Post on 24-Dec-2015
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?