Roofing type including large span structures

Roofing

1. A shell structure is one in which the strength reloads into the outer surface. They are usually lighter than frame structures. Thin-shell structures are light weight constructions using shell elements. These elements are typically curved and are assembled to large structures. A shell structure is a thin curved membrane or slab usually of reinforced concrete that functions both as structure and covering. The term “shell” is used to describe the structures which possess strength and rigidity due to its thin, natural and curved form such as shell of egg, a nut, human skull, and shell of tortoise. SHELLS OCCURING IN NATURE Shell Structure

2. HT = Horizontal thrust of the arch LT = Line of thrust which represents the successive action of the voussoirs W = Vertical weight of the masonry and overload (dead and live) T = Thrust, resultant force of the horizontal thrust and weight Forces acting in arches and vaults

3. CYLINDRICAL BARREL VAULTS barrel vaults are perhaps the most useful of the shell structures because they can span upto 45 metres with a minimum of material the curve of the cross section of the barrel is usually a circle; however, any other form maybe used, such as the ellipse, a parabola, or a funicular curv e which fits the thrust line of the applied load; each curve has its particular structural and aesthetic qualities a number of terms have been developed to describe cylindrical shells: if the span is large in comparison to the width, the form is called a long shell if the length is short, it is called a short shell an arbitrary ratio for long shells is a span/radius ratio of 5; short shell has a span/radius ratio less than 1 and shells between these limits are called intermediate shells.

4. Basic Elements SHORT SHELLS cylindrical shell having a large radius in comparison to the length components: the arch structure (stiffener) the shell spanning between arches edge beam the principal structural element is the stiffener, usually a reinforced concrete arch, although steel arches or trusses have been used

5. if this structure is to be used as a canopy SHORT SHELLS Pure Arch and Shell

6. SHORT SHELLS Massive Abutments if the abutments are made heavy and rigid, then the arch may be lighter; so it may be more economical to use the large mass of concrete at the lower elevation to save concrete in the arches

7. SHORT SHELLS Rigid Frame short shells may be used with reinforced concrete rigid frames as the principal structural element it is not necessary to have the spans of all the rigid frames equal, and the bending moments in the frames may be reduced if shorter side spans are used

8. SHORT SHELLS Cantilever Abutments

9. INTERSECTION SHELLS made up by combining portions of the previous types arranged to form more stable combinations than the individual elements alone termed "intersection shell" because the surfaces that produce the shell appear to meet at an intersection any of the basic types may be used in this manner but the barrel shell is the most familiar and useful the structural efficiency of the intersection shell depends on the angle of the intersection of the surfaces; if the angle is small (sharp), then a natural rib is formed by the adjacent elements of the basic shells which is much stiffer than the adjacent shells on each side an intersection for which the angle is very large is called a shallow intersection an intersection of 90 degrees is optimum because it gives a stiff rib on large structures with shallow intersections, massive ribs may be necessary which are very evident and detract from the light appearance

10. INTERSECTION SHELLS Square in Plan Shallow Intersection triangular pieces of a cylindrical shell arranged in the form of a square the best type of dome to cover a square area loads are carried by the cross ribs formed by the intersection and by the stiffening element created by the edge beam the bottom of the shell requires tensile reinforcement as in a short shell.

11. INTERSECTION SHELLS Polygonal Plan, Shallow Intersection this form is suitable for a dome of large span which must be nearly circular in plan if more than six sides are used, the rib formed by the shell gets rather shallow so additional ribs are required a thrust ring must be added to take the forces in the ribs windows may be placed in the shell except at the lowest points

12. the groined vault is an intersection shell composed of four triangular pieces of cylindrical shells, arranged in a cross form so that there are arches on each of the sides this is one of the most ancient of masonry arch structures and still used for underground water reservoirs of concrete without any reinforcing Groined Vault, Square in Plan double barrel vault or cross vault the structure obtains its rigidity by the large angle between the shell components at the intersections which creates a very strong rib the size of these structures is almost unlimited because the form is inherently very strong and is stiffened by six complete arches INTERSECTION SHELLS

13. Groined Vault, Polygonal Plan INTERSECTION SHELLS

14. Intersection Shell – Folded Plate INTERSECTION SHELLS

15. CONICAL SHELLS

16. CF = Circular force in every ring LT = Line of thrust of “an arch” of the dome HT = Horizontal thrust of “an arch” of the dome W = Vertical weight of “an arch” and the overload T = Thrust, resultant force of the horizontal thrust and weight of “an arch” P = Peripheral tension which is created by the combination of the horizontal thrusts of all the arches, that are radiating from the centre Forces acting in domes

17. DOMES OF REVOLUTION Sphere Segment - Column Supports the shell thickness is a minimum and may be 2 1/2 to 3 inches for spans up to 150 ft due to the double curvature of domes, buckling is seldom a factor in the design domes have been built with a thickness of 6 inches for a span of about 300 feet.

18. Half Sphere – Vertical Walls DOMES OF REVOLUTION

19. Domes – Square in Plan spherical dome with portions sliced off to form a square or rectangle most areas to be covered are rectangular so a circular dome is not always a good solution to the planning requirements this dome is supported by four rigid frames and would only be suitable for small spans because the frames would get quire large for long spans, it is necessary to place a tie between the knees of the frame DOMES OF REVOLUTION

20. Multiple Domes DOMES OF REVOLUTION

21. Folded Plate Domes

22. Translation Domes TRANSLATION DOMES This structure looks very much like the square dome shown previously except the shape is generated by an entirely different method a translation shell is generated by a vertical curve sliding along another vertical curve; the curves can be circles, elipses , or parabolas the vertical sections are all identical as opposed to a circular dome in which all vertical sections vary in height; this is a big advantage in construction of the formwork most of the load is carried by the side arches with some coming directly to the corners

23. HYPERBOLOIDS OF REVOLUTION OF ONE SHEET

24. HYPERBOLIC PARABOLOIDS

25. Hyperbolic Paraboloidal Saddle Dome HYPERBOLIC PARABOLOIDS

26. Trumpet Shell HYPERBOLIC PARABOLOIDS

27. Groined Vault HYPERBOLIC PARABOLOIDS

28. CONOID

29. Folded Plate Folded plate structures consist of flat components, or plates, that are interconnected at some dihedral angle. Structures composed of rectangular plates are said to be prismatic. In modern construction practice the most widely used folded plate structures are made of cast-in-situ or precast reinforced concrete. The structures are used as roofs for industrial and public buildings. The main advantage of folded plate structures over other shells (such as cylindrical) is the simplicity of manufacture.

30. Folded Plate Structural system for roofing large span Column free areas Simple formwork as compare to shell structures Derive their strength from the inherent stiffness of the folds. They usually have triangular or trapezoidal zig zag cross sectional shape.

31. Assignment : Sketch any 2 types of each of the following on A2 sheets Folded plate Short Shell Intersection shell Domes Hyperbolic Paraboloids

32. Thank You…