US3798849A - Hyperbolic paraboloid roof structure - Google Patents

Hyperbolic paraboloid roof structure Download PDF

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Publication number
US3798849A
US3798849A US00268599A US26859972A US3798849A US 3798849 A US3798849 A US 3798849A US 00268599 A US00268599 A US 00268599A US 26859972 A US26859972 A US 26859972A US 3798849 A US3798849 A US 3798849A
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United States
Prior art keywords
section
roof
roof structure
edges
outer edges
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Expired - Lifetime
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US00268599A
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English (en)
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D Biggs
E Konkel
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Individual
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Individual
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Publication date
Priority to CA118,864A priority Critical patent/CA949716A/en
Priority to FR7127139A priority patent/FR2099588B1/fr
Application filed by Individual filed Critical Individual
Priority to US00268599A priority patent/US3798849A/en
Application granted granted Critical
Publication of US3798849A publication Critical patent/US3798849A/en
Anticipated expiration legal-status Critical
Expired - Lifetime legal-status Critical Current

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    • E—FIXED CONSTRUCTIONS
    • E04—BUILDING
    • E04B—GENERAL BUILDING CONSTRUCTIONS; WALLS, e.g. PARTITIONS; ROOFS; FLOORS; CEILINGS; INSULATION OR OTHER PROTECTION OF BUILDINGS
    • E04B1/00—Constructions in general; Structures which are not restricted either to walls, e.g. partitions, or floors or ceilings or roofs
    • E04B1/32—Arched structures; Vaulted structures; Folded structures
    • E—FIXED CONSTRUCTIONS
    • E04—BUILDING
    • E04B—GENERAL BUILDING CONSTRUCTIONS; WALLS, e.g. PARTITIONS; ROOFS; FLOORS; CEILINGS; INSULATION OR OTHER PROTECTION OF BUILDINGS
    • E04B7/00—Roofs; Roof construction with regard to insulation
    • E04B7/08—Vaulted roofs
    • E04B7/10—Shell structures, e.g. of hyperbolic-parabolic shape; Grid-like formations acting as shell structures; Folded structures
    • E04B7/102—Shell structures
    • E—FIXED CONSTRUCTIONS
    • E04—BUILDING
    • E04H—BUILDINGS OR LIKE STRUCTURES FOR PARTICULAR PURPOSES; SWIMMING OR SPLASH BATHS OR POOLS; MASTS; FENCING; TENTS OR CANOPIES, IN GENERAL
    • E04H6/00—Buildings for parking cars, rolling-stock, aircraft, vessels or like vehicles, e.g. garages
    • E04H6/44—Buildings for parking cars, rolling-stock, aircraft, vessels or like vehicles, e.g. garages for storing aircraft
    • E—FIXED CONSTRUCTIONS
    • E04—BUILDING
    • E04B—GENERAL BUILDING CONSTRUCTIONS; WALLS, e.g. PARTITIONS; ROOFS; FLOORS; CEILINGS; INSULATION OR OTHER PROTECTION OF BUILDINGS
    • E04B1/00—Constructions in general; Structures which are not restricted either to walls, e.g. partitions, or floors or ceilings or roofs
    • E04B1/32—Arched structures; Vaulted structures; Folded structures
    • E04B2001/3235—Arched structures; Vaulted structures; Folded structures having a grid frame

Definitions

  • ABSTRACT A roof structure for a hanger or the like in which first and second roof sections having the shapes of parts of triangular cross sections made up of hyperbolic paraboloid surfaces joined by vertical edges.
  • roof structures which will effectively cover a large area at a relatively low cost without the use of intermediate supports.
  • the roof have the shape of a hyperbolic paraboloid, which may be described as a surface having parabolic contours when intersected with vertical planes at 45 to the grid lines and having hyperbolic contours when intersected by horizontal planes.
  • a hyperbolic paraboloid which may be described as a surface having parabolic contours when intersected with vertical planes at 45 to the grid lines and having hyperbolic contours when intersected by horizontal planes.
  • the hyperbolic paraboloid roof is made large enough in area to accommodate a large modern aircraft, its shape renders it unsuitable for that purpose. That is, over a given area and for certain vertical exterior dimensions, the stress condition of the roof is so high that excessive deflection results. This condition could only be overcome by use of a curvature which, while it reduces the stress, results in excessive exterior vertical dimensions.
  • Use of a plurality of hyperbolic paraboloid structures of limited area with intermediate supporting columns obviously defeats the intended purpose of thestructure.
  • a hyperbolic paraboloid is a structure which generally has great strength and rigidity except along the edges of the structure.
  • the stiffness of the edges might be increased by increasing the curvature of the body but again, the permissible external vertical dimensions would be exceeded.
  • a hyperbolic paraboloid roof structure which effectively covers a large area without the use of intermediate vertical supports.
  • Our structure effectively covers an extended area without incorporating inordinately great vertical dimensions.
  • Our structure incorporates stiff edges without requiring excessive vertical dimensions and without adding an inordinate weight to the structure.
  • Our roof permits an air.- craft hangar to be constructed in such a way as most efficiently to use the available space while accommodating extremely large aircraft.
  • One object of our invention is to provide an improved roof structure for covering a large area without requiring the use of intermediate vertical supports within the perimeter of the area.
  • Another object of our invention is to provide a hyperbolic paraboloid roof structure especially adapted for use in an aircraft hangar.
  • a further object of our invention is to provide a hyperbolic paraboloid roof structure which effectively covers an extended area without requiring excessively great exterior vertical dimensions.
  • Still another object of our invention is to provide a hyperbolic paraboloid roof structure having stiff edges without excessive vertical dimensions.
  • Yet another object of our invention is to provide a hyperbolic paraboloid roof structure having edges which are reinforced without adding materially to the weight of the basic structure.
  • our invention contemplates the provision of ahyperbolic paraboloid roof structure in which first and second roof sections shaped as portions of respective first and second hyperbolic paraboloidsare joined along an arch which is common to the two paraboloids. Portions of other hyperbolic paraboloids together with the edge portions of the first and second paraboloids and vertical edges form reinforcing girders of hollow, generally triangular cross section extending-around the edge of the structure.
  • FIG. 1 is a side elevation of an aircraft hangar incorporating our hyperbolic paraboloid roof structure.
  • FIG. 2 is a front elevation of the hangar shown in FIG. 1 taken along the line 2 2 of FIG. 1.
  • FIG. 3 is a diagrammatic view illustrating the manner in which a roof section can be taken from a hyperbolic paraboloid.
  • FIG. 4 is a diagrammatic view of a first hyperbolic paraboloid on which one of our roof sections is based as viewed from the right front thereof.
  • FIG. 5 is a diagrammatic view of a second hyperbolic paraboloid on which a second section of our roof structure is based as viewed from the right front thereof.
  • FIG. 6 is a diagrammatic view illustrating a compound figure made up by joining the paraboloids of FIGS. 3 and 4 along an arch common to the two.
  • FIG. 7 is a diagrammatic view of another hyperbolic paraboloid from which we obtain one side of a reinforcing girder of our hyperbolic paraboloid roof structure.
  • FIG. 8 is a diagrammatic view illustrating the manner in which a structure derived from the paraboloid of FIG. 6 cooperates with a portion of the arrangement of FIG. 5 in forming a reinforcing girder.
  • FIG. 9 is a perspective view illustrating our finished hyperbolic paraboloid roof structure.
  • This area has two corners at points on the parabola at the saddle and two other corners at distances h and h. from points p and p on the curve in the x 1 plane. It will be understood that in practice the area to be covered as well as minimum and maximum permissible heights are predetermined.
  • a first roof section surface indicated generally by the reference character may be formed with reference to a square grid indicated generally by the reference character 12'which may for example be 15 feet square to provide 255 squares defined by the intersecting lines of the grid.
  • the surface of our roof is derived from a hyperbolic paraboloid. Such a surface contains two families of straight lines and has a saddle point at the origin.
  • the hyperbolic paraboloid In generating the surface for the first section of ourroof we select a portion of the hyperbolic paraboloid providing respective high points 14 and 16 at the corners l8 and 20 of the grid I2and low points ofzero elevation at the other corners 22 and 24 of the grid.
  • the paraboloid surface has a hyperbolic curvature in planes passing through corners 18 and 20 and a parabolic contour in planes passing through corners 22 and 24.
  • the surface can be entirely 'made up of a plurality of straight lines 26. In effect, the entire 225 feet square with the 15 ft. grid is raised to conform to the high and low points resulting in the hyperbolic paraboloid surface.
  • work stringers need not be placed parallel to the straight lines 26 to form the surface, but may extend in any direction.
  • the front section terminates along a paraboloidal arch 30 shown in FIG. 4 so that the portion of the surface to the right of that line in FIG. 3 need not be constructed.
  • high point 14 has an elevation 108.6 ft.
  • FIG. 5 we generate another hyperbolic paraboloid surface indicated generally by the reference character 32 with reference to the same grid 12.
  • Surface 32 is made up of a plurality of straight lines 34 but the form work stringers need not be laid parallel to these lines in constructing the rear section of the roof.
  • the surface 32 contains an arch 36 which is identical with the arch 30. We connect the two sections along this arch so that we need not actually construct the portion of surface 32 to the left of the line 36 in FIG. 5.
  • Surface 32 is so selected as to provide a desired high point 38 in the nose area of the hangar and a theoreticalhigh point 40 at the other end of the surface with low points of zero at the corners 22 and 24 of the grid. In a particular example, we provide a high point 38 having an elevation of 66 ft. above the corner 20 and a theoretical high point 40 having an elevation of 210.6 ft. above the corner 18.
  • FIG. 6 we have illustrated the manner in which the surfaces 10 and 32 can be joined along an arch 40 which is common to both arches 30 and 36 to form a composite structure.
  • arch 40 which is common to both arches 30 and 36 to form a composite structure.
  • hyperbolic paraboloids generally have great strength and rigidity except along the edges thereof.
  • FIGS. 7 to 9 we generate a portion 42 of an edge reinforcing beam structure from a third hyperbolic paraboloid surface indicated generally by with it at about thirty feet for example, back from the front edge.
  • the paraboloid from which the surface portion 42 is derived may have high points at 1 15 ft. and at 392.25 ft. above the corners Band 20 of the grid.
  • additional surfaces 50, 52, 54 and 56 for other edges of the composite roof structure.
  • flat surfaces 58 are provided around the edge between the outer edge of surface 10 and of surface 42 for example to provide a hollow reinforcing girder entirely around the edge of the roof structure.
  • Abutments 60 and 62 may also be added to the structure.
  • the roof section per se is now complete.
  • FIGS. 1 and 2 in an actual installation of our hyperbolic paraboliod roof indicated generally by the reference character 64 including sections 10 and 32 in a hangar the roof is erected on a tie beam 66 and may be provided with wind columns 68.
  • Section 10 forms the entrance of the hangar while the left hand portion of section 32 as viewed in FIG. 1 forms the nose area.
  • Siding 70 across the upper portion of the front of section 10 is formed with an opening 72 for admitting the tail of an aircraft indicated in phantom at 74. Suitable doors and the like may be used to close the front of the hangar. Since the other portions of the hangar structure do not per se form part of our invention they will not be described in detail.
  • a roof in accordance with our invention, starting with given vertical dimensions for the front entrance, for the nose area and for the central arch, we first determine the surfaces of the sections and 32. Next, the reinforcing form work stringers are laid parallel to the surfaces. These stringers run in various directions and intersect each other. Next, the building material such for example as concrete is applied. So that said arch portions define a common arch therebetween. ln the course of that operation the reinforcing beam surfaces such as 42 and the vertical surfaces which close the beams are applied until the roof is complete. It will then accommodate an aircraft 74 with a minimum of waste space.
  • a first section cementitious having the shape of a predetermined part of a hyperbolic paraboloid generated with reference to a preselected grid, said first section having outer edge terminating outlying portions and an arch portion;
  • a second section cementitious having the shape of a predetermined part ofa hyperbolic paraboloid generated with reference to said preselected grid, said second section having outer edge terminating outlying portions and an arch portion that is substantially identical to the arch portion of said first section, the arch portion of said second section being positioned adjacent to the arch portion of said first section, so that said arch portions define a common arch therebetween;
  • a third section having the shape of a predetermined part of a hyperbolic paraboloid, said third section having one portion positioned adjacent to predetermined outlying portions of said first section and having another portion positioned adjacent to predetermined outlying portions of said second section with said one portion of said third section outwardly terminating at outer edges spaced. with respect to the outer edges of said first section and inwardly terminating at inward edges in contact with said first section inwardly of the outer edges thereof, and said another portion. of said third section outwardly terminating at outer edges spaced with respect to the outer edges of said second sec tion and inwardly terminating at inward edges in contact with said second section inwardly of the outer edges thereof; and
  • joining means having one portion joining outer edges of said first and third sections and another portion joining outer edges of said second and third sections whereby a roof structure reinforcing member is formed about said outer edged of said roof structure.

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  • Engineering & Computer Science (AREA)
  • Architecture (AREA)
  • Civil Engineering (AREA)
  • Structural Engineering (AREA)
  • Physics & Mathematics (AREA)
  • Electromagnetism (AREA)
  • Road Paving Structures (AREA)
US00268599A 1970-07-24 1972-07-03 Hyperbolic paraboloid roof structure Expired - Lifetime US3798849A (en)

Priority Applications (3)

Application Number Priority Date Filing Date Title
CA118,864A CA949716A (en) 1970-07-24 1971-07-22 Hyperbolic paraboloid roof structure
FR7127139A FR2099588B1 (enrdf_load_stackoverflow) 1970-07-24 1971-07-23
US00268599A US3798849A (en) 1970-07-24 1972-07-03 Hyperbolic paraboloid roof structure

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
US5806570A 1970-07-24 1970-07-24
US00268599A US3798849A (en) 1970-07-24 1972-07-03 Hyperbolic paraboloid roof structure

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US3798849A true US3798849A (en) 1974-03-26

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US00268599A Expired - Lifetime US3798849A (en) 1970-07-24 1972-07-03 Hyperbolic paraboloid roof structure

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CA (1) CA949716A (enrdf_load_stackoverflow)
FR (1) FR2099588B1 (enrdf_load_stackoverflow)

Cited By (12)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3909993A (en) * 1973-05-14 1975-10-07 Vredevoogd Jon Arch supported membrane structure
US4542759A (en) * 1982-09-22 1985-09-24 Kyner Jr Paul R Portable shelter
US4597925A (en) * 1985-07-05 1986-07-01 Loggy Albert D Method of constructing a modular reinforced building structure
US5020287A (en) * 1989-12-22 1991-06-04 Woods Ray A Structural building components incorporating integrated hyperbolic paraboloid elements
WO2004099517A1 (en) * 2003-05-06 2004-11-18 Borchio Piergiovanni Three-dimensional structure formed by joining straight members
US20040261953A1 (en) * 2001-10-16 2004-12-30 Hart Garry Randall Sail shaped awnings
GB2407329A (en) * 2003-10-15 2005-04-27 Moonburst Structures Ltd Building structure with a tensile membrane
USD544104S1 (en) * 2005-10-31 2007-06-05 Christopher Lee Grotbeck Paneled hypar canopy
US20070251161A1 (en) * 2004-12-21 2007-11-01 Florian Tuczek Double-curved shell
US20110197940A1 (en) * 2010-02-12 2011-08-18 Gerhard Allan Warner Saddle shaped tent with portico
US8869464B2 (en) * 2012-11-24 2014-10-28 Dennis John Newland Correlated hyperbolic paraboloid structural members
US10100510B1 (en) * 2017-03-21 2018-10-16 Imam Abdulrahman Bin Faisal University Expandable shade and shelter system

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109812022B (zh) * 2019-01-28 2021-04-09 中国五冶集团有限公司 双斜拱承双曲抛物面索网结构施工方法

Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US2511974A (en) * 1950-06-20 Hangar tent
US2928360A (en) * 1956-10-16 1960-03-15 Jr Edmund C Heine Flexural tension framing system and structural unit thereof
US2961802A (en) * 1957-02-18 1960-11-29 William T Mongan Stressed structural unit
US3137097A (en) * 1960-04-14 1964-06-16 Zeinetz Bertil Olov Roof structure
US3206895A (en) * 1961-03-27 1965-09-21 Reynolds Metals Co Hyperbolic paraboloidal roof and method of making the same
US3215153A (en) * 1963-06-10 1965-11-02 Carl F Huddle Architectural structure
US3263322A (en) * 1959-01-07 1966-08-02 Arthur T Brown Method of producing shell roof structure

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
FR792145A (fr) * 1934-09-22 1935-12-23 Perfectionnements aux constructions métalliques

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US2511974A (en) * 1950-06-20 Hangar tent
US2928360A (en) * 1956-10-16 1960-03-15 Jr Edmund C Heine Flexural tension framing system and structural unit thereof
US2961802A (en) * 1957-02-18 1960-11-29 William T Mongan Stressed structural unit
US3263322A (en) * 1959-01-07 1966-08-02 Arthur T Brown Method of producing shell roof structure
US3137097A (en) * 1960-04-14 1964-06-16 Zeinetz Bertil Olov Roof structure
US3206895A (en) * 1961-03-27 1965-09-21 Reynolds Metals Co Hyperbolic paraboloidal roof and method of making the same
US3215153A (en) * 1963-06-10 1965-11-02 Carl F Huddle Architectural structure

Cited By (15)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3909993A (en) * 1973-05-14 1975-10-07 Vredevoogd Jon Arch supported membrane structure
US4542759A (en) * 1982-09-22 1985-09-24 Kyner Jr Paul R Portable shelter
US4597925A (en) * 1985-07-05 1986-07-01 Loggy Albert D Method of constructing a modular reinforced building structure
US5020287A (en) * 1989-12-22 1991-06-04 Woods Ray A Structural building components incorporating integrated hyperbolic paraboloid elements
US20040261953A1 (en) * 2001-10-16 2004-12-30 Hart Garry Randall Sail shaped awnings
WO2004099517A1 (en) * 2003-05-06 2004-11-18 Borchio Piergiovanni Three-dimensional structure formed by joining straight members
GB2407329A (en) * 2003-10-15 2005-04-27 Moonburst Structures Ltd Building structure with a tensile membrane
GB2407329B (en) * 2003-10-15 2007-02-14 Moonburst Structures Ltd Building structure with a tensile membrane
US20070251161A1 (en) * 2004-12-21 2007-11-01 Florian Tuczek Double-curved shell
US7591108B2 (en) * 2004-12-21 2009-09-22 Florian Tuczek Double-curved shell
USD544104S1 (en) * 2005-10-31 2007-06-05 Christopher Lee Grotbeck Paneled hypar canopy
US20110197940A1 (en) * 2010-02-12 2011-08-18 Gerhard Allan Warner Saddle shaped tent with portico
US8701689B2 (en) * 2010-02-12 2014-04-22 0798555 B.C. Ltd. Saddle shaped tent with portico
US8869464B2 (en) * 2012-11-24 2014-10-28 Dennis John Newland Correlated hyperbolic paraboloid structural members
US10100510B1 (en) * 2017-03-21 2018-10-16 Imam Abdulrahman Bin Faisal University Expandable shade and shelter system

Also Published As

Publication number Publication date
FR2099588A1 (enrdf_load_stackoverflow) 1972-03-17
FR2099588B1 (enrdf_load_stackoverflow) 1974-03-29
CA949716A (en) 1974-06-25

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