shape optimization study for a lattice column

SHAPE OPTIMIZATION STUDY FOR A LATTICE COLUMN CRITERIA AND APPROACH POINT LOAD KARAMBA DEFINITION Grad Structures 1 Class Project / Citylab Orlando / Summer 2019 Students: Carly Chavez, Jon Clark, Margaret Logas, Ka’Nard Robinson LATERAL LOAD KARAMBA DEFINITION Abstract This graduate level structures project introduces students to the application of parametric modeling, stress and deformation visualization, shape optimization, and digital fabrication in the analysis of complex structural elements and systems. The lattice column, similar to a diagrid or a truss column, exhibits unique qualities of lightness and simple spatial elegance; yet its underlying behavior as a vertical support element is deceivingly complex. To model the project, a thin walled cylinder with an adaptive lattice grid geometry mapped onto its surface was developed as a generative starting point for the lattice structure. The overall shape of the generative structure is modified into four varying shapes to compare and contrast the intricately distributed tensile and compressive stresses over the structural elements. The resultant structure is statically indeterminate and an approximate numerical solution for the stress distribution and deformation can be accomplished using finite element analysis software. With the comparative study, the material properties (steel), effective length and method of restraint for the column iteration are constant while the moment of inertia and the material area are allowed to adapt to each iteration (the smaller the diameter, the higher the area). The column modeling analysis is visualized in three iterative modes; the first was unrestrained in the z axis to develop stress in the members without column buckling, the second allowed the structure to deform or buckle under the vertical load, and in the third iteration the x axis was unrestrained to simulate deformation laterally. As precedent and inspiration for the study, projects by renowned architects Toyo Itto, Massimiliano Fuksas, Norman Foster, Pelli Clarke and others were reviewed. Further studies are planned to validate the numerical results and advance the single component into an integrated system of vertical and horizontal supports. Toyo Ito, Mediatheque, Sendai, Japan. 1998-201 Sasaki Structural Consultants Soviet Transmission Tower. 1922 Pelli Clarke, Winter Garden, NYC. 2014 Thornton Tomasetti PRECEDENT / INSPIRATION Massimiliano Fuksas, Milan, Italy. 2002 - 2005. Structural: Schlaich Bergmann Norman Foster, 30 St. Mary Axe, London. 2001 - 2003. Arup and Partners Kuenstle Summer 2019 Orlando LARGE CYLINDER 1 2 L = 18’ STRESS DISTRIBUTION CONVEX CYLINDER 1 2 L = 18’ STRESS DISTRIBUTION STRAIGHT CYLINDER STRESS DISTRIBUTION L = 18’ 2 CONCAVE CYLINDER L = 18’ 1 2 STRESS DISTRIBUTION 1 2 1

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SHAPE OPTIMIZATION STUDY FOR A LATTICE COLUMN

CRITERIA AND APPROACH

POINT LOADKARAMBA DEFINITION

Grad Structures 1 Class Project / Citylab Orlando / Summer 2019Students: Carly Chavez, Jon Clark, Margaret Logas, Ka’Nard Robinson

LATERAL LOADKARAMBA DEFINITION

AbstractThis graduate level structures project introduces students to the application of parametric modeling, stress and deformation visualization, shape optimization, and digital fabrication in the analysis of complex structural elements and systems. The lattice column, similar to a diagrid or a truss column, exhibits unique qualities of lightness and simple spatial elegance; yet its underlying behavior as a vertical support element is deceivingly complex. To model the project, a thin walled cylinder with an adaptive lattice grid geometry mapped onto its surface was developed as a generative starting point for the lattice structure. The overall shape of the generative structure is modified into four varying shapes to compare and contrast the intricately distributed tensile and compressive stresses over the structural elements. The resultant structure is statically indeterminate and an approximate numerical solution for the stress distribution and deformation can be accomplished using finite element analysis software. With the comparative study, the material properties (steel), effective length and method of restraint for the column iteration are constant while the moment of inertia and the material area are allowed to adapt to each iteration (the smaller the diameter, the higher the area). The column modeling analysis is visualized in three iterative modes; the first was unrestrained in the z axis to develop stress in the members without column buckling, the second allowed the structure to deform or buckle under the vertical load, and in the third iteration the x axis was unrestrained to simulate deformation laterally. As precedent and inspiration for the study, projects by renowned architects Toyo Itto, Massimiliano Fuksas, Norman Foster, Pelli Clarke and others were reviewed. Further studies are planned to validate the numerical results and advance the single component into an integrated system of vertical and horizontal supports.

Toyo Ito, Mediatheque, Sendai, Japan. 1998-201Sasaki Structural Consultants

Soviet Transmission Tower. 1922

Pelli Clarke, Winter Garden, NYC. 2014Thornton Tomasetti

PRECEDENT / INSPIRATION

Massimiliano Fuksas, Milan, Italy. 2002 - 2005.Structural: Schlaich Bergmann

Norman Foster, 30 St. Mary Axe, London. 2001 - 2003.Arup and Partners

Kuenstle Summer 2019 Orlando

LARGE CYLINDER

L =

18’

STRESS DISTRIBUTION

CONVEX CYLINDER