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## The variant analysis of the planetary dome

### Paweł Pestka

#### Abstract

Domes have been used in buildings and architecture since the ancient times, mainly to cover temples and palaces. Probably the oldest example of using domes is igloo, which is a construction made of snow, usually on a circular base, widely known among the Inuit Indian tribe. The most known domes built hundreds years ago in Rome are: Pantheon (built in year 125 B.C, the diameter of the dome is 43.3 m), Saint Peter's Basilica (the diameter of 42 m, hight of 52 m, built in year1547 A.D) as well as Hagia Sophia in Istanbul (of the diameter of 32.6, high 52 m, built in the years 532-563 A.D.) The materials used in that times were most often stone blocks and ceramic materials. The oldest known nonreinforced concrete construction is abovementioned Roman Pantheon. In modern times instead of such constructions we use mainly steel or reinforced concrete construction. There are mantles, frameworks and gratings made of reinforced concrete. They are often used as planetary or hall roofs. The most interesting one is geodesic dome frameworks. The geometrical shape of geodesic dome is used in various architectural constructions as it is attractive and self-supporting (they do not need external pillars). Some examples of using geodesic domes is Złote Tarasy in Warsaw. In the PROJECT part of this paper I will present a steel construction of such dome. It has the diameter of 40m and the hight of 20m and it is used as a planetary roof. In case of this type of construction the way they look is very important. The dome after constructing it and covering it with galvanized sheet will look extraordinary. Such attraction will have a great chance to win many planetary visitors. Pipe bars were used to construct a special assembly which enables us to regualte the lenght of bars and their angle. Such construction allows an easy and fast installation at the construction site. The construction elements (on condition they are not damaged) can be used again. Also repairing such construction is easier that in case of welded bars. The technical instruction infroms us how the bars should be installed and how the elements should be located. Not fulfilling these instructions may make the whole construction not stable. It is very important to install the bars correctly as here negligence can also cause instability of the construction.All works need very detailed supervision. Constructing elements are shown on technical charts.The dome consists of 525 bars of diameter of 88.9 mm and lenght (theoretical) from 3.81m to 4.33 m. The total weight of the whole construction, the roof weight and ceiling, pressure caused by wind and snow were included in the calculations. The dome is built in Płock. In the part ANALYSIS the power of mantle was calculated with the pressure of wind and snow. The calculations were made basing on the membrane state of stress. Next the construction of the dome, in part PROJECT of this paper, was slightly changed. Finally both domes, the one before changes, and the one after the changes, were compared as to assess how much they differed (see tables and charts). I also wanted to find out if there is a way to calculate the powers in the dome with the same method as for the membrane state of stress. In Conclusions I proposed the way how to create such a method, as well as I discussed the results of my assumptions on the results of the calculations made onassumptions of the membrane state of stress. Many data calculations in this work needed very advanced mathematical instruments. Therefore the paper includes the description of the way I prepared the charts and tables. There are also chapters where I explain, step by step, all used mathematical instruments and mathematical patterns.
Record ID
WUTebb3f0e73f4a4df0a35d251f576a8840
Diploma type
Master of Science
Author
Paweł Pestka Paweł Pestka,, Undefined Affiliation
Title in Polish
Supervisor
Andrzej Dzięgielewski (FCEMP/ICEn) Andrzej Dzięgielewski,, Insitute of Civil Engineering (FCEMP/ICEn)Faculty of Civil Engineering, Mechanics and Petrochemistry (FCEMP)
Andrzej Dzięgielewski (FCEMP/ICEn) Andrzej Dzięgielewski,, Insitute of Civil Engineering (FCEMP/ICEn)Faculty of Civil Engineering, Mechanics and Petrochemistry (FCEMP)
Certifying unit
Faculty of Civil Engineering, Mechanics and Petrochemistry (FCEMP)
Affiliation unit
Insitute of Civil Engineering (FCEMP/ICEn)
Study subject / specialization
, Budownictwo
Language
(pl) Polish
Status
Finished
Defense Date
17-01-2012
Issue date (year)
2012
Keywords in Polish
planetarium, kopuła, analiza porównawcz
Abstract in Polish
Celem niniejszej pracy jest przede wszystkim wykonanie analizy (porównania) wyników obliczeń statycznych uzyskanych dla różnych schematów statycznych konstrukcji nośnej kopuły przeznaczonej do budynku planetarium, z jednoczesnym zaprojektowaniem tej konstrukcji. Porównaniu będą poddane wyniki uzyskane dla przypadków obciążeń o zbliżonym rozkładzie na powierzchni kopuły. Ma to na celu sprawdzenie w jakim stopniu założenie błonowego stanu naprężeń opisuje bliski prawdziwemu (Autodesk Robot Structural Analysis Professional 2009) rozkład sił w konstrukcji prętowej kopuły. Konstrukcją tą jest kratownica przestrzenna nazywana kopułą geodezyjną, której osie prętów i węzły pokrywają się z krawędziami i wierzchołkami półsfery geodezyjnej szóstego stopnia stworzonej na bazie dwudziestościanu foremnego, a wpisanej w sferę o promieniu o średnicy 40m. Rozważony również został wpływ reakcji jakimi na skutek danego obciążenia odpowiada podpora kopuły na wartości obliczonych sił wewnętrznych.
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Pestka Paweł p. magisterska 669.pdf
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Uniform Resource Identifier
https://repo.pw.edu.pl/info/master/WUTebb3f0e73f4a4df0a35d251f576a8840/
URN
urn:pw-repo:WUTebb3f0e73f4a4df0a35d251f576a8840

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