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8/9/2019 Static Model Bra

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Suspension structures Prof Schierle 1

S

uspens ion t ruc t u res

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Suspension structures Prof Schierle 2

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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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 anglesA 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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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 load

w= 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 in2

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 =(270 2+72 2)1/2 T=279 k

Assume: Suspension cables spaced 20 ft

Allowable cable stress Fa = Fy/3 Fa = 70 ks

LL = 12 psf (60% of 20 psf for trib. area>600 ft2

DL = 18 psf = 30 psf

Horizontal reaction

H= 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 Eo/Em ration

Try model cross sectionAm = Sg

2Ao Eo/EmAm = 0.0001x 4.16 x 0.759 Am = 0.0003157

Model wire size

= 2(Am/)1/2 = 2(0.0003157/)1/2 = 0.0200Use available wire size = 0.02

Am = 0.012 Am = 0.0003142

Force scale

Sf= AmEm/(AoEo)= 0.0003142 x 29000/(4.16x22000)

Sf= 0.0001 Sf= 1:10,000

Model load

Original load Po = w L = 0.6klf x240 Po = 144 k

Sf= Pm/Po Pm = Pc SfPm = Po Sf= 144k x 1000 # / 10,000 Pm = 14.4 #

Load per cup

Assume 12 load cups (one cup per stay cable)

Pcup = Pm/12 = 14.4#/12 Pcup = 1.2#

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

Eo/Em = 22/29 Eo/Em = 0.759

Original cross section area

Strand 2 3/4 (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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Uniform suspender 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+438 2)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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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 Munich

Architect: Ackermann

Engineer: Schlaich / Bergermann

A prismatic steel truss arch of 100 m span, rising

from 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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Assume

All. strand stress Fy/3 = 210/3 Fa = 70 ksi

DL = 5 psf 5 psf on arch 5 psf

LL = 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 moment

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

Horizontal reaction

H = 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 (8.6 2 + 7.6 2 )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 stress

f = 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 reaction

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

Vertical reaction

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

Arch force

C= (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 k

Try 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 Coliseum

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