Supporting Structure for Freeform Surfaces in Buildings

Abstract

Supporting structure ( 8 ) for curved envelope geometries in buildings consisting of support elements ( 4 ) which are each combined to form N-sided polygons (N=3,4, . . . ) which span the envelope geometry and which each enclose a planar surface element ( 5 ), and the support elements ( 4 ) of adjacent N-sided polygons each form a common node region ( 3 ) in which the support elements ( 4 ) abut, and the plane of a surface element ( 5 ) and the respective planes of the surface elements ( 5 ) of two N-sided polygons which adjoin in non-parallel spatial directions lie in different planes in at least one portion of the envelope geometry. According to the invention, the support elements ( 4 ) in this portion each form 4- or 6-sided polygons, and the support elements ( 4 ) each have a longitudinal axis (L) which extends in a straight line between in each case two node regions ( 3 ) and runs parallel to the imaginary intersection line of the surface element planes associated with said portion, wherein the cross section of the support elements ( 4 ) normal to their longitudinal axis in each case has a relative twist angle of 0° along the entire longitudinal axis of the support element ( 4 ).

1 . A supporting structure ( 8 ) for curved envelope geometries in buildings, consisting of support elements ( 4 ) which are each combined to form N-gons which span the envelope geometry and which each enclose a planar surface element ( 5 ), and the support elements ( 4 ) of adjacent N-gons each form a common node region ( 3 ) in which the support elements ( 4 ) abut, and the plane of a surface element ( 5 ) and the respective planes of the surface elements ( 5 ) of two N-gons which adjoin in non-parallel spatial direction lie in different planes in at least one section of the envelope geometry, wherein the support elements ( 4 ) form in this section 4-gons or 6-gons each, and the support elements ( 4 ) each have a longitudinal axis (L) which extends in a straight line between two node regions ( 3 ) each and runs parallel to the imaginary line of intersection of the surface element planes associated with the same, with the cross section of the support elements ( 4 ) normal to their longitudinal axis in each case having a relative twist angle of 0° along the entire longitudinal axis (L) of the support element ( 4 ). 
   
   
       2 . A supporting structure according to  claim 1 , wherein the angular sum of respectively opposing angles is equal in the point of intersection of the imaginary lines of intersection of four surface element planes adjoining in a node region ( 3 ). 
   
   
       3 . A supporting structure according to  claim 1 , wherein the angular sum of respectively opposite angles between the surface normals of two adjoining surface element planes of four surface element planes adjoining in a node region ( 3 ) is equal. 
   
   
       4 . A supporting structure according to  claim 1 , wherein the support elements ( 4 ) have a rectangular cross-sectional shape or can be inscribed into a rectangular cross-sectional shape. 
   
   
       5 . A supporting structure according to  claim 1 , wherein at least two surface elements ( 5 ) are held on the support elements ( 4 ). 
   
   
       6 . A method for determining a supporting structure ( 8 ) for curved envelope geometries in buildings, consisting of support elements ( 4 ) in which a predetermined curved envelope geometry is approximated by a continuous network of N-gons (N=3,4, . . . ) which each define a planar mesh ( 1 ), with respectively adjoining N-gons having a common node (X), and the mesh plane of an N-gon and the respective mesh planes of two N-gons adjoining in non-parallel spatial directions lie in different planes in at least one section of the structural shape, wherein the approximation of the predetermined curved envelope geometry occurs with the help of a first continuous network of 4-gons or 6-gons which can be transferred to a further continuous network of 4-gons or 6-gons by parallel displacement in a direction normal to the mesh plane of the respective 4-gon or 6-gon, with two respective adjoining N-gons having a common boundary line ( 2 ) which determines the progression of the longitudinal axis of one support element ( 4 ) associated with said N-gons, and the dimensions of a support element ( 4 ) perpendicular to said boundary line ( 2 ) being determined by the distance (d) of the respective boundary line ( 2 ) of the first network to that of the further, parallel displaced network. 
   
   
       7 . A method for determining a supporting structure ( 8 ) according to  claim 6 , wherein the angular sum of respectively opposite angles between the boundary lines ( 2 ) of four adjoining 4-gons is equal in their common node (X). 
   
   
       8 . A method for determining a supporting structure ( 8 ) according to  claim 6 , wherein the angular sum of respectively opposite angles between the surface normals of two adjoining mesh planes of four surface element planes adjoining in a node (X) is equal. 
   
   
       9 . A method for determining a supporting structure ( 8 ) according to  claim 6 , wherein in a section of the supporting structure ( 8 ) at least one second continuous network of 4-gons or 6-gons is determined which each define a planar mesh plane, with the 4-gons or 6-gons of the second network being formed by parallel displacement of the 4-gons or 6-gons of the first network in a direction normal to the mesh plane of the respective 4-gon or 6-gon.