S[tr/c]u[c/lp]ture workshop Sapienza 11 04 2015 intro

April 11 2015April 11 2015Sapienza University of RomeSapienza University of RomeSchool of Engineering School of Engineering

// // Sapienza and DTU workshopSapienza and DTU workshop ////Sapienza University of RomeSapienza University of Rome, , School of EngineeringSchool of Engineering, , April April 11 201511 2015

Structural optimization in parametricsStructural optimization in parametrics

Optimal lines on free-form surfacesOptimal lines on free-form surfaces

IntroductionIntroduction

Konstantinos GkoumasKonstantinos Gkoumas

StroNGER srl co-founder and partnerStroNGER srl co-founder and partner



THE UNIVERSITY

• Founded in 1303 by Pope Boniface

• 63 Departments

• 11 Faculties

• 2 University Hospitals

• 154 Bachelor courses

• 120 Master courses

• 243 Prof. Master courses

• 86 PhD courses

• 128,963 students

• 3997 Professors (including assistant-associate)

• 914 International agreements

• 20 double degrees

• 100 visiting professors

• 183 FP7 programs in 2007-2013


THE FACULTY OF CIVIL AND INDUSTRIAL ENGINEERING

• Founded in 1817 by Pope Pius VII

• In 1935, the School became the Faculty of Engineering

• Nowadays: “Faculty of Civil and Industrial Engineering”


THE ST. PETER IN CHAINS BASILICA

• first rebuilt on older foundations in 432–440 to house the relic of the chains that bound Saint Peter

• It houses Michelangelo's Moses statue (completed in 1515)


THE ST. PETER IN CHAINS BASILICA


THE CLOISTER

Giuliano da Sangallo15th century


THE CLOISTER


THE CLOISTER


THE CLOISTER


THE GROUP OF STRUCTURAL ANALYSIS AND DESIGN

Franco Bontempi, PhDProf. of Structural Analysis and DesignSapienza University of Rome

Stro N

GERwww.stronger2012.com

Academic research Industry research - R&D

University courses Professional courses

Big group Small group


THE GROUP OF STRUCTURAL ANALYSIS AND DESIGN


THE TECHNICAL UNIVERSITY OF DENMARK

• Founded in 1829

• Today ranked among Europe's leading engineering institutions

• Academic staff: 2,003

• Administrative staff: 1,540

• Students: 11,190

• Undergraduates: 6,803

• Doctoral students:1,200


VANKE PAVILION

RAMBOLL Computational Design


VANKE PAVILION



VANKE PAVILION



VANKE PAVILION



WORKSHOP PROGRAM OUTLINE

09.15-09.45 Introduction: the Pierluigi Nervi inspiration Konstantinos

09.45-11.15 Grasshopper introduction and exercises Salma & Kareem

11.15-11.30 Morning break

11.30-13.00 Karamba introduction and exercises•Simple beams (cantilever and simply supported), cross sections, loads, materials, joints / truss elements•Introduction to 2nd order analysis, buckling modes, eigenfrequencies •Mesh and shell elements (importance of good mesh qualities and exercises in shell elements)•Shell analysis tool (force-flow, principal stress, principal bending)

Kristjan & Mariam

13.00-14.00 Lunch break

14.00-17.00 Design exercise•Analyze existing structure(s)•Design of new free-form shed covering the open space over the Sapienza Engineering Faculty Cloister

17.00-18.00 Group presentations


isostatic lines – Nervi’s inspiration


Isostatic lines define the directions of principal stress to visualize the stress trajectories in beams and other elements. In other words, they indicate by their direction at any point, the direction of one of the principal stresses.

Beam with isostatic lines (thick compression lines and thin tension lines)

isostatic lines – a brief recall

Cantilever beam


Lines of stress within a material subject to compressive loading graphically describing the isostatic lines around a hole – in the far right case with a stiffer infill.

"Hole Force Lines" by Kaidor ‘Form and Forces’, by Edward Allen and Waclaw Zalewski

isostatic lines – “force follows stiffness”


stress trajectory: a line showing the continuous change in the orientation of a principal stress throughout a body.

although trajectories may curve, their intersections with other principal stresses remain perpendicular.

isostatic lines: stress trajectories in surfaces


isostatic lines: stress trajectories in surfaces

D'Aloisio, Righi, Modelli matematici per l’architettura e il calcolo numerico 2013 \\ 2014Dr. Luca Sgambi, Politecnico di Milano


Considering (Arcangeli) that a 2D continuous body subjected to normal forces produces two families of orthogonal curves (isostatics), tangential to the principal bending moment trajectories, along which torsional moments are equal to zero.

If this continuous body is replaced by ribs oriented along the isostatics, then the rib structure and the continuous body would have identical structural behavior under identical loading and support conditions.

isostatic lines – Nervi’s inspiration

Isostatic inspiration for the rib patterns of Nervi’s floor systems

Isostatic Ribbed Floor Slab


Source: Nervi, P.L., Aesthetics and Technology in Building, Harvard University Press (1965).

Each 5m x 5m slab of the Gatti Wool Factory is supported by a central column. All slabs are monolithically joined along the perimeter edges.

• red lines: primary isostatics, corresponding to the maximum principal bending moments

• blue lines: represent the secondary isostatics, corresponding to the minimum principal bending moments.

Gatti Wool Factory floorsDesign: Nervi, Arcangeli, Cesteli Guidi

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C.C. Guidi e P.L. Nervi

Lanificio Gatti Roma 1951-53 solaio a

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Source: Nervi, P.L., Aesthetics and Technology in Building, Harvard University Press (1965).

Each 10m x 10m slab is supported by columns at the four corners and the isostatic patterns follow one-eighth symmetry

Palace of Labor (Palazzo del Lavoro), TurinDesign: Nervi, Arcangeli, Cesteli Guidi

Source: Project Nervi - Aesthetics and Technology, Dale Clifford, Carnegie Mellon University


Analogy between natural and artificial forms: in nature there is a “natural reinforcement” along the most stresses zones

A similarity in nature (?)


A similarity in nature (?)

left: Wolff’s Law traces bone growth along principle stress trajectoriesright: cross section of a human femur

Wolff’s Law developed the theory that bone grows in response to stress or put another way, the internal patterning of bone is transformable and responsive to external loading from the environment. The converse is also true, that bone will degenerate if not subject to loading.

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Palazzetto dello Sport di Roma

A. Vitellozzi eP.L. Nervi

Palazzetto dello SportRoma 1956-57

sezioni schematiche


A. Vitellozzi e P.L. NerviPalazzetto dello Sport

Roma 1956-57particolare del pilastro a forcella





// // Sapienza and DTU workshopSapienza and DTU workshop ////Sapienza University of RomeSapienza University of Rome, , School of EngineeringSchool of Engineering, , April April 11 201511 2015

Structural optimization in parametricsStructural optimization in parametrics

Optimal lines on free-form surfacesOptimal lines on free-form surfaces

IntroductionIntroduction

Konstantinos GkoumasKonstantinos Gkoumas

StroNGER srl co-founder and partnerStroNGER srl co-founder and partner


Extra slides


curved surfaces – tangent plane

The tangent plane to a point on a given surface, is the plane that goes through that point and that it is tangent to the surface at that point.

Let F(x,y,z) define a surface that is differentiable at a point (x0,y0,z0), then the tangent plane to F(x,y,z) at

(x0 ,y0 ,z0) is the plane with normal vector: Grad

F(x0,y0,z0) that passes through the point (x0,y0,z0).

In Particular the equation of the tangent plane is:

Grad F(x0,y0,z0) . ( x - x0 , y - y0 , z - z0) = 0

All tangent lines to a point p on a surface will fall on the tangent plane to the surface at that point.

Any curve embedded in the surface that passes through that point will have a tangent at that point which falls in this tangent plane.


curved surfaces – normal plane, principal curvatures

A normal plane at point p is one that contains the normal vector, and will therefore also contain a unique direction tangent to the surface and cut the surface in a plane curve, called normal section. This curve will in general have different curvatures for different normal planes at p.

The principal curvatures at p, denoted k1 and k2, are the maximum and minimum values of this curvature, and they measure the maximum and minimum “bending” of the surface at that point. They are the eigenvalues of the Hessian

The lines of curvature are curves which are always tangent to a principal direction (they are integral curves for the principal direction fields).

Eigenvalues of H: k1 k2


curved surfaces – mean and Gaussian curvature


Surfaces with zero mean curvature are called minimal surfaces.

Minimal surfaces tend to be saddle-like since principal curvatures have equal magnitude but opposite sign.

The saddle is also a good example of a surface with negative Gaussian curvature.

curved surfaces – specific cases

Surfaces with zero Gaussian curvature are called developable surfaces because they can be “developed” or flattened out into the plane without any stretching or tearing.

For instance, any piece of a cylinder is developable since one of the principal curvatures is zero.

The hemisphere is one example of a surface with positive Gaussian curvature


curved surfaces – Gaussian curvature example surfaces

From left to right:

•a surface of negative Gaussian curvature (hyperboloid);

•a surface of zero Gaussian curvature (cylinder), and;

•a surface of positive Gaussian curvature (sphere).

"Gaussian curvature" by Jhausauer - English wikipedia,. Licensed under Public Domain via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:Gaussian_curvature.PNG#/media/File:Gaussian_curvature.PNG

S[tr/c]u[c/lp]ture workshop Sapienza 11 04 2015 intro

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