ASIAN JOURNAL OF CIVIL ENGINEERING (BUILDING AND HOUSING) VOL. 13, NO.

1 (2012)
PAGES 97-112

NONLINEAR DYNAMIC ANALYSIS OF CHIMNEY-LIKE TOWERS

M.R. Tabeshpour*
Faculty of Engineering, Sabzevar Tarbiat Moallem University, Sabzevar, Iran
Received: 5 September 2010, Accepted: 5 July 2011

ABSTRACT

Evaluation of seismic vulnerability of very flexible structures such as high-rise petro-

chemical and refinery stacks (chimney) and power plant chimneys is a challenging problem
in earthquake engineering. Their equipments and structures are often considered as vital
facilities and thus they must be fully functional after even very strong ground motions. From
other point of view, numerical modeling of such mega-structures with numerous elements
may not allow to consider all details of mechanical characteristics of consisting materials,
particularly nonlinear performance of elements during large deformations. Therefore, a
simplified model corresponding to dynamic characteristics of whole structure is
substantially needed to investigate seismic performance and failure modes of these essential
structures subjected to strong ground motions. The procedure for developing a 2-D
simplified nonlinear model based on moment-curvature in some plane-sections of a 3-D
sophisticated model but linear system having almost identical dynamic properties is
discussed. If micro elements be used for structural modeling of the chimney like structures,
static nonlinear analysis or dynamic linear analysis will be economically suitable for
assessment investigation. But of the most important problems in earthquake behavior of the
structures is hysteretic behavior of material and section properties. The significance of this
study, if any, is mainly concentrated on model simplification that provides sufficient
accuracy based on a nonlinear discrete model. Tous power-plant chimney is investigated
numerically as an example.

Keywords: High-rise structures; seismic vulnerability; damage index; nonlinear model

1. INTRODUCTION

Some special structures such as high-rise towers and power plant chimneys and their
equipments and/or in-charge facilities are often considered to be fully functional after even
very strong ground motions. Consequently, seismic assessment for actual performance of
structures during earthquakes, the nonlinear dynamic analysis is required. Then the damage

*
E-mail address of the corresponding author: tabesh_mreza@yahoo.com (M.R. Tabeshpour)
98 M.R. Tabeshpour

indices of structure have to be calculated, using appropriate damage models since these
indices could be numerical representation of damage states of the structures. However,
numerical modeling of such mega-structures with numerous elements may not be allowed to
include all details of mechanical characteristics of consisting materials, particularly
nonlinear performance of elements during large deformations. Therefore, a simplified model
corresponding to dynamic characteristics of whole structure is substantially needed to
investigate seismic performance and failure modes of these essential structures subjected to
strong ground motions.
In this paper a practical method to assessment chimney like towers such as smoke stacks,
minarates and TV towers is presented based on nonlinear dynamic analysis considering
appropriate hysteretic behavior of section and material properties. Damage analysis is
presented as well. Such an analysis is required for fragility curve of the structure. Many
nonlinear dynamic analyses are required for fragility cures. Only using simple reliable
macro (beam-column element) model can achieve such a goal. Some examples of damaged
towers in previous earthquakes show the necessity of the nonlinear dynamic analysis of
these types of structures.

1.1 Seismic Behavior of Minarates

Classification and description of damage were documented for 64 historical and monumental
structures surveyed after the August 17 (Kocaeli) and November 12 (Düzce), 1999
earthquakes (Turkey) by Sezen et al. [1-2]. The levels of damage recorded, construction type,
and locations of the surveyed mosques and minarets were reported. Survey results indicated
that the majority (70%) of the masonry and reinforced concrete minarets surveyed in Düzce
was observed to sustain damage of intensity severe to collapse. Collapse of the minarets, which
are tall slender towers, constituted a hazard to life and to surrounding buildings. Horizontal
circumferential cracks and spalling of concrete near the bottom of minaret cylinder (Figure 1)
were the common types of damage reported for reinforced concrete minarets. In most cases,
damage was observed within a diameter above the intersection of the cylindrical portion of the
minaret and the pyramid-shaped section providing the transition from a cube to cylinder. The
location of failure in the reinforced concrete minarets that collapsed was found to be near the
bottom of the cylinder where the longitudinal reinforcing bars were spliced (Figure 2). Less
frequently, transition segment, mid-height of the cylinder (Figure 1), and top of the minaret
were among the sections where minarets sustained significant damage.

1.2 Seismic Behavior of Chimneys

During the Ismit (Kocaeli) Earthquake of August 17, 1999, a 115 m. high reinforced
concrete chimney or heater stack, located at the Tüpras Refinery, collapsed. The falling
debris cut 63 pipes, which contributed to interrupted production for more than 14 months.
This stack was designed and constructed according to international standards and is
representative of similar structures at refineries throughout the world, including those in
earthquake-prone regions. The opening was located about 1/3 of the height above the base
and appeared to be the region of initiation of the collapse. The debris cut many lines, which
fueled fires that shut down the refinery for months. The collapsed stack was 115 m. The
remnants of the stack are shown more clearly in Figure 3, where it is evident that the failure
 NONLINEAR DYNAMIC ANALYSIS OF CHIMNEY-LIKE TOWERS 99

occurred in the vicinity of the opening.

Figure 1. Damage to cylinder mid-height Figure 2. Collapse of minarets due to failures

near the bottom of the cylinders

Figure 3. Remnants of failed stack

The investigation is focused on the dynamic response of the stack due to an earthquake
motion recorded at a nearby site. Gould et al. [3] and Huang and Gould [4] presented
interesting results of analysis of the Tüpras stack. They presented nonlinear static analysis
of the collapsed stack using a demand-collapse comparison. The demand was represented by
an acceleration-displacement response spectrum based on the recorded motion as well as
some smoothed adaptations typical of design spectra, while the capacities were calculated
from pushover curves using a nonlinear reinforced concrete finite element analysis. The
results confirm that the stack could readily fail under the considered earthquake and were
also consistent with the debris pattern. Pushover results shown in Figure 4 are cracking
patterns for the model with and without opening in a step. Of course, a full nonlinear
100 M.R. Tabeshpour

dynamic analysis would be necessary to more completely simulate the failure.

Figure 4. Cracking pattern for the model with and without opening [3]

1.3 Vibration Test

Yamamoto and Maeda [5] presented measured micro-tremor to acquire vibration
characteristics, which was used to construct FE model for the superstructure by simulating
base-fixed horizontal natural frequencies of the brick chimney of the height of 23m in
Tokoname (Japan) which was built in 1922 (Figure 5). Soil-foundation interaction was
treated by installing soil springs which were determined by simulating soil-coupled
frequency. With the soil-coupled FE model, linear dynamic response analysis was carried
out for four kinds of input ground motions. It was found that the base of the chimney will
have damage at maximum acceleration from 41 to 77 Gal, should the collapse be caused by
excessive tensile stress at mortal joints.

Figure 5. Appearance of the chimney

1.4 soil-structure interaction
Generally a fixed base model is adopted for seismic design when the effect of soil-structure
 NONLINEAR DYNAMIC ANALYSIS OF CHIMNEY-LIKE TOWERS 101

interaction is considered negligible. When this effect is taken into account, the use is
commonly made of a sway rocking model for the structures with spread or short-pile
foundation. The SSI effect on the structure as well as piles, however, is considered
significant in case of long piles in soft ground. In such a case, some coupled system should
be adopted for the seismic design model. A finite element model would be powerful in
evaluating the SSI effect if it were linear. Also as a simple model a lumped mass-spring-
beam model can be considered appropriate for taking into account the major SSI effect as
well as the material non-linearity in the structure and the ground [6]. Figure 6 shows the
models mentioned above. Halabian and Kabiri have investigated the effect of soil structure
interaction on the response of stack like structures [7].

Figure 6. Models of preliminary analyses as candidates for the seismic design

In this paper, an exclusive review of relevant modeling and methodology for estimation
of damage indices in special RC structures has been carried out. A procedure for developing
a 2-D simplified nonlinear model based on moment-curvature in some plane-sections of a 3-
D sophisticated model but linear system having almost identical dynamic properties is
developed.
The significance of this study, if any, is mainly concentrated on model simplification that
provides sufficient accuracy based on a nonlinear discrete model. Damage indices under
different hazard levels of excitations provide the database for vulnerability and seismic risk
analyses for the both elements and whole of structures. For instance, from relative
displacement responses of nonlinear model, one may estimate the most probable modes of
failure under MCE level of input excitation.
As noted above, the damage indices of structure have to be calculated, using appropriate
damage models. It is because of the fact that damage indices are quantitative values for damage
states of the structures. These models are usually based on the maximum deformations,
hysteretic energies and structural deteriorations. Damage indices are appropriate tools for
quantifying numerically the damage in structures sustained under earthquake loading. Many
researchers have defined various damage indices. Damage indices may be defined locally for
102 M.R. Tabeshpour

elements or globally for whole the structure. An extensive review of defined damage indices
for various types of structures has been carried out [9-10]. Vulnerability of an existing
structure based on seismic hazard analysis has been assessed [11].
Park-Ang damage index [12], considered in IDARC [13], is the most usual damage index
for damage analysis of reinforced concrete structures. It can be calculated in the element,
storey and overall scales. An important point is that the damage indices of stories are
calculated based on hysteretic energy weighting factors and therefore the structural
importance of beams and columns are the same. Also overall damage index of structure is
calculated by summation of the storey damage indices on the basis of hysteretic energy of
each storey.
Seismic vulnerability and damage analysis of special structures have been carried out
successfully using IDARC program [14-15]. The key idea of structural modeling of the
special structures is to develop a simplified 2-D model using beam-column elements based
on moment-curvature in some plane sections. Appropriate results have been achieved by
nonlinear dynamic analysis of these simplified models.
Some special structures such as high rise towers are often analyzed elastically using shell
or solid elements, ignoring the effect of nonlinear properties. But it is clear that in order to
understand the actual behavior of the structure, nonlinear dynamic analysis must be carried
out. To investigate the structural behavior of towers under future earthquakes, the structure
should be modeled as a way to perform the seismic behavior properly. The structural
modeling can be carried out using various types of elements. Among these elements beam-
column element is an appropriate type considering both the complexity of the structural
performance and the time consuming of the analyses.
In this paper the seismic performance of Tous power-plant chimney, which is located in a
seismically active zone, has been evaluated.

2. STRUCTURAL MODELING

As mentioned earlier, it is possible to model the structure using various types of elements.
But it is clear that nonlinear dynamic analysis of structure is required for seismic
vulnerability. It is possible to use various types off elements to model high rise cantilever
type towers. The beam-column element is the most appropriate method for structural
modeling, because of limitations in the computation time. Figure 7 shows the discrete model
of the structure using lumped mass and beam-column elements. Beam-column elements are
modeled considering flexural, shear and axial deformations. Flexural and shear components
of the deformation are modeled using three parameter Park model described later. The axial
deformation component is modeled using a linear-elastic spring.
 NONLINEAR DYNAMIC ANALYSIS OF CHIMNEY-LIKE TOWERS 103

Figure 7. Discrete structural beam element model

3. NONLINEAR MODELING OF MATERIALS

Softening of the concrete under deformation near its limit state of resistance is an important
property that must be considered in nonlinear dynamic analysis. The moment–curvature
relation method is one of the specialty approaches used to express the real behavior of
concrete structures when deformed. This method could widely serve all general cross-
sectional shapes that may be used as different geometric cross-sections in towers. The
longitudinal concrete stresses can be found from the longitudinal concrete strains by using
the appropriate concrete stress–strain relationship in compression. Figure 8 shows the
relation between stress and strain for steel and concrete materials.

(a) (b)
Figure 8. Stress – strain relationship for steel (a) and concrete (b)

Assuming that there is appropriate reinforcement such that the collapse of the tower will
be due to crushing of concrete in primary stress arising from axial load and flexure, it can be
used from the moment - curvature diagram in order to damage analysis.
104 M.R. Tabeshpour

4. PUSHOVER ANALYSIS

The nonlinear pushover analysis, or collapse mode analysis, is a simple and efficient
technique to predict the seismic response of prior to a full dynamic analysis. A pushover
analysis can establish the sequence of component yielding, the potential ductility capacity,
and the adequacy of the lateral strength of the structures. The pushover analysis option
performs an incremental analysis of the structure subjected to a distribution of lateral forces.
The pushover analysis may be carried out using force control or displacement control. In
the former option, the structure is subjected to an incremental distribution of lateral forces
and the incremental displacements are then calculated. In the latter option, the structure is
subjected to a displacement profile, and the lateral forces that needed to generate the
deformation are calculated. Typically, since the deformed profile is not known, and an
estimate of the lateral distribution of forces can be made, force control is commonly used.
For displacement control, the user must specify the target maximum deformation profile of
the structure. This profile is internally divided by the number of steps specified by the user,
and then incrementally applied to the structure. In the force control option the user must
specify the maximum force distribution, or select one of the force distributions available in
the program: Uniform Distribution, Inverted Triangular Distribution, Generalized Power
Distribution Modal Adaptive Distribution.
The generalized power distribution was introduced to consider different variation of the
storey accelerations with the storey elevation. This distribution was introduced to capture
different modes of deformation, and the influence of higher modes in the response. The
force increment at floor “i” is calculated according to:

Wi hik
Fi  N
Vb (1)

j 1
W j h kj

where Wi and hi are the storey weight and the storey elevation, respectively, and Vb is the
increment of the building base shear and k is the parameter that controls the shape of the
force distribution. The recommended value for k may be calculated as a function of the
fundamental period of the structure (T):
k  1.0 for T  0.5 (2a)

k  2.0 for T  2.5 (2b)

T  0.5
k  1.0  otherwise (2c)
2

5. NONLINEAR DYNAMIC ANALYSIS

The nonlinear dynamic analysis is carried out using a combination of the Newmark-Beta
 NONLINEAR DYNAMIC ANALYSIS OF CHIMNEY-LIKE TOWERS 105

integration method, and the pseudo-force method. The viscous damping matrix is calculated
in the program using one of the following options: Mass or Stiffness proportional damping
and Rayleigh damping. In the program IDARC the circular frequency corresponding to the
first mode of vibration is used for the mass and stiffness proportional damping, while the
circular frequencies corresponding to the first and second modes are used for the Rayleigh
damping type. Under these conditions, mass proportional damping will yield a smaller
damping ratio for the higher modes, while stiffness proportional and Rayleigh damping may
result in a higher critical damping ratio for the higher modes.
Modeling the hysteretic behavior of structural elements is one of the core aspects of a
nonlinear structural analysis program. The three parameter Park hysteretic model is as part
of the original release of IDARC. The hysteretic model incorporates stiffness degradation,
strength deterioration, non-symmetric response, slip-lock, and a trilinear monotonic
envelope. The model traces the hysteretic behavior of an element as it changes from one
linear stage to another, depending on the historey of deformations. The model is therefore
piece-wise linear. Each linear stage is referred to as a branch. Figures 9 shows the effect of
various parameters on the shape of the hysteretic loops.

6. DAMAGE ANALYSIS

In order to damage analysis, it is necessary to quantify the structural damage and therefore
damage index must be defined. Many damage indices have been defined. The most usual
damage index is the Park-Ang model. It is defined as combination of maximum deformation
and hysteretic energy [12]:
 
 u  u Py 
DI  m  dE h (3)

in which m is the maximum deformation of the element (nonlinear dynamic analysis),  u is

the ultimate deformation (push-over analysis),  is a model constant parameter (0.1-.015),

 dE h is the hysteretic energy absorbed by the element during the earthquake, Py is the
yield strength of the element. Park-Ang damage model can be extended to the storey and
overall scales. Park-Ang damage indices for various damage states are shown in Table 1.

Table 1: The relation between damage index and damage state

Degree of Damage Damage Index State of Building

Slight <0.1 No Damage
Minor 0.1-0.25 Minor Damage
Moderate 0.25-0.4 Repairable
Severe 0.4-1.0 Beyond Repair
Collapse >1.0 Loss of Building
106 M.R. Tabeshpour

stiffness degradation strength deterioration pinching

Figure 9. Control parameters for the three parameter hysteretic model [15]

7. CASE STUDY

The chimney has cylindrical shape with 100m height, and external diameter of 10 meter.
The cylindrical shell thickness is 80cm from base to the elevation of 17.5m and then it is
reduced to 30cm in upper part. The schematic view of the chimney has been presented in
Figure 10.

Figure 10. Schematic view and photograph of chimney

Seismic hazard analysis has been performed to determine the peak ground acceleration
(PGA) in both case studies. For instance for return periods of 75, 500, 1000 and 2500 years
at the site of chimney, PGA values resulted in 0.13, 0.26, 0.33, and 0.43g, respectively.
In order to determine the periods and the effects of different modes of the structure,
eigenvalue analysis must be performed. For the studied chimney the periods of the first three
modes associated to 1.67, 0.30 and 0.11 sec, respectively. It is important to note that the
mode shapes and frequencies of the structure were measured using Ambient Vibration
Survey (AVS) [16]. The first and second frequencies resulted in 1.48 and 0.29 sec
 NONLINEAR DYNAMIC ANALYSIS OF CHIMNEY-LIKE TOWERS 107

respectively. The third mode of AVS test has been associated to the torsional mode, and
therefore it is not comparable with numerical results. Figure 11 shows the flexural mode
shapes. It is clear from the first mode that the considered power distribution of lateral force
is appropriate for pushover analysis.

Figure 11. Mode shapes of chimney

The results of the pushover analyses for various types of lateral force have been
presented in Figure 12. As shown in this Figure, the uniform distribution of lateral load
gives the maximum base shear. Also the base shear of the triangle distribution is more than
that of the power distribution for the power factors equal to 1.5, 1.625 and 2 that are
corresponding to the periods of 1.5, 1.75 and 2.5 sec, respectively. Note that the
fundamental period of the structure is 1.67 sec. It is seen that the ultimate strength of the
structure is approximately 19% of weight.

Figure 12. Comparison of pushover analyses of chimney

108 M.R. Tabeshpour

For all kinds of distribution proposed for lateral loads, the mechanism is similar to Figure
13, in which the plastic hinge occurs in the elevation 17.5m, the section that thickness
changes sharply.

Figure 13. Failure Mode of chimney (position of plastic hinge)

Nonlinear dynamic analysis has been performed under the input motions shown in Figure 14.

Figure 14. Acceleration time history records

Nonlinear dynamic analysis has been performed under the input motions shown in Figure
14. Time history responses at top of the structure for input motion scaled to PGA level of 75
years return period are given in Figure 15.
 NONLINEAR DYNAMIC ANALYSIS OF CHIMNEY-LIKE TOWERS 109

Figure 15. Time history responses at top of the structure for input motion scaled to PGA level of
75 years return period

The effect of input motion is observed clearly. Overall drift of the structure for PGA
values of 0.1g-0.6g has been shown in Figure 16. It is seen that for PGAs less than 0.3g,
there is no considerable difference among the responses of various input motions, but for
PGAs greater than 0.3g, the input motion characteristic has a strong influence on the
response of the structure.
110 M.R. Tabeshpour

Figure 16. Relation between PGA and top displacement ratio

Global damage index of the structure for PGA values of 0.1-0.6g has been shown in
Figure 17. It is observed that for PGAs greater than 0.2g, the input motion has an obvious
influence on the damage of the structure. Also for PGAs greater than 0.6g structural collapse
may occur under some records consisting of low frequency content.

Figure 17. Relation between PGA and global damage index

 NONLINEAR DYNAMIC ANALYSIS OF CHIMNEY-LIKE TOWERS 111

8. CONCLUSIONS

The nonlinear dynamic analysis is essentially needed for seismic assessment in evaluation of
actual performance of complicated structures during earthquakes. Then the damage indices
of structure had to be calculated, using appropriate damage models, since these indices
would be numerical representation of damage states of the structures. However, numerical
modeling of such mega-structures with numerous elements would not be allowed to include
all details of mechanical characteristics of consisting materials, particularly in large
deformations. Therefore, a simplified model corresponding to dynamic characteristics of
whole structure was developed to investigate seismic performance and failure modes of
these essential structures subjected to strong ground motions. The simplified model provided
sufficient accuracy based on a nonlinear discrete model. To verify the proposed modeling
procedure, two case studies were investigated numerically. Acceleration time histories
scaled to different hazard levels were used as input excitations. Among the results,
distribution of damage indexes could verify the most probable mode of failure under the
severe excitation.

REFERENCES

1. Sezen H, Firat GY, Sozen MA. Investigation of the performance of monumental

structures during the 1999 Kocaeli ans Duzce Earthquakes, 5th National Conference on
Earthquake Engineering, Istanbul, Turkey, Paper No: AE-020, 2003.
2. Sezen H, Acarb R, Dogangunb A, Livaogluc R. Dynamic analysis and seismic
performance of reinforced concrete minarets, Engineering Structures, 30(2008) 2253–64.
3. Gould PL, Huang W, Martinez R, Johnson GS. Nonlinear analysis of a collapsed heater
stack, 13th World Conference on Earthquake Engineering, Vancouver, B.C., Canada,
Paper No. 2153, 2004.
4. Huang W, Gould PL. A case study considering a 3-D pushover analysis procedure, 14th
World Conference on Earthquake Engineering, Beijing, China, 2008.
5. Yamamoto T, Maeda T. Earthquake safety assessment of a tall brick chimney in
Tokoname based on the mircro-tremor measurement, 14th World Conference on
Earthquake Engineering, Beijing, China, 2008.
6. Mori S. Design and actual performance of a super high R/C smokestack on soft ground,
Proceedings Third UJNR Workshop on Soil-Structure Interaction, Menlo Park,
California, USA, 2004.
7. Halabian AM, Kabiri S. Soil structure interaction effects on inelastic response of R/C
stack like structures, 13th World Conference on Earthquake Engineering, Vancouver,
B.C., Canada, Paper No. 2759, 2004.
8. Cajiao P, Sherstobitoff J, Wong M. Seismic upgrade of chimney stack at Lions Gate
Hospital, 13th World Conference on Earthquake Engineering, Vancouver, B.C.,
Canada, Paper No. 2410, 2004.
9. Williams MS, Sexsmith RG. Seismic damage indices for concrete structures: A state-of-
the art review, Earthquake Spectra, 11(1995) 391-49.
112 M.R. Tabeshpour

10. Ghobarah H, Abou-Elfath, Biddah A. Response-based damage assessment of structures,

Earthquake Engnging and Structural Dynamics, 28(1999) 79-104.
11. Golafshani AA, Bakhshi A, Tabeshpour MR. Vulnerability and damage analysis of
existing buildings, Asian Journal of Civil Engineering (Building and Housing), 6(2005)
85-100.
12. Park YJ, Ang AHS. Mechanistic seismic damage model for reinforced concrete.
Journal of Structural Engineering, ASCE, 111(1985) 722-39.
13. Reinhorn AM, Kunnath SK, Valles-Mattox R. IDARC 2D Version 4.0: users manual.
Department of civil Engineering, State University of New York at Bufallo, 1996.
14. Tabeshpour MR, Bakhshi A, Golafshani AA. Seismic vulnerability of Tehran TV
tower, Proceedings of the 4th International Conference on Seismology and Earthquake
Engineering, IISEE, Tehran, Iran, 2003 (in Persian).
15. Tabeshpour MR, Bakhshi A, Golafshani AA. Nonlinear dynamic analysis and seismic
vulnerability of special structures, 13th World Conference on Earthquake Engineering,
Vancouver, Canada, 2004.
16. Aghababaei AR. Investigation of dynamic properties of power-plant structures.
Proceedings of the 4th International Conference on Seismology and Earthquake
Engineering, IISEE, Tehran, Iran, 2003 (in Persian).