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Hi, everyone Welcome back to NPTEL online course on Structure, Form, and Architecture: The Synergy Today we are at Lecture Number-24 and we will be talking on Dome Structures So, in the last lecture we have seen types of vaults, their use, the fundamentals and we also came to know about the construction of a vault, it is basically a series of arches Now in this, we will also get to know about the evolve of that particular dome and it is again in this case like we have to take an arch and then we revolve it So, we just rotate it 360 degree we can get to the shape or else we can just cut a hollow sphere and we can get it So, we will get into this a dome and we will try to understand the materials, the use of that, different components of a dome, the purpose of using dome and then different types with some images ,some examples So, let get started this lecture So, this is a very introductory slide So, if you just search dome, the first in the Google so, what exactly the definition you will get from the dictionary.com it is a rounded vault forming the roof of a building or a structure typically with a circular base So, what exactly it is like a rounded vault is basically when we create this space it is the vault even the cross-arch vault is being represented like a dome and then it is normally being used and the circular base So, in this circular base I take a rise this is one arch and I just revolve it 360 degree So, multiple arch like this we just tried to create and then basically whatever the form will get that is the dome Like this is some example that is there with us; so, this is if you just try to simplify it So, it is some dome not really having a very semicircular, hemispherical dome So, like there is some other components added So, we will come to that as well Now, here you can see a crystal dome in this So, dome is an architectural element that resembles hollow upper half of a sphere So, that already explained Starting from a prehistory to the modern age, dome have been constructed using mud, snow, that we cannot ignore the construction of igloo that is basically the dome structure, then wood, brick, concrete, metal, glass, plastic and now like anything Even we all have played with the plastic ball or some kind of a cricket ball So, if you cut this that will be a solid dome, but we all are aware about this particular form So, dome is formed through revolution of an arch, self-supporting, stabilized by the force of gravity acting on their self weight hold them in compression Useful to cover the large span, it is again the same So, starting from the dome that we can see in Taj Mahal or maybe the dome that we have seen in Pantheon in Rome So, it is basically helping us to have a column less structure So, vault doing the same purpose, but for the corridor or maybe an area of that kind, but dome being used for a larger span The dome load transfer: how it transfers the load so, let us understand this And, here you get a schematic and corresponding color will have the indication the type of force that it is dealing with So, the component that we have is basically these meridional portions So, this are your meridional component of your dome and that is taking the compression So, basically if you take one a plastic ball or something a ball made of a light material

and you try to put the pressure from the top so, these fibers are always in compression Then, what you have the upper loop so, upper loop they will also try to compress So, they will also be in compression, but the bottom surface when you press it ok The bottom surface will always try to go away from each other and they that is why it is in tension and then the vertical and lateral loads transferred to the down So, this what we can compared with your latitude longitude similar kind of thing so, you have a series of compression and tension which can be dealt with the dome So, this is one example that I picked up This is a dome made of some temporary wood and then the grass or something It is very old a kind of practice to make this kind of structure, but the overall form is again a dome shape So, it is basically giving you a volume as well as like you do not need to really give much support in between Move on So, this is some famous example and I am repeating this example in many cases because it is worth of repeating of its many features We can explain many things with this the use of like this lighting is one component, but here the intention is to show you the dome So, this dome is basically the dome for the pantheon and then here like it can accommodate the gathering So, this is being used to have a like column less space This is something really, I need no explanation the beauty of it, the aesthetics of it and the centralized dome So, basically this is a type of dome we refer as the onion dome, we will come to that when we discuss it So, this is another application of the dome This is your Hagia Sophia So, here also you can see the series of domes in a different pattern So, time to time from the history to the modern, the pattern of dome, the ornamentation of dome it differs And, in the modern age also we can have something which is a pneumatic dome; that means, somewhere we also discuss; the typology the pneumatic means it is filled with the air and then create a form of a dome This is another example of a dome but here you can see that instead of your lattice and the hoop you have something different like a triangulation of that multiple triangles they form it So, this kind of form is also called geodesic dome So, we will also discuss this when the type of domes will be discussed in upcoming slides Now, coming to the elements of dome so, here you have some information which are little bit not similar to the vault component or arch So, we have coffer, we have cupola, lantern, oculus, rotunda, tholobate, pendentive, then squinch and whispering gallery So, what exactly they are? Though the names are little bit difficult to remember I know, but looking at the photo we will try to identify what exactly and I am sure that we can really get idea with the some of the forms and the names and the what exactly it means So, before that in this, it is very simple So, the lantern is the upper part that initial picture that I have shown here at the very beginning slide so, this particular portion is now referring as your lantern it is similar to that and not only looking at the shape, but it has a function as well So, this will be used to create some puncture So, light can enter to this and then the interior can be getting some daylight So, like when we have a lantern something like this, we hold it and then there is a lamp So, we can get the light it is something like that The cupola is the similar kind of thing that we will do and this is basically when a dome to be placed on a part of a cylinder So, this is basically the drum shape Then whenever you have to change like you have to place a different kind of dome on our square base So, you have to make changes at that junction So, pendentive will be formed and squinch of arches that will be formed

So, let us try to discuss it Now, coffer is basically the series of sunken panel So, this is basically what you can see in order to reduce the volume of the self weight of the dome, we can also have something like this So, this is basically the coffer, sometimes we call in this case it is the component is called the coffer part of that, we also refer as the coffer ceiling So, then where we can really reduce the volume of the concrete So, suppose this is a solid section and then if you use the coffer slab is basically something like this So, looking at the load it can carry so, we can reduce this volume So, this is basically the cross section I am referring So, it being used in the modern building Also, the coffer is the terminology to just represent the series of sunken panel Then cupola is basically what we can relate with the cup So, the shape if you just put the cup in this position, something like this, so, it is the small most often dome like a structure on top of the building So, something like this you just put on top of it So, in many buildings like where you have a very similar route pattern and top of that you can use this Move to that the lantern cupola used to allow the daylight it is a similar thing that the top of each the cupola in this case having the transparent glass so that daylight can easily enter And, not only the daylights sometimes even at nighttime, it can get a good lighting, some ambience, good view of this particular building Now, coming to the oculus this is where the circular opening in the center of a dome or a wall So, that we can see in again the example this is basically the view recreated from again the pantheon and this particular puncture So, if you go back to the example of this so, this is basically the oculus Now, what is Rotunda? Rotunda is basically any building with a circular ground plan and covered by a dome So, in state of many buildings you will find that a dome is placed at the center So, that it will look like something like these or maybe if you use some drums so, it may look like this But, here it is the same where the plan is itself a cylindrical form or it is basically the whole volume is a cylindrical form and the plan is circular So, you can see if you just try to make the drawing of this is a circular plan and then in top of it you have this Then, coming to the tholobate, it is the upright part of a building drum like on which dome is raised So, this portion is a basically the tholobate., this is basically also alternatively that we have seen it is called drum So, pendentive is basically constructive device which allows the placement of a circular dome on a square room So, basically if you have a like some room like this and when you place the dome on top of it So, it is basically you can take the midpoint of that, you can make the circle and you can make the dome, but now this particular portion to be managed So, in that case what we can do? We can just take out those material or we just create the portion, we transform that portion and this particular puncture where form you will take out the material that will be pendentive So, this is basically the pendentive be created Where the squinch is something were construction filling in the upper angles of a square room to form a base to receive a dome So, again here some things we have to fill so, that is the squinch Whispering gallery is something where it is a circular or hemispherical enclosure often beneath the dome ok So, it is basically a area where you can stand we have where we can you can go and which will help to whisper and if you just make a noise in this and that will take a surrounding sound and you can stand here and listen to this So, this is being there even in India this kind of things we can observe in your Gol

Gumbaz in South So, if you have visited that also you experienced this or else in upcoming days if you plan to visit you can get it and this is something which is also a part of a dome sometimes where we can create this kind of scenario Coming to the materials, so, as I already mentioned it can be mud, it can be snow, it can be brick masonry, it can be stone masonry, wood, concrete or steel and in this case you can see this being created a temporary dome being created with a bamboo So, this is how beautifully they have been creating it and this is igloo being formed with the comprised block and then this dome been created Now, the types of domes So, go to different search you will get different kind of list of the dome The my point is here I have a specified the domes which are very popular in nature, but definitely there will be some addition to this list and I will be happy listen from you if I just missed out some of the dome and you can add on to this particular list So, it started with the corbelled dome, crossed-arch dome which is also like the ripped vault that we discussed; the geodesic dome, onion dome, oval dome, rotational dome, saucer dome, this is really interesting, umbrella dome, cable net dome, inflated domes So, what exactly they are and how to really remember? So, I will try to just relate with the terminologies So, let start with the corbelled dome So, corbelled dome is basically where we put the layers of your brick or stone one after another ok And, then we just take some kind of offset and we just create this type of hollow space inside So, the more offside view it will look very like pyramidical shape, but if you reduce this particular space between two layers So, definitely it will give you the form of a dome So, this is something a very old kind of structure where without any mortar this being created and here it is something where in a temple this being again created to make a circular form and final ornamentation is a different thing, but basically out is the same So, we take the span, we have like a particular cylindrical form and all So, we just try to feel the first layer, then the second layer, third layer, fourth layer So, likewise we will go for this kind of corbelled dome Now, the crossed-arch dome is basically where it is the similar that we have seen that multiple arches they are creating an octagonal shape or sometimes even more arches will give more polygonal shape and then this is being supported with some kind of wall or something So, this dome being created is the crossed arch dome So, this one is one of the earliest types of ribbed vault rips instead of meeting the dome center are intervened to the polygons that we have also seen in that ribbed and clustered vault Coming to the geodesic I have shown you one example a lit take this example this is as a model where like triangle being placed one after another to create this kind of form Another example that I can give you the formation of the dome that many of us we also like played football or maybe we watch football So, football if you see like basically it is a sphere ok, but in formation of this what we need? We need pentagons and then we need a hexagon So, with one pentagon so, we just create the five hexagons and like that we create the this particular curvature But, instead of that if you use the triangle and we can just create this kind of volume So, this is also very popular nowadays many such steel structure, geodesic dome being created So, sphere like structure consistent of a network of different triangles provide a self-balancing between the structures This is very useful; these joints are how it is being made those are very crucial so, firm anchor how it is being placed to form this So, the application of this kind of dome is quite modern and there are many examples that we can come across So, this is one of them Coming to the onion dome is the easiest thing to remember we all know the onion and the

shape is something like this So, this is a white onion So, the color may vary, but this shape I just place it here Earlier I have given an example of Taj Mahal Now, this is something like this Even if you take example of the Disney Land so, there also you get this towers and then the form is something like this Even we have something seen in those documentary video of Aladdin or some Disney movie So, this is something where we can get it So, this is basically the cathedral domes from Russia so, where the form is being easily visible So, it is look like a golden onion, but yes this can also be used as a form Coming to the oval as it is coming from in the shape of an oval so, like something like this So, here sometimes for some interior space the change, the plan in state of a circle, the profile is the oval So, basically an oval dome may be defined as a dome whose plan or profile has an oval form The geometry is defined as using combination of circular arch that transition at tangential points So, basically in this case we have to reduce it like this So, that we will finally, get the oval form on the series of oval So, this is one oval, this is another one and this been connected to that sub plan here it is basically a wall and then on top of it we have this So, this is oval Now, coming to the rotational dome It is basically where I have started like we take with one particular circular form and this is center you take a rise then you take one arch and then you try to revolve it 360 degree So, after revolving whatever you will get is basically a hemisphere spherical dome if you take this arch and the rise in that panel So, it is basically the half cut of a sphere So, it is something the example that is from the dome of the Jerusalem Rock Shrine So, here it is example of the rotation So, rotating arch So, if you find that if these are visible of few of the arches merging to a particular point if you increase more So, basically it is starting from a point and ending to the same point the revolve of this So, that is the rotational dome Saucer dome is basically where it is also referred as the segmental dome So, we talked about the rise So, this is your support and then whatever the height will get so, this is basically the rise So, for the saucer dome it is a segmental So, the rise is something which is not lying in this line maybe from some bottom of that and from there we make this particular arch So, the center of this arch is basically below that So, a dome having the form of a segment of a sphere with the center well, below the springing line So, this is the line that we have talked about the springing line even in the vault so, this particular portion is the saucer vault So, here you can see that how flat almost it is there So, it is the saucer dome Coming to the umbrella dome it is also known as ribbed or parachute dome So, what exactly it is we know the form of a parachute is something like this and also the umbrella So, where it is basically started with a very simple dome and then the ribbed will actually guide it to like take a form of this umbrella So, if you just take this example this is United State Capitol from US So, it the example of this umbrella dome Coming to the cable net dome So, it is also very important that this particular Millennium Dome we have discussed earlier as well in when we discussed about that tensile structure So, in this case these vertical members they are used as compressive members and very finally, if you see these images so, they are fixed with some cables some multiple cables they are giving the tension and this is the fabric material So, huge dome being created which very few numbers of such post or mast we refer technically

The mast it is only taking the compression and the rest of the arch tensioned So, with the cable this can also be formed The cable net structure can adopt an overall dome shape, albeit individual section is generally flat or anticlastic form So, we have discussed the anticlastic thing, but again we are just discussing it Anticlastic form is when the two curvatures of the plane they are acting in opposite directions So, basically, I have given example of a chips So, it is sometimes you just take any example of chip So, it is something like this something like this So, here I am trying to explain this with this example So, this is anticlastic means you have a curvature of this particular arch like this and then you have curvature of the top like this So, this is basically the anticlastic form that we will follow when we discuss the fabric structure as a form we will discuss in detail the anticlastic and synclastic curvature their advantages and disadvantages, but to understand it basically two curvature in opposite direction So, this is from the cable net dome Coming to the inflated dome, can you guess the material of this dome? So, looking at the image from a distance it looks similar to a concrete dome, but it is not So, this is basically the inflated dome being created So, inflated structures are formed by pressurizing a volume of air, enclosed by a lightweight fabric membrane So, sometimes even I have given this cited this example before that for a game zone in a shopping mall or it may be a local fair So, we will get something like a structure for the kids like you have a Mickey Mouse kind of things So, people are jumping over it So, it is nothing, but a membrane so, they put air inside this to give the form which is sells sustaining and adjusting automatically and when you release it will be just flatted So, this inflated dome being created This is the Qatar Inflatable Fabric dome It is a fabric being used, the air is used to give the form and it has been created So, this is not the only for a structure even these kinds of technique now being used to create as a shuttering to create the dome Now, obviously, for this concave structure or the huge dome, unless you go for the core building is very difficult to make the shuttering at certain height, and also to maintain the perfect symmetry So, what we need to do? We can use take example of this kind of balloon kind of form and then we just put the pressure, we just cast the dome as we want or then we just take it out the we release the pressure, so that this is this will be formed very smoothly So, this is a very good example and its low scale if you use this dome kind of structure, they are again mostly taking the compression and at the bottom hoops, you will get some kind of tension This is also proven to be good for seismic zone So, in state of having rectangular this dome can be used for that even for the wind So, they will also help to have a better air flow So, taking the aerodynamics and oscillation and also this kind of shapes are being useful So, not only as just the root purpose of any building as a decoration, even for a normal structure as a building structure we can also made So, we will discuss on when we discuss about the structure that is preferable for such disaster zone area will come back again with this kind of dome form Coming to the summary, so, basically in this we have discussed about the dome and here it is like the basic dome being formed, like it is half the section of your hollow sphere this is one idea that we had and the other one we discussed on the rotation So, you have one arch and then you revolve it 360 degree and then we get the form of this dome We have also discussed about the material, the mud I have also shown you some dome made of your some branches of the tree as well as some grasses to give the form and then also we discussed about the igloo which is made up snow and later on brick masonry, concrete masonry, even the steel, even the cable and then the last example that I have shown you is just some air pressure

So, due to pressurized air so, inflation of these things being done and the type of dome that is a series of dome and, but we can relate it So, where the rotational dome we also discuss the onion dome that been used in Taj Mahal or even in the Disney Land somewhere we have also seen that particular umbrella or ribbed thing that we have discussed for your what we call the Saint Peter’s or maybe sometimes like the example have taken for the US State Capital that is there and then sometimes the dome can be of your corbelled So, where like you have to align that particular layer of bricks or masonry in so, taking some offset in such a way that it will create a form of arch and finally, it revolved and then we can get this dome Now, coming to the advantage of the dome definitely; taking the example of the pantheon So, it will be used like it is very useful for covering a large span with minimum obstruction, but the disadvantage that we have that we cannot use the upper portion So, that is where normally being used for the roof for the case and then like it can be easily formed and mostly it is like self-adjusting, transferring the load to the support like this And, then the last point that we discussed that this kind of dome or curvde form that is very useful for the windy area or earthquake prone areas to tackle with that can also be used as a like small unit of as residence And, then also we discuss in modern days in state of this a heavy construction we just go each some triangulation of your structure with the steel member and then we form the geodesic dome which is being used to create it So, we can we have some examples on that as well So, this is the discussion on the dome and their uses from the history to the modern world, and there is no end of getting the examples of that Please do that exercise to put the more examples to this and if I missed out some of the category which is very predominant you can also suggest me in the forum, we will get back to you that positively And, these are some reading materials that been repeated so, you can go with that So, these structural analyses of historical construction there you will in this book you will get some example of construction of dome and all how these being done So, the main idea to discuss each type of structure one by one to get the advantages, their applications, the type so, not only the structural forms or they are capable to take more load, more span is feasible, but as well as the like the ornamentation that also we need to understand because this subject is basically the synergy between the form, architecture and these aesthetics as well as the structure So, we should also take that point that how beautifully like ornamentation of world then the arches and then now the dome being created and we can definitely simplify that We can go with the classical one or else taking the new materials and create some good form and that will make a proper synergy without compromising the structural safety of our building, we can do some great creation with some new materials, new techniques and all So, again I would like to thank you for take part in this course and next we will be meeting with a new discussion on the grid structures So, moving from arch, vault and then dome and then we will discuss about the grid and their limitations and their advantages and then slowly move over to the membrane structure and other structural forms that will be a useful lecture that will help us to take a decision on the type of structure to be selected depending on the purpose and we can make the synergy between all these form architecture and structure So, till then bye

Thank you

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