Moderné vzdelávanie pre vedomostnú spoločnosť/ Projekt je spolufinancovaný zo zdrojov EÚ Aktívne využitie modelovania so softvérovou podporou pri rieš

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1 Moderné vzdelávanie pre vedomostnú spoločnosť/ Projekt je spolufinancovaný zo zdrojov EÚ Aktívne využitie modelovania so softvérovou podporou pri riešení výskumných úloh modul Inžinierske konštrukcie a dopravné stavby Stavebná fakulta doc. Ing. Michal Tomko, PhD. Ing. Peter Vernársky 1

2 Táto publikácia vznikla za finančnej podpory z Európskeho sociálneho fondu v rámci Operačného programu VZDELÁVANIE. Opatrenie 1.1. Príprava študijných materiálov a realizácia metód do študijných programov pre ich zatraktívnenie Názov projektu: Balík zlepšení kvality TUKE prostredníctvom sietí ITMS Názov: Aktívne využitie modelovania so softvérovou podporou pri riešení výskumných úloh modul Inžinierske konštrukcie a dopravné stavby Autori: doc. Ing. Michal Tomko, PhD., Ing. Peter Vernársky Vydavateľ: Technická univerzita v Košiciach Rok: 2015 Vydanie: Prvé Počet výtlačkov: 10 Rozsah: 21 Rukopis neprešiel jazykovou úpravou. Za odbornú a obsahovú stránku zodpovedajú autori. 2

3 Úvod Cieľom tohto učebného textu je priblížiť študentom Stavebnej fakulty možnosti moderného a progresívneho riešenia membránových a pneumatických konštrukcií s využitím komplexného softvérového balíka EASY. Novodobý trend stavebných konštrukcií je zameraný na efektivitu výstavby, architektonickú kompozíciu pri znižovaní finančnej náročnosti na celkové stavebné dielo a na zefektívnenie stavebných prác. Neustály posun vpred v oblasti vedy, techniky a informačných technológii, predurčuje efektivitu projekčných prác, aplikáciou sofistikovaných programových balíkov, ktoré dokážu minimalizovať vznik chýb a celkovo spresňujú výsledný projekt stavebného diela. V tomto učebnom texte sa zameriame na teóriu a prax pri využívaní softvéru na nelineárnu statickú, dynamickú, tvarovú a strihovú analýzu predpätých membránových nosných sústav. Problém ľahkých stavieb, teda stavieb, ktoré dokážu prenášať dané zaťaženie, pri menšej vlastnej hmotnosti ako klasické konštrukcie, si vyžaduje pomerne citlivý a presný prístup. Ako pri každej stavebnej konštrukcii, aj pri membránových či pneumatických konštrukciách, existuje množstvo zjednodušených riešení, napr. metóda prútovej aproximácie. Tieto metódy sú pomerne presné a dobre využiteľné, ale na druhej strane sú veľmi náročné. Z toho dôvodu je lepšie voliť špecializovaný program na výpočtovú, ale aj na projekčnú časť úlohy navrhovania predpätých membránových či pneumatických konštrukcií. Medzi najkomplexnejšie programy v tejto oblasti patrí program EASY. Program obsahuje moduly, ktoré zabezpečujú možnosť navrhovania konštrukcie od form-findingu, cez statickú a dynamickú analýzu, až po konečné strihové plány použitej membrány. Výsledný efekt je spracovaný vo forme prehľadných a pre prax použiteľných výstupov. Program umožňuje riešenie samostatných membrán bez alebo v kombinácii s tuhými prvkami v tlaku, ťahu alebo v ohybe. V prípade špecifických požiadaviek alebo v prípade nedostatočného pokrytia riešenej oblasti programom EASY, je možné aplikovať plynulé prepojenie programu EASY s programom DLUBAL. Takto fungujúce prepojenie dvoch programov zabezpečuje dostatočne široké pokrytie aj pre náročných užívateľov alebo v prípade náročných a komplexných úloh, ktoré sa v stavebnej praxi bežne vyskytujú. Program sa zameriava na jednoduchosť a intuitívnosť ovládania, s čím sa zabezpečuje zvýšená efektivita práce a presnosť. Tieto poznatky sú aplikované so zreteľom na požiadavky praxe a taktiež na požiadavky vedeckej činnosti v tejto oblasti. Dalo by sa povedať, že program je výsledkom spolupráce inžinierov z praxe a inžinierov zaoberajúcich sa výskumom membránových a pneumatických konštrukcií. Na Stavebnej fakulte TUKE je tento program využívaný pri vedeckých prácach so zameraním na teóriu a navrhovanie inžinierskych konštrukcií. Využíva sa na predbežné analýzy a na stanovenie počiatočného tvaru membránovej konštrukcie. Program je skôr orientovaný pre prax ako na vedeckú činnosť, z toho dôvodu slúžia výstupy z programu EASY ako vstupné parametre do ďalších, vedeckých programových balíkov. Tento fakt, možnosť použitia výstupov pre vedecké účely, poukazuje na vysoké kvalitatívne vlastnosti balíka. Program je dostupný v anglickom jazyku. Z toho dôvodu je návod k tomuto programu predkladaný tiež v anglickom jazyku. Návod sa zaoberá teoretickým popisom metód výpočtov, ktoré program realizuje. Popisuje možnosti jednotlivých dostupných modulov a charakterizuje oblasť ich použitia a aplikácie na niektoré základné tvarové typy membránových konštrukcií. 3

4 1 INTRODUCTION The design of free forms, the statical analysis and the subsequent cutting pattern generation is guaranteed by the software. Easy is a fully comprehensive suite of software modules for the complete design of lightweight structures. Due to the engineering system Easy you'll find the optimal software solution for planning, design and calculation of lightweight surface structures. Easy is the market leader in the domain of lightweight surface structures planning and design. The sketch of free shapes, the static analysis and cutting pattern calculation for textile membranes and ETFE foils are supported in the Easy system. The simultaneous calculation of membrane or ETFE foil with stiff primary structure elements generally made-of steel ensure an economic and efficient material usage. The calculation of pneumatic structures like airhalls or foil cushions can be done with Easy very user-friendly: The possible allowance of different types of physical laws affords the accurate evaluation of the required material usage, which hence becomes optimal. 1.1 EASY A COMPLETE SYSTEM FOR LIGHTWEIGHT STRUCTURES The Easy program system is composed of 5 modules: Easy.Form: Formfinding is a process to evaluate the geometry of a stressed surface: it is only required for lightweight surface structures, 4

5 because a separation of geometry and physical behavior isn't possible. The geometry of conventional structures can be defined by an architect at the drawing-board. In Easy.Form a stress harmonic surface will be configured under consideration of user-defined conditions. Easy.Stat: The function of the static analysis is to materialize the surfaces created by the Formfinding process (i.e. To assign material properties to the membrane), to consider the external causes resulting of the statutory provisions (e.g. Self-weight, wind and snow loads) and to calculate the inner stresses and deformations: Thus the stability of the overall structure can be verified. Easy.Cut: The cutting pattern generation is a task which is well known in a similar way from map projection. The map projection doctrine treats the projection of the earth into plane maps. In the cutting pattern generation of fabrics the three-dimensional surfaces being in equilibrium are also projected into a plane; here too distortions should become as small as possible. Easy.Beam: Only a combined calculation of beam structures together with prestressed textile surfaces (respectively cable nets or foils) guarantees an efficient and optimal utilization of all cross-sections. The separation of static systems into subsystems for lightweight surface structures with non-linear behaviourproduces in general wrong results. The simultaneous calculation of the complete system in Easy.Beam is the only correct method for this circumstance and optimizes resources. Easy.Vol: The calculation of pneumatic structures is characterized by pressure which affects the surface permanently. This pressure must be included in all calculations. In the Formfinding process it plays a decisive role as shape giving factor. In the statical analysis it is effective together with all the other parameters: due to the fact that the pressure can change in case of extraneous causes, physical gas laws are essential for exact modelling. RSTAB:Easy determines all internal forces and designs the membrane. When designing the supporting understructure, RSTAB and the respective add-on modules come into play. By means of an integrated interface, the entire model inclusive of the internal forces is transferred to RSTAB. In this program, the stress design and, if necessary, the evaluation of stability can then be completed. As the rigidities can have an enormous effect on the forces in the membranes, the optimized cross-sections of RSTAB have to be transferred to Easy for a new calculation run. This iterative process ensures that the model is close to reality. RSTAB also serves as a tool to document the design results graphically and numerically. RSTAB is a software product of Dlubal GmbH, Germany. 5

6 Summary Easy.Form comprises the programs used for data generation together with force density form-finding. When the Easy.Stat programs are additionally installed structural analysis of non-linear structures becomes possible, these are limited to membrane elements, cables and struts. If bending stiff elements should be added to the calculation of the overall system Easy.Beam will be required. The Easy.Cut functionality enables the generation of high quality planar cutting patterns from Easy.Form output. Easy.Vol is used for pneumatic structures. For designing the supportingstructure, RSTAB from Dlubal GmbH can be used. 6

7 1.2 COMPANY PROFILE Technet GmbH is a company that provides both software and consulting to its clientele. For engineers, we offer solutions in the areas of lightweight structural design, integration of Geo-Data, engineering surveying, photogrammetry and surface analysis. Our know-how comes from the extensive experience in surveying and mapping, civil engineering, computer sciences and physics. Since being founded in 1988 technet GmbH has developed into a worldwide operating company. In addition to the headquarter in Berlin we have satellite offices in Stuttgart and a representation in Beijing. Our intention is to ensure sustainable success to our customers through continued development of our products. The competitive advantage of our customers takes center stage in our efforts. The customers of technet GmbH are planners, architects, land surveying offices and authorities from more than 40 nations worldwide. 1.3 THE EASY-TEAM Program coordination, programming Dr. D. Stroebel Dr. P. Singer Dipl. Ing. J. Holl Consulting Prof. Dr.-Ing.Dr. h.c. L. Gründig Programming Dipl. Ing. (FH) A. Stark Dipl. Ing (FH) B. Simmler Program supervision Manuals - Help system Dipl. Ing. U. Gründig-Tsoukalas Dipl. Ing. U. Keck-Maute Technical support and training Dr. D. Stroebel Dr. P. Singer Dipl. Ing. J. Holl Management, administration and sales Dipl. Ing B. Aschoff Dipl. Geogr.(FH) M. Müller-Kolbe 2 A SHORT HISTORICAL OVERVIEW The theories being used in the Easy system are related to a lot of persons. Here are some of the most famous ones, for which publications may be found in all libraries. Material law 1660 Hooke First geodetic networks 1800 C. F. Gauß Law of stress and strain 1800 Kirchoff Principal of minimal energy 1875 Castigliano Adjustment theory - statical analysis 1903 Finsterwalder Net of distances - elastically systems 1961 Linkwitz Topology description of networks 1963 Fenves, Branin Method of Finite Elements 1965 Argyris, Zienkiewicz Numerical Methods 1976 Schek, Gründig Additional research in this field was done especially at the Technical University in Stuttgart, Germany. The famous institute IL (Institute of Lightweight structures) of Frei Otto founded the well-known Sonderforschungsbereich 64 Weitgespannte Flächentragwerke (SFB 64) in 1970; this was a group of architects and engineers focusing the aim to increase the knowledge of lightweight structures with respect to theory and practise. The Olympic Games took place 1972 in Munich, Germany; the Olympic Stadion was covered by a cable-network offering an excellent possibility to the SFB 64 to gain experiences with the design and practical realization of a big lightweight structure. The design of this roof was done empirically, and also a model (scale 1:125) was built. The coordinates of the model s surface has been measured with the highest accuracy by means of photogrammetry. The results of this measurement were used as starting values for the nonlinear Formfinding procedure and also for the statical analysis. Because of the fact, that this procedure - physical model and an additional very precise measurement - is in general too expensive, theories for an analytical Formfinding were tried to develop. Schek and Linkwitz finally found an analytical method, later on known as Force-Density-Method. Gründig improved and implemented this theory in a software tool. The SFB 234 Natürliche Konstruktionen - 7

8 Leichtbau in Architektur und Natur ( ) - also located in Stuttgart generated new ideas and concepts concerning the lightweight structures. 3 THE EASY SHELL 8

9 3.2 MODULES 3.3 CALCULATION PROGRAMS 9

10 3.4 4 EDITORS BASICS The next paragraph will explain some basics in membrane construction. 4.1 STRUCTURAL BEHAVIOUR Membranes have a special structural behaviour. The material is flexible and only tensile forces can be carried. We have to use the membrane in a way that loads can be transferred only by tensile forces. This can be achieved by a double curved geometry and the introducing of prestress. 10

11 4.2 ANTICLASTIC AND SYNCLASTIC FORMS How can prestress be introduced to a membrane? Mechanically,which leads to an anticlastic form. The two principle curvatures are opposite. This form gets its stiffness through its anticlastic form. Pneumatically supported, which leads to a synclastic form. The two principle curvatures are equal oriented. This form gets its stiffness through its synclastic form and the inner pressure. 4.3 FORMS OF PRESTRESSEDMEMBRANE STRUCTURES Some remarks to the forms of membrane construction: Membrane structures are form active. There is a direct relationship between form and force distribution and the forms are figures of equilibrium. The internal forces and external forces are balanced. Which forms can be designed and how can we influence the forms of membrane structures? Figure 18 shows the possibilities to influence the forms of membrane structures. Where are the support points located? How is the boundary defined? How is the orientation of the warp and weft direction of the fabric set? How is the prestress set? 11

12 4.4 PROTOTYPES Two criteria are mainly responsible for the shape of the form: Arrangement of the boundary: The boundary can be flexible or rigid 4.5 Support of the surface: It can be selective by points, linear by cable or arch, areal by pressure MODELS To study the appearance and to control the shape of the covered space, as well as defining the precise geometry for calculations and cutting patterns we need three dimensional models.this can be a physical model and/or a computer model In the case of computer models a formfinding procedure is needed. Easy.Form calculates the figure of equilibrium with the force density method. It is a linear calculation method which finds the result in one calculation step without starting values. 12

13 4.6 FORCE VECTOR DIRECTED ALONG A LINE FORCE AS A CARTESIAN VECTOR r r F is the force which is directed along the cord AB. We can formulate F as a Cartesian vector r by realizing that it has the same direction and sense as the position vector rab directed from point A to r point B on the cord. This common direction is specified by the unit vector u 13

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17 5 FORMFINDING Opposite to the design of conventional structures a formfinding procedure is needed withrespect to textile membrane surfaces because of the direct relationship between form and force distribution ( form follows force ). In general there are two possibilities to perform the formfindingprocedures: the physical formfinding procedure and the analytical one. The physical modelling of lightweight structures has limitations with respect to numbers for the coordinates of the surfaces: a scale problem exists. Therefore the computational modelling of lightweight structures becomes more and more important; without this technology lightweightstructures cannot be built. 5.1 FORCE DENSITY METHOD - BASIC PRINCIPLE The Force Density Method is a mathematical strategy for solving the equations of equilibrium for any type of cable network, without requiring any initial coordinates of the structure. This is achieved through the exploitation of a mathematical trick. The essential ideas are as follows: 6 COMPARISON OF THE TOPOLOGY AND THE RESULT OF THE FORMFINDING PROCESS For a comparison of the prepared topology and the result of the formfinding you have to add the result of the program ZUSN (zusn.ein) to the graphical editor GED. Select File/Add/EIN File in the graphical editor GED to add the file zusn.ein to the existing file fofin.ein. 17

18 The file zusn.ein shows a flat net structure (geometry) with the defined fixed points, fofin.ein shows your membrane structure as a figure of equilibrium (result of the formfinding process) calculated with your special parameters. 7 GENERATING SURFACE ELEMENTS The generation of surface elements is not necessary for the formfinding calculation but it will later be used for the statical calculation or for the calculation of the surface areas, contour lines, etc. after the formfinding process. The surface elements are calculated with the program LOOP2D and with the program PUTZ: 18

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20 8 STATICAL ANALYSIS WITH EXTERNAL LOADS After the Preparation and the calculation of the Statical Analysis without loads, the Statical Analysis for each load case can be achieved as follows: Create a new loadcase (e.g. snow, wind,..). Enter the load data and calculate the external load vectors. Perform the nonlinear Statical Analysis. The approximate values, which are needed in this nonlinear process, are given by the formfinding result. 9 CREATE LOAD CASE NEW(4) To create a new loadcase we can use the Easy Expert. Each loadcase will create a new subdirectory called load case name in your project folder. In this example a loadcase with four different load zones is calculated. You will find the results of the Statical Analysis withloads in the Easy installation folder..\ EasyTrainingProjects\ Example 2\new(4). Right click (context menu) on the loadcase button in the Easy expert and select Add new load case

21 Export the model and the load case data to Rstab. Make sure that the previous Rstab window is closed before exporting. Check critical cross sections and links. 10 WIND LOAD Click Loads] New Load Case. The New Load Case tabsheet opens, fill in the name of the load case wind and select a DRE file, then click OK. Edit the load case, click Loadzones on the Project Explorer panel left side then select loadzone 1 on the Project Explorer panel right side. Click Focus on the Parameters panel, select wind load, wind direction should be y-axis, select mode of loading area load. Fill in a wind load value of 0,1kN/m², and then Start Loadgen. The loadvectors are calculated. Click Create and load Result on the toolbar. Now the form of equilibrium of the model under wind load is visible on the View panel. Check the program report of Beam3D on the Console panel. Be sure that your model is in balance! Check the residual for forces value if the value is still larger than your stop criterion value in Beam3D Parameters, increase the number of iterations. 21