Arch-supported tensile structures with a special suspension system

Krisztián Hincz

CONTENTS

Existing arch-supported tensile structures The block and tackle suspension system Main steps of the numerical analysis Dynamic relaxation method Numerical examples Future plans

BoA Pavilion, MA

BoA Pavilion, MA

BLOCK AND TACKLE SUSPENSION SYSTEM

Árpád KOLOZSVÁRY, Roof Arches Without Bending Moments, 2006.

THE ARCH LOADS

Conventional suspension system

Block and tackle suspension system

In practice, how much can the bending moment of the arches (due to tipical external loads) be decreased?

THE ANALYSED STRUCTURES

Cable net Suspension system Truss arches Safety cables

STRUCTURAL UNITS OF THE ANALYSED STRUCTURES

MODELLING OF THE BLOCK AND TACKLE SUSPENSION SYSTEM

MODELLING OF THE BLOCK AND TACKLE SUSPENSION SYSTEM

MAIN STEPS OF THE ANALYSIS

1. Truss arch and cable net topology generation (Initial shape)

2. Form finding of the cable net with constant cable forces (Theoretical shape)

3. Calculation of the stress-free lengths of the cables

4. Determination of the construction shape (prestress+dead load)

5. Load analysis (prestress, dead load, snow load, wind load)

DINAMIC RELAXATION METHOD

Step-by-step Nonlinear, static problems, determination of

equilibrium positions of tensile structures Fictitious motion from the initial position to the

equilibrium shape Fictitious masses Unbalanced (resultant) nodal forces

(member forces + external forces) Newton’s II. law Kinetic damping

TOPOLOGY GENERATION, INITIAL SHAPE

Initial data: Geometrical data of the truss arches (radius, angle,

depth, width) Number of suspended points Initial (constant) distance of the upper and lower

suspension points

FORM FINDING OF THE CABLE NET

Constant force in the snow and wind cables The breakpoints of the ridge cables are fixed Coordinates, cable forces unbalanced nodal forces

Calculation of the stress-free (cutting) lengths

CONSTRUCTION SHAPE

Constant suspension force Current coordinates, stress-free lengths, stiffness (+self weight) unbalanced

nodal forces

Stress-free lengths of the suspension cables

LOAD ANALYSIS

Unbalanced nodal forces: Meteorological loads Member forces Self-weight

Loads: Total snow load Two types of partial snow load Wind load(+Self-weight and prestress)

MOVEMENT OF THE PULLEYS

1

1

Upper pulleys roll if:

ori i

i i

S SR r R r

S R r S R r

1

1

Lower pulleys roll if:

cot(45 arcsin or2

cot(45 arcsin2

i

i

i

i

S r

S R

S r

S R

0 01 1

Displacement:

, , , , i i i il l l l EA S i+1

iS

2R

2r

S i+1iS

2R

2r

EXAMPLE STRUCTURE I.

Individual suspension cables ↔ Block and tackle suspension system

Idealised pulleys

Covered area: 120m·120m

MEMBER FORCES IN CASE OF PARTIAL SNOW LOAD TYPE 1

MAXIMUM OF THE INTERNAL FORCES AND BENDING MOMENTS

  Normal Force [kN] Shear Force [kN] Bending Moment [kNm]

Load ISC BTSS BTSS/ISC ISC BTSS BTSS/ISC ISC BTSS BTSS/ISC

Construction shape

-7289 -7289 1.00 69 69 1.00 265 265 1.00

Total snow load

-14808 -17833 1.20 -1074 36 -0.03 31001 783 0.03

Partial snow load 1

-12393 -14459 1.17 -1427 118 -0.08 42528 3523 0.08

Partial snow load 2

-9384 -11973 1.28 -512 53 -0.10 15554 512 0.03

Wind load -9264 -10216 1.10 736 92 0.12 -19248 -1317 0.07

EXAMPLE STRUCTURE II.

How does the friction affect the elimination of bending moments?

INTERNAL FORCES IN CASE OF WIND LOAD

INTERNAL FORCES IN CASE OF PARTIAL SNOW LOAD TYPE 1

CONCLUSIONS

By the help of the developed procedures, arch supported tensile roofs with block and tackle suspension system can be analysed. The developed procedures converge in every step of the analysis.

The numerical results show that the block and tackle suspension system reduces radically the in-plane bending moments of the supporting arches.

FUTURE PLANS

Topology of the cable net Theoretical shape of the cable net Number of suspension points Experiments to validate the numerical results.

K. HINCZ: ARCH-SUPPORTED TENSILE STRUCTURES WITH VERY LONG CLEAR SPANS, JOURNAL OF THE INTERNATIONAL ASSOCIATION FOR SHELL AND SPATIAL STRUCTURES, Vol. 48 No. 2, 2007

0

1000

2000

3000

4000

5000

6000

7000

8000

125 150 175 200 225 250 275 300 325

initial prestress in the suspension cables [kN]

max

imum

com

pres

sion

for

ce [

kN]

PBSS_TSnow ISC_TSnow PBSS_PSnow1

ISC_PSnow1 PBSS_PSnow2 ISC_PSnow2

PBSS_Wind ISC_Wind Prestress

0

0.5

1

1.5

2

125 150 175 200 225 250 275 300 325

initial prestress in the suspension cables [kN]

max

imum

dis

plac

emen

t [m

]

PBSS_TSnow ISC_TSnow PBSS_PSnow1 ISC_PSnow1

PBSS_PSnow2 ISC_PSnow2 PBSS_Wind ISC_Wind

0

1000

2000

3000

4000

5000

6000

7000

8000

0 1 2 3 4 5 6 7

initial suspension length [m]

max

imum

com

pres

sion

forc

e [k

N]

PBSS_TSnow ISC_TSnow PBSS_PSnow1

ISC_PSnow1 PBSS_Wind ISC_Wind

Prestress

0

200

400

600

800

1000

1200

1400

1600

0 1 2 3 4 5 6 7

initial suspension length [m]

max

imum

com

pre

ssio

n f

orc

e [k

N]

PBSS_TSnow ISC_TSnow PBSS_Psnow1

ISC_Psnow1 PBSS_Wind ISC_Wind

Prestress

QUESTIONS

How much can the bending moment of the arches be decreased? How do the tangential and out-of-plane movements of the pulleys and the friction affect the elimination of bending moments?

Can the cable net be prestressed during construction by tensioning the suspension cables only?

What effect does the prestress level have on the behaviour of the structure?

What effect does the distance of the upper and lower pulleys have?

MOTION OF THE BLOCK AND TACKLE II.

1 ,0 1,0

,0 1,0

*,0

*,0 ,0

1,0 ,0

( ) ( )S=

( )

(e.g. 10)

n ni i i i

n ni i

n ii

n ni i

n ni i

l l l lEA

l l

l EAl

S EA

l l

l lk

S i+1

iS

R

r

l i

i,0l

l i+1,0

i+1l

EXAMPLE STRUCTURE I.

Individual suspension cables ↔ Block and tackle suspension system

Force in the suspension cables: 25kN - 300kN Suspension length: 1m - 6m Idealised pulleys

QUESTIONS

How much can the bending moment of the arches be decreased?

How do the tangential and out-of-plane movements of the pulleys and the friction affect the elimination of bending moments?

What effect does the prestress level have on the behaviour of the structure?

What effect does the distance of the upper and lower pulleys have?