psf

Horizontal reactionH= M/f= 4320/16 H= 270 k

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Static model

Assume:Piano wire as model cables

Geometric scale Sg = 1:100

Strain scale Ss = 1 (due to large deflections)

Force scale

Sf= Am Em / (Ao Eo)

To keep Ss = 1 adjust Am by Em / Eo ration

Try model cross section

Am = Sg2Ao Em/Eo

Am = 4.16 x 1.32/10,000 Am = 0.000549

Model wire size

= 2(Am/)1/2 = 2(0.000549/)1/2 = 0.026

Consider available size use 0.025

Am = r2 = (0.025/2)2 Am = 0.00049in

2

Force scale

Sf= AmEm/(AoEo)= 0.00049x29000/(4.16x22000)Sf= 0.0001553 Sf= 1 : 6441

Model load

Original load Po

= w L = 0.6klf x240 Po

= 144k

Sf= Pm/Po Pm = Pc SfPm = Po Sf= 144k x 1000# / 6441 Pm = 22#

Load per cup

Assume 12 load cups (one cup per stay cable)Pcup = Pm/12 = 22#/12 Pcup = 1.83#

Original strand Eo = 22,000ksiPiano wire Em = 29,000ksi

Em/Eo = 29/22 Em/Eo = 1.32

Original cross section area

Strand 23/4 (70% metallic)

Ao = 0.7 r2 = 0.7 (2.75/2)2 Ao = 4.16in

2

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Exhibit Hall Hanover

Architect: Thomas Herzog

Engineer: Schlaich Bergermann

Suspended steel bands of 3x40 cm (1.2x16 inch) supportprefab wood panels, filled with gravel to resist wind uplift.

In width direction the roof is slightly convex for drainage;

which also provides an elegant interior spatial form.

Curtain wall mullions are pre-stressed between roof andfooting to prevent buckling under roof deflection.

Unequal support height is a structural disadvantage since

horizontal reactions of adjacent bays dont balance; but it

provides natural lighting and ventilation for sustainability

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Uniformsuspender load

w= 1.7 kN/m2

x 5.5m w = 9.35 kN/mGlobal moment

M=wL2/8= 9.35 x 642 / 8 M= 4787 kN-m

Horizontal reaction

H= M/f= 4787/7 H = 684 kN

Vertical reaction R (max.)

Reactions are unequal; use R/H ratio

(similar triangles) to compute max. RR / H= (2f+h/2) / (L/2), hence

R= H (2f+h/2) / (L/2)

R= 684 (2x7+13/2)/(64/2) R= 438 kN

Exhibit Hall Hanover

Suspender tension (max.)T= (H2+R2)1/2= (6842+4382)1/2 T= 812 kN

Given LL = 0.5 kN/m2 (10 psf)

DL = 1.2 kN/m

2

(25 psf) = 1.7 kN/m2 (35 psf)

Suspenders 3x40 cm (~1x16), spaced at 5.5 m (18)

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Suspender tension

(from previous page) T = 812 kN

Suspender stress

f=T/A= 812/0.012= 67,667 kPa f = 68 MPa

US units equivalent

68 MPa x 0.145 = f = 9.9 ksi

9.9 < 22 ksi, OK

Graphic method

Draw vector of total vertical load W = w L

Suspender cross section area

A= 0.03 x 0.4 m) A = 0.012 m2

Draw equilibrium vectors parallel to cable tangents

Draw equilibrium vectors for right support

Draw equilibrium vectors for left support

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Dulles Airport Terminal (1963)

Architect: Ero Saarinen

Engineer: Ammann and Whitney

150x600, 40-65 high Concrete/suspension cable roof

Support piers spaced 40

D ll Ai t T i l

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Dulles Airport Terminal

Span L = 150

Sag f = 15

Support height differential h = 25

Strand spacing e = 5

Allowable strand stress Fa = 70 ksi

DL = 38 psf

LL = 12 psf

= 50 psfUniform strand load

w = 50psf x5/1000 w = 0.25 klf

Horizontal reaction H = wL2/(8f)

H = 0.25x1502

/(8x15) H = 46.9 kMax. vertical reaction

R=H(2f+h/2)/(L/2)

R = 46.9(30+12.5)/(75) R = 26.6 k

Strand tension T =(H2+R2)1/2

T =(46.92+ 26.62)1/2 T = 53.9 k

Cross section required (70% metallic)

A = 53.9/(0.7x70) ksi A = 1.1 in2

Strand diameter = 2(A/ )1/2

=2(1.1/3.14)1/2 = 1.18Use = 1 3/16

L

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Skating rink MunichArchitect: AckermannEngineer: Schlaich / Bergermann

A prismatic steel truss arch of 100 m span, risingfrom concrete piers, support anticlastic cable nets

A translucent PVC membrane is attached to wood

slats that rest on the cable net

Glass walls are supported by pre-stressed strandsto avoid buckling under roof deflection

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AssumeAll. strand stress Fy/3 = 210/3 Fa = 70 ksiDL = 5 psf 5 psf on arch 5 psfLL = 20 psf 12 psf on arch uplift 21 psf

= 25 psf 17 psf on arch 16 psf

Cable net

Uniform load (cable spacing 75 cm = 2.5)

Gravity w= 25 psf x2.5/1000 w = 0.0625 klf

Wind p= 16 psf x 2.5/1000 p = 0.040 klf

Global momentM= w L2/8= 0.0625 x 1102/8 M = 95 k

Horizontal reactionH = M / f = 95 / 11 H = 8.6 k

Vertical reaction

R/H= (2f+h/2 ) / (L/2); R= H (2f+h/2 ) / (L/2)R= 8.6 (2x11+53/2)/(110/2) R = 7.6 k

Gravity tension (add 10% residual prestress)

T = 1.1 (H2

+ R2

)1/2

T = 1.1 (8.62+ 7.62 )1/2 T = 11.5 k

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Gravity tension (from previous slide) T = 11.5 k

Wind tension (10% residual prestress)Wind suction is normal to surface, hence

T= 1.1 p r= 1.1 x 0.04 x 262 Wind T = 12 k12 > 11.5 Wind governs

Metallic cross section area(assume twin net cables, 70% metallic)Am = 0.7x2r2= 0.7x2(0.5/2)2 Am= 0.28 in2

Cable stressf = T/Am= 12 k / 0.28 f = 43 ksi

43 < 70, ok

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Truss arch design (prismatic truss of 3 steel pipes)

Floor area 4,200 m2 / 0.30482 45,208ft2

Arch load

w = (45,208x17psf/328)/1000+0.26klf arch DL)w = 2.6klf

Horizontal reactionH= M/d = wL2/(8d)= 2.6x3282/(8x53) H= 660k

Vertical reactionR= w L/2 = 2.6 x 328 / 2 R = 426k

Arch forceC= (H2+ R2)1/2 = (6602+ 4262)1/2 C = 786k

Panel bar length (K=1) KL = 7

3 bars, P ~ C / 3 ~ 786 / 3 ~ 262 kTry 10 extra strong pipe Pall = 328 > 262

3xP 10 ok

(244/25.4 = 9.6)

(267/25.4 = 10.5)

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Oakland ColiseumArchitect/Engineer:

Skidmore Owings and Merrill

Radial cables, suspended from a concretecompression ring and tied to a steel tensionring, are stabilized against wind uplift andnon-uniform load by prefab concrete ribs.

AssumeAllowable cable stress Fa= 70 ksi(1/3 of 210 ksi breaking strength)

Cables spaced 13 @ outer compression ring

LL reduced to 60% of 20 psf per UBC

for tributary area > 600 sq. ft.)LL = 12 psf (60% of 20 psf)DL = 28 psf (estimate) = 40 psf

+ 0.12 klf for concrete ribs(0.15kcf x 4 x 29/144 uniform load)

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Distributed load

w = 40 psf x 13/1000 w = 0 to 0.52 klf

Global moment (due to triangular roof load)

(cubic parabola with origin at mid-span)Mx = w L2/24 (1 8 X3 / L3 )

For max. M at mid-span, X=0, hence

M = wL2 / 24= 0.52 x 4202 / 24 M = 3,822 k

Horizontal reaction

H = M/f= 6,468/30 H = 216 k

Vertical reaction

R = wL/2 = (0.52/2+0.12) x 420/2 R = 80 k

Cable tension (max.)

T = (H2 + R2)1/2 = (216 2 + 80 2 )1/2 T = 230 k

Metallic cross section requiredAm = T/Fa= 230/70 ksi Am = 3.3 in

2

Global moment (due to uniform rib load)

M = w L2/8 = 0.12 klf x 4202/8 M = 2,646 k

Moments = 3,822 + 2,646 M = 6,468 k

Recycling Center Vienna (1981)

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Recycling Center, Vienna (1981)

Architect: L. M. LangEngineer: Natterer and Diettrich

This recycling center is a wood structure of 170 m (560 ft)

diameter of 67 m (220 ft) height concrete mast.The roof consists of 48 radial laminated wood ribs that

carry uniform roof load in tension but asymmetrical loads

may cause bending in the semi-rigid tension bands.

The mast cantilevers from a central foundation, designedto resist asymmetrical erection loads and lateral wind load.The peripheral pylons are triangular concrete walls.

1 Cross section2 Roof plan

3 Top of central support mast4 Tension rib base support

A Laminated wood ribs, 20x80-110 cm (7.8x32-43 in)B Laminated wood ring beams, 12x39 cm (5x15 in)C Wood joistsD Steel tension ringE Steel anchor bracket

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Clifton Suspension Bridge, UK, 214 m span, 1831

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Danube Bridge, Budapest, 220 m span, 1840

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Golden Gate Bridge, San Francisco, 4200 m main span, 1934

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Tacoma Narrows Bridge, 853 m span, 7, 1, 1940 - 11, 7, 1940http://www.youtube.com/watch?v=3mclp9QmCGs

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Exhibit Hall 8/9, Hanover, Germany, 245x345m, 1998

Architect: GMP

Engineer: Schlaich Bergermann

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suspended cable car

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