1 Hannu Hirsi : Structures Wood Shell Structures Form and statics. Structures and connections. Analyses and construction. Ver. 2013 Objectives 1 : Rather than technology as well as art, architecture is and must be a synthesis of technology and art. The structure that does not follow the simplest and most efficient schemes or a construction detail that does not consider the specific character of the material with which it is built will only with great difficulty achieve good aesthetic expression. Hannu Hirsi 2
2 Objectives 2 : The core of the problem is how to develop in students a static understanding,, the indispensable basis of intuition of structural imagination. The architect need not have a specific knowledge of all details but... must have a clear knowledge of every branch of the building industry orchestra conductor Hannu Hirsi 3 Objectives 3 : It seem to me that this relationship can be defined in the following manner : The objective data of the problem, technology and static suggest the solutions and forms. The aesthetic sensitivity of the designer welcomes the sugges- tion and models it, emphasizes it, proportions it, in a personal manner which constitutes the artistic element in architecture. ( Pier Luigi Nervi ) Hannu Hirsi 4
3 Objectives in this lecture : To give an appreciation of the opportunities to create exciting building forms in timber Using as a basis the structural principles of shells, large clear spans without internal supports. Exciting curved forms in buildings. Not in this lecture Neither Double Layer Space Truss, nor timber pole space frames. Mora & Candela : Chapel San Vicente de Paul Coyoacan. Hannu Hirsi 5 Structures : Hannu Hirsi 6
4 Shells : Shells are thin and stiff curved membranes which act alone to provide a complete structure, including : The form of the surface, the primary load-bearing stiff structural system and the isolating surface between outdoor and indoor climate. Variety of shapes is infinite. Should be considered whenever an elegant, architecturally appealing solution is needed. Hannu Hirsi 7 1. Membrane : Series of thicknesses of material Laid at an angle to one another In building site nail-glued together timber boards laid side by sides, plywood and laminated veneer lumber. Hannu Hirsi 8
5 2. Edge beams : Normal stiff load bearing structural elements. Paraboloid or elliptical arc forms. prefabricated structural elements: Glued laminated timber or LVL. Hannu Hirsi 9 3. Stiffening ribs : Boards nailed together, Glued laminated timber, LVL. Hannu Hirsi 10
6 4. Connections : Nail-glued connec- tions. Steel plates and nails, screws or bolts. Steel, concrete and timber connections. Hannu Hirsi 11 Tension shells : Easier to design because we have no problems with stability. Modelling methods are the same. Nowicki & Deitrick & Severud :Raleigh- Arena. Hannu Hirsi 12
7 Form : Hannu Hirsi 13 Choice of form, back to basics : Conic sections: Ellipse and circle. Parabola. Hyperbola. Lines and points. These are all we need! Hannu Hirsi 14
8 Ellipses and circles : One equation gives one curve. The curvature is between certain limits or the same: Not too much or too little. Start point and end point are the same. I recommend warmly. 5 y 3y2 + x2 = 9 4 y2 + 3x2 +3x = 4 y2 +xy + x2 = 9 3 2 1 0-3 -2-1 0 1 2 3 x -1-2 -3-4 Hannu Hirsi -5 15 Hyperbolas : One equation gives four different curves. The curvature is all the time coming bigger after turn point: Very quickly straight line. Start point and end point are different. y 5 4 3 2 1 0-3 -2-1 0 1 2 3 x -1-2 y2 - x2 = 3 y2 - x2 +2x = 2 yx = 0.5 Sorry, not so good. -3-4 -5 Hannu Hirsi 16
9 Parabolas : One equation gives one curve. The curvature is all the time coming smaller after turn point: Never straight line Start point and end point are different. y 5 4 3 2 1 0-3 -2-1 0 1 2 3 x -1-2 y = -x2 + 2x + 3 y = x2-3 y = x2 x = x2-2xy + y2-3 Ok, if you like it. -4-5 Hannu Hirsi 17 Quadric surfaces 1: In one and two direction Curved surfaces: Sphere. Ellipsoids. Paraboloids: Circular and elliptic paraboloids Hyperbolic paraboloid: Edges bisecting directions of generators. Edges parallel to generators. Sphere Hyperbolic paraboloid Ellipsoid Hannu Hirsi 18
10 Quadric surfaces 2: In two direction Curved surfaces : Hyperboloid of one sheet: Hyperbolic, parabolic, elliptical and circular cylinders. Circular and elliptic cones. Hyperboloid of two sheets. Conoids. Torus. Cylinders Torus Hyperboloids Hannu Hirsi 19 Woodstudio 2005 HDW Info- Pavilion Tkk Holz-Glas-Studio 2004-2005 Antti Lehto & Teemu Seppänen Hannu Hirsi 20
11 HDW-paviljonki (Antti Lehto & Al) Hannu Hirsi 21 Ruled Surfaces : Ex. of different ruled surfaces calculated with AutoLISP and drawn with AutoCAD. Hyperbolic paraboloid Hyperboloid of one sheet Raiski & Hirsi & Salokangas Hannu Hirsi 22
12 Hannu Hirsi 23 Geodesic surfaces : Classification of geodesic surfaces : Hannu Hirsi 24
13 Icosahedron based geodesic domes : Most common geodesic domes : Hannu Hirsi 25 Octahedron based Geodesic domes : Less uniform structure : Hannu Hirsi 26
14 Tetrahedron based domes : Degenerated structures. Hannu Hirsi 27 Geodesics surfaces : Icosahedron based geodesic spheres calculated with AutoLISP and drawn with AutoCAD. Hannu Hirsi 28
15 Free surfaces : NURBS-curves and -surfaces: Here is the future? Hannu Hirsi 29 Tape test of surfaces : Geodesics of the cylinder and conic : Hannu Hirsi 30
16 Affinity : Scaling and zooming. Examples of vertical affinity of a: 0.5-1.0-1.5-2.0 Examples of horizontal affinity (same factors) : Hannu Hirsi 31 Affinity : Paraboloid of revolution Projections in plane are hexacons. Ortogonal and polar projections. Hannu Hirsi 32
17 Geometrical modelling : Hannu Hirsi 33 Example : Modeling the triangle shell : Phase 1: Modelling the new structures with splines and changing these to polylines Phase 2 : Orthogonal projection of polylines to ellipsoid Hannu Hirsi 34
18 Phases of the design of shell (Mechanical view): 1. Choose the basic surfaces. 2. Clip the parts you need. 3. Join them together to get a seamless structure. 4. Trim the structures with splines or some other methods. Hannu Hirsi 35 Example : Choose the basic surfaces. Clip the parts you need. Join them together Trim the structures Galgary Olympic Saddledome Hannu Hirsi 36
19 Structural modelling : Hannu Hirsi 37 Structures, basic idea 1 : Beams and arcs form the bearing system of shell structure : Beam-effect effect locally. Arc-effect globally. Inside bearing system forces choose always the most rigid direction. Arc Compression kn Bending Shear N1 Hannu Hirsi 38
20 Local and global features of shells : Globally normal force Normal force and moment Locally normal force, moment, shear and torsion. Hannu Hirsi 39 Structures, basic idea 2 : Dividing the forces and stiffening the structure with triangles Three layers in different directions. Two layers and a surface structure. We have triangles In the scale of whole structure. Ring beam inside and in the edge of structure forms triangles. Hannu Hirsi 40
21 Shell structure with stiffening triangles : Whole structure is like plate structure. Compression forces of the beams Bending moments of the beams Hannu Hirsi 41 Shell structure without stiffening triangles : Bars act like column structures. Compression forces of the beams Bending moments of the beams Hannu Hirsi 42
22 Shell structures and stiff edge beam : Stiff edge beam forms triangles Compression force of the beams X Y Z Bending moments of the bars X Y Z Hannu Hirsi 43 Arc effect : Important to have continuous and symmetric structures and loadings X Y Z N27 X =-10.450 kn Y = 13.000 kn Z = 0.000 kn Y M X = FREE X Z M Y = FREE M Z = FREE N1 X =10.450 kn Y =13.000 kn Z = 0.000 kn M X = FREE M Y = FREE M Z = FREE Hannu Hirsi 44
23 Arc effect in shells : Self weight 1 point load in the middle 1 point load near the edge X YZ X Y Z Hannu Hirsi 45 Beam effect in shells : Point forces on the bars means only local effects Y X Z Shear forces Y X Z Bending moments Normal forces Hannu Hirsi 46
24 Beam and arc effect in ring beams : Moment diagram Ring beam Y Z X Deflections Largest in the edges Z Y X Hannu Hirsi 47 Span ratio : Stiffness ratio Use symmetrical structures Span ratio ( l 2 / l 1 ) Reactions 1.00 1.50 2.00 3.00 Beam b ( l 1 ) R 1 0.5 x F 0.77 x F 0.89 x F 0.96 x F Beam a ( l 2 ) R 2 0.5 x F 0.23 x F 0.11 x F 0.04 x F Hannu Hirsi 48
25 Stability : a. Bar buckling b. Node instability c. Line instability d. General instability Minimum curvature of bar! Hannu Hirsi 49 Unstability : Erosion of unstable component : Class 0 Critical load has no unstable components Class 1 There is a moderate erosion < 25 % Class 2 There is a strong erosion < 50 % Class 3 There is a very strong erosion > 75 Theoretical Actual Hannu Hirsi 50
26 Stability of shell structures : Stability is a complex phenomenon. Space structures are unique. The loss of stability occurs spontaneously in most cases, without any preliminary indications of an imminent catastrophe. Instability occurs in a region with strong geometrical and material non-linearities linearities. Influence of imperfections,, the most important factors, is very significant. Checking the structure experimentally is very difficult Design codes and standards are scarce. Hannu Hirsi 51 Displacements of the shell : Y X Z Hannu Hirsi 52
27 Strength reduction for curvature : Reduction 1 0.95 0.9 0.85 0.8 0.75 100 135 170 205 240 Ril 120 kuva 5.8 Min = 100 Maximum curvature of bar! =R/t Hannu Hirsi 53 Analysis of shell structures : Phase 1 : Surface tension analogy (1750 - ) All forces are assumed to lie within the shell surface, no bending moments exist Phase 2 : Analytical membrane theory solutions of basic mathematical forms (1850 - ) Cylindrical shells,conoidal shells,dome shells,elliptical parabolas,hyperbolic parabolas Phase 3 : Numerical, computational solutions of forces ( 1950 - ) Job Information Difference methods Engineer Checked Approved Finite-element element methods Name: Date: 17-Mar-03 Non-Linear methods Structure Type SPACE FRAME Number of Nodes 134 Highest Node 367 Hannu Hirsi Number of Elements 328 54 Highest Beam 369
28 Economically feasible dimensions : Shell form Width (span m) Length Hyperbolic paraboloid 7.2-24 7.2-24 Elliptic paraboloid 7.2-30 7.2-30 Barrel-vault shell 7.2-20 12-36 Conoid 12-27 7.2-12 Hannu Hirsi 55 Production planning of shell structures : Much easier to build than design. Oulu Raksila Dome Hannu Hirsi 56
29 Summary : Hannu Hirsi 57 Summary : If the picture is worth 1000 words, then a simple model is worth 1000 calculations. There are only few basic structural systems for post and beam structures. For the shell structures there are thousands, each require a unique approach to design. Shell structures get their strength by shape and not by high strength of material. The supports for the shell are more important than the shell. Shell structures can be understood as a set of beams, arches and catenaries (ketjukäyrä). Stiffest path concept is most useful. There is always a simple method to check the precise, complicated computer analyses. Hannu Hirsi 58