07_TensiNet

DESIGNLOADING CONDITIONS

Chapter 7

Markus Balz, Mike Dencher

DESIGN LOADING CONDITIONS

I 2 I

7.1 Lightweight Structures Subject to External Loading

By the very nature of lightweight structures, the ratio of applied loading to self-weight is usu-ally many times larger than that of conventional building structures. Changes in the magni-tude of wind and snow loading are therefore likely to have a proportionately larger impacton the size of the structural members required and the scale of deflections experienced.

Consequently the selection of suitable loading patterns for the design of membrane struc-tures has to be carefully considered. Furthermore the codes are written for standardisedbuilding shapes and building behaviour, usually making the application of a single code verydifficult. As a consequence more time and effort needs to be spent in defining load cases.

As described in the previous chapter, due to the flexibility of membrane forms the designof such structures needs to vary from the new European Codes.

7.2 Prestress

The level of prestress in a membrane surface affects all the elements within the supportingstructure (masts, frames, cables etc.). Prestress is an inherent part of its structural behaviour.The prestress levels are chosen as a result of the “form finding” process, and have to beachieved and sustained during the erection and life of the structure. These forces have to beincluded in all other load cases.

The prestress of membrane structures is a fundamental part of the shape and structuralbehaviour. This is explained in more detail in Chapter 2.

Long term effects, such as creep of the membrane material may alter prestress levels.Foundation settlement may also, though rarely, be an influence. These effects must be con-sidered and appropriate measures taken to ensure the retention of sufficient prestress.

Generally the minimum required prestress of membrane surfaces depends on the stiffnessand strength of the material and the efficiency of the membrane surface (i.e. curvature).Furthermore prestress levels lower than those given may lead to an uneven or wrinklyappearance as not all fibres in the surface may be sufficiently stretched.

For PVC coated Polyester membrane structures, a ‘rule of thumb’ is that the prestress shouldnot be less than 1.3% of the average tensile strip capacity of the material in both the warpand weft directions. This value can be applied to satisfy the minimum requirement forprestress of permanent membrane structures made of the following PVC types

Minimum Prestress Levels for PVC coated Polyester membrane structuresType I 0.70 KN/mType II 0.90 KN/mType III 1.30 KN/mType IV 1.60 KN/mType V 2.00 KN/m

European Design Guide for Tensile Surface Structures

I 3 I

The prestress can be chosen with higher values to minimise deflections of inefficient curvedmembrane forms, with the increased prestress marginally reducing the allowable working stressrange. Temporary or special case membrane structures might be designed using lower prestress.

The prestress values for PTFE coated glass fibre membrane structures tend to be higher asthe material is stiffer. The prestress should not be lower then 2.0kN/m and the strongestcurrently available membrane PTFE coated glassfibre membrane is often prestressed attypically 5.0kN/m (and for very flat surfaces perhaps up to 10kN/m).

A “rule of thumb” is that the prestress should not be less than 2.5% nor greater than 6%of the average tensile strip capacity of the material in both warp and fill directions.

The above values can be applied to satisfy the basic requirement for prestress of permanentmembrane structures.

The level of prestress in the membrane surface affects the support structures (e.g. mast,frames and cables) and is an inherent part of the structural behaviour. Prestress ratios areselected during the form finding process and their levels are validated during analysis of thedesign loadcases. The prestress forces have, of course, to be included in all load cases.

Different prestress levels between warp and weft may alter the shape to a certain degree andmay improve the structural behaviour. This strategy is in effect a fine-tuning for structuresthat have a “design-dictating” imposed load in one direction and a moderate load in theother opposite direction. However choosing more suitable geometric boundary conditionsand more curvature will always be a more successful way of improving structural behaviour.

For conical membrane shapes varying prestress levels are a necessity, as the membraneshape would “neck-in” around the ring support.

Generally the prestress ratios should not vary by more than 1:4 or 4:1.

7.2.1 COMPENSATION

Membrane structures are usually ‘compensated’ so that thefabric will achieve the predefined prestress levels at the cor-rect geometry once the creep of the membrane has occurred.The compensation process accounts for the elastic stretch ofmembrane and cables, and for the creep of the membrane.

A “force-controlled” prestress regime is one in which all ele-ments including the membrane reach their pre-defined pre-stress values, but will need to be subjected to re-tensioningafter the early creep has occurred, see Fig. 7.1. Alternatively, a“geometrically controlled” prestress regime will slightly overstress the membrane until sufficient creep has occurred. Highlyprestressed membranes may reach their working capacity fora short period of time while they are stretched into position


TensiNet

Fig. 7.1 Force-controlled pre stressregime of membrane structureusing hydraulic jacks © LandrellFabric Engineering


I 4 I

without time to creep and should therefore be installed in a force-controlled manner or using a“time stepped” geometrically-controlled prestress regime. The structure does not have to bere-tensioned after installation provided appropriate compensation values are applied and accounthas been taken of likely long-term movements such as foundation settlement and drift.

Using a geometrically-controlled prestress regime requires detailed analysis to avoid overstres-sing the membrane should it be subjected to high external loading shortly after installation.

7.2.2 REPLACEMENT OF THE MEMBRANE

The procedures for membrane renewal and maintenance need to be considered during thedesign stage. Where for instance a panel of the membrane may need to be replaced theconsequential effects on the remaining structure, in terms of changes to membrane stres-ses, element forces and movements, should be considered.

In such circumstances lower levels of imposed load may be satisfying when judged in rela-tion to a reduced period of exposure to such load.

7.3 Selfweight

The selfweight of the membrane is commonly between 0.7 and 2.0 kg/m2.

It is not usual to include the self-weight in the form finding process because this may intro-duce some additional mechanical freedom into the response of the membrane to wind upliftloadings. Although this is usually a trivial effect, in some cases it may be significant – forexample in relatively lightly stressed membrane surfaces using heavier grade fabrics.

Whether or not self-weight is included in the form finding process (to define an initial geo-metrical state) it must be included in all applied load cases.

7.4 Wind

Wind, especially in the form of uplift, is regularly the critical case for membrane and cablestresses in lightweight membrane structures. It is generally considered as a static load case,defined by a dynamic pressure multiplied by a pressure coefficient (Cp). It is also assumedthat the membrane undergoes only slight changes to its geometry such that changes to Cpfactors are small enough to be safely ignored.

This approach may not be appropriate if the membrane form is deflection sensitive and/orlarge deflections are the case. This case is discussed in more detail later in 7.4.5.

7.4.1 SITE WIND SPEED

The site wind speed and dynamic pressure can be derived as described in EC1, part 2.4.


I 5 I

7.4.2 Cp VALUES

Membrane structures are single layer elements with wind load often exerted on both facessimultaneously. The local Cp values for both internal and external surfaces can be derivedusing appropriate codes and papers. The summed effects of the internal and external Cpvalues used are to be applied to the analysis model. Pressures need to be applied normalto the deflected surface.

Membrane structures that enclose buildings behave differently to open canopies since onlythe external side of the fabric is exposed directly to the dynamic wind pressure. Howeverthe internal pressure / internal suction has also to be taken into account. This will be sig-nificant when large openings in wall or roof are present. Consequently high internal Cp fac-tors can be expected.

With air-inflated structures the dynamic wind pressure due to wind loading acts only on oneside of the membrane, as the inflation equipment controls the internal pressure.

7.4.3 Cp VALUES FOR SMALL AND SIMPLY-SHAPED STRUCTURES

The building form described in the relevant codes will not usually match the form-foundshape of the membrane structure. Therefore when using these sources conservative assump-tions need to be made when considering the various possible configurations of Cp’s.Literature available for guidance includes:a) EC1 – Part 2.4b) BS 6399 Part 2c) DIN 1055 Part 4d) N J Cook, ‘The Designers Guide to Wind Loading of Building Structures – Part 2’ publ.

BRE/Butterworthse) Zuranski, Windeinflüsse auf Baukonstruktionen.

Examples of pressure distributions for typical tensile shapes are provided in Appendix A1.

7.4.4 Cp VALUES FOR OPEN STADIUM ROOFS

Examples of pressure distributions for a variety of Open Stadium Roofs are given inAppendix A2.

7.4.5 Cp VALUES FOR COMPLEX AND IRREGULAR FORMS, INCLUDING LONG-SPANSTRUCTURES

Wind Tunnel tests need to be used to derive Cp values when:

1. The membrane shape and form is sufficiently different from those described in the codesand available literature that a reliable estimate of the Cp values cannot be made.

Or

2. The conservative approach renders a complex structure too expensive to construct.


TensiNet


I 6 I

A wind tunnel test can investigate the local pressure coefficients and improve the reliabilityof the design loading. The majority of wind tunnel tests are carried out on rigid models thatdo not take into account changes in the applied pressure distribution due to deflection ofthe membrane surface. Hence rigid model tests are not the most suitable type for deflection-sensitive membrane surfaces, but generally the only option.

A more complex “aero-elastic” wind tunnel test to investigate dynamic effects, such as gal-loping and flutter, could be more suitable for such a structure. This would incorporate in themodel a surface that deflects in a similar way to the full size structure. However, these modelsare very complex to build and do not always provide very consistent answers. Currentresearch is attempting to assess the aerodynamic stability using coupled numerical analysisfor wind flow (Computational Fluid Dynamics CFD analysis) and structural interaction (FiniteElement Modelling FEM). However, their application to prove the feasibility of very soft mem-brane structures responding to wind will be an aspect for future research.

The wind tunnel should represent the appropriate atmospheric boundary layer to accom-modate gust effects including those resulting from dominant buildings and other obstruc-tions in the surrounding area.

Generally the wind tunnel is able to provide local pressure loads including Cp values,dynamic amplification factors and size effects. Their results are based on the following infor-mation provided by the structural engineer:

a) the structurally important mode shapes and their natural frequenciesb) maximum deflections based on established loadsc) load application areas (overall, secondary elements, cladding etc.)d) specific areas of interest for loads.


Fig. 7.2 Wind tunnel model stadium, © Wacker Ingenieure

I 7 I

The test results need to be filtered appropriately to find the most critical load cases for thestructure. The most critical wind load case for a membrane structure will not necessarily berelated to the mode shapes, which is often the case for more standard structures.

7.4.6 DYNAMIC EFFECTS

Typically the structural calculations will be undertaken using statically applied loads.However in rare cases dynamic effects of the wind may need to be considered.

In relation to “global resonant behaviour” membrane structures have low natural frequencies(Nf) and values of 1.5 to 0.5 are typical. However, due to their very low weight and their welldamped behaviour, negative effects like dynamic amplifications are very small and can beneglected in most cases. They are also commonly seen as lightly damped structures in termsof their structural damping ratio. However, tests on aero-elastic wind tunnel models1 parti-cularly for enclosed membrane structures illustrate a highly damped behaviour that does notcause aerodynamic instability. Similarly, for open sided structures it seems that a large degreeof damping is provided by the moving air volumes. For the estimation of dynamic amplifi-cation factors the wind tunnel experts assume damping ratios between 1.5% and 3%– neglecting aerodynamic damping. However, within the membrane structure industry highervalues of damping are thought to be appropriate as the composite nature of the material andthe crimp interchange between the yarns will naturally cause high damping due to friction.

Free membrane edges are susceptible to localdynamic issues. Care shall be taken with frontedges and membrane boundaries lying parallelwith the leeward exposed airflow, because the Cpfactors on these edges can change dramaticallywith only a small change in the flow’s “angle ofattack”. This effect is called “flutter” (figure 7.3)and occurs particularly in the naturally flat bound-ary areas or in edge areas with low tension in thefabric.The increased movement of the fabric surfacereduces the lifespan of the membrane and maywell disconcert the observer. To minimise theseeffects it is recommended to limit the free spansof boundary edge cables to not greater than 20m.


TensiNet

Fig. 7.3 Flutter along a freemembrane edge


I 8 I

Similar to all major design load cases, sufficient curvature of the membrane surface is thekey to minimising wind excited flutter, though high prestress values to stabilise flat mem-brane surfaces are sometimes an alternative. The following equation provides a good indi-cation of the stiffness available to react against applied pressure loads D measured off anequilibrated form-found model.

Nwarp = Prestress in Warp Direction (kN/m)Nweft = Prestress in Weft Direction (kN/m)Rwarp = positive Radius in Warp Direction (m)Rweft = positive Radius in Weft Direction (m)D = Stiffness of Surface (kN/m2)

Membrane structures with sound structural behaviour were typically found to have D greaterthan 0.3kN/m2. On some membrane surfaces, with D of around 0.15kN/m2 and less, it hasbeen observed that small travelling waves were excited on the surface by wind. Membranestructures having D < 0.2kN/m2 over large areas can show deflection-sensitive behaviour andmay require detailed investigation into the structural behaviour under environmental loads.

On pneumatic structures, such as air halls2, 3, 4, having low positive gaussian curvature andrelatively flat membrane surfaces, travelling waves can occur even under steady winds asthe internal pressure is often set low to reduce running costs. The stiffness of the surfaceD is for air halls equivalent to the internal pressure.

7.5 Snow

Ground snow load should be investigated using guidance from EC1. For long-span structures,it is recommended that the ground snow load be investigated using available data from thelocal meteorological office.

In areas not subjected to snow loads, a nominal uniformly distributed load of 0.3kN/m2

should nevertheless be considered. This figure may be reduced for structures with spansover 50m by applying a detailed statistical investigation accounting for loading by rain,fallen leaves, sand/dirt etc.


D ≈ Nwarp

Rwarp

Nweft

Rweft+

I 9 I

7.5.1 SNOW LOAD DISTRIBUTION

Snow can be deposited uponroofs under calm or windyconditions.

Under calm conditions aneven layer will tend to bedeposited over the entireroof. EC1 gives guidance onthe value of the coefficientsto be used.

Under windy conditions thesnow will tend to drift apply-ing an uneven loading to theroof. The nature of thisuneven loading depends onthe roof profile in the direc-tion of the wind.

In the case of a roof consisting of a series of ridges and valleys under windy conditions thesnow will drift away from the ridges into the valleys. EC1 gives coefficients for the peakamount of snow at the valley base and for the minimum amount of snow at the ridge. Thiseffect is difficult to predict and care must be taken.

Alternative possible load distributions need to be considered and design undertaken for themost onerous. The likelihood of numerous snowfalls compounding the load case also needsto be considered. In EC1 the concept of “single snow events” and “multiple snow events” areused. “Single snow events” occur in regions where there is a reasonable expectation that thesnow deposited on roofs will thaw between the arrival of one weather system and the next.

The wind blown snow loading to large wide-span structures can be modelled in a wind tun-nel or flume to predict the redistribution of the snow on the roof. It is generally assumed thatthe total snow load on the roof would remain the same but that under wind action snow maydrift in the valleys of the roof increasing the loading to those areas.

7.5.2 SNOW SLIDING

The effects of snow sliding over smooth surfaces into the valleys shall be considered. Therisk of snow falling from the roof and endangering people shall also be considered. Thereis a higher perceived risk with fabric structures since their smooth surfaces can effectivelybe lubricated by melting snow.


TensiNet

Fig. 7.4 Snow load distribution on conical membrane structure (foreground) and acrylicglass clad cable net roof (background) © Atelier Kinold


I 10 I

7.5.3 PONDING

As explained above, snow will drift and slideinto the valleys and towards the boun-daries. With a large snow load, the structuremay develop deflections such that a down-ward slope becomes reversed.

This can produce what is generally referred to as ‘ponding’ since the slope no longer allowsthe runoff of rain and melting snow. Due to the flexibility of the membrane, the retention ofrainwater and snow leads to larger deflections. This then leads to the further attraction ofrainwater and snow. Large loads are experienced and for this reason, ponding must beavoided in membrane structures. It should be demonstrated that the application of snowloads will not result in ponding. It is not sufficient to consider surface slopes purely in theprestress state since the geometry of the surface may change significantly under loading.

7.5.4 SNOW CLEARING

The procedures for snow clearance must be considered. Reduced snow loads can only beapplied where a “limiting depth” can be assured by a practical means of snow removal.Additional access loads may be larger than the snow load, but smaller structures allow alter-native means of clearing the snow.

One method is to use a hosepipe to wash down the snow after a snowfall. Another, which isoften used to clear the snow round smooth surface air halls, is to heat the internal surfaceof the membrane as the snow is able to slide off easily in all directions. All other methodsof trying to melt the snow have been found to be unsuccessful and unreliable.

7.6 Temperature

Temperature effects in respect of overall structural behaviour and load analysis are usuallyfound to be less significant on fabric structures when compared with rigid construction.Temperature change manifests itself in relatively small ± variation in prestress levels. However,temperature effects are more important for steel cable nets.


Fig. 7.5 Ponding Snow on Membrane Roof, Pennsylvania(by courtesy of Geiger Engineers5)

I 11 I

7.7 Seismic Loading

In general seismic loads are not a problem as membrane structures weigh so little and sowill not pick up substantial acceleration forces under seismic action. Should the structurecontain relatively massive components such as struts or connections, then these will be sub-ject to accelerations under seismic loading.

7.8 Construction Tolerance

The European codes for construction tolerances vary, but generally it can be said that thetolerances provided by standard concrete works are by no means sufficient to erect staticallyindeterminate structures upon. Therefore the tightest tolerances have to be chosen or struc-tural adjustment measures have to be taken to ensure the connection points (i.e. base plates,mast footing or wall connection) are accurate. Stiff structures or highly pretensioned elementsmay require high fabrication tolerances especially in the axial force direction, to ensure thatpredefined prestress forces and geometry of the structure can be confirmed. Sensitivity ana-lysis involving shortening or lengthening crucial structural elements can be used to definethe required construction tolerances for the base. The bases (i.e. grouted up base plates etc.)should be surveyed prior to installation of a membrane structure.

Further tolerances have to be expected within the membrane structure and cables. Themembrane surface, being less stiff, is usually more forgiving to small dimensional inaccura-cies than the cables.

In general the tension members of a cable structure do not allow adjustment of their lengthto compensate for fabrication tolerance. Hence the fabrication tolerance on the length of thecomplete assembly with end fittings is critical. Any error in cable length will result in diffe-rences between actual and design prestress forces within the cables once fully erected.

If the cables are generally shorter than designed then the prestress forces will be larger,resulting in:

a) possible overloading of cables when the structure is loaded

b) larger jacking forces required to connect the cables as the latter must be ‘stretched’ intoposition. The larger the diameter of the cable the greater will be the extra jacking loadrequired to stretch the cable by a given proportion of its length – hence the tolerance onlength of larger diameter short cables is more critical than smaller long cables.

Alternatively if the cables are generally longer than designed the forces will be smaller,resulting in:

c) cables may go slack when structure is loaded (or even in prestress-only state) giving alack of structural stiffness.


TensiNet


I 12 I

A typical tolerance on a cable cut under preload and with end fittings attached is:

Tolerance = ± (‹(L/1000) + 5 mm) where L is cable length in mm.

To achieve these construction tolerances the cables are typically cut to length under theirdesign prestress load. It is therefore important that the design prestress loads used areaccurate to the loads that will be in the cables in the erected prestressed state.

Not all cable manufacturers are able to manufacture to these tolerances and a structural sen-sitivity study would need to be done.

7.9 Load Combinations

To take account of the large deflections of membrane structures, analysis has to be madeusing unfactored loads. It is very important that the results of a load combination are foundby adding loads and then analysing, rather than analysing each load separately and thenadding the results.

The prestress and self-weight loads should be part of all load cases. This is a deviation fromthe EC Codes as the self-weight of the membrane need not be reduced for wind uplift casesas it is negligible.

Example load cases to be considered:

a) self weight + prestress b) self weight + prestress + snow c) self weight + prestress + windd) self weight + prestress + wind (downward pressures) + snowe) etc.

The load combinations should generally be applied in accordance with the national appli-cation document of EC1 neglecting the partial safety factors on the loading as described inChapter 6. However, for load combinations including multiple imposed live loads (i.e. winddownward + snow) one of the applied loads might reasonably be reduced.

7.10 Disproportionate Collapse

The design of membrane structures to avoid disproportionate collapse should be considered.

Once the likely failure modes have been identified the membrane structure will need to bemodelled in the partially failed state in order to prove that further failure and collapse willnot occur. This situation can be considered to be an additional load case although theanalysed models will obviously be of the variously identified partial collapse states. In theseloadcases, the Factor of Safety (F.o.S.) on the materials may be reduced from those used inthe main loadcases.


I 13 I

REFERENCES:

(1) H.P.A.H Irwin R.L. Wardlaw – “A Wind Tunnel Investigation of a Retractable RoofFor The Montreal Olympic Stadium”, The Second Canadian Workshop for WindEngineering, Varennes, Quebec, Sept. 1978.

(2) British Standards Institution BS 6661: 1986 Guide for the design, constructionand maintenance of single skin air-supported structures, (withdrawn 1997).

(3) L. Mabon and C.J.K. Williams – Proceedings of conference on “Wind-Over-WaveCouplings: Perspectives and Prospects”, Salford, April 1997.

(4) IL University Stuttgart and School of Arch. And Build. Engineering UniversityBath – IL 15 Air Hall Handbook, August 1983 ISBN 3-7828-2015-0.

(5) D.M. Campbell, “Snow induced ponding of Textile Membrane Roof Structures”,TensiNet Symposium Designing Tensile Architecture, sept. 2003,ISBN 9-789090-173443.


TensiNet


I 14 I European Design Guide for Tensile Surface Structures

Documents

07_TensiNet