SURFACE STRUCTURES including SAP2000
Prof. Wolfgang Schueller
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, (1) The Design of Building Structures (Vol.1, Vol. 2), rev. ed., PDF eBook by Wolfgang Schueller, 2016, published originally by Prentice Hall, 1996, (2) 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
Surfaces in nature
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
- SHELLS: solid shells, grid shells CYLINDRICAL SHELLS THIN SHELL DOMES HYPERBOLIC PARABOLOIDS
- 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)
Slabs resisting gavity loads
Flat plate building
New National Gallery, Berlin, 1968, Mies van der Rohe Arch
Notre Dame du Haut, Ronchamp, France, 1955, Le Corbusier Arch, Arup Struct Eng
Shear walls resisting wind
Cite Picasso, Nantere, Paris, 1977, Emile Aillaud Arch
Whitney Museum of American Art, New York, 1966, Marcel Breuer Arch
Everson Museum, Syracuse, NY, 1968, I. M. Pei Arch
Auditorium Maximum TU Munich, 1995,Rudolf Wienands Arch, Seiler-Stephan-Bloos Struct Eng
Delft University of Technology Aula Congress Centre, 1966, Jaap Bakema Arch
St. Engelbert, Cologne-Riehl, Germany, 1932, Dominikus Böhm Arch
Design Museum, Nuremberg, Germany, 1999, Volker Staab Arch
Schlumberger Research Center, Cambridge, UK, 1985, Hopkins/ Hunt
Stress contour of structural piping
Boston Convention Center, Boston, 2005, Vinoly and LeMessurier
Incheon International Airport, Seoul. 2001, Fentress Bradburn Arch.
MUDAM, Museum of Modern Art, Luxembourg, 2007, I.M. Pei
Armchair 41 Paimio by Alvar Aalto, 192933, laminated birchwood
Eames Plywood Chair, 1946, Charles and Ray Eames Designers
Panton Molded Plastic Chair, Denmark, 1960, Verner Panton Designer
Ribbon Chair, Model CL9, Bernini, 1961, Cesare Leonardi & Franca Stagi designers
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!
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.
LINE COMPONENT
PLANAR COMPONENT
SOLID COMPONENT
Possibilities for Modeling a Simple Structure CONTINUOUS MODELS DISCRETE MODEL
LINE ELEMENT
TYPICAL PLANAR ELEMENTS
TYPICAL SOLID ELEMENTS
a.
b.
c.
d.
Basics of Modeling
e.
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
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!
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.
FMIN
FMAX
Axis 2
J4 J3 F22 Axis 1
F12 F11
F12
J2 J1
MEMBRANE FORCES
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
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 dropdown box, then type 0.0624 in the Multiplier edit box, then click OK.
MEMBRANES • BEAMS • BEARING WALLS and SHEAR WALLS
National Gallery of Art, East Wing, Washington, 1978, I.M. Pei Arch
ey
Fy
Fy
Fy Mp
Cp
d/2
d/2 d/2
Bending Stresses
Tp b
ey
Fy
Fy
Fy
1
2
3
e.
Glulam beams
Build-up wood beams
Equivalent stress distribution for typical singly reinforced concrete floor beams at ultimate loads
Shear force resistance of vertical stirrups
Design of concrete floor structure (see Examples 3.17 and 3.18)
4'
1 K/ft
40'
2'
10 k
8'
(2) EXAMPLES: 12.1, 12.2
4'
1 K/ft
40'
a.
b.
c.
EXAMPLE: 12.1: Beam membrane
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.
±1.01 ksi
92 psi
EXAMPLE: 12.1: Beam membrane
2'
10 k
8'
EXAMPLE 12.2: Cantilever beam membrane
Pu= 500 k 10'
Pu= 500 k 10'
a.
10'
strut: Hcu z = 0.9h = 10.8'
u
D
12'
wh
Hcu
Du
wd
θ = 47.20
b.
tie: Htu
Mu
Htu 30' R = 500 k
R = 500 k
EXAMPLE 12.3 Deep Beam; Flexural Stress S11
Arbitrary membrane structure – S11 stresses – displacements contour lines – displacements contour fill
BEARING WALLS and SHEAR WALLS
Luther house, Eisenach, Germany, ca. 500 years old
Wartburg, Eisenach (Germany), center for medieval poetry and minnegesang, Luther translated the New Testament
National Assembly, Dacca, Bangladesh, 1974, Louis Kahn
Kaiserbad Building, Aachen, Germany,1994, Ernst Kasper & Klaus Klever Arch.
Songzhuang Artist Residences, Beijing, 2009, DnA_Design and Architecture
Wall behavior
World War II bunker transformed into housing, Aachen, Germany
Dormitory of Nanjing University, Zhang Lei Arch., Nanjing University, Research Center of Architecture
Seismic action
Shear-wall or Cantilever-column
LATERAL DEFLECTION OF SHEAR WALLS
Shear Wall Behavior
Frame Behavior
Shear Wall and Frame
Shear Wall and Frame Behavior
Shear Wall and Truss Behavior
25 k
25 k
h = 16'
h
L = 32'
L = 8'
a.
b.
LONG WALL 10.5 k
CANTILEVER WALL 9 k/ft
10ft
10ft
INTERMEDIATE WALL Example 12.4: Effect of shear wall proportion
Long wall: axial stresses, shear stresses, bending stresses
From shallow to deep beam
shallow beam
deep beam
Deep concrete beams
Effect of shear wall proportion, S22 axial stresses, S12 shear stresses
S22 axial gravity stress – S12 wind shear stress – S22 flexural wind stress
EXAMPLE: 12.4: Bearing wall
Typical Long-wall structure
Typical shear wall structure
The behavior of ordinary shear walls
Fig. 12.8, Problem 12.2: Stresses S22 (COMB1), S12 (COMB2), S22 (COMB3)
The response of exterior brick walls to lateral and gravity loading
The effect of lateral load action upon walls with openings
Shear Wall
Shear Wall or Frame ?
Shear Wall or Frame
Frame
Very Small Openings may not alter wall behavior
Medium Openings may convert shear wall to Pier and Spandrel System
Beam
Spandrel
Wall
Very Large Openings may convert the Wall to Frame
Column Pier
Pier
Openings in Shear Walls
Openings in Shear Walls - Planer
Shear Wall Behavior
Pier and Spandrel System
Frame Behavior
27 ft
3 ft
4 ft
4 ft
4 ft
4 ft
ww = 0.4 k/ft
4 ft
4 ft
wD = 1k/ft, wL = 0.6 k/ft at roof and floor levels
7 SP@ 3 ft = 21 ft
Problem: 12.3: Bearing wall with openings
LATERAL DEFLECTION OF WALLS WITH OPENINGS
PIER-SPANDEL SYSTEMS
Multiple Shear Panels
Shear Wall-Frame Interaction: Lateral Deflection (top), Wind Moments (bottom)
Plate-Shell Model
Rigid Frame Model
Modeling Walls with Opening
Truss Model
Truss model for shear walls
Rigid frame model for shear walls
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.
THE STRUCTURE OF GLASS WALL SKINS
Cologne/Bonn Airport, Germany, 2000, Helmut Jahn Arch., Ove Arup USA Struct. Eng.
Cottbus University Library, Cottbus, Germany, 2005, Herzog & De Meuron Arch
Max Planck Institute of Molekular Cell Biology, Dresden, 2002, Heikkinen-Komonen Arch
Xinghai Square shopping mall, Dalian, China
Sony Center, Potzdamer Platz, Berlin, 2000, Helmut Jahn Arch., Ove Arup USA Struct. Eng
Shopping Center, Jiefangbei business district, Chongqing, China
PLATES • SLABS
• RETAINING WALLS
A visual investigation of floor structures
Slab structures: the effect of support and boundaries
Joist floor
Introduction to two-way slabs on rigid supports
Design of two-way slabs on stiff beams
Flat slab building structures
Design of flat plates and post-tensioned slabs
Mixed Path Slab On Walls Slab On Beams Beams on Walls
Complex Path
Three Step Path
Slab on Beams Slab on Walls Beams on Beams Beams on Columns
Slab On Ribs Ribs On Beams Beams on Columns
Single Path
Single Path
Dual Path
Slab On Walls
Slab on Columns
Slab On Beams, Beams on Columns
Gravity Load Transfer Paths
Type of Slab Systems in SAFE
Square and Round Concrete Slabs
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).
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
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
a. WALL SUPPORT
b. DEEP BEAMS
c. SHALLOW BEAMS
SLAB SUPPORT ALONG EDGES
d. NO BEAMS
a
b
c
d
e
f
EXAMPLE: 12.5: Square concrete slabs
Punching shear
#4 @ 12"
#13 @ 305 mm
#3 @ 9" #10 @ 229 mm 12 in 305 mm
15 ft 4.57 m
Example 4.10 one-way slab cross section
12 in
ETABS template
SAFE template
There are no slab templates in SAP2000 – planar objects must be modeled
Gatti Wool Factory, Rome, Italy, 1953, Pier Luigi Nervi
Floor systems of Palace of Labor, Large Sports Palace, Gatti Wool Factory, Pier Luigi Nervi
Schlumberger Research Center, Cambridge, 1985, Michael Hopkins, Anthony Hunt, Ove Arup
Dead + PT LC: vertical deflection plot of slab
34"
18"x18"
15"
GI 16/24
BM 12/24
BM 12/24
EXAMPLE 4.10: Design of one-way slab
15"
GI 16/24
BM 12/24
Retaining wall
Example of slab steel reinforcement layout
Example of steel reinforcement layout
Ramp (STRAP)
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
Folded plate structure systems
Examples 7.1 and 7.2: slab action
Examples 7.1 and 7.2: beam action
Triangular folded plates
(1) Figs 7.6, 7.7, 7.8
Folded plate architecture
Saint John's Abbey, Collegeville, Minnesota, 1961, Marcel Breuer Arch
American Concrete Institute Building (ACI), Detroit. Michigan, 1959, Minoru Yamasaki Arch
NIT, Ningbo
Neue Kurhaus, Aachen, Germany
Unesco Auditorium, Paris, 1958, Marcel Breuer, Pier Luigi Nervi
Turin Exhibition Hall, Salone Agnelli, 1949, Pier Luigi Nervi
St. Loup Chapel, Rompaples VD, Switzerland, 2008, Danilo Mondada Arch
St. Foillan, Aachen, Germany, 1958, Leo Hugot Arch.
Wallfahrtskirche "Mariendom" , Neviges, Germany, 1972, Gottfried Boehm Arch
St. Gertrud, Cologne, Germany, 1965, Gottfried Boehm Arch
St. Hubertus, Aachen, Germany, 1964, Gottfried Böhm Arch
Riverside Museum, Glasgow, Scotland, 2011, Zaha Hadid Arch, Buro Happold Struct. Eng
Pukovo Airport Roof Detail, Saint Petersburg, Russia, 2014, Grimshaw Arch, Arup Struct Eng
SHELLS: solid shells, grid shells • CYLINDRICAL SHELLS • THIN SHELL DOMES • HYPERBOLIC PARABOLOIDS
Curvilinear Patterns
Surface classification 1
Surface classification 2
Arches as enclosures
Development of long-span roof structures
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);
Pantheon, Rome, Italy, c. 123 A.D.
Hagia Sofia, Constantinople (Istanbul), 537 A.D., Anthemius of Tralles and Isodore of Miletus
Santa Maria del Fiore, Florence, Italy. Begun in 1296. Dome added by Filippo Brunelleschi in 1436
Saint Peter's Basilica, Rome, 15061626, Rome, Michaelangelo, 1546; hanging chain” analysis of Dome of St Peter’s, by Giovani Poleni, 1742
St Paul’s Cathedral, London (16751708),Christopher Wren Arch
Frauenkirche, Dresden, Germany, 1743/2005, George Bähr Arch
St. Mary, Pirna, Germany, 1616
Casa Mila, Barcelona, Spain, 1912, Antoni Gaudi Arch (catalan vaulting)
Versuchsbau einer doppelt gekruemmtan Zeiss-Dywidag Schale (1.5 cm thick): Franz Dischinger & Ulrich Finsterwalder, Dyckerhoff & Widmann AG, Jena, 1931
Bent surface structures
UNESCO Concrete Portico (conoid), Paris, France, 1958, Marcel Breuer, Bernard Zehrfuss, Pier Luigi Nervi
Hipodromo La Zarzuela, 1935, Eduardo Torroja
Kresge Auditorium, MIT, 1955, Eero Saarinen Arch, Amman & Whitney Struct. Eng
deflected structure under its own weight
Kresge Auditorium, MIT, Eero Saarinen/Amman Whitney, 1955, on three supports
Suspended models by Heinz Isler
Autobahnraststätte, Deitingen, Switzerland, 1968, Heinz Isler
Gartenhaus Center, Zuchuil, Switzerland, 1962, Heinz Isler
Bubble Castle, Theoule, France, 2009, Designer Antti Lovag
Earth House Estate Lättenstrasse, Dietikon, Switzerland, 2012, VETSCH ARCH
Sydney Opera House, 1973, Jørn Utzon, Arup - Peter Rice
Jubilee Church, Rom, Italy, 2000, Richard Meier Arch, Ove Arup Struct. Eng.
Eden Project, Cornwall, UK, 2001, Sir Nicholas Grimshaw Arch, Anthony Hunt Struct. Eng
Shell surfaces in plastics
Basic concepts related to barrel shells
Barrels
Cylindrical shell beam structures
Vaults and short cylindrical shells
R2 = z2 + x2 Circular cylindrical surface
Kimball Museum, Fort Worth, TX, 1972, Louis Kahn Arch, August E. Komendant Struct. Eng
Shonan Christ Church, Fujisawa, Kanagawa, Japan, 2014, Takeshi Hosaka Arch, HITOSHI YONAMINE / OVE ARUP Struct Eng
Stadelhofen, Zurich, Switzerland, 1983, Santiago Calatrava Arch
Shanghai Grand Theater, Shanghai, 1998, Jean-Marie Charpentier
College for Basic Studies, Sichuan University, Chengdu, 2002
CNIT Exhibition Hall, Paris, 1958, Bernard Zehrfuss Arch, Nicolas Esquillon Eng
P&C Luebeck, Luebeck, 2005, Ingenhoven und Partner, Werner Sobek Struct. Eng
Cristo Obrero Church, Atlantida, Uruguay, 1960, Eladio Dieste Arch+Struct Eng
World Trade Centre Dresden, 1996, Dresden, nps + Partner
Glass Roof for DZ-Bank, Berlin, 1998, Schlaich Bergermann Struct. Eng
Railway Station "Spandauer Bahnhof“, BerlinSpandau, 1997, Architect von Gerkan Marg und Partner, Scdhlaich Bergermann
Greenhouse Dalian
Garden Exhibition Shell Roof, Stuttgart, 1977, Hans Luz und Partner, Schlaich Bergermann
St. Louis Abbey Priory Chapel, Missouri, 1962, Gyo Obata of (HOK) and Pier Luigi Nervi
St. Louis Airport, 1956, Minoru Yamasaki, Anton Tedesko, a cylindrical groin vault
Ecole Nationale de Ski et d'Alpinisme (ENSA), Chamonix-Mont Blanc, France, 1974, Roger Taillibert Arch, Heinz Isler Struct. Eng.
Dalian
Social Center of the Federal Mail, Stuttgart, 1989, Roland Ostertag Arch, Schlaich Bergermann Struct. Eng
The Tunnel, Buenos Aires, Argentine, Estudio Becker-Ferrari Arch
Slab action vs beam action
From the joist slab to shell beam
Long vs short barrel shell
Behavior of short barrel shells
Behavior of long barrel shell
Rectangular beam vs shell beam
a.
b.
a.
b.
c.
d.
Transverse S22 stresses and longitudinal S11 stresses in short barrel shells
Pipe connected to plate - stress contour of structural piping
Barrel shells with or without edge beams
Various cylindrical shell types
Museum of Hamburg History Glass Roof, Hamburg, 1989, von Gerkan Marg, Partner,Sclaich Bergermann
x2 +y2 + z2 = R2 surface geometry of spherical surface
x2 +y2 + z2 = R2
Don Bosco Church, Augsburg, Germany, 1962, Thomas Wechs Arch
MUDAM: Futuro House (or UFO), 1968, Finland, Matti Suuronen
Little Sports Palace, 1960 Olympic Games, Rome, Italy, Pier Luigi Nervi
State Farm Center (Assembly Hall), University of Illinois, Urbana-Champaign, 1963, Harrison & Abramovitz Arch, Ammann & Whitney Struct. Eng
St. Rochus Kirche, Düsseldorf, Germany, 1954, Paul SchneiderEsleben Arch
National Grand Theater, Beijing, 2007, Paul Andreu Arch
Schlüterhof Roof, German Historical Museum, Berlin, glazed grid shell, 2002, Architect I.M. Pei, Schlaich Bergermann
Keramion, Frechen, Germany, 1971, Peter Neufert Arch, Stefan Polónyi Struct. Eng.
Reichstag, Berlin, Germany, 1999, Norman Foster Arch. Leonhardt & Andrae Struct. Eng
Schlüterhof Roof, German Historical Museum, Berlin, Germany, 2002, I.M. Pei Arch, Schlaich Bergermann Struct. Eng
Braced dome types
Dome structure cases
Major dome systems
Membrane forces in a spherical dome shell due to live load q
Membrane forces in a dome shell due to self-weight w
Dome shells on polygonal base
Schwedler dome (Example 8.6)
Elliptic paraboloid
Junction of dome shell and support structure
a.
a.
b.
b.
shallow and hemispherical shells
Cylindrical grid with domical ends
Allianz Arena, Munich, 2006, Herzog & Meuron Arch, Arup Struct Eng
Mineirão Stadium Roof, Belo Horizonte, Brazil, 2012, Gerkan, Marg + Gustavo Penna Arch, Schlaich Bergermann Struct. Eng.
Climatron Greenhouse, St. Louis, 1960, Murphy and Mackey Arch, Synergetics Designers
Biosphere, Toronto, Expo 67, Buckminster Fuller, 76 m, double-layer space frame
Geodesic dome
MUDAM, Museum of Modern Art, Luxembourg, 2006, I.M. Pei Arch
Burnham Plan Centennial Eco-Pavilion, Chicago, 2009, Zaha Hadid Arch
Japanese pavilion at shanghai expo 2010, Yutaka Hitosaka Arch
Pennsylvania Station Redevelopment / James A. Farley Post Office, New York, 2003, SOM
Luce Memorial Chapel, Taichung, Taiwan, 1963, I. M. Pei Arch
Cologne Mosque, Cologne, Germany, 2014, Paul und Gottfried Boehm Arch
Case study of hypar roofs
Hyperbolic paraboloid
Félix Candela
Hyperbolic parabolid with curved edges
Hyperbolic parabolid with straight edges.
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.
Hypar units on square grids
Membrane forces in basic hypar unit
Some hypar characteristics
Examples 8.9 and 8.10
The equation defining the surface of a regular hypar
z = (f/ab)xy = kxy
5/8 in. concrete shell, Cosmic Rays Laboratory, U. of Mexico, 1951, Felix Candela
Hypar umbrella structures, Mexico, 1950s, Felix Candela
Hypar roof for a warehouse, Mexico, 1955, Felix Candela
Zarzuela Racecourse Grandstand, Madrid, 1935, Eduardo Torroja, Carlos Arniches Moltó, Martín Domínguez Esteban Arch, Eduardo Torroja Struct Eng: overhanging hyperboloidal sectors
More umbrella hypars by Felix Candela
Iglesia de la Medalla Milagrosa, Mexico City, 1955, Felix Candela
Iglesia de la Virgen Milagrosa, Mexico City, 1955, Felix Candela
Chapel Lomas de Cuernavaca, Cuernavaca, Mexico, 1958, Felix Candela
Bacardí Rum Factory, Cuautitlán, Mexico, 1960, Felix Candela
Los Manantiales, Xochimilco , Mexico, 1958, Felix Candela
Alster-Schwimmhalle, HamburgSechslingspforte, 1967, Niessen und Störmer Arch, Jörg Schlaich Struct. Eng
The Cathedral of St. Mary of the Assumption, San Francisco, California, USA, 1971, Pietro Belluschi + Pier-Luigi Nervi Design
St. Mary’s Cathedral, Tokyo, Japan, 1963, Kenzo Tange, Yoshikatsu Tsuboi
Shanghai Urban Planning Center, Shanghai, China, 2000, Ling Benli Arch
Law Courts, Antwerp, Belgium, 2005, Richard Rogers, Arup Struct. Eng
Bus shelter, Schweinfurt, Germany
a.
b.
c..
d.
Intersecting shells
Other surface structures
Heidi Weber Pavilion, Zurich (CH), 1963, Le Corbusier Arch
Teepott Seebad, Warnemünde, Rostock, Germany, 1968, Erich Kaufmann Arch, Ulrich Müther Struct. Eng
Lehman College Art Gallery, Bronx, New York, 1960, Marcel Breuer Arch
Philips Pavilion, World's Fair, Brussels (1958), Le Corbusier Arch
Membrane forces - elliptic paraboloid
Multihalle Mannheim, Mannheim, Germany, 1975, Frei Otto Arch
TWA Terminal, JFK Airport, New York, NY, 1962, Eero Saarinen Arch, Amman and Whitney Struct. Eng
EXPO-Roof, Hannover, Germany, 2000, Thomas Herzog Arch, Julius Natterer Struct. Eng,
Japan Pavilion, Hannover Expo 2000, 2000, Shigeru Ban Arch
Centre Pompidou-Metz, 2010, France, Shigeru Ban Arch
Pompidou Museum II, Metz, France, 2010, Shigeru Ban
Sydney Opera House, Australia, 1972, Joern Utzon/ Ove Arup
Museum of Contemporary Art (Kunsthaus), Graz, Austria, 2003, Peter Cook - Colin Fournier Arch
Wünsdorf Church, Wünsdorf, Germany, 2014, GRAFT Arch, Happold Struct. Eng
Beijing National Stadium, 2008, Herzog and De Meuron Arch, Arup Eng
BMW Welt Munich, 2007, Coop Himmelblau Arch, Bollinger und Grohmann Struct. Eng
Heydar Aliyev Centre, Bakı, Azerbaijan, 2012, Zaha Hadid Architects, Tuncel Engineering, AKT (Structure), Werner Sobek (Façade)
Busan Cinema Center, Busan, South Korea, 2012, CenterCoop Himmelblau Arch, Bollinger und Grohmann Struct Eng
DZ Bank auditorium, Berlin, Germany ,2001, Frank Gehry Arch, Schlaich Bergemann Struct. Eng
Guangzhou Opera House, China, 2010, Zaha Hadid Arch, KGE Struct Eng
Museo Soumaya, Mexico City, 2011, Fernando Romero Arch, Ove Arup and Frank Gehry engineering
Railway station Spandau, Berlin, Germany, 1998, Gerkan, Marg Arch, Schlaich, Bergemann
Alvin and Marilyn Lubetkin House, Mo-Jo Lake, Texas, 1972, Ant Farm (Richard Jost, Chip Lord, Doug Michels)
Endless House, 1958, Frederick Kiesler Arch
MUDAM, Museum of Modern Art, Luxembourg, 2007
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
Tensile membrane roof structures
Georgia Dome, Atlanta, 1995, Weidlinger, Structures such as the Hypar-Tensegrity Dome, 234 m x 186 m
Millenium Dome (365 m), London, 1999, Rogers + Happold
Tent architecture
Hybrid tensile surface structures
Point-supported tents
Edge supports for cable nets
Examples 9.9 and 9.10
German Pavilion, Expo ’67, Montreal, Canada, Frei Paul Otto and Rolf Gutbrod, Leonhardt + Andrä Struct. Eng.
Olympic Parc, Munich, Germany, 1972, Frei Otto, Leonhardt-Andrae
Soap models by Frei Otto
Structural study model for the Munich Olympic Stadium (1972), Behnisch Architekten, with Frei Otto
Sony Center, Potzdamer Platz, Berlin, 2000, Helmut Jahn Arch., Ove Arup
2010 London Festival of ArchitecturePrice & Meyers Arch
Rosa Parks Transit Center, Detroid, 2009, Parson Brinkerhoff Arch
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)
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.
There are several types of weaving methods. The common place plainweave 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 orthogonal yarns so that the fabric may be considered isotropic for preliminary design purposes, similar to cable network with triangular meshes, plastic skins and metal skins.
The scale of the structure, from a structural point of view, determines the selection of the tensile membrane type. The approximate design tensile strengths in the warp and fill directions, of the most common coated fabrics may be taken as follows for preliminary design purposes:
PVC-coated nylon fabric (nylon coated with vinyl): 200 – 400 lb/in (350 – 700 N/cm) PVC-coated polyester fabric:
300 – 700 lb/in.(525 – 1226 N/cm)
PVC-coated fiberglass fabric:
300 – 800 lb/in.(525 – 1401 N/cm)
PTFE-coated fiberglass fabric: (e.g. Teflon-coated fiberglass) 300 – 1000 lb/in.(525 – 1751 N/cm)
Strength Properties Samples taken from any roll will possess the following minimum ultimate strength values. Warp5700 N/50mmWeft (fill)5000 N/50mm
The 50mm width shall be a nominal width which contains the theoretical number of yarns for 50mm calculated from the overall fabric properties. (f) Design Life of Membrane
Membrane Properties
Tensile only: no shear or compression •Strength (38.5 ounce per square yard PTFE coated Fibreglass Fabric)
Warp: 785 lb/in. Fill: 560 lb/in.
•Creep •Modulus of Elasticity (E) E=stress/strain (stress=force/area,strain=dL/L)
•Poisson’s Ratio: ratio of strain in x and y directions Bi-axial testing of every roll of raw goods.
Which Fabric do I Use? Easy! There are five types of fabrics being used today for tensile fabric structures and they all have special qualities. Below are descriptions of these fabrics, but there may be other fabrics that are not listed here. These fabrics are (1) PVC coated polyester fabric, (2) PTFE coated glass fabric, (3) expanded PTFE fabric, (4) Polyethylene coated polyethylene fabric, and (5) ETFE foils. PVC polyester fabric is a cost effective fabric having a 10 to 20 year lifespan. It has been used in numerous applications worldwide for over 40 years and it is easy to move for temporary building applications. Top films or coatings can be applied to keep the fabric clean over time. It meets building codes as a fire resistive product and light translucencies range between zero and 25%. PVC meets B.S 7837 for Fire Code. Typical woven roll width is 2.5 meters. PTFE glass fabrics have a 30 year lifespan and are completely inert. They do not degrade under ultra violet rays and are considered non combustible by most building codes. PTFE meets B.S 476 Class 0 for fire code. They are used for permanent structures only and can not be moved once installed. The PTFE coating keeps the fabric clean and translucencies range from 8 to 40%. They are woven in approximately 2.35m or 3.0 meter widths. ETFE foils are used in inflated pillow structures where thermal properties are important. The foil can be transparent or fritted much like laminated glass products to allow any level of translucency. Its fire properties lie somewhere between that of PTFE glass and PVC polyester fabrics and it is used in permanent applications. PVC glass fabrics are used for internal tensile sails, such as features in atriums, glare control systems. Their maintenance is minimal and meet B.S 476 Class 0 for Fire Code.
LOADS Tensile structures are generally of light weight. The magnitude of the roof weight is a function of the roof skin and the type of stabilization used. The typical weights of common coated polyester fabrics are in the range of approximately 24 to 32 oz/yd2 (0.17 to 0.22 psf, 8 to 11 Pa). The roof weight of a fabric membrane on a cable net may be up to approximately 1.5 psf (72 Pa). The lightweight nature of membrane roofs is clearly expressed by the air-supported dome of the 722-ft-span Pontiac Stadium in Michigan, weighing only 1 psf (48 Pa = 4.88 kg/m2).
Since the weight of typical pretensioned roofs is relatively insignificant, the stresses due to the superimposed primary loads of wind (laterally across the top and from below for open-sided structures), snow, and temperature change tend to control the design. These loads may be treated as uniform loads for preliminary design purposes and the structure weight can be ignored. The typical loads to be considered are snow loads, wind uplift, dynamic load action (wind, earthquake), prestress loads, erection loads, creep and shrinkage loads, movement of supports, temperature loads (uniform temperature changes and temperature differential between faces), and possible concentrated loads. The prestress required to maintain stability of the fabric membrane, depending on the material and loading, is usually in the range of 25 to 50 lb/in (88 N/cm).
STRUCTURAL BEHAVIOR Soft membranes must adjust their shape (because they are flexible) to the loading so that they can respond in tension. The membrane surface must have double curvature of anticlastic geometry to be stable. The basic shape is defined mathematically as a hyperbolic paraboloid. In cable-nets under gravity loads, the main (convex, suspended, lower load bearing) cable is prevented from moving by the secondary (concave, arched, upper, bracing, etc.) cable, which is prestressed and pulls the suspended layer down, thus stabilizing it. Visualize the initial surface tension analogous to the one caused by internal air pressure in pneumatic structures. Arched, prestress membrane force
wp f
T1
T1 w
T2 Suspended, load-carrying membrane force
f
T2
Design Process The design process for soft membranes is quite different from that for hard membranes or conventional structures. Here, the structural design must be integrated into architectural design. Geometrical shape: hand sketches are used to first pre-define a geometry of the surface as based on geometrical shapes(e.g. conoid, hyperbolic paraboloid) including boundary polygon shape as based on functional and aesthetical conditions. Equilibrium shape: form is achieved possibly first by using physical modeling and applying stress to the membrane (e.g. through edge-tensioning, cabletensioning, mast-jacking), where the geometry is in balance with its own internal prestress forces, and then by computer modeling. Computational shape: structural analysis is performed to find the resulting surface shape due to the various load cases causing large deformations of the flexible structure. The resulting geometry is significantly different from the initially generated form; the biaxial properties of the fabric (elastic moduli and Poisson’s ratios) are critical to the analysis. Not only the radius of curvature changes, but also the actual forces will be different. Modification of surface shape Cutting pattern generation of fabric membrane (e.g. linear patterning for saddle roofs, radial patterning for umbrellas)
General purpose finite element programs such as SAP can only be used for the preliminary design of cablenet and textile structures however the material properties of the fabric membrane in the warp- and weft directions must be defined. Special purpose programs are required for the final design such as Easy, a complete engineering design program for lightweight structures by technet GmbH, Berlin, Germany (www.technet-gmbh.com). The company also has second software, Cadisi, for architects and fabricators for the quick preparation of initial design proposals for the conceptual design of surface stressed textile structures especially of saddle roofs and radial high-point roofs.
Double Curvature
Large radius of curvature results in large forces.
PNEUMATIC STUCTURES Air-supported structures Air – inflated structures: air members Hybrid air structures
Classification of pneumatic structures
Pnematic structures
Low-profile, long-span pneumatic structures
Effect of internal pressure on geometry
Soap bubbles
The spherical membrane represents a minimal surface under radial pressure, since not only stresses and mean curvature are constant at any point on the surface, but also because the sphere by definition represents the smallest surface for the given volume. Some examples in nature are the sea foam, soap bubbles floating on a surface forming hemispherical shapes, and flying soap bubbles. The effect of the soap film weight on the spherical form may be neglected.
Traveling exhibition
Example 9.12
Effect of wind loading on spherical membrane shapes
Air-inflated members and Example 9.14
Air-supported structures
high-profile ground-mounted air structures
berm- or wall-mounted air domes
low-profile roof membranes Air-supported structures form synclastic, single-membrane structures, such as the typical basic domical and cylindrical forms, where the interior is pressurized; they are often called low-pressure systems because only a small pressure is needed to hold the skin up and the occupants don’t notice it. Pressure causes a convex response of the tensile membrane and suction results in a concave shape. The basic shapes can be combined in infinitely many ways and can be partitioned by interior tensile columns or membranes to form chambered pneus. Air-supported structures may be organized as high-profile groundmounted air structures, and berm- or wall-mounted, low-profile roof membranes.
In air-supported structures the tensile membrane floats like a curtain on top of the enclosed air, whose pressure exceeds that of the atmosphere; only a small pressure differential is needed. The typical normal operating pressure for airsupported membranes is in the range of 4.5 to 10 psf (0.2 kN/m2 to 0.5 kN/m2 = 0.5 kPa) or 2 mbar to 5 mbar, or roughly 1.0 to 2.0 inches of water as read from a water-pressure gage.
p
T = pR
EXAMPLE: 12.10 Air-supported cylindrical membrane
T = pR
US Pavilion, EXPO 70, Osaka, DavisBrody Arch, Geiger – Berger Struct. Eng.
US Pavilion, EXPO 70, Osaka, DavisBrody
Pontiac Metropolitan Stadium , Detroit, 1975, O'Dell/Hewlett & Luckenbach Arch, Geiger Berger Struct. Eng.
Metrodome, Minneapolis, 1982, SOM Arch, Geiger-Berger Struct. Eng
See also packing of soap bubbles
Examples of pneumatic structures
'Spirit of Dubai' Building in front of Al Fattan Marine Towers, Dubai, 2007
'Sleep and Dreams' Pavilion, 2006, Le Bioscope, France
To house a touring exhibition
Using inflatable moulds and spray on polyurethane foam
Kiss the Frog: the Art of Transformation, inflatable pavilion for Norway’s National Galery, Oslo, 2001, Magne Magler Wiggen Architect,
Air – inflated structures: air members Air inflated structures or simply air members, are typically, lower-pressure cellular mats: air cushions high-pressure tubes
Air members may act as columns, arches, beams, frames, mats, and so on; they need a much higher internal pressure than air-supported membranes
inflatable Ethylene Tetrafluoro Ethylene (ETFE) clad facade cushions
Allianz Arena, Munich, 2005, Herzog and Pierre de Meuron, Arup
Roof for Bullfight Arena - Vista Alegre, Madrid, 2000, Schlaich Bergemann
Expo 02 , Neuchatel, Switzerland, Multipack Arch, air cussion, ca 100 m dia.
Roman Arena Inflated Roof, Nimes, France, 1988, Architect Finn Geipel, Nicolas Michelin, Paris; Schlaich Bergermann und Partne; internal pressure 0.4…0.55 kN/m2
15' 15'
200'
EXAMP LE: 12.11: Air cushion roof
Hybrid air structures Hybrid air structures are formed by a combination of the preceeding two systems or when one or both of the pneumatic systems are combined with any kind of rigid support (e.g. arch supported).
In double-walled air structures, the internal pressure of the main space supports the skin and must be larger than the pressure between the skins, which in turn, must be large enough to withstand the wind loads. This type of construction allows better insulation, does not show the deformed state of the outer membrane, and has a higher safety factor against deflation. It provides rigidity to the structure and eliminates the need for an increase of pressure inside the building.
Fuji Pavilion, Expo 1970, Osaka, air pressure 500…..1000 mbar = 50……1000 kN/m2
Airtecture, Festo AG, Esslingen, Germany, 1999 Axel Thallemer Arch, Festo AG Struct. Eng
Surface structures tensioned by cables and masts are of permanent nature with at least 15 to 20 years of life expectancy (and tents or other clear-span canvas structures which are often massproduced) have an anticlastic surface geometry, where the two opposing curvatures balance each other. In other words, the prestress in the membrane along one curvature stabilizes the primary load-bearing action of the membrane along the opposite curvature. The induced tension provides stability to form, while space geometry, together with prestress, provides strength and stiffness.
The membrane supports may be rigid or flexible; they may be point or line supports located either in the interior or along the exterior edges. The following organization is often used based on support conditions: • Edge-supported saddle surface structures • Arch-supported saddle surface structures • Mast-supported conical (including point-hung) membrane structures (tents) • Hybrid structures, including tensegrity nets The lay out of the support types, in turn, results in a limitless number of new forms, such as,
• Ring-supported saddle roofs • Parallel and crossed arches as support systems • Parallel and radial folded plate point-supported surfaces • Multiple tents on rectangular grids
The pre-tensioning mechanisms range from edge-tensioning systems (e.g. clamped fabric edges) to cable-tensioning and mast-jacking systems. Since flexible structures can resist loads only in pure tension, their geometry must reflect and mirror the force flow; surface geometry is identical with force flow. Membranes must have sufficient curvature and tension throughout the surface to achieve the desired stiffness and strength under any loading condition. In contrast to traditional structures, where stresses result from loading, in anticlastic tensile structures prestress must be specified initially so that the resulting membrane shape can be determined. Tensile membranes can be classified either according to their surface form or to their support condition.. Basic anticlastic tensile surface forms are derived from the mathematical geometrical shapes of the paraboloid of revolution (conoid), the hyperbolic paraboloid or the torus of revolution. In more general terms, textile surface structures can be organized as, •
• •
Saddle-shaped and stretched between their boundaries representing orthogonal anticlastic surfaces with parallel fabric patterns Conical-shaped and center supported at high or low points representing radial anticlastic surfaces with radial fabric patterns The combination of these basic surface forms yields an infinite number of new forms
Dorton (Raleigh) Arena, 1952, North Carolina, Matthew Nowicki Arch, Frederick Severud Struct. Eng
Schwarzwaldhalle, Karlsruhe, Germany, 1954, Ulrich Finsterwalder + Franz Dischinger
Dreifaltigkeitskirche, Hamburg-Hamm, Germany, 1957, Reinhard Riemerschmid Arch
Yoyogi National Gymnasium, Tokyo, 1964, Kenzo Tange Arch, Yoshikatsu Tsuboi Struct. Eng
Minor Olympic Stadium, Tokyo, 1964, Kenzo Tange Arch, Yoshikatsu Tsuboi Struct. Eng
Ice Hokey Rink, Yale University, 1959, Eero Saarinen Arch, Fred N. Severud Struct. E.
Dance Pavilion, Federal Garden Exhibition, 1957, Cologne, Germany, Frei Otto Arch
University of La Verne Campus Center, La Verne (CA), 1973, The Shaver Partnership Arch, T. Y. Lin, Kulka, Yang Struct. Eng
One of the first architectural applications of PTFE coated Fibreglass fabrics developed in 1972. Fabric was tensile tested after 20 years at 70% fill/80% warp of original strength.
Ice Rink Roof, Munich, 1984, Architect Ackermann und Partner, Schlaich Bergermann Struct. Eng
Schlumberger Research Center, Cambridge, UK, 1985, Michael Hopkins Arch, Anthony Hunt Struct. Eng
Haj Terminal, Jeddah, Saudi Arabia, 1982, SOM/ Horst Berger Arch, Fazlur Khan/SOM Struct. Eng
Denver International Airport Terminal, 1994, Denver, Horst Berger/ Severud
San Diego Convention Center Roof, 1990, Arthur Erickson Arch, Horst Berger consultant for fabric roof
Nelson-Mandela-Bay-Stadion , Port Elizabeth , South Africa, 2010, Gerkan, Marg Arch , Schlaich Berger Struct. Eng
Rhoen-Clinic Medical Center, Bad Neustadt, Germany, 1997, Lamm-WeberDonath Arch, Werner Sobek Struct Eng
Moses Mabhida Stadion , Durban, South Africa, 2009, Gerkan, Marg und Partner
King Fahd International Stadium, Riyadh, Saudi Arabia, 1986, Ian fraser, John Roberts Arch, Geiger Berger Struct. Eng
Inchon Munhak Stadium, Inchon, South Korea, 2002, Adome Arch, Schlaich Bergermann Struct. Eng.
Canada Place, Vancouver, 1986, Eberhard Zeidler/ Horst Berger
Stellingen Ice Skating Rink Roof, Hamburg-Stellingen, 1994, Schlaich Bergermann Arch
Rhoen Clinikum, Bad Neustadt/Germany, 1997, Lamm, Weber, Donath & Partner Arch, Werner Sobek Struct Eng
Ningbo
Max Planck Institute of Molekular Cell Biology, Dresden, 2002, Heikkinen-Komonen Arch
Subway Station Froettmanning, Munich, 2005, Bohn Architect, PTFE-Glass roof
Cirque de Soleil, Disney World, Orlando, FL, 2000, FTL (Nicholas Goldsmith)/Happol d + Birdair
Rosa Parks Transit Center, Detroit, 2009, Parson Brinkerhoff + FTL Design and Engineering Studio
West Germany Pavilion at Expo 67, Montral, 1967, Frei Otto + Rolf Gutbrod Arch
Munich Olympic Stadium, 1972, Frei Otto and Gunther Behnisch
The prestress force must be large enough to keep the surface in tension under any type of loading, preventing any portion of the skin or any other member to slack because the compression being larger than the stored tension. In addition, the magnitude of the initial tension should be high enough to provide the necessary stiffness, so that the membrane deflection is kept to a minimum. However, the amount of pretensioning not only is a function of the superimposed loading but also is directly related to the roof shape and the boundary support conditions. The prestress required to maintain stability of the fabric membrane, depending on the material and loading, is usually in the range of 25 to 50 lb/in (44 to 88 N/cm). Flexible structures do not behave in a linear manner, but resist loads by going through large deformations and causing the magnitude of the membrane forces to depend on the final position in space.
For preliminary design of shallow membranes, all external loads (snow, wind) can be treated as normal loads, are assumed to be carried by the suspended portion of the surface, when the arched portion has lost its prestress and goes slack. Also notice that at least one-half of the permitted tension in the membrane is consumed by the initial stored tension. T2 = Tmax = wR = wL2/8f
The design of the arched cable system or yarn fibers is derived, in general, from the loading condition where maximum wind suction, ww, causes uplift and increases the stored prestress tension, which is considered equal to one-half of the full gravity loading, minus the relatively small effect of membrane weight. In other words, under upward loading, the maximum forces occur in the arched portion of the membrane T1 = Tmax = (wp + ww)R =(wp + ww)L2/8f
Problem 12.6: Tensile membrane hypar structure
COMB1
COMB2
COMB3
a.
b.
COMB1
COMB2
COMB3
Form Finding Methodologies There are three main methods used to find the equilibrium shape. All lead to the same result, which is an minimum surface for a given pre-stress, membrane characteristics, and edge and support conditions. Modern programs can take into account structural characteristics of supports, uneven loading, and non-linear membrane characteristics.
For a constant membrane thickness taking into account the weight of the membrane, no curved surface exists whereby all points on the surface have equal tension. It is possible, however, to obtain a curved surface where the shearing force at every point is zero. An important component of design is the analysis of the equilibrium surface, based on varying load scenarios. The final form the designer chooses may vary from the equilibrium surface so as to be optimized for estimated load extremes and considerations of on-site construction and pre-stressing methods.
