8th Hellenic National Conference of Steel Structures

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

Giulia MilanaPierluigi OlmatiKonstantinos GkoumasFranco Bontempi

Sapienza University of RomeDipartimento di Ingegneria Strutturale e Geotecnica

8th Hellenic National Conference of Steel Structures Tripoli (Greece) 2-4 October 2014

Konstantinos Gkoumas03/10/2014


SustainabilityOverview

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)



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

SustainabilityUse of steel and structural form



SustainabilityTall 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 structures



SustainabilityTall 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 structures Exterior structures



SustainabilityDiagrid structures

Capital Gate, Abu Dhabi - RMJM

Milan Trade Fair - Fuksas Atlas Building, Netherlands - Rafael Vinoly ArchitectsWesthafen, Frankfurt Tower - Schneider & Schumacher



Diagrid structureDiagrid 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



Diagrid structureInitial configuration and diagrid schemes

Outrigger Structure Diagrid Structures

42° 60° 75°

160

m

36 m



Original Structure:Outrigger

Improved Structure:Diagrid

PerimetralStructure

InternalStructure

Numerical resultsStructural configuration



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°



Outrigger 42° 60° 75°

P(ton)

8052 6523 5931 5389

Saving(%)

- 19 26 33

0

1000

2000

3000

4000

5000

6000

7000

8000

9000Weight

P (

ton

)

Numerical resultsAnalyses and comparisons



Numerical resultsModal analysis

T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12

Outrigger 3.741908 3.624657 2.478095 1.162387 1.084865 0.795965 NaN NaN NaN NaN NaN NaN

Diagrid 42° 3.105204 3.083854 1.724092 0.994648 0.958515 0.782728 NaN NaN NaN NaN NaN NaN



0.25

0.75

1.25

1.75

2.25

2.75

3.25

3.75

First six periods

T (

s)

Traslational in Y

direction

Traslational in X

direction

Rotationalaround Z

axis

Traslational in Y

direction

Traslational in X

direction

Rotationalaround Z

axis



Numerical resultsSLS - 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

Out

rigge

r

Dia

grid

42°

Dia

grid

60°

Dia

grid

75°



Diagrid 42°

Diagrid Structure with inclination of diagonal members of

42°

Diagrid 60°


60°

Diagrid 75°


75°



Numerical resultsHorizontal displacements

0

16

32

48

64

80

96

112

128

144

160

0 20 40 60 80 100 120 140 160 180

Diagrid 42° Diagrid 60° OutriggerDiagrid 75° SLS limit

U1 (m)

Z (

m)

Out

rigge

r

Dia

grid

42°

Dia

grid

60°

Dia

grid

75°



Numerical resultsULS - load combinations, pushover

Out

rigge

r

Dia

grid

42°

Dia

grid

60°

Dia

grid

75°



Diagrid 42°


42°

Diagrid 60°


60°

Diagrid 75°


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



Numerical resultsDiagrid 60°: Pushover (YZ Sections)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

20000

40000

60000

80000

100000

120000

140000

160000

180000Pushover

Step25

Step28

Step37

Step44

Step51

Step67

U1 (m)

F (

kN)

Step 67Step 51Step 44Step 37Step 25



Numerical resultsDiagrid 60°: Pushover+Vert (YZ Sections)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

20000

40000

60000

80000

100000

120000

140000

160000

180000

Pushover+Vert

Step11

Step16

Step39

Step47

Step55

U1 (m)

F (

kN)

Step 47 Step 55Step 39Step 11

VERT



Numerical resultsComparison of capacity curves

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

20000

40000

60000

80000

100000

120000

140000

160000

180000

Pushover

U1 (m)

F (

kN)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Pushover+Vert

Outrigger

Diagrid 42°

Diagrid 60°

Diagrid 75°

U1 (m)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Pushover+Dead

U1 (m)

DEAD VERT



Numerical resultsDefinition of significant properties

R=Fmax (Strength)

K=Fy/Dy

(Stiffness)

m=Dmax/Dy (Ductility)



Numerical resultsComparison 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



Numerical resultsComparison of Mechanical Properties

R/R0

K/K0

m/m0

1,2 ((P0-P)/P0+1) 0

2

4

Pushover+Vert




Preliminary robustness checksElimination of diagonal elements on Diagrid 60°

D1,L1

D1,L2

D2,L1

D2,L2

D3,L1

D3,L2

0 0.5 1 1.5 2 2.5 30

20000

40000

60000

80000

100000

120000

140000

Pushover

D1,L1D1,L2D2,L1D2,L2D3,L1D3,L2INTATTA

U1 (m)

F (

kN

)



DiagridOngoing research – apply simplified robustness indexes (1)

Kun λiun

Eigenvalues

Kdam λidam

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.



DiagridOngoing research – apply simplified robustness indexes (2)

d1d2d3

d4d5

d7

d6

37

5942 45

35 3823

63

4158 55

65 6277

0

20

40

60

80

100

1 2 3 4 5 6 7

Rob

ustn

ess

%

ScenarioCf max Robustness

83 87 88

5360

86

64

17 13 12

4740

14

36

0

20

40

60

80

100

1 2 3 4 5 6 7

Rob

ustn

ess

%

ScenarioCf max Robustness

Damage scenario Damage scenariod1 d2 d3 d4 d5 d6 d7 d1 d2 d3 d4 d5 d6 d7

Pier 6Pier 7

North

Pier 6

Thank [email protected]



mailto:[email protected]



Numerical resultsCOMB 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%

ShearInterior ColumnsDiagrid/ Edge Col-umnsCorner Columns

11%

45%

44%

NormalInterior ColumnsDiagrid/ Edge Col-umnsCorner Columns

5%

95%

Shear

Interior Columns

Diagrid

7%

93%

Normal

Interior Columns

Diagrid

Diagrid 60°

Diagrid 75°

Interior Columns

Interior Columns



Additional slides - DiagridMaterials

S275 (UNI EN 10025-2)

Modulus of Elasticity E 210000 N/mm2

Poisson’s Ratio n 0,3

Yield Strength fyk275 N/mm2

Tensile Strength fyk430 N/mm2

S460N/NL (UNI EN 10025-3)

Modulus of Elasticity E 210000 N/mm2

Poisson’s Ratio n 0,3

Yield Strength fyk430 N/mm2

Tensile Strength fyk540 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



Additional slides - DiagridOutrigger 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)

a1 a2 a3 b1 b2 b3



Additional slides - DiagridOutrigger structure - beams



Additional slides - DiagridOutrigger structure – columns



Additional slides - DiagridWind 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

-1.5 -1 -0.5 0 0.5 1 1.5 2 2.50

20

40

60

80

100

120

140

160

We

We,u

We,l



Additional slides - DiagridSAP 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.



Additional slides - DiagridSAP 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.

8th Hellenic National Conference of Steel Structures

Engineering

Transcript of 8th Hellenic National Conference of Steel Structures