Structural behavior and robustness assessment of tall buildings: the case of diagrid systems

1. Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
8th Hellenic National Conference of Steel Structures
Tripoli (Greece) 2-4 October 2014
Giulia Milana
Pierluigi Olmati
Konstantinos Gkoumas
Franco Bontempi
Sapienza University of Rome
Dipartimento di Ingegneria Strutturale e Geotecnica

2. Konstantinos Gkoumas
03/10/2014
Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
Page 2
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)

3. End of Life
Sustainability
Use of steel and structural form
• Easy dismantling
• Reusability/Reciclability
Konstantinos Gkoumas
03/10/2014
Material
Used
Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
Page 3
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
Source: Foster + Partners Hearst Tower USA, 2000 - 2006
SUSTAINABILITY
IN
STRUCTURES
Resource
Efficient
Site
Planning
Non
Pollution
Structural
Form
Energy
Efficiency

4. Konstantinos Gkoumas
03/10/2014
Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
Interior structures
Page 4
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.

5. Konstantinos Gkoumas
03/10/2014
Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
IEnxteterrioiorr s strturucctutureress
Page 5
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.

6. Konstantinos Gkoumas
03/10/2014
Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
Page 6
Sustainability
Diagrid structures
Capital Gate, Abu Dhabi - RMJM
Milan Trade Fair - Fuksas Atlas Building, Netherlands Westhafen, Frankfurt Tower - Schneider & Schumacher - Rafael Vinoly Architects

7. effect of overturning moment
Konstantinos Gkoumas
03/10/2014
effect of gravity load
effect of shear force
Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
Page 7
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.

8. Konstantinos Gkoumas
03/10/2014
Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
Page 8
Diagrid structure
Initial configuration and diagrid schemes
Outrigger Structure Diagrid Structures
42° 60° 75°
160 m
36 m

9. Konstantinos Gkoumas
03/10/2014
Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
Page 9
Original Structure:
Outrigger
Improved Structure:
Diagrid
Perimetral
Structure
Internal
Structure
Numerical results
Structural configuration

10. 9000
8000
7000
6000
5000
4000
3000
2000
1000
Konstantinos Gkoumas
03/10/2014
Acronym Description Color
Outrigger Outrigger Structure
Diagrid
42°
Diagrid Structure with inclination
of diagonal members of 42°
Diagrid
60°
Diagrid Structure with inclination
of diagonal members of 60°
Diagrid
75°
Diagrid Structure with inclination
of diagonal members of 75°
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
Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
Page 10
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
Outrigger 42° 60° 75°
P
(ton)
8052 6523 5931 5389
Saving
(%)
- 19 26 33
0
P (ton)
Weight
Numerical results
Analyses and comparisons

11. Konstantinos Gkoumas
03/10/2014
First six periods
Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
Page 11
Numerical results
Modal analysis
T1 T2 T3 T4 T5 T6
4.00
3.50
3.00
2.50
2.00
1.50
1.00
0.50
0.00
T (s)
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
Traslational
in Y
direction
Traslational
in X
direction
Rotational
around Z
axis
Traslational
in Y
direction
Traslational
in X
direction
Rotational
around Z
axis

12. Konstantinos Gkoumas
03/10/2014
Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
Page 12
Numerical results
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
COMB
HORIZONTAL
DISPLACEMENTS
Outrigger
Diagrid 42°
Diagrid 60°
Diagrid 75°
Acronym Description Color
Outrigger Outrigger Structure
Diagrid
42°
Diagrid Structure with inclination of
diagonal members of
42°
Diagrid
60°
Diagrid Structure with inclination of
diagonal members of
60°
Diagrid
75°
Diagrid Structure with inclination of
diagonal members of
75°

13. Konstantinos Gkoumas
03/10/2014
Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
Page 13
Numerical results
Horizontal displacements
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
160
144
128
112
96
80
64
48
32
16
0
U1 (m)
Z (m)
Diagrid 42° Diagrid 60° Outrigger Diagrid 75° SLS limit
Outrigger
Diagrid 42°
Diagrid 60°
Diagrid 75°

14. Konstantinos Gkoumas
03/10/2014
Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
Page 14
Numerical results
ULS - load combinations, pushover
Outrigger
Diagrid 42°
Diagrid 60°
Diagrid 75°
Acronym Description Color
Outrigger Outrigger Structure
Diagrid
42°
Diagrid Structure with inclination of
diagonal members of
42°
Diagrid
60°
Diagrid Structure with inclination of
diagonal members of
60°
Diagrid
75°
Diagrid Structure with inclination of
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
DEAD VERT

15. Step 25 Step 37 Step 44 Step 51 Step 67
Konstantinos Gkoumas
03/10/2014
Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
Page 15
Numerical results
Diagrid 60°: Pushover (YZ Sections)
180000
160000
140000
120000
100000
80000
60000
40000
20000
0
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

16. Step 11 Step 39 Step 47 Step 55
Konstantinos Gkoumas
03/10/2014
Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
Page 16
Numerical results
Diagrid 60°: Pushover+Vert (YZ Sections)
180000
160000
140000
120000
100000
80000
60000
40000
20000
0
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
VERT

17. Pushover+Vert
Konstantinos Gkoumas
03/10/2014
Pushover
Pushover+Dead
Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
Page 17
Numerical results
Comparison of capacity curves
180000
160000
140000
120000
100000
80000
60000
40000
20000
0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
F (kN)
U1 (m)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
U1 (m)
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)
DEAD VERT

18. Konstantinos Gkoumas
03/10/2014
Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
K=Fy/Dy
(Stiffness)
Page 18
Numerical results
Definition of significant properties
R=Fmax
(Strength)
m=Dmax/Dy
(Ductility)

19. W.A. 4,20 5,97 7,25 5,08
Konstantinos Gkoumas
03/10/2014
Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
Page 19
Numerical results
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

20. Konstantinos Gkoumas
03/10/2014
R/R0
4
3.5
3
2.5
2
1.5
1
0.5
Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
Page 20
Numerical results
Comparison of Mechanical Properties
0
K/K0
m/m0
1,2 ((P0-
P)/P0+1)
Pushover+Vert
Outrigger Diagrid 42° Diagrid 60° Diagrid 75°

21. Pushover
Konstantinos Gkoumas
03/10/2014
D3,L2
D3,L1
D2,L2
D2,L1
D1,L2
140000
120000
100000
80000
60000
40000
20000
Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
Page 21
Preliminary robustness checks
Elimination of diagonal elements on Diagrid 60°
D1,L1
0
0 0.5 1 1.5 2 2.5 3
F (kN)
U1 (m)
D1,L1
D1,L2
D2,L1
D2,L2
D3,L1
D3,L2
INTATTA

22. Konstantinos Gkoumas
03/10/2014
Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
Eigenvalues
Page 22
Diagrid
Ongoing research – apply simplified robustness indexes (1)
Kun λi
un
Kdam λi
dam
Consequence factor
Robustness index
Nafday, A.M. (2011), “Consequence-based structural design approach for black swan events”, Structural Safety, Vol. 33, No.
(1), pp. 108-114.
Olmati, P., Gkoumas, K., Brando, F. and Cao, L., (2013). Consequence-based robustness assessment of a steel truss bridge.
Steel and Composite Structures, Vol. (14), No (4), pp. 379-395.

23. Pier 7 Pier 6
d3 d4 d5 d6 d7 d1 d2 d3 d4 d5 d6 d7
Damage scenario Damage scenario
Konstantinos Gkoumas
03/10/2014
100
100
80
80
60
60
40
40
20
20
Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
Page 23
Diagrid
Ongoing research – apply simplified robustness indexes (2)
d1
d3 d2
d4
d5
d7
d6
37
59
42 45
35 38
23
63
41
58 55
65 62
77
0
1 2 3 4 5 6 7
Robustness %
Scenario
Cf max Robustness
42 45
35 38
23
58 55
65 62
77
3 4 5 6 7
Scenario
Cf max Robustness
83 87 88
53
60
86
64
17 13 12
47
40
14
36
0
1 2 3 4 5 6 7
Robustness %
Scenario
Cf max Robustness
North
Pier 6

24. Thank you!
konstantinos.gkoumas@uniroma1.it
Konstantinos Gkoumas
03/10/2014
Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
Page 24

25. Konstantinos Gkoumas
03/10/2014
Diagrid 42° Interior Columns
1%
Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
Page 25
Numerical results
COMB 5 U.L.S.
DIAGRID
42°
DIAGRID
60°
DIAGRID
75°
3%
97%
Shear
Interior
Columns
Diagrid
11%
89%
Normal
Interior
Columns
Diagrid
2%
97%
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

26. Konstantinos Gkoumas
03/10/2014
Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
Page 26
Additional slides - Diagrid
Materials
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

27. a1 a2 a3 b1 b2 b3
Konstantinos Gkoumas
03/10/2014
Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
Page 27
Additional slides - Diagrid
Outrigger structure
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)

28. Konstantinos Gkoumas
03/10/2014
Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
Page 28
Additional slides - Diagrid
Outrigger structure - beams

29. Konstantinos Gkoumas
03/10/2014
Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
Page 29
Additional slides - Diagrid
Outrigger structure – columns

30. 160
140
120
100
80
60
40
20
We
Konstantinos Gkoumas
03/10/2014
Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
Page 30
Additional slides - Diagrid
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
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
We,u
We,l

31. Konstantinos Gkoumas
03/10/2014
Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
Page 31
Additional slides - Diagrid
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.

32. Konstantinos Gkoumas
03/10/2014
Structural behavior and robustness assessment
of tall buildings: the case of diagrid systems
Page 32
Additional slides - Diagrid
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.