1. Structural forms

2. “The human environment, both natural and manufactured, provides an ideal resource for graphic investigation, study and analysis”

3. By examining structures in nature we can see how principles in their design are incorporated in man made structures Munich Olympic Stadium, Frei Otto Epcot centre, Florida Spherical structure of Carbon atoms An insects eye

4. Exercise 1 Select one of the following well known Architects and investigate if nature has been an influencing factor in creating some of their designs. Outline the link between nature and one of their structures. Pier Luigi Nervi Felix Candella Santiago Calatrava Antoni Gaudí Frank Llyod wright Tadao Ando

5. “ Investigation of the historical development of common structural forms, including the arch, dome and vault, together with the representation of these and other structures using line diagrams”

6. An Arch is a structure that spans a space while supporting weight

7. A Vault is an architectural term for an arched form used to provide a space with a ceiling or roof Barrel Vault, Egypt Annular Vault, The section is translated along a straight line profile The section is translated along a curved profile

8. A Dome is a structural element of architecture that resembles the hollow upper half of a sphere. Dome of the Rock, Jerusalem

9. Exercise 2 The image shows a Monolithic home in New Mexico. The main structure is based on a Dome, the entrance porch is based on a Barrel vault. (a) Using neat freehand sketches draw the orthographic views of the structure. (b) Draw the outline view of the home when it is cut by both a horizontal section plane containing the top of the window and a vertical section plane containing the front door.

10. Surfaces A surface is generated by the movement of a straight line or curved line. The resulting surfaces can be defined as either Ruled or doubly curved.

11. A Ruled surface is generated by moving a straight line, the generatrix. An infinite number of straight lines can be drawn through any one point on a planar surface

12. Singly-Ruled surface If you select any point on a singly-ruled surface, you can only draw one straight line through this point. A singly-ruled surface can be developed so that the complete surface will lie on a plane. The most familiar examples are the curved surface of a cylinder or cone. Other examples are the right conoid and the helicoid. Helicoid Cylinder Cone Conoid

13. Doubly-Ruled surface A surface is doubly ruled if through every one of its points there are two distinct lines that lie on the surface. The Hyperbolic Paraboloid and the Hyperboloid of revolution of one sheet are examples of doubly ruled surfaces.

14. Hyperboloid of revolution The surface can be generated by revolving: (1)A straight line about another non-parallel, non-intersecting line as its axis (conjugate axis) (2)A hyperbola about the conjugate axis Can the cone and cylinder be generated by revolving straight lines? The throat circle is the shortest horizontal distance between the two skew lines

15. Learning outcomes This sheet shows three different ways of producing the Hyperbolae in elevation. Link to Technical graphics Key principles The surface is made up of an infinite number of straight line elements Each element in plan is tangential to the throat circle Link to Conic sections

16. Are there any links between the Cylinder, Cone and Hyperboloid of revolution when each is sectioned by a horizontal, vertical and inclined cutting planes?

17. Key principle The asymptote is an element of the surface, is tangential to the throat circle and is seen as a true length when it is an asymptote to the hyperbola. The true length of any element is seen when the plane that contains it is seen as a true shape True length

18. Hyperboloid Paraboloid Hyperbolic paraboloid are often referred to as "saddles,". Their name stems from the fact that their vertical cross sections are parabolas, while the horizontal cross sections are hyperbolas. It is a warped surface and cannot be developed. The surface can be generated by: (1) Translating a parabola contained on a vertical plane along another parabola also contained on a vertical plane. (2) By a straight line (generatrix) that moves along two non-parallel, non-intersecting lines known as linear directrices. The generatrix as it moves must always remain parallel to a plane, called the plane director. Parabolic profile Guide Parabola