Research on Ribbed Domes

Here is the research that we did for our final asssignment for our Arch241 class. Our structural element is Dome. And every section is devided into groups so we are researching Ribbed Dome. We are going to do a model of this structural element and here is the information that we will use while doing it.

Ribbed dome is Type of vault giving the effect of a dome, or where the under-surface of a dome or cupola is subdivided by radiating ribs.

Rib : a three dimensional arch which projects from the dome’s interior surface.Arch: the geometric shape of the rib especially when it forms half a circle extending from the base on one side to the base on the other side of the dome.

Ribbed dome:  a dome with ribs that rotate around its vertical axis.

When arches are rotated around a dome’s vertical axis, the intersection point at the apex of the dome becomes more congested as the number of arches increases When arches are rotated around a dome’s vertical axis, the intersection point at the apex of the dome becomes more congested as the number of arches increases. This problem can be avoided by using a pair of arches instead of only one, and leaving an open space in the apex where the node of intersecting ribs used to be . Increasing the number of rotated arches to 3, 4, 5 or more arches creates more complex patterns, but causes two effects which were not satisfactory to Arab builders: the first is a physical one, where the resulting arches have different radii because of their location on the dome surface. , this meant that more varied and extensive forms are required for building. A more import-ant effect, however, is a visual one, where the arches intersect in ways that did not appeal to Arab- Muslim tastes.

 

2.1. Mathematical Properties

Depending on the distance between the arches in a pair, the rotation creates polygonal or star shapes, which are divided into a number of cells. These cells are uniform in shape around the circumference, and become smaller in size starting from the outside and progressing towards the center. The number of star vertices is obviously twice the number of rotations of a pair of arches: n = 2r

Where n is the number of star vertices, and r is a whole number of rotations required until the last pair is superimposed over the first, and ranges from 3 to almost 50. The exterior angle (the angle farthest away from the star center) of each of the kite shaped cells corresponds to the number of rotations that created the star. The outermost angle is equal to the angle of rotation, and is given by this equation: a1 = 360°/ 2r

Where a1 is the angle, and r is the number of rotations as defied in the preceding equation the exterior angle for subsequent cells is given by this equation: ax = x a1

Where ax is the angle, x is the cell sequence number from outside towards inside, where the outermost cell number is 1; a1 is the angle of rotation obtained by the pre-ceding equation.

The cells in the last interior layer which adjoins the central polygon, are always triangles rather than kite shaped. The number of different cells in a star, including the central polygon, equals to the number of rotations that created the star.

star motifs can be produced by joining points equally distributed around the circumference of a circle. These stars can be described by a concise notation giving the data on three quantities: the number of initial vertices n , the method of joining up the vertices to produce the original star (i.e., joining every 2nd point, 3rd point, and so on) d , and the number of cells remaining in the star motif (since some cells can be removed)

2.2. Basic Types of Ribbed Domes

the rotation of a pair of arches 90° produces a square shape. This is a static form un-less placed on the diagonal of a square base. Three rotations produce a hexagonal star or polygon. This is the minimum number of rotations to produce a star motif.  by rotating a pair of arches four times, the most popular ribbed dome is created, because of its simple and pleasing proportions, its dynamic qualities, and its balanced relationship to the square and the circle in the same time. Other popular domes are the 12-pointed and 16-pointed stars.

If the framing be of a form less convex than the curve of equilibrium, the weight will have a tendency to crush the ribs inwards, but this pressure may be effectually overcome by strutting between the ribs; and hence it is important that the struts be so placed as to form continuous horizontal circles.

A ribbed dome consists of a number of identical meridional girders or trusses, interconnected at the crown by compression ring

The dome has vertical compression along their meridians, but horizontally experience compression only in the portion above 51.8 degrees from the top. Below this point, the hemispherical dome experiences tension horizontally.