Chapter 6 Design Basis and Safety Criteria National and Euro Codes - Limit State Approach  For structures entailing softening behaviour (cracking of concrete, plasticity in steel) limit state approach safer and more accurate. Tensile Structures  Large deformations - geometry dependent on magnitude & distribution of loading.  Stiffening Systems.  Large factors need to be applied to quoted rupture strengths (to allow for material variabilities, degredation, tear strength etc).

Design Basis  Design loads to be taken as the characteristic loads (or maximum service loadings)  Tensile fabric, cables and webbings to be assessed on a Permissible Stress basis. Recommended factors based on a review of European and other codes fpr tensile structures.  Tear strength / tear propagation.  Creep rupture of seams under high temperatures.  Rigid / semi-rigid support components (eg steel masts, beams, arches etc) to be checked against Euro Codes with appropriate limit state factors applied to design case forces and moments.

Stability Checks (Limit State)  For tensile structures employing support systems which may be subject to snap-through buckling (eg slender arch supported nets or membranes) apply, in addition to the above code checks, ultimate load stability checks. Other Limit State Checks  Avoidance of progressive collapse due to failure of any component.  Security of heavy components in the event of partial failure of a membrane.  Avoidance of Ponding due to snow / snow melt. Commentary : Design Guide - not intended for regulation but consensus

CHAPTER 8 : FORM-FINDING, LOAD ANALYSIS AND PATTERNING Characteristics and Modelling of Tension Structures (surface stiffness and curvatures, load carrying directions, long & short term loadings, prestress levels, stressing out, response to dynamic loading, damping characteristics, form controls : support systems and prestress ratios, numerical modelling : networks and continua, shearing strains and stress flows, on/off material non- linearities, crimp interchange, fabrication patterning and geodesic seam lines; Gaussioan curvature and the effect of panel widths on shearing angle at seams).

Form-Finding There may also be sound engineering reasons for aiming at a uniform state of stress: For example, under the long term prestress state there will be creep of the fabric and some relaxation of the prestress - if the fabric is stressed in a reasonably uniform state initially there will be less deformation of the form due to change in the stress ratios and perhaps in consequence less liklihood of local wrinking. However, the more important issue is to do with ensuring gradual variations in stress where these are necessary to achieve a desired form; deliberate variations in stress ratios throughout a surface can be necessary for both structural economy and increased security. A classic case is that of a conic in which, for an intended difference in height between the cone ring and outer boundary, the ring diameter is insufficient to allow uniform stress.

Physical Modelling Numerical Methods for Form-Finding and Analysis The most widely reviewed and applied methods which can be used for both the form-finding and fully non-linear analysis of tensile structures are:  The Force- Density Method (references A)  Non-linear Finite Element Methods (references B), and  Dynamic Relaxation (references C) Numerical Models for Fabric Stress / Strain Properties Crimp Interchange Effects Assessment of Material Properties and Test Procedures Fabrication Patterning

panels divided further into triangular regions according to inter-set nodes on panel definition lines regions divided further into triangular facets according to subdivision density as set by user field boundaries defined by scallop/ridge cables panel 2 panel 1 warp control lines – panel edges warp line segments follow geodesics on the surface, triangle bases follow warp direction