Nowadays, tending to use super high-rise steel buildings has increased the need for finding efficient and economical lateral load resisting systems. The diagrid structural system is widely used for medium- and super-high-rise buildings due to its structural efficiency. The aim of this study was to find the optimal diagrid angle to minimize the lateral drift in high-rise building. Five different diagrid angle configurations (27o, 45o, 56o, 72o, and 81o) have been considered for 24, 48 and 72-storey steel buildings. The results were tabulated by performing finite element analysis using ETABS version 15 in the form of lateral displacement and storey drift. It is shown that the optimal diagrid angle is smaller than 56o for 24-storey model, and between (56o- 72o) for 48-storey model, and 72o for 72-storey model.

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International Journal of Civil Engineering and Technology (IJCIET)
Volume 6, Issue 11, Nov 2015, pp. 01-10, Article ID: IJCIET_06_11_001
Available online at
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=6&IType=11
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
© IAEME Publication
___________________________________________________________________________
OPTIMAL DIAGRID ANGLE TO MINIMIZE
DRIFT IN HIGH-RISE STEEL BUILDINGS
SUBJECTED TO WIND LOADS
Khalid K. Shadhan
University of Babylon - College of Engineering
ABSTRACT
Nowadays, tending to use super high-rise steel buildings has increased the
need for finding efficient and economical lateral load resisting systems. The
diagrid structural system is widely used for medium- and super-high-rise
buildings due to its structural efficiency. The aim of this study was to find the
optimal diagrid angle to minimize the lateral drift in high-rise building. Five
different diagrid angle configurations (27o
, 45o
, 56o
, 72o
, and 81o
) have been
considered for 24, 48 and 72-storey steel buildings. The results were tabulated
by performing finite element analysis using ETABS version 15 in the form of
lateral displacement and storey drift. It is shown that the optimal diagrid
angle is smaller than 56o
for 24-storey model, and between (56o
- 72o
) for 48-
storey model, and 72o
for 72-storey model.
Key words: Steel Buildings, Wind loads and Drift
Cite this Article: Shadhan, K. K. Optimal Diagrid Angle to Minimize Drift in
High-Rise Steel Buildings Subjected to Wind Loads. International Journal of
Civil Engineering and Technology, 6(11), 2015, pp. 01-10.
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=6&IType=11
_____________________________________________________________________
1. INTRODUCTION
The rapid growth of urban population and limitation of available land, the taller
structures are preferable now a day. So when the height of structure increases then the
consideration of lateral wind load is very much important. For that the lateral load
resisting system becomes more important than the structural system that resists the
gravitational loads. There are numerous structural lateral systems used in medium-
and super-high-rise building design such as: shear frames, shear trusses, frames with
shear core, framed tubes, trussed tubes, mega frames etc. Recently the diagrid
(diagonal grid) structural system is widely used for high-rise buildings due to its
structural efficiency and aesthetic potential provided by the unique geometric
configuration of the system (Moon et. al, 2007).

2. Khalid K. Shadhan
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The difference between typical exterior-braced frame structures and current diagrid
structures is that, for diagrid structures, almost all the vertical columns are eliminated.
This is possible because the diagonal members in diagrid structural systems can carry
gravity loads as well as lateral forces owing to their triangulated configuration, whereas
the diagonals in typical braced frame structures carry only lateral loads (Figure 1).
Figure 1 Braced tube vs. Diagrid structure (Moon et. al, 2007)
One of the biggest tasks of the structural designer in high-rise building design
simply reduces to limiting the lateral drift that is associated with wind loads. If a
building takes on too much lateral drift, significant damage can be realized in other
systems such as curtain walls or the partitions. Additionally, large displacements in a
building can induce P-delta moments which can have an adverse effect on structure
stability. Further, if lateral displacements can be felt by the users of the building not
only may the safety be questioned, but motion sickness may also create an issue.
ASCE/SEI 7-10 (Minimum Design Loads for Buildings and Other Structures, 2010)
suggested in the serviceability considerations section, the current practice is to limit the
drift index, deflection divided by the corresponding height, to between 1/600 and 1/400
of the building or storey height. Additionally, an absolute limit on storey drift may also
need to be imposed in light of evidence that damage to nonstructural partitions,
cladding, and glazing may occur if the storey drift exceeds about 10 mm (3/8 inch).
While a significant number of researches had been made on traditional structural lateral
resisting systems, a much fewer number were made for diagrid system (Moon et. el., 2007,
Montuori et. el., 2013, Panchal and Patel, 2014, Singh et. el., 2014, Mele et. el., 2014).
2. OBJECTIVE
The primary objective of this study was to use the Etabs v.15 finite element software
to model medium- and super high-rise steel building, subjected to lateral wind loads,
and determine the most advantageous configuration in which to supply diagrid
structural system. More specifically, this study looks at the optimal diagrid angle to
minimize the lateral drift.
3. DESCRIPTION OF MODELS
3.1. Typical Geometric Parameters
This study has utilized finite element high-rise building models having 42m width
dimensions with diagrid structural system. Three high-rise building types were
examined, medium-, high-, and super-high-rise building models. The storey height is
kept uniform of 3.5 m for all adopted models. The diagrid members to base
connections were assumed fully restrained. To compare the performances of different
diagrid models at equal basis, the same sections were considered for the diagrid

3. Optimal Diagrid Angle to Minimize Drift in High-Rise Steel Buildings Subjected to Wind
Loads
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members and beams in each model type. For diagrid members, Grade 50 steel pipe
with three different cross section, 700mm, 600mm, and 500mm diameter with 40mm,
30mm, and 20mm thick for 24-,48- and 72-storey building models ,respectively.
Grade 36, W18×76 steel section is selected for the beams in all models.
ASCE/SEI 7-10 is used to estimate the lateral wind load. The building models are
assumed to be in Babylon, Iraq and within category III, which implies that there is a
substantial hazard to human life in the event of failure. Based on the available
climatic data, the basic wind speed is assumed 100 km/hr. Based on real 3D building
model with 42m×42m plan, lateral load 0.450 kN/m2
was chosen, its equivalent to
30kN concentrated force in each storey level in 2D model.
3.2. Diagrid Inclination Angle
The diagonal members in diagrid structural systems carry both gravity loads as well as
lateral forces owing to their triangulated configuration. The geometry of the basic
triangle model plays a major role in the internal axial force distribution, as well as in
conferring global shear and bending rigidity to the building structure. Since the optimal
angle of the columns for maximum bending rigidity is 90o
, (i.e. vertical columns in
traditional buildings) and that of the diagonals for maximum shear rigidity is about 27o
(only one storey stacked per basic triangle model), it is expected that the optimal angle
of diagonal members for diagrid structures will fall between these angles.
The angle of diagrid depends on the number of stories stacked per model. In this
study, 1, 2, 3, 6 and 12 stories are stacked per diagrid triangle model with typical
3.5m storey height which gives an inclination angle 27o
, 45o
, 56o
, 72o
and 81o
,
respectively as shown in Figures (2).
3.3. Aspect Ratio
Short buildings of low aspect ratio (height/width) behave like shear beams, and tall
buildings of high aspect ratio tend to behave like bending beams. Thus, it is expected
that the optimal diagrid angle directly affected by the total height (or number of
stories) of the building. In order to examine the effect of the aspect ratio on the
optimal diagrid inclinations angle, a set of 24-storey (aspect ratio H/b = 2) buildings
having various diagrid angles are analyzed using 2D finite element model. Then, the
analysis is repeated for 48- and 72-storey (aspect ratio H/b = 4 and 6, respectively) as
shown in Figure (3) and (4). Due to the fact that there are not strict guidelines on what
is actually considered a high-rise structure, it was hoped, this range safely keeps it
from being considered either a medium -rise or super-high-rise building.
4. RESULTS AND DISCUSSION
Lateral displacement is studied generally in two cases, building top (roof) lateral
displacement and storey drift (relative displacement between floors). The results
obtained from 2D finite element analysis are tabulated as follows:
4.1. Lateral Displacement
The graphs of lateral displacement versus storey number are plotted in Figure (5), (6)
and (7) for 24-, 48-, and 72-storey model, respectively. It is observed that the lateral
displacements are effected by the diagrid angle to largest extent especially for 24- and
48-storey building models. While the displacement is maximum for models with 27o
and 81o
diagrid angle, the displacement are reduced sequentially for models with
diagrid angle between 45o
and 72o
.

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Figure 2 Diagrid angles in 24-Storey models (Aspect ratio=2)
Figure 3 Diagrid angles in 48-Storey models (Aspect ratio=4)
Figure 4 Diagrid angles in 72-Storey models (Aspect ratio=6)
24-Storey 27 O
45 O
56 O
72 O
81 O
48-Storey 27 O
45 O
56 O
72 O
81 O
72-Storey 27 O
45 O
56 O
72 O
81 O

5. Optimal Diagrid Angle to Minimize Drift in High-Rise Steel Buildings Subjected to Wind
Loads
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From Table (1), it can be observed that the minimum building top displacement
value is obtained with 56o
diagrid angle in 24-storey model, and with 72o
diagrid
angle for 48- and 72-storey model.
Table 1 Comparison results of building top displacement (mm)
Model
Aspect
ratio
Angle of diagrid System
27o
45o
56o
72o
81o
24-storey 2 12.8 11.9 11.7 16.2 36.1
48-storey 4 96.3 88.2 80.1 78.2 122.6
78-storey 6 303.5 280.0 250.8 216.9 272.5
Figure 5 Lateral displacement for 24-storey models (Aspect ratio=2)
4.2. Storey Drift Ratio
As per Section 11.2 in current ASCE/SEI 7-10 (2010), storey drift can be defined as
the lateral displacement at the top of the storey relative to the bottom of the storey,
while the storey drift ratio is define as the storey drift divide by the storey height.
The storey drift ratios are shown in in Figure (8), (9) and (10) for 24-, 48-, and 72-
storey model, respectively. It is clear that the storey drift ratio at storey coincide with
the apex of triangle is less than those in other adjacent stories. Also, the storey drift
ratio is very low in bottom stories, very high at the middle stories and finally
decreases towards the upper stories.
0
5
10
15
20
25
30
0 5 10 15 20 25 30 35 40 45
STOREYNO.
LATERAL DISPALACEMENT (MM)
27-Degree 45-Degree 56-Degree 72-Degree 81-Degree

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Figure 6 Lateral displacement for 48-storey models (Aspect ratio=4)
Figure 7 Lateral displacement for 72-storey models (Aspect ratio=6)
Table 2 Comparison results of Max. Storey drift ratio (mm/mm)
Model
Aspect
ratio
Angle of diagrid System
27o
45o
56o
72o
81o
24-storey 2 0.000182 0.000178 0.000211 0.000382 0.001008
48-storey 4 0.000733 0.000658 0.000617 0.000705 0.001631
78-storey 6 0.001575 0.001454 0.001297 0.001112 0.00196
0
10
20
30
40
50
60
0 20 40 60 80 100 120 140
STOREYNO.
LATERAL DISPLACEMENT (MM)
27-Degree 45-Degree 56-Degree 72-Degree 81-Degree
0
10
20
30
40
50
60
70
80
0 50 100 150 200 250 300 350
STOREYNO.
LATERAL DISPLACEMENT (MM)
27-Degree 45-Degree 56-Degree 72-Degree 81-Degree

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Figure 8 Storey drift ratios for 24-storey models (Aspect ratio=2)
Figure 9 Storey drift ratios for 48-storey models (Aspect ratio=4)
4.3. Optimal Diagrid Angle
In medium- and super-high-rise building, lateral displacement decreasing is an urgent
criterion. Lateral displacement is studied generally in two approaches, building top
lateral displacement and storey drift. In this study in order to determine optimum
diagrid angle, the results for these two approaches has been used as measurable
parameters. For this reason building top lateral displacement and maximum storey
drift are plotted versus the diagrid angles and the results are shown in Figure (11) and
(12), respectively.
0
5
10
15
20
25
30
0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012
STOREYNO.
STOREY DRIFT RATIO (MM/MM)
27-Degree 45-Degree 56-Degree 72-Degree 81-Degree
0
10
20
30
40
50
60
0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.0016 0.0018
STOREYNO.
STOREY DRIFT RATIO (MM/MM)
27-Degree 45-Degree 56-Degree 72-Degree 81-Degree

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Figure 10 Storey ratios for 72-storey models (Aspect ratio=6)
The optimal angle of the diagrid members for maximum bending rigidity is 90o
,
(i.e. vertical traditional columns) and that of the diagonals for maximum shear rigidity
is about 27o
(only one storey stacked per basic triangle model), it is expected that the
optimal angle of the diagonal members of diagrid structures will fall between these
angles.
The optimum diagrid angle is where the building top lateral displacement and
storey drift ratio are minimum. It can observed that the optimum diagrid for 24-storey
model is smaller than 56o
while optimum angle is 72o
for both 48- and 72-storey
models.
Figure 11 Building top displacement vs. Diagrid angle
0
10
20
30
40
50
60
70
80
0 0.0005 0.001 0.0015 0.002 0.0025
STOREYNO.
STOREY DRIFT RATIO (MM/MM)
27-Degree 45-Degree 56-Degree 72-Degree 81-Degree
0
50
100
150
200
250
300
350
20 30 40 50 60 70 80 90
Max.LateralDisplacement(mm)
Diagrid angle (Degrees)
24-Storey
48-Storey
72-Storey

9. Optimal Diagrid Angle to Minimize Drift in High-Rise Steel Buildings Subjected to Wind
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Figure 12 Max. Storey drift ratio vs. Diagrid angle
5. CONCLUSIONS
This study examined the lateral behavior of diagrid high-rise building models
under lateral wind loads from which the following conclusions can be drawn based on
the above results:
1. The diagrid angle has a critical influence on the lateral behavior of the high-rise
building models under lateral load. The structural efficiency of diagrids can be
maximized by configuring the building model to have optimum grid geometries.
2. The storey drift ratio at storey coincide with the apex of triangle is less than those in
other adjacent stories.
3. Optimum diagrid angle resulted from finite element analysis for 24-storey model
(aspect ratio=2) is smaller than 56o
while optimum angle is 72o
for both 48- (aspect
ratio =4) and 72-storey (aspect ratio=6) models.
4. The optimal range of diagrids angle is reduced as the building aspect ratio
(height/width) decreases.
REFERENCES
[1] ASCE/SEI 7-10; Engineers, A. S. Minimum Design Loads for Buildings and
Other Structures. American Society of Civil Engineers, 2010.
[2] Montuori, G. M., Mele, E., Brandonisio, G. and De Luca, A. Design Criteria for
Diagrid Tall Buildings: Stiffness versus Strength. The Structural Design of Tall
and Special Buildings, Published online in Wiley Online Library, DOI:
10.1002/tal.1144, 2013.
[3] Mele, E., Toreno, M., Brandonisio, G. and De Luca, A. Diagrid Structures for
Tall Buildings: Case Studies and Design Considerations. The Structural Design
of Tall and Special Buildings, 23, 2007, pp. 124–145.
[4] Moon, K. S., Connor J. J. and Fernandez, J. E. Diagrid Structural System for Tall
Buildings: Characteristics and Methodology for Preliminary Design. The
Structural Design of Tall and Special Buildings,16(2), 2007, pp. 205–230.
0
0.0005
0.001
0.0015
0.002
0.0025
20 30 40 50 60 70 80 90
Max.Storeydrift(mm/mm)
Diagrid angle (Degrees)
24-Storey
48-Storey
72-Storey

10. Khalid K. Shadhan
http://www.iaeme.com/IJCIET/index.asp 10 editor@iaeme.com
[5] Panchal, N. B. and Patel V. R. Diagrid Structural System: Strategies to Reduce
Lateral Forces on High-Rise Buildings. International Journal of Research in
Engineering and Technology, 3(4), 2014, pp. 374–378.
[6] Singh, R. K., Garg, V. and Sharma, A. Analysis and Design of Concrete Diagrid
Building and its Comparison with Conventional Frame Building. International
Journal of Science, Engineering and Technology, 2(6), 2014, pp. 1330–1337.
[7] Mathew, J. and Babu, N. Topology Optimisation of Braced Frames for High-Rise
Buildings. International Journal of Civil Engineering and Technology, 5(12),
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