2015.12.17 kg diagrid

CORSO DI
COSTRUZIONI METALLICHE
Sustainability of
tall buildings:
issues and
structural design
Konstantinos Gkoumas,
Ph.D., P.E.
Docente: Franco Bontempi,
Ph.D., P.E.
Facoltà di Ingegneria
Sapienza Università di Roma
CORSO DI COSTRUZIONI METALLICHE
Konstantinos Gkoumas
17/12/2015

CORSO DI
COSTRUZIONI METALLICHE Page 2Sustainability of tall buildings:
the case of diagrid structures
17/12/2015
Sustainability
Overview
SUSTAINABILITY
SOCIAL
ENVIRONMENTAL
ECONOMIC
SUSTAINABLE DEVELOPMENT:
“Development that meets the needs of the
present without compromising the ability of
future generations to meet their own needs.”
(Brundtland Commission, 1987)

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Steel Material
• 40% of resources
from recycling
• Manufacturing
process with
controlled
environmental
impact
• Material durability
• High recycling rate
Construction
Phase
• prefabrication/
offsite manufacture
Design and Service Life
• Weight reduction of structure
• Creation of versatile spaces
• Longevity and robustness of
steel components
• Simple incorporation of
renewable energy generation
systems
End of Life
• Easy dismantling
• Reusability/Reciclability
Source: Foster + Partners Hearst Tower USA, 2000 - 2006
SUSTAINABILITY
IN
STRUCTURES
Material
Used
Resource
Efficient
Site
Planning
Non
Pollution
Energy
Efficiency
Structural
Form
Sustainability
Use of steel and structural form

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17/12/2015
SUSTAINABILITY
IN
STRUCTURES
Material
Used
Resource
Efficient
Site
Planning
Non
Pollution
Energy
Efficiency
Structural
Form
Sustainability
Building automation and energy harvesting

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17/12/2015
SUSTAINABILITY
IN
STRUCTURES
Material
Used
Resource
Efficient
Site
Planning
Non
Pollution
Energy
Efficiency
Structural
Form
Sustainability
Diagrid, building automation and energy harvesting
Diagrid: double façade - chimney effect

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17/12/2015
Sustainability
Tall buildings
Ali, M. M., Moon, K. S. (2007). Structural Development in Tall Buildings: Current Trends and Future Prospects. Architectural
Science Review,Vol. 50, pp. 205-223.
Interior structuresExterior structures

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Sustainability
Diagrid structures – what about
“Nature’s own system of coordination [is] based on triangles,”
R. Buckminster Fuller
“A series of triangles that combine gravity and lateral support into one,
making the building stiff, efficient, and lighter than a traditional high-rise.”
Yoram Eilon, project manager on Foster’s Hearst Tower
“It’s the image of sustainability.”
Craig Schwitter, managing director for design consultant Buro Happold.
“What diagrid does is take the structure of a continuous shell, which
works in any direction, and pair it with the constructability of the discrete
element, the beam-and-stick approach. It’s a discretized shell.”
Dominic Munro, ARUP, structural engineer on the Swiss Re project.

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Sustainability
Diagrid structures – precursor
The World's First Hyperboloid
Lattice Shell structure.
The Russian engineer and
architect Vladimir Shukhov was
the first in the world to invent and
use in construction hyperboloid
towers.
For the 1896 All-Russia industrial
and art exhibition in Nizhniy
Novgorod Shukhov built the steel
lattice 37-meter tower, which
became the first hyperboloid
structure in the world.
© By Arssenev (Own work) [CC BY-SA 3.0
(http://creativecommons.org/licenses/by-sa/3.0) or
GFDL (http://www.gnu.org/copyleft/fdl.html)], via
Wikimedia Commons

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Sustainability
Further development of lattice
structures and their wide
implementation in architecture
started after the 1950s.
The most famous example is a
structure called the Biosphere that
Buckminster Fuller presented at
the Montreal Expo in 1967.
The construction was made with
tubular steel elements, was 60 m
tall and had a diameter of 75 m.
© Archdaily
Buckminster Fuller's geodesic dome built as the
United States Pavillion for the 1967 International
and Universal Exposition or Expo 67 held in
Montreal, Canada

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17/12/2015
Sustainability
Further development of lattice
structures and their wide
implementation in architecture
started after the 1950s.
The most famous example is a
structure called the Biosphere that
Buckminster Fuller presented at
the Montreal Expo in 1967.
The construction was made with
tubular steel elements, was 60 m
tall and had a diameter of 75 m.
© FLICKR
Montreal, Canada

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Sustainability
© FLICKR
Montreal, Canada

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17/12/2015
Sustainability
Diagrid structures - office buildings
An early example of the diagrid
structure is the IBM Building (now
United Steelworkers Building) in
Pittsburgh built in the early 1960s.
With its 13-story building height,
this building was not given much
attention by architects and
engineers.
Curtis & Davis, architects - IBM building,
Pittsburgh, PA, 1961-63 (Engineers: John
Skilling and Leslie Robertson, Seattle)
© 2006Teenie Harris Archive
http://teenie.cmoa.org

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NEO Bankside
A multi award winning set of four
prestigious apartment blocks beside the
Tate modern art gallery designed by Rogers
Stirk Harbour + Partners.
The towers feature an external bracing
system that forms a rigid diagrid across the
facade.This bracing has allowed the
removal of internal structural walls and
provides greater flexibility for the internal
space.
Sustainability
Diagrid structures - residential buildings
NEO Bankside / Rogers Stirk Harbour +
Partners. Image © Edmund Sumner

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Sustainability
NEO Bankside / Rogers
http://www.daversteels.co.u
k/project-
showcase/commercial-
projects/neo-bankside-
london-uk.html
NEO Bankside:
compression strut
and tie bars

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Sustainability
k/project-
london-uk.html
NEO Bankside:
compression strut
and tie bars

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17/12/2015
Sustainability
k/project-
london-uk.html
NEO Bankside:
compression strut
and tie bars design
scheme

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Sustainability
Diagrid structures – landmark buildings
30 St Mary Axe, known fondly as “The
Gherkin”, is one of the most dramatic
landmarks in London. Situated in the
main financial district, the 40-storey 180
meters tall office has won a unique place
in the affections of many, as well as a
host of awards.
The building’s concept was generated
from its circular plan which embodied
radial geometry inspiring the architects
to widen the building’s profile as you
move up and slowly lessen it as you
approach the top most lens.
It received the Royal Institute of British
Architects (RIBA) Stirling Prize in 2004.
© Foster and Partners

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17/12/2015
Sustainability
30 St Mary Axe, known fondly as “The
Gherkin”, is one of the most dramatic
landmarks in London. Situated in the
main financial district, the 40-storey 180
meters tall office has won a unique place
in the affections of many, as well as a
host of awards.
The building’s concept was generated
from its circular plan which embodied
radial geometry inspiring the architects
to widen the building’s profile as you
move up and slowly lessen it as you
approach the top most lens.
It received the Royal Institute of British
Architects (RIBA) Stirling Prize in 2004.
© Foster and Partners

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Sustainability
©FosterandPartners

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17/12/2015
Sustainability
The CCTV Headquarters is a 234m,
44-story skyscraper in the Beijing
Central Business District (CBD).The
tower serves as headquarters for
China CentralTelevision (CCTV).
Groundbreaking took place on 1 June
2004 and the building's facade was
completed in January 2008.The
Headquarters has been finally
completed in May 2012.
The CCTV Headquarters won the
2013 Best Tall BuildingWorldwide
from the Council onTall Buildings and
Urban Habitat.
© Rem Koolhaas and OMA

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Sustainability
Diagrid structures – functioning scheme
http://1.bp.blogspot.com/-
5EpcNaDo_Uw/U3JAvantNHI/AAAAAAAAAUE/Ti_omxg1p3Y/s1600/diagram+model+
2.jpg

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Diagrid structure
Diagrid module
Mele, E., Toreno, M., Brandonisio, G. and Del Luca, A. (2014). Diagrid structures for tall buildings: case studies and design
considerations.The Structural Design of Tall and Special Buildings.Wiley Online Library,Vol. 23, No. 2, pp. 124-145.
effect of gravity load
effect of overturning moment
effect of shear force

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Diagrid structure
Initial configuration and diagrid schemes
Outrigger Structure Diagrid Structures
42° 60° 75°
160m
36 m

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Original Structure:
Outrigger
Improved Structure:
Diagrid
Perimetral
Structure
Internal
Structure
Diagrid structure
Structural configuration

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S275 (UNI EN 10025-2)
Modulus of Elasticity E 210000 N/mm2
Poisson’s Ratio n 0,3
Yield Strength fyk 275 N/mm2
Tensile Strength fyk 430 N/mm2
S460N/NL (UNI EN 10025-3)
Modulus of Elasticity E 210000 N/mm2
Poisson’s Ratio n 0,3
Yield Strength fyk 430 N/mm2
Tensile Strength fyk 540 N/mm2
 S275 used for all profiles of
outrigger structure and for the
interior structure of diagrid
buildings
 S460N/NL with better mechanical
properties, is used for perimeter
structure of diagrid buildings
Diagrid structure
Materials

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17/12/2015
a – sections XZ (a1-Y=0m; a2-Y=9,5m; a3-Y=19,5m)
b – sections XZ (b1-X=0m; b2-X=4m; b3-X=13,5m)
a1 a2 a3 b1 b2
b3
Diagrid structure
Outrigger structure

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Diagrid structure
Outrigger structure - beams

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Diagrid structure
Outrigger structure - columns

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SLS Dead Gk Tamp Qk Qn W+X W-X W+Y W-Y
COMB5 1 1 1 0,7 0,5 1 - - -
COMB6 1 1 1 0,7 0,5 - 1 - -
COMB7 1 1 1 0,7 0,5 - - 1 -
COMB8 1 1 1 0,7 0,5 - - - 1
ULS Dead Gk Tamp Qk Qn W+X W-X W+Y W-Y
COMB5 1,3 1,3 1,3 1,05 0,75 1,5 - - -
COMB6 1,3 1,3 1,3 1,05 0,75 - 1,5 - -
COMB7 1,3 1,3 1,3 1,05 0,75 - - 1,5 -
COMB8 1,3 1,3 1,3 1,05 0,75 - - - 1,5
Acronym Description Color
Outrigger Outrigger Structure
Diagrid
42°
Diagrid Structure with inclination
of diagonal members of 42°
Diagrid
60°
Diagrid
75°
Outrigger 42° 60° 75°
P
(ton)
8052 6523 5931 5389
Saving
(%)
- 19 26 33
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
P(ton)
Weight
Diagrid structure
Analyses and comparisons

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Diagrid structure
Modal analysis
T1 T2 T3 T4 T5 T6
Outrigger 3,7 3,6 2,5 1,2 1,1 0,8
Diagrid 42° 3,1 3,1 1,7 1,0 1,0 0,8
Diagrid 60° 3,3 3,3 1,9 1,0 1,0 0,9
Diagrid 75° 3,7 3,6 2,8 1,3 1,2 1,2
0,00
0,50
1,00
1,50
2,00
2,50
3,00
3,50
4,00
T(s)
First six periods
Traslational
in Y
direction
Traslational
in X
direction
Rotational
around Z
axis
Traslational
in Y
direction
Traslational
in X
direction
Rotational
around Z
axis

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Wind load
Z
(m)
q
(kN/m2)
We,l
(kN/m2)
We,u
(kN/m2)
Z
(m)
q
(kN/m2)
We,l
(kN/m2)
We,u
(kN/m2)
0 0,94 0,787 -0,972 80 1,95 1,639 -0,972
4 0,94 0,787 -0,972 84 1,98 1,66 -0,972
8 0,94 0,787 -0,972 88 2,00 1,68 -0,972
12 1,09 0,919 -0,972 92 2,02 1,699 -0,972
16 1,21 1,018 -0,972 96 2,04 1,718 -0,972
20 1,31 1,097 -0,972 100 2,07 1,735 -0,972
24 1,38 1,163 -0,972 104 2,09 1,752 -0,972
28 1,45 1,22 -0,972 108 2,11 1,769 -0,972
32 1,51 1,271 -0,972 112 2,12 1,785 -0,972
36 1,57 1,316 -0,972 116 2,14 1,8 -0,972
40 1,62 1,357 -0,972 120 2,16 1,815 -0,972
44 1,66 1,394 -0,972 124 2,18 1,83 -0,972
48 1,70 1,429 -0,972 128 2,20 1,844 -0,972
52 1,74 1,461 -0,972 132 2,21 1,858 -0,972
56 1,78 1,491 -0,972 136 2,23 1,871 -0,972
60 1,81 1,52 -0,972 140 2,24 1,884 -0,972
64 1,84 1,546 -0,972 144 2,26 1,897 -0,972
68 1,87 1,571 -0,972 148 2,27 1,909 -0,972
72 1,90 1,595 -0,972 152 2,29 1,921 -0,972
76 1,93 1,618 -0,972 156 2,30 1,933 -0,972
80 1,95 1,639 -0,972 160 2,31 1,944 -0,972
0
20
40
60
80
100
120
140
160
-1,5 -1 -0,5 0 0,5 1 1,5 2 2,5
We
We,u
We,l
Diagrid structure

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Diagrid structure
Horizontal displacements
0 0,1 0,2 0,3 0,4
0
16
32
48
64
80
96
112
128
144
160
U1 (m)
Z(m)
Outrigger
0 0,1 0,2 0,3 0,4
0
16
32
48
64
80
96
112
128
144
160
U1 (m)
Z(m)
Diagrid 42°
0 0,1 0,2 0,3 0,4
0
16
32
48
64
80
96
112
128
144
160
U1 (m)
Z(m)
Diagrid 60°
0 0,1 0,2 0,3 0,4
0
16
32
48
64
80
96
112
128
144
160
U1 (m)
Z(m)
Diagrid 75°

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Diagrid structure
Horizontal displacements
0 0,05 0,1 0,15 0,2 0,25 0,3 0,35
0
16
32
48
64
80
96
112
128
144
160
U1 (m)
Z(m)
Diagrid 42° Diagrid 60° Outrigger Diagrid 75° SLS limit
Outrigger
Diagrid42°
Diagrid60°
Diagrid75°

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Diagrid structure
SLS - load combinations
SLS Dead Gk Tamp Qk Qn W+X W-X W+Y W-Y
COMB5 1 1 1 0,7 0,5 1 - - -
COMB6 1 1 1 0,7 0,5 - 1 - -
COMB7 1 1 1 0,7 0,5 - - 1 -
COMB8 1 1 1 0,7 0,5 - - - 1
HORIZONTAL
DISPLACEMENTS
COMB
Outrigger
Diagrid42°
Diagrid60°
Diagrid75°
Diagrid
42°
Diagrid Structure with inclination of
diagonal members of
42°
Diagrid
60°
diagonal members of
60°
Diagrid
75°
diagonal members of
75°

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Diagrid structure
ULS - load combinations, pushover
Outrigger
Diagrid42°
Diagrid60°
Diagrid75°
Diagrid
42°
diagonal members of
42°
Diagrid
60°
diagonal members of
60°
Diagrid
75°
diagonal members of
75°
ULS Dead Gk Tamp Qk Qn W+X W-X W+Y W-Y
DEAD 1 - - - - - - - -
VERT 1 1 1 - - - - - -
+STATIC PUSHOVER FORCES
PUSHOVER
DEA
D
VERT

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Diagrid structure
COMB 5 U.L.S.
DIAGRID
42°
DIAGRID
60°
DIAGRID
75°
Diagrid 42° Interior Columns
3%
97%
Shear
Interior
Columns
Diagrid
11%
89%
Normal
Interior
Columns
Diagrid
2%
97%
1%
Shear
Interior
Columns
Diagrid/
Edge
Columns
11%
45%
44%
Normal
Interior
Columns
Diagrid/
Edge
Columns
5%
95%
Shear
Interior
Columns
Diagrid
7%
93%
Normal
Interior
Columns
Diagrid
Diagrid 60°
Diagrid 75°
Interior Columns
Interior Columns

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SAP 2000 plastic hinges
Axial hinges, used for all
elements of the outrigger
structures and the perimetral
system in the diagrid structures,
and, bending hinges for the
internal columns in the diagrid
structures.
For the axial hinges the
constitutive equation is rigid and
perfectly plastic, with a yield
stress equal to fyk (430 MPa for
diagrid structures and 275 MPa
for the outrigger structure) and
an ultimate deformation (eu) of
5%.These hinges are placed in
the middle of the elements, with
a relative length of 1, i.e. the
hinges extend for the entire
length.
Diagrid structure

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SAP 2000 plastic hinges
For the bending hinges the behavior is defined starting from a moment-curvature diagram
with a rigid and hardening-plastic constitutive equation, extrapolated using FEMA356.
Diagrid structure

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Diagrid structure
Diagrid 60°: Pushover (YZ Sections)
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5
F(kN)
U1 (m)
Pushover
Step25
Step28
Step37
Step44
Step51
Step67
Step 67Step 51Step 44Step 37Step 25

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Diagrid 60°: Pushover+Vert (YZ Sections)
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5
F(kN)
U1 (m)
Pushover+Vert
Step11
Step16
Step39
Step47
Step55
Step 47 Step 55Step 39Step 11
VERT
Diagrid structure

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Diagrid structure
Comparison of capacity curves
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5
F(kN)
U1 (m)
Pushover
0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5
U1 (m)
Pushover+Vert
Outrigger
Diagrid
42°
Diagrid
60°
Diagrid
75°
0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5
U1 (m)
Pushover+Dead
DEAD VERT

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Diagrid structure
Definition of significant properties
R=Fmax
(Strength)
K=Fy/Dy
(Stiffness)
m=Dmax/Dy
(Ductility)

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Diagrid structure
Comparison of significant properties
Outrigger Diagrid 42° Diagrid 60° Diagrid 75°
Pushover+Vert Pushover+Vert Pushover+Vert Pushover+Vert
Strength
(R) – kN
94775 110185 104972 97131
Stiffness
(K) – kN/m
77143 80615 71306 60897
Ductility
(m)
1,535 3,587 5,681 2,564
Weight
(P) - Ton
8052 6523 5931 5389
Weighted average (W.A.) of significant properties
Pushover+Vert Pushover+Vert Pushover+Vert Pushover+Vert
Strength
(R) – kN
94775 110185 104972 97131
Stiffness
(K) – kN/m
77143 80615 71306 60897
Ductility
(m)
1,535 3,587 5,681 2,564
Weight
(P) - Ton
8052 6523 5931 5389
W.A. 4,20 5,97 7,25 5,08

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Diagrid structure
Comparison of Mechanical Properties
0
0,5
1
1,5
2
2,5
3
3,5
4
R/R0
K/K0
m/m0
1,2 ((P0-
P)/P0+1)
Pushover+Vert

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Diagrid structure
Diagrid 60°: Robustness checks
D1,L1
D1,L2
D2,L1
D2,L2
D3,L1
D3,L2
Analysis interruption: two cases:
• «first plastic hinges»
• «last plastic hinges»

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Diagrid structure
Diagrid 60°: Robustness checks
D1,L1
D1,L2
D2,L1
D2,L2
D3,L1
D3,L2
0
20000
40000
60000
80000
100000
120000
140000
0 0,5 1 1,5 2 2,5 3
F(kN)
U1 (m)
Pushover
D1,L1
D1,L2
D2,L1
D2,L2
D3,L1
D3,L2
INTATTA

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References
• J.R. Ehrenfeld. “Sustainability by Design: A Subversive Strategy for Transforming Our
Consumer Culture”, Yale University Press, New Haven, 2008.
• United Nations World Commission on Environment and Development. “Report of the World
Commission on Environment and Development: Our Common Future”. UN - United Nations,
1987.
• Berardi, U. “Clarifying the new interpretations of the concept of sustainable building”.
Sustainable Cities and Society, 8, pp. 72-78, 2013. DOI: 10.1016/j.scs.2013.01.008.
• Robin, C.P.Y., Poon, C.S. “Cultural shift towards sustainability in the construction industry of
Hong Kong”. Journal of Environmental Management, 90(11), pp. 3616-3628, 2009. DOI:
10.1016/j.jenvman.2009.06.017.
• Moon, K.S. “Diagrid Structures for Complex-Shaped Tall Buildings”. Procedia Engineering, 14,
pp. 1343-1350, 2011. DOI: 10.1016/j.proeng.2011.07.169.
• Mele, E., Toreno, M., Brandonisio, G., Del Luca, A. “Diagrid structures for tall buildings: case
studies and design considerations”. The Structural Design of Tall and Special Buildings, 23(2),
pp. 124–145, 2014. DOI: 10.1002/tal.1029
• Richie, I. “Diagonal Architecture: Diagrid Structures”. 2012. E-architect, available online at:
http://www.e-architect.co.uk
• Leonard, J. “Investigation of Shear Lag Effect in High-rise Buildings with Diagrid System”.
Master thesis, Massachusetts Institute of Technology, 2007.

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References
• Milana, G., Olmati, P., Gkoumas, K., Bontempi, F. (2015) “Ultimate capacity of diagrid
systems for tall buildings in the nominal configuration and the damaged state”, Periodica
Polytechnica Civil Engineering, Vol.59, No. 3, pp. 381 - 391.
• Foster and Partners – The Hearst Tower, available online at:
www.fosterandpartners.com/projects/hearst-tower
• Moon, K.S. “Stiffness-based design methodology for steel braced tube structures: A
sustainable approach”. Engineering Structures, 32(10), pp. 3163-3170, 2010. DOI:
10.1016/j.engstruct.2010.06.004
• Moon, K.S., Connor, J.J., Fernandez, J. E. “Diagrid structural systems for tall buildings:
characteristics and methodology for preliminary design”. The Structural Design of Tall and
Special Buildings, 16(2), pp. 205-230, 2007. DOI: 10.1002/tal.311.
• Montuori, G.M., Mele, E., Brandonisio, G., De Luca, A. "Geometrical patterns for diagrid
buildings: Exploring alternative design strategies from the structural point of view".
Engineering Structures, 71, pp. 112-127, 2014 DOI: 10.1016/j.engstruct.2014.04.017.
• Montuori, G.M., Mele, E., Brandonisio, G., De Luca, A. "Secondary bracing systems for
diagrid structures in tall buildings". Engineering Structures, 75, pp. 477-488, 2014. DOI:
10.1016/j.engstruct.2014.06.011.
• Pinho, R. “Using pushover analysis for assessment of building and bridges”. Pecker, A, editor,
Advanced earthquake engineering analysis, CISM International Centre for Mechanical
Sciences, 494, Springer, Vienna, pp. 91-120, 2007. DOI: 10.1007/978-3-211-74214-3_6.

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17/12/2015
Resources
https://www.pinterest.com/gkoumas/strcting-diagonal-grid

CORSO DI
17/12/2015
Sustainability of
tall buildings:
issues and
structural design
Thank you!
konstantinos.gkoumas@uniroma1.it

2015.12.17 kg diagrid

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2015.12.17 kg diagrid