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

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

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

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 ISCBTSSBTSS/ISCISCBTSSBTSS/ISCISCBTSSBTSS/ISC Construction shape Total snow load Partial snow load Partial snow load Wind load

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

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.

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?