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The lecture is in support of:
(1) The Design of Building Structures (Vol.1, Vol. 2), rev. ed., PDF eBook by Wolfgang Schueller, 2016
(2) Building Support Structures, Analysis and Design with SAP2000 Software, 2nd ed., eBook by Wolfgang Schueller,
The SAP2000V15 Examples and Problems SDB files are available on the Computers & Structures, Inc. (CSI) website: http://www.csiamerica.com/go/schueller

The lecture is in support of:
(1) The Design of Building Structures (Vol.1, Vol. 2), rev. ed., PDF eBook by Wolfgang Schueller, 2016
(2) Building Support Structures, Analysis and Design with SAP2000 Software, 2nd ed., eBook by Wolfgang Schueller,
The SAP2000V15 Examples and Problems SDB files are available on the Computers & Structures, Inc. (CSI) website: http://www.csiamerica.com/go/schueller

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Surface Structures, including SAP2000

  1. 1. SURFACE STRUCTURES including SAP2000 Prof. Wolfgang Schueller
  2. 2. For SAP2000 problem solutions refer to “Wolfgang Schueller: Building Support Structures – examples model files”: https://wiki.csiamerica.com/display/sap2000/Wolfgang+Schueller%3A+Building+Su pport+Structures+- If you do not have the SAP2000 program get it from CSI. Students should request technical support from their professors, who can contact CSI if necessary, to obtain the latest limited capacity (100 nodes) student version demo for SAP2000; CSI does not provide technical support directly to students. The reader may also be interested in the Eval uation version of SAP2000; there is no capacity limitation, but one cannot print or export/import from it and it cannot be read in the commercial version. (http://www.csiamerica.com/support/downloads) See also, Building Support Structures, Analysis and Design with SAP2000 Software, 2nd ed., eBook by Wolfgang Schueller, 2015. The SAP2000V15 Examples and Problems SDB files are available on the Computers & Structures, Inc. (CSI) website: http://www.csiamerica.com/go/schueller
  3. 3. Surfaces in nature
  4. 4. SURFACE STRUCTURES - MEMBRANES BEAMS BEARING WALLS and SHEAR WALLS - PLATES slabs, retaining walls - FOLDED SURFACES RIBBED VAULTING LINEAR and RADIAL ADDITIONS parallel, triangular, and tapered folds CURVILINEAR FOLDS
  5. 5. - TENSILE MEMBRANE STUCTURES Pneumatic structures Air-supported structures Air-inflated structures (i.e. air members) Hybrid air structures Anticlastic prestressed membrane structures Edge-supported saddle roofs Mast-supported conical saddle roofs Arch-supported saddle roofs Hybrid tensile surface structures (including tensegrity) - SHELLS: solid shells, grid shells CYLINDRICAL SHELLS THIN SHELL DOMES HYPERBOLIC PARABOLOIDS
  6. 6. Slabs resisting gavity loads
  7. 7. Flat plate building
  8. 8. New National Gallery, Berlin, 1968, Mies van der Rohe Arch
  9. 9. Art Museum of Sao Paulo, Sao Paulo, Brazil, 1968, Lina Bo Bardi Arch (prestressed concrete beams)
  10. 10. Shear walls resisting wind
  11. 11. Cite Picasso, Nantere, Paris, 1977, Emile Aillaud Arch
  12. 12. Whitney Museum of American Art, New York, 1966, Marcel Breuer Arch
  13. 13. Everson Museum, Syracuse, NY, 1968, I. M. Pei Arch
  14. 14. Delft University of Technology Aula Congress Centre, 1966, Jaap Bakema Arch
  15. 15. St. Engelbert, Cologne-Riehl, Germany, 1932, Dominikus Böhm Arch
  16. 16. Design Museum, Nuremberg, Germany, 1999, Volker Staab Arch
  17. 17. Schlumberger Research Center, Cambridge, UK, 1985, Hopkins/ Hunt
  18. 18. Stress contour of structural piping
  19. 19. Boston Convention Center, Boston, 2005, Vinoly and LeMessurier
  20. 20. Incheon International Airport, Seoul. 2001, Fentress Bradburn Arch.
  21. 21. MUDAM, Museum of Modern Art, Luxembourg, 2007, I.M. Pei
  22. 22. Armchair 41 Paimio by Alvar Aalto, 1929- 33, laminated birchwood
  23. 23. Eames Plywood Chair, 1946, Charles and Ray Eames Designers
  24. 24. Panton Molded Plastic Chair, Denmark, 1960, Verner Panton Designer
  25. 25. Ribbon Chair, Model CL9, Bernini, 1961, Cesare Leonardi & Franca Stagi designers
  26. 26. MODELING OF SURFACE STRUCTURES Introduction to Finite Element Analysis The continuum of surface structures must be divided into a temporary mesh or gridwork of finite pieces of polygonal elements which can have various shapes. If possible select a uniform mesh pattern (i.e. equal node spacing) and only at critical locations make a transition from coarse to fine mesh. In the automatic mesh generation, elements and their definitions together with nodal numbers and their coordinates, are automatically prepared by the computer. Shell elements are used to model thin-walled surface structures. The shell element is a three-node (triangular) or four- to nine-node formulation that combines separate membrane and plate bending behavior; the element does not have to be planar. Structures that can be modeled with shell elements include thin planar structures such as pure membranes and pure plates, as well as three-dimensional surface structures. In general, the full shell behavior is used unless the structure is planar and adequately restrained. Membrane and plate elements are planar elements. Keep in mind that three-dimensional shells can also be modeled with plane elements if the mesh is fine enough and the elements are not warped!
  27. 27. In general, the plane element is a three- to nine-node element for modeling two-dimensional solids of uniform thickness. The plane element activates three translational degrees of freedom at each of its connected joints. Keep in mind that special elements are required when the Poisson’s ratio approaches 0.5! An element performs best when its shape is regular. The maximum permissible aspect ratio (i.e. ratio of the longer distance between the midpoints of opposite sides to the shorter such distance, and longest side to shortest side for triangular elements) of quadrilateral elements should not be less than 5; the best accuracy is achieved with a near to 1:1 ratio. Usually the best shape is rectangular. The inside angle at each corner should not vary greatly from 900 angles. Best results are obtained when the angles are near 900 or at least in the range of 450 to 1350. Equilateral triangles will produce the most accurate results.
  28. 28. LINE COMPONENT PLANAR COMPONENT SOLID COMPONENT DISCRETE MODEL CONTINUOUS MODELS LINE ELEMENT TYPICAL PLANAR ELEMENTS TYPICAL SOLID ELEMENTS a. b. c. d. e. Basics of Modeling Possibilities for Modeling a Simple Structure
  29. 29. Planar elements: MEMBRANE: pure membrane behavior, only the in-plane direct and shear forces can be supported (e.g. wall beams, beams, shear walls, and diaphragms can be modeled with membrane elements, i.e. the element can be loaded only in its plane. Planar elements: PLATE: pure plate behavior, for out-of plane force action; only the bending moments and the transverse force can be can be supported (e.g. floor slabs, retaining walls), i.e. the element can only be loaded perpendicular to its plane. Bent planar elements: SHELL: for three-dimensional surface structures, i.e. full shell behavior, consisting of a combination of membrane and plate behavior; all forces and moments can be supported (e.g. three- dimensional surface structures, such as rigid shells, vaults). Solid elements
  30. 30. The accuracy of the results is directly related to the number and type of elements used to represent the structure although complex geometrical conditions may require a special mesh configuration. As mentioned above, the accuracy will improve with refinement of the mesh, but when has the mesh reached its optimum layout? Here a mesh-convergence study has to be done, where a number of successfully refined meshes are analyzed until the results converge. Computers have the capacity to allow a rapid convergence from the initial solution as based, for instance, on a regular course grid, to a final solution by feeding each successive solution back into the displacement equations that is a successive refinement of a mesh particularly as effected by singularities. Keep in mind, however, that there must be a compromise between the required accuracy obtained by mesh density and the reduction file size or solution time!
  31. 31. Finite element computer programs report the results of nodal displacements, support reactions and member forces or stresses in graphical and numerical form. It is apparent that during the preliminary design stage the graphical results are more revealing. A check of the deformed shape superimposed upon the undeflected shape gives an immediate indication whether there are any errors. Stress (or forces) are reported as stress components of principal stresses in contour maps, where the various colors clearly reflect the behavior of the structure as indicated by the intensity of stress flow and the distribution of stresses. The shell element stresses are graphically shown as S11 and S22 in plane normal stresses and S12 in-plane shear stresses as well as S13 and S23 transverse shear stresses; the transverse normal stress S33 is assumed zero. The shell element internal forces (i.e. stress resultants per unit of in-plane length) are the membrane direct forces F11 and F22, the membrane shear force F12, the plate bending moments M11 and M22, the plate torsional moment M12, and the plate transverse shear forces V13 and V23. The principal values (i.e. combination of stresses where only normal stresses exist and no shearing stresses) FMAX, FMIN, MMAX, MMIN, and the corresponding stresses SMAX and SMIN are also graphically shown. As an example are the membrane forces shown in Fig. 10.3. The Von Mises Stress SVM (FVM) is identified in terms of the principal stress and provides a measure of the shear, or distortional, stress in the material. This type of stress tends to cause yielding in metals.
  32. 32. FMIN FMAX F11 F22 F12 F12 Axis 2 Axis 1 J4 J1 J3 J2 MEMBRANE FORCES
  33. 33. COMPUTER MODELING Define geometry of structure shape in SAP- draw surface structure contour using only plane elements for planar structures. click on Quick Draw Shell Element button in the grid space bounded by four grid lines or click the Draw Rectangular Shell Element button, and draw the rectangular element by clicking on two diagonally opposite nodes or click the Quadrilateral Shell Element button for four-sided or three-sided shells by clicking on all corner nodes If just the outline of the shell is shown, it may be more convenient to view the shell as filled in click in the area selected, then click Set Elements button, then check the Fill Elements box under shells click Escape to get out of drawing mode, click on the beam on screen go to Edit, then Mesh Shells choose Mesh into, then type the number of elements into the X- direction on top, and then Z-direction on bottom for beams or Y-direction on bottom for slabs; use an aspect ratio close to the proportions of the surface element but less than the maximum aspect ratio of about 1/4 to 1/5, click OK, click Save Model button or for the situation where a grid is given and reflects the meshing, choose Mesh at intersection of grids to mesh the elements later into finer elements, just click on the Shell element and proceed as above. adding new Shell elements: (1) click at their corner locations, or (2) click on a grid space as discussed before
  34. 34. Define MEMBER TYPES and SECTIONS : click Define, then click Shell Sections click Add New Section button, then type in new name go to Shell Sections, then define Material, then type thickness in Membrane and Bending box (normally the two thicknesses are the same) in kip-ft if dimensions are in kip-ft select Membrane option for beam action or Plate option for slab action or Shell option for bent surface structures, then click OK, then click Save Model button Define STATIC LOAD CASE Click Static Load Cases, then assign zero to Self Weight Multiplier, then click Change Load, OK , or type DL in the Load edit box (or leave LOAD1 then click the Change Load button, in other words self-weight is not set to zero Type LL in the Load edit box then type 0 in the Self Weight Multiplier edit box, then click the Add New Load button Assign LOADS Single loads are applied at nodes. Uniform loads act along mid-surface of the shell elements for membrane elements, in other words are applied as uniformly distributed forces to the mid-surfaces of the plane elements that is load intensities are given as forces per unit area (i.e. psi). Assign joint loads click on joint, then click on Assign click at Joint Static Loads, then click on Forces, then enter Force Global Z (P for downward in global z-box), then click Add to existing loads, then click OK Assign uniform loads select All, then click Assign, then click Shell Static Loads, then click Uniform choose w (psf), Global Z direction ( i.e. Direction: Gravity), for spatial membranes project the loads on the horizontal projection, then click OK Assign loads to the pattern click Assign, then select Shell Static Loads, and Select Pressure from the Shell Pressure Loads dialog box select the By Joint Pattern option, then select e.g. HYDRO fro the drop- down box, then type 0.0624 in the Multiplier edit box, then click OK.
  35. 35. MEMBRANES • BEAMS • BEARING WALLS and SHEAR WALLS
  36. 36. National Gallery of Art, East Wing, Washington, 1978, I.M. Pei Arch
  37. 37. ey Fy Fy Fy e. ey Fy Fyb d/2 1 2 Fy Mp d/2 Cp Tp 3 d/2 Bending Stresses
  38. 38. Glulam beams
  39. 39. Build-up wood beams
  40. 40. Equivalent stress distribution for typical singly reinforced concrete floor beams at ultimate loads
  41. 41. Shear force resistance of vertical stirrups
  42. 42. Design of concrete floor structure (see Examples 3.17 and 3.18)
  43. 43. 1 K/ft 4' 40' 10 k 8' 2' (2) EXAMPLES: 12.1, 12.2
  44. 44. 1 K/ft 4' 40' a. b. c. EXAMPLE: 12.1: Beam membrane
  45. 45. The maximum bending moment is, Mmax = wL2/8 = 1(40)2/8 = 200 ft-k The section modulus is, S = bh2/6 = 6(48)2/6 = 2304 in3 The maximum shear stress (S12) occurs at the neutral axis at the supports, fv max = 1.5(V/A) = 1.5(20000)/(6)48 =104 psi (0.72 MPa or N/mm2) ≤ 165 psi OK The SAP shear stresses (c) are, S12 = 101 psi. The maximum longitudinal bending stresses (S11) occur at top and bottom fibers at midspan and are equal to, ± fb max = M/S = 200(12)/2304 = 1.04 ksi (7.17 MPa or N/mm2) ≤ 1.80 ksi OK The SAP longitudinal stresses (c) are, S11 = ±1.046 ksi. Or, the maximum stress resultant force F11 = ± 6.28 k, which is equal to stress x beam width = 1.046(6) = 6.28 k/inch of height.
  46. 46. ±1.01 ksi 92 psi EXAMPLE: 12.1: Beam membrane
  47. 47. 10 k 8' 2' EXAMPLE 12.2: Cantilever beam membrane
  48. 48. 30' 12' 10' 10' 10' Pu= 500 k R = 500 k R = 500 k θ = 47.20 z=0.9h=10.8' Hcu Htu Pu= 500 k D u Du strut: Hcu tie: Htu wd wh Mu a. b. EXAMPLE 12.3 Deep Beam; Flexural Stress S11
  49. 49. Arbitrary membrane structure – S11 stresses – displacements contour lines – displacements contour fill
  50. 50. BEARING WALLS and SHEAR WALLS
  51. 51. National Assembly, Dacca, Bangladesh, 1974, Louis Kahn
  52. 52. Wall behavior
  53. 53. World War II bunker transformed into housing, Aachen, Germany
  54. 54. Dormitory of Nanjing University, Zhang Lei Arch., Nanjing University, Research Center of Architecture
  55. 55. Seismic action
  56. 56. Shear-wall or Cantilever-column
  57. 57. LATERAL DEFLECTION OF SHEAR WALLS
  58. 58. Shear Wall and Frame Shear Wall Behavior Frame Behavior
  59. 59. Shear Wall and Frame Behavior
  60. 60. Shear Wall and Truss Behavior
  61. 61. LONG WALL CANTILEVER WALL INTERMEDIATE WALL 10.5 k 9 k/ft 10ft 10ft 25 k 25 k a. L = 32' h = 16' h b. L = 8' Example 12.4: Effect of shear wall proportion
  62. 62. Long wall: axial stresses, shear stresses, bending stresses
  63. 63. From shallow to deep beam
  64. 64. shallow beam deep beam
  65. 65. Deep concrete beams
  66. 66. Effect of shear wall proportion, S22 axial stresses, S12 shear stresses
  67. 67. S22 axial gravity stress – S12 wind shear stress – S22 flexural wind stress
  68. 68. EXAMPLE: 12.4: Bearing wall
  69. 69. Typical Long-wall structure
  70. 70. Typical shear wall structure
  71. 71. The behavior of ordinary shear walls
  72. 72. Fig. 12.8, Problem 12.2: Stresses S22 (COMB1), S12 (COMB2), S22 (COMB3)
  73. 73. The response of exterior brick walls to lateral and gravity loading
  74. 74. The effect of lateral load action upon walls with openings
  75. 75. Shear Wall or Frame Shear Wall FrameShear Wall or Frame ?
  76. 76. Openings in Shear Walls Very Large Openings may convert the Wall to Frame Very Small Openings may not alter wall behavior Medium Openings may convert shear wall to Pier and Spandrel System Pier Pier Spandrel Column Beam Wall
  77. 77. Openings in Shear Walls - Planer
  78. 78. Shear Wall Behavior Pier and Spandrel System Frame Behavior
  79. 79. D L ww=0.4k/ft 4ft4ft4ft4ft4ft3ft4ft 27ft 7 SP@ 3 ft = 21 ft w = 1k/ft, w = 0.6 k/ft at roof and floorlevels Problem: 12.3: Bearing wall with openings
  80. 80. LATERAL DEFLECTION OF WALLS WITH OPENINGS PIER-SPANDEL SYSTEMS
  81. 81. Multiple Shear Panels
  82. 82. Shear Wall-Frame Interaction: Lateral Deflection (top), Wind Moments (bottom)
  83. 83. Modeling Walls with Opening Plate-Shell Model Rigid Frame Model Truss Model
  84. 84. Truss model for shear walls Rigid frame model for shear walls
  85. 85. In ETABS single walls are modeled as cantilevers and walls with openings as pier/spandrel systems. Use the following steps to model a shear wall in ETABS: • Files > New Model > model outline of wall • Edit grid system by right-clicking the model and use: Edit Reference Planes (or go to Edit >), Edit Reference Lines (or go to Edit >), and possibly Plan Fine Grid Spacing (or go to Options > References > Dimensions/Tolerances Preferences) • Define as in SAP: Material Properties, Wall/Slab/Deck Sections, Static Load Cases, and Load Combinations • Draw the entire wall, then select the wall > Edit > Mesh Areas > Intersection with Visible Grids, then create window openings by deleting the respective panels. • Assign pier and spandrel labels to the wall: Assign > Shell Areas > Pier Label command and then the same process for Spandrel Label. • Assign the loads to the wall. • Run the Analysis. • View force output: go to Display > Show Member Forces/Stress diagram > Frame/Pier/Spandrel Forces > check Piers and Spandrels > e.g. M33 • Design: Options > Preferences > Shear Wall Design > check Design Code, Start: Design > Shear Wall Design > Select Design Combo, then click Start Design/Check of Structure. • Once design is completed, design results are displayed on the model. A right-click on one of the members will bring up the Interactive Design Mode form, then click Overwrites, if changes have to be made.
  86. 86. THE STRUCTURE OF THE SKIN: GLASS SKINS
  87. 87. Cologne/Bonn Airport, Germany, 2000, Helmut Jahn Arch., Ove Arup USA Struct. Eng.
  88. 88. Cottbus University Library, Cottbus, Germany, 2005, Herzog & De Meuron Arch
  89. 89. Max Planck Institute of Molekular Cell Biology, Dresden, 2002, Heikkinen-Komonen Arch
  90. 90. Xinghai Square shopping mall, Dalian, China
  91. 91. Sony Center, Potzdamer Platz, Berlin, 2000, Helmut Jahn Arch., Ove Arup USA Struct. Eng
  92. 92. Shopping Center, Jiefangbei business district, Chongqing, China
  93. 93. PLATES • SLABS • RETAINING WALLS
  94. 94. A visual investigation of floor structures
  95. 95. Slab structures: the effect of support and boundaries
  96. 96. Joist floor
  97. 97. Introduction to two-way slabs on rigid supports
  98. 98. Design of two-way slabs on stiff beams
  99. 99. Flat slab building structures
  100. 100. Design of flat plates and post-tensioned slabs
  101. 101. Square and Round Concrete Slabs
  102. 102. Investigate a square 6-in. (15 cm) concrete slab, 12 x 12 ft (3.66 x 3.66 m) in size that carries a uniform load of 120 psf (5.75 kPa or kN/m2, COMB1), that is a dead load of 75 psf (3.59 kPa) for its own weight (SLABDL taken care by self weight) and an additional dead load 5 psf (0.24 kPa, TOPDL), and a live load of 40 psf.(1.92 kPa, LIVE). The concrete strength is 4000 psi (28 MPa) and the yield strength of the reinforcing bars is 60 ksi (414 MPa). Solve the problem by using 2 x 2 ft (0.61 x 0.61 m) plate elements. Check the answers manually using approximations. Compare the various slab systems that is study the effect of support location on force flow. a. Assume one-way, simply supported slab action. b. Assume a two-way slab, simply supported along the perimeter. c. Assume the slab is clamped along the edges to approximate a continuous interior two-way slab. d. Assume flat plate action where the slab is simply supported by small columns at the four corners. e. Assume cantilever plate action with four corner supports for a center bay of 8x 8 ft (2.44 x 2.44 m).
  103. 103. Assume one-way, simply supported slab action. Checking the SAP results according to the conventional beam theory: The total slab load is: W = 0.120(12)12 = 17.28 k The reactions are: R = W/2 = 17.28/2 = 8.64 k = wL/2 = 0.120(12/2) = 0.72 k/ft or, at the interior nodes Rn= 2(0.72) = 1.44 k The maximum moment is: Mmax = wL2/8 = 120(12)2/8 = 2160 lb-ft/ft Checking the stresses, which are averaged at the nodes, S = tb2/6 = 6(12)2/6 = 144 in.3 ±fb = M/S = 2(2160(12)/144) = 360 psi According to SAP, the critical bending values of the center slab strip at mid-span are: M11 = 2129 lb-ft/ft, S11 = ± 354 psi
  104. 104. Assume a two-way slab, simply supported along the perimeter. Checking the results approximately at the critical location at center of plate according to tables (see ref. Timoshenko), is Ms ≈ wL2/22.6= 120(12)2/22.6 = 764 lb-ft/ft The critical moment values according to SAP are: M11 = M22 = MMAX = 778 lb-ft/ft Notice the uplift reaction forces in the corners causing negative diagonal moments at the corner supports, M12 = -589 lb-ft/ft Assume the slab is clamped along the edges to approximate a continuous interior two-way slab. The critical moment values are located at middle of fixed edge according to tables (ref. Timoshenko), are Ms ≈ - wL2/20 = -120(12)2/20 = -864 lb-ft/ft The critical moment values according to SAP are: M11 = M22 = MMIN = -866 lb-ft/ft
  105. 105. b. DEEP BEAMS c. SHALLOW BEAMSa. WALL SUPPORT d. NO BEAMS SLAB SUPPORT ALONG EDGES
  106. 106. a d b e c f EXAMPLE: 12.5: Square concrete slabs
  107. 107. Punching shear
  108. 108. #4 @ 12" #3 @ 9" 15 ft 12 in 12 in #13 @ 305 mm #10 @ 229 mm 4.57 m 305 mm Example 4.10 one-way slab cross section
  109. 109. ETABS template SAFE template There are no slab templates in SAP2000 – planar objects must be modeled
  110. 110. Gatti Wool Factory, Rome, Italy, 1953, Pier Luigi Nervi
  111. 111. Floor systems of Palace of Labor, Large Sports Palace, Gatti Wool Factory, Pier Luigi Nervi
  112. 112. Schlumberger Research Center, Cambridge, 1985, Michael Hopkins, Anthony Hunt, Ove Arup
  113. 113. Dead + PT LC: vertical deflection plot of slab
  114. 114. GI GI BM BM BM 16/24 16/24 12/24 12/24 12/24 34" 15"15" 18"x18" EXAMPLE 4.10: Design of one-way slab
  115. 115. Retaining wall
  116. 116. Example of slab steel reinforcement layout
  117. 117. Example of steel reinforcement layout
  118. 118. Ramp (STRAP)
  119. 119. FOLDED SURFACES The folded surfaces of the following building cases many the early modern period are constructed of reinforced concrete while most of the later periods are of framed steel or wood construction (e.g. trusses)! • RIBBED VAULTING • LINEAR and RADIAL ADDITIONS parallel, triangular, and tapered folds • CURVILINEAR FOLDS
  120. 120. Folded plate structure systems
  121. 121. Examples 7.1 and 7.2: slab action
  122. 122. Examples 7.1 and 7.2: beam action
  123. 123. Triangular folded plates
  124. 124. (1) Figs 7.6, 7.7, 7.8
  125. 125. Folded plate architecture
  126. 126. Saint John's Abbey, Collegeville, Minnesota, 1961, Marcel Breuer Arch
  127. 127. American Concrete Institute Building (ACI), Detroit. Michigan, 1959, Minoru Yamasaki Arch
  128. 128. NIT, Ningbo
  129. 129. Neue Kurhaus, Aachen, Germany
  130. 130. Unesco Auditorium, Paris, 1958, Marcel Breuer, Pier Luigi Nervi
  131. 131. Turin Exhibition Hall, Salone Agnelli, 1949, Pier Luigi Nervi
  132. 132. St. Loup Chapel, Rompaples VD, Switzerland, 2008, Danilo Mondada Arch
  133. 133. St. Foillan, Aachen, Germany, 1958, Leo Hugot Arch.
  134. 134. Wallfahrtskirche "Mariendom" , Neviges, Germany, 1972, Gottfried Boehm Arch
  135. 135. St. Gertrud, Cologne, Germany, 1965, Gottfried Boehm Arch
  136. 136. St. Hubertus, Aachen, Germany, 1964, Gottfried Böhm Arch
  137. 137. Riverside Museum, Glasgow, Scotland, 2011, Zaha Hadid Arch, Buro Happold Struct. Eng
  138. 138. SHELLS: solid shells, grid shells • CYLINDRICAL SHELLS • THIN SHELL DOMES • HYPERBOLIC PARABOLOIDS
  139. 139. Curvilinear Patterns
  140. 140. Surface classification 1
  141. 141. Surface classification 2
  142. 142. Arches as enclosures
  143. 143. Development of long-span roof structures
  144. 144. St. Peters (1590 by Michelangelo), Rome; US Capitol (1865 by Thomas U. Walther), Washington; Epcot Center, Orlando, (1982by Ray Bradbury ) geodesic dome; Georgia Astrodome, Atlanta (1980);
  145. 145. Pantheon, Rome, Italy, c. 123 A.D.
  146. 146. Hagia Sofia, Constantinople (Istanbul), 537 A.D., Anthemius of Tralles and Isodore of Miletus
  147. 147. St. Mary, Pirna, Germany, 1616
  148. 148. Casa Mila, Barcelona, Spain, 1912, Antoni Gaudi Arch (catalan vaulting)
  149. 149. Versuchsbau einer doppelt gekruemmtan Zeiss-Dywidag Schale (1.5 cm thick): Franz Dischinger & Ulrich Finsterwalder, Dyckerhoff & Widmann AG, Jena, 1931
  150. 150. Bent surface structures
  151. 151. UNESCO Concrete Portico (conoid), Paris, France, 1958, Marcel Breuer, Bernard Zehrfuss, Pier Luigi Nervi
  152. 152. Hipodromo La Zarzuela, 1935, Eduardo Torroja
  153. 153. Kresge Auditorium, MIT, 1955, Eero Saarinen Arch, Amman & Whitney Struct. Eng
  154. 154. Kresge Auditorium, MIT, Eero Saarinen/Amman Whitney, 1955, on three supports deflected structure under its own weight
  155. 155. Suspended models by Heinz Isler
  156. 156. Autobahnraststätte, Deitingen, Switzerland, 1968, Heinz Isler
  157. 157. Gartenhaus Center, Zuchuil, Switzerland, 1962, Heinz Isler
  158. 158. Bubble Castle, Theoule, France, 2009, Designer Antti Lovag
  159. 159. Earth House Estate Lättenstrasse, Dietikon, Switzerland, 2012, VETSCH ARCH
  160. 160. Sydney Opera House, 1973, Jørn Utzon, Arup - Peter Rice
  161. 161. Jubilee Church, Rom, Italy, 2000, Richard Meier Arch, Ove Arup Struct. Eng.
  162. 162. Eden Project, Cornwall, UK, 2001, Sir Nicholas Grimshaw Arch, Anthony Hunt Struct. Eng
  163. 163. Shell surfaces in plastics
  164. 164. Basic concepts related to barrel shells
  165. 165. Barrels
  166. 166. Cylindrical shell beam structures
  167. 167. Vaults and short cylindrical shells
  168. 168. R2 = z2 + x2 Circular cylindrical surface
  169. 169. Kimball Museum, Fort Worth, TX, 1972, Louis Kahn Arch, August E. Komendant Struct. Eng
  170. 170. Shonan Christ Church, Fujisawa, Kanagawa, Japan, 2014, Takeshi Hosaka Arch, HITOSHI YONAMINE / OVE ARUP Struct Eng
  171. 171. Stadelhofen, Zurich, Switzerland, 1983, Santiago Calatrava Arch
  172. 172. Shanghai Grand Theater, Shanghai, 1998, Jean-Marie Charpentier
  173. 173. College for Basic Studies, Sichuan University, Chengdu, 2002
  174. 174. CNIT Exhibition Hall, Paris, 1958, Bernard Zehrfuss Arch, Nicolas Esquillon Eng
  175. 175. P&C Luebeck, Luebeck, 2005, Ingenhoven und Partner, Werner Sobek Struct. Eng
  176. 176. Cristo Obrero Church, Atlantida, Uruguay, 1960, Eladio Dieste Arch+Struct Eng
  177. 177. World Trade Centre Dresden, 1996, Dresden, nps + Partner
  178. 178. Glass Roof for DZ-Bank, Berlin, 1998, Schlaich Bergermann Struct. Eng
  179. 179. Railway Station "Spandauer Bahnhof“, Berlin- Spandau, 1997, Architect von Gerkan Marg und Partner, Scdhlaich Bergermann
  180. 180. Greenhouse Dalian
  181. 181. Garden Exhibition Shell Roof, Stuttgart, 1977, Hans Luz und Partner, Schlaich Bergermann
  182. 182. St. Louis Abbey Priory Chapel, Missouri, 1962, Gyo Obata of (HOK) and Pier Luigi Nervi
  183. 183. St. Louis Airport, 1956, Minoru Yamasaki, Anton Tedesko, a cylindrical groin vault
  184. 184. Ecole Nationale de Ski et d'Alpinisme (ENSA), Chamonix-Mont Blanc, France, 1974, Roger Taillibert Arch, Heinz Isler Struct. Eng.
  185. 185. Dalian
  186. 186. Social Center of the Federal Mail, Stuttgart, 1989, Roland Ostertag Arch, Schlaich Bergermann Struct. Eng
  187. 187. The Tunnel, Buenos Aires, Argentine, Estudio Becker-Ferrari Arch
  188. 188. Slab action vs beam action
  189. 189. From the joist slab to shell beam
  190. 190. Behavior of short barrel shells Long vs short barrel shell
  191. 191. Behavior of long barrel shell
  192. 192. Rectangular beam vs shell beam
  193. 193. a. b.
  194. 194. a. b. c. d. Transverse S22 stresses and longitudinal S11 stresses in short barrel shells
  195. 195. Pipe connected to plate - stress contour of structural piping
  196. 196. Barrel shells with or without edge beams Various cylindrical shell types
  197. 197. Museum of Hamburg History Glass Roof, Hamburg, 1989, von Gerkan Marg, Partner,Sclaich Bergermann
  198. 198. x2 +y2 + z2 = R2 surface geometry of spherical surface
  199. 199. x2 +y2 + z2 = R2
  200. 200. Don Bosco Church, Augsburg, Germany, 1962, Thomas Wechs Arch
  201. 201. MUDAM: Futuro House (or UFO), 1968, Finland, Matti Suuronen
  202. 202. Little Sports Palace, 1960 Olympic Games, Rome, Italy, Pier Luigi Nervi
  203. 203. St. Rochus Kirche, Düsseldorf, Germany, 1954, Paul Schneider- Esleben Arch
  204. 204. National Grand Theater, Beijing, 2007, Paul Andreu Arch
  205. 205. Schlüterhof Roof, German Historical Museum, Berlin, glazed grid shell, 2002, Architect I.M. Pei, Schlaich Bergermann
  206. 206. Keramion, Frechen, Germany, 1971, Peter Neufert Arch, Stefan Polónyi Struct. Eng.
  207. 207. Reichstag, Berlin, Germany, 1999, Norman Foster Arch. Leonhardt & Andrae Struct. Eng
  208. 208. Schlüterhof Roof, German Historical Museum, Berlin, Germany, 2002, I.M. Pei Arch, Schlaich Bergermann Struct. Eng
  209. 209. Braced dome types
  210. 210. Dome structure cases
  211. 211. Major dome systems Membrane forces in a spherical dome shell due to live load q
  212. 212. Membrane forces in a dome shell due to self-weight w Dome shells on polygonal base
  213. 213. Schwedler dome (Example 8.6) Elliptic paraboloid
  214. 214. Junction of dome shell and support structure
  215. 215. a. b. a. b. shallow and hemispherical shells
  216. 216. Cylindrical grid with domical ends
  217. 217. Allianz Arena, Munich, 2006, Herzog & Meuron Arch, Arup Struct Eng
  218. 218. Mineirão Stadium Roof, Belo Horizonte, Brazil, 2012, Gerkan, Marg + Gustavo Penna Arch, Schlaich Bergermann Struct. Eng.
  219. 219. Climatron Greenhouse, St. Louis, 1960, Murphy and Mackey Arch, Synergetics Designers
  220. 220. Biosphere, Toronto, Expo 67, Buckminster Fuller, 76 m, double-layer space frame
  221. 221. Geodesic dome
  222. 222. MUDAM, Museum of Modern Art, Luxembourg, 2006, I.M. Pei Arch
  223. 223. Burnham Plan Centennial Eco-Pavilion, Chicago, 2009, Zaha Hadid Arch
  224. 224. Pennsylvania Station Redevelopment / James A. Farley Post Office, New York, 2003, SOM
  225. 225. Luce Memorial Chapel, Taichung, Taiwan, 1963, I. M. Pei Arch
  226. 226. Cologne Mosque, Cologne, Germany, 2014, Paul und Gottfried Boehm Arch
  227. 227. Case study of hypar roofs
  228. 228. Hyperbolic paraboloid
  229. 229. Hyperbolic parabolid with curved edges Hyperbolic parabolid with straight edges. Félix Candela The Hyperbolic Paraboloid The hyperbolic-paraboloid shell is doubly curved which means that, with proper support, the stresses in the concrete will be low and only a mesh of small reinforcing steel is necessary. This reinforcement is strong in tension and can carry any tensile forces and protect against cracks caused by creep, shrinkage, and temperature effects in the concrete. Candela posited that “of all the shapes we can give to the shell, the easiest and most practical to build is the hyperbolic paraboloid.” This shape is best understood as a saddle in which there are a set of arches in one direction and a set of cables, or inverted arches, in the other. The arches lead to an efficient structure, but that is not what Candela meant by stating that the hyperbolic paraboloid is practical to build. The shape also has the property of being defined by straight lines. The boundaries, or edges, of the hypar can be straight or curved. The edges in the second case are defined by planes “cutting through” the hypar surface.
  230. 230. Hypar units on square grids
  231. 231. Membrane forces in basic hypar unit
  232. 232. Some hypar characteristics
  233. 233. Examples 8.9 and 8.10
  234. 234. z = (f/ab)xy = kxy The equation defining the surface of a regular hypar
  235. 235. 5/8 in. concrete shell, Cosmic Rays Laboratory, U. of Mexico, 1951, Felix Candela
  236. 236. Hypar umbrella structures, Mexico, 1950s, Felix Candela
  237. 237. Hypar roof for a warehouse, Mexico, 1955, Felix Candela
  238. 238. Zarzuela Racecourse Grandstand, Madrid, 1935, Eduardo Torroja, Carlos Arniches Moltó, Martín Domínguez Esteban Arch, Eduardo Torroja Struct Eng: overhanging hyperboloidal sectors
  239. 239. More umbrella hypars by Felix Candela
  240. 240. Iglesia de la Medalla Milagrosa, Mexico City, 1955, Felix Candela
  241. 241. Iglesia de la Virgen Milagrosa, Mexico City, 1955, Felix Candela
  242. 242. Chapel Lomas de Cuernavaca, Cuernavaca, Mexico, 1958, Felix Candela
  243. 243. Bacardí Rum Factory, Cuautitlán, Mexico, 1960, Felix Candela
  244. 244. Los Manantiales, Xochimilco , Mexico, 1958, Felix Candela
  245. 245. Alster-Schwimmhalle, Hamburg- Sechslingspforte, 1967, Niessen und Störmer Arch, Jörg Schlaich Struct. Eng
  246. 246. The Cathedral of St. Mary of the Assumption, San Francisco, California, USA, 1971, Pietro Belluschi + Pier-Luigi Nervi Design
  247. 247. St. Mary’s Cathedral, Tokyo, Japan, 1963, Kenzo Tange, Yoshikatsu Tsuboi
  248. 248. Shanghai Urban Planning Center, Shanghai, China, 2000, Ling Benli Arch
  249. 249. Law Courts, Antwerp, Belgium, 2005, Richard Rogers, Arup Struct. Eng
  250. 250. Bus shelter, Schweinfurt, Germany
  251. 251. a. b. c.. d.
  252. 252. Intersecting shells
  253. 253. Other surface structures
  254. 254. Heidi Weber Pavilion, Zurich (CH), 1963, Le Corbusier Arch
  255. 255. Teepott Seebad, Warnemünde, Rostock, Germany, 1968, Erich Kaufmann Arch, Ulrich Müther Struct. Eng
  256. 256. Lehman College Art Gallery, Bronx, New York, 1960, Marcel Breuer Arch
  257. 257. Philips Pavilion, World's Fair, Brussels (1958), Le Corbusier Arch
  258. 258. Membrane forces - elliptic paraboloid
  259. 259. Multihalle Mannheim, Mannheim, Germany, 1975, Frei Otto Arch
  260. 260. TWA Terminal, JFK Airport, New York, NY, 1962, Eero Saarinen Arch, Amman and Whitney Struct. Eng
  261. 261. EXPO-Roof, Hannover, Germany, 2000, Thomas Herzog Arch, Julius Natterer Struct. Eng,
  262. 262. Japan Pavilion, Hannover Expo 2000, 2000, Shigeru Ban Arch
  263. 263. Centre Pompidou-Metz, 2010, France, Shigeru Ban Arch
  264. 264. Pompidou Museum II, Metz, France, 2010, Shigeru Ban
  265. 265. Sydney Opera House, Australia, 1972, Joern Utzon/ Ove Arup
  266. 266. Museum of Contemporary Art (Kunsthaus), Graz, Austria, 2003, Peter Cook - Colin Fournier Arch
  267. 267. Wünsdorf Church, Wünsdorf, Germany, 2014, GRAFT Arch, Happold Struct. Eng
  268. 268. Beijing National Stadium, 2008, Herzog and De Meuron Arch, Arup Eng
  269. 269. BMW Welt Munich, 2007, Coop Himmelblau Arch, Bollinger und Grohmann Struct. Eng
  270. 270. Heydar Aliyev Centre, Bakı, Azerbaijan, 2012, Zaha Hadid Architects, Tuncel Engineering, AKT (Structure), Werner Sobek (Façade)
  271. 271. Busan Cinema Center, Busan, South Korea, 2012, CenterCoop Himmelblau Arch, Bollinger und Grohmann Struct Eng
  272. 272. DZ Bank auditorium, Berlin, Germany ,2001, Frank Gehry Arch, Schlaich Bergemann Struct. Eng
  273. 273. Museo Soumaya, Mexico City, 2011, Fernando Romero Arch, Ove Arup and Frank Gehry engineering
  274. 274. Railway station Spandau, Berlin, Germany, 1998, Gerkan, Marg Arch, Schlaich, Bergemann
  275. 275. Alvin and Marilyn Lubetkin House, Mo-Jo Lake, Texas, 1972, Ant Farm (Richard Jost, Chip Lord, Doug Michels)
  276. 276. Endless House, 1958, Frederick Kiesler Arch
  277. 277. MUDAM, Museum of Modern Art, Luxembourg, 2007
  278. 278. Tensile Membrane Structures In contrast to traditional surface structures, tensile cablenet and textile structures lack stiffness and weight. Whereas conventional hard and stiff structures can form linear surfaces, soft and flexible structures must form double-curvature anticlastic surfaces that must be prestressed (i.e. with built-in tension) unless they are pneumatic structures. In other words, the typical prestressed membrane will have two principal directions of curvature, one convex and one concave, where the cables and/or yarn fibers of the fabric are generally oriented parallel to these principal directions. The fabric resists the applied loads biaxially; the stress in one principal direction will resist the load (i.e. load carrying action), whereas the stress in the perpendicular direction will provide stability to the surface structure (i.e. prestress action). Anticlastic surfaces are directly prestressed, while synclastic pneumatic structures are tensioned by air pressure. The basic prestressed tensile membranes and cable net surface structures are
  279. 279. Tensile membrane roof structures
  280. 280. Georgia Dome, Atlanta, 1995, Weidlinger, Structures such as the Hypar-Tensegrity Dome, 234 m x 186 m
  281. 281. Millenium Dome (365 m), London, 1999, Rogers + Happold
  282. 282. Tent architecture
  283. 283. Hybrid tensile surface structures
  284. 284. Point-supported tents Edge supports for cable nets
  285. 285. Examples 9.9 and 9.10
  286. 286. German Pavilion, Expo ’67, Montreal, Canada, Frei Paul Otto and Rolf Gutbrod, Leonhardt + Andrä Struct. Eng.
  287. 287. Olympic Parc, Munich, Germany, 1972, Frei Otto, Leonhardt-Andrae
  288. 288. Structural study model for the Munich Olympic Stadium (1972), Behnisch Architekten, with Frei Otto Soap models by Frei Otto
  289. 289. Sony Center, Potzdamer Platz, Berlin, 2000, Helmut Jahn Arch., Ove Arup
  290. 290. 2010 London Festival of ArchitecturePrice & Meyers Arch
  291. 291. Rosa Parks Transit Center, Detroid, 2009, Parson Brinkerhoff Arch
  292. 292. TENSILE MEMBRANE STUCTURES Pneumatic structures Air-supported structures Air-inflated structures (i.e. air members) Hybrid air structures Anticlastic prestressed membrane structures Edge-supported saddle roofs Mast-supported conical saddle roofs Arch-supported saddle roofs Hybrid tensile surface structures (possibly including tensegrity)
  293. 293. MATERIALS The various materials of tensile surface structures are: • films (foils) • meshes (porous fabrics) • fabrics • cable nets Fabric membranes include acrylic, cotton, fiberglass, nylon, and polyester. Most permanent large-scale tensile structures use fabrics, that is, laminated fabrics, and coated fabrics for more permanent structures. In other words, the fabrics typically are coated and laminated with synthetic materials for greater strength and/or environmental resistance. Among the most widely used materials are polyester laminated or coated with polyvinyl chloride (PVC), woven fiberglass coated with polytetrafluoroethylene (PTFE, better known by its commercial name, Teflon) or coated with silicone.
  294. 294. There are several types of weaving methods. The common place plain- weave fabrics consists of sets of twisted yarns interlaced at right angles. The yarns running longitudinally down the loom are called warp yarns, and the ones running the crosswise direction of the woven fabric are called filling yarns, weft yarns, or woof yarns. The tensile strength of the fabric is a function of the material, the number of filaments in the twisted yarn, the number of yarns per inch of fabric, and the type of weaving pattern. The typical woven fabric consists of the straight warp yarn and the undulating filling yarn. It is apparent that the warp direction is generally the stronger one and that the spring-like filler yarn elongates more than the straight lengthwise yarn. From a structural point of view, the weave pattern may be visualized as a very fine meshed cable network of a rectangular grid, where the openings clearly indicate the lack of shear stiffness. The fact of the different behavioral characteristics along the warp and filling makes the membrane anisotropic. However, when the woven fabric is laminated or coated, the rectangular meshes are filled, thus effectively reducing the difference in behavior along the orthog