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Article

Structural Analysis of the Historical Sungurlu Clock Tower

by
Ahmet Gökdemir
1,* and
Zülküf Baki
2
1
Department of Civil Engineering, Faculty of Technology, Gazi University, Ankara 06560, Türkiye
2
Graduate School of Natural and Applied Sciences, Gazi University, Ankara 06560, Türkiye
*
Author to whom correspondence should be addressed.
Appl. Sci. 2024, 14(16), 7085; https://doi.org/10.3390/app14167085
Submission received: 5 July 2024 / Revised: 2 August 2024 / Accepted: 7 August 2024 / Published: 12 August 2024
(This article belongs to the Section Civil Engineering)

Abstract

:
Background: The strength of historical buildings built in different centuries with various materials and construction techniques and harboring many structural problems depends on the structural system, geometrical condition, and material properties. Sungurlu clock tower, whose system and geometry are in good condition, has been damaged under environmental and climatic effects, earthquakes, and other loads, and has survived to the present day by preserving its structural integrity to a great extent with the repairs it has undergone. Methods: In addition to static analysis, the robustness and durability of the design of the tower were tested by dynamic analysis with the SAP2000 program. In the model that will represent the actual system behavior of the tower, the lengths of the elements; nodal points; bearings; joints; shapes such as bars, shells, and plates; characteristic values of the materials to be used; as well as the system, element sections, and all loads and combinations of masses or dynamic forces acting on the system are defined. Results: In the reports presented visually, the moment, shear force, axial forces, and other forces to which the tower was exposed after the architectural and structural problems were eliminated were seen in a diagram. Since the effects of the damage could not be predicted, in this study, to measure the reaction of the building against earthquakes and other loads, the numerical model representing its original condition was prepared and analyzed according to the theoretical method and assumptions made by the restitution, survey, and static observation reports. Conclusions: With this program, which allows for the preparation of this model, it was concluded that the loads coming to the structure according to the principles of ductility, rigidity, and strength could be safely transferred to the ground without causing damage to the structural system and its elements. From the deformation, stress, velocity, acceleration, and reaction force graphs obtained, it was understood that the tower exhibited the expected structural behavior under its own weight and live loads. The stress and reaction force graphs showed that the structural materials are adequate for the resistance of the structure and system against the existing loads and possible earthquakes.

1. Introduction

Time not only increases the value of historical buildings but also causes strains and damages as a result of aging, wear, loss of properties, deterioration, and inadequacy of the material due to effects such as climate, environmental factors, earthquakes, vertical and lateral loads, and lack of maintenance [1]. To minimize the adverse effects of time, it is necessary to act according to the laws and rules accepted in the scientific framework, written or unwritten. The main principle in repairing and conserving historic buildings is to keep the intervention to a minimum level so that the building does not lose its originality. The conservation of a building should cover its layout, all plan and sectional features, materials, construction system, and structural system [2]. An irreversible intervention in any of these cannot be called conservation. The point that should always be remembered in the works to be carried out for the repair and protection of historical monuments is that these buildings have historical, cultural, monumental, aesthetic, symbolic, social, and even psychological value [3]. Interventions to be made in the light of these data should fulfill the following sine qua non conditions.
  • The methods and materials used should be in harmony with the structure. Interventions that may cause the structure to decay or collapse due to the selection of materials incompatible with the structure should be avoided [4].
  • The life of the repairs should be as long as the life of the building; if this cannot be achieved, they should be of a quality that can be repeated at specific intervals [5].
  • Repair and conservation work started with good intentions may bring bad results due to any mistake that may be made.
  • Experiments and calculations must demonstrate that the intervention achieves the desired result [6]. Reversibility: Repair and strengthening work started with good intentions may bring bad results due to any mistake that may be made. For this issue, which requires expertise and experience, the reversibility flexibility of the selected technique should not be ignored.
  • Every conscious and responsible individual should show sensitivity in protecting and preserving all cultural assets that we have inherited and have become a part of our lives [7].
It is one of today’s most critical problems to keep the cultural values that make up the historical environment alive and to transfer them to future generations with their original qualities. The aim is to prevent further deterioration of the old buildings and ensure that they are transferred to the next generations in a healthy condition [8].
It is only possible for historic buildings to maintain their existence for centuries or even millennia and to be passed on to future generations by ensuring periodic maintenance and repair. For this reason, severe damage may occur in abandoned buildings that are not used for a long time due to a lack of maintenance, and in some cases, the building may even be lost entirely. Another important factor that reduces the structural resistance of masonry structures against natural or physical effects is the human interventions and additions that the structure encounters during its lifetime [9].
Slender geometry and irregular structures such as clock towers are very sensitive to seismic loads. Severe damage or sudden collapses may occur under earthquake loads [10,11,12]. Structural analysis of the seismic vulnerability of historic buildings is critical, especially in earthquake-zone countries. The importance of FE modeling approaches developed to comprehensively investigate the actual structural behavior of historic structures under seismic effects is increasing. Defining and analyzing appropriate structural models is a specialized subject. In particular, nonlinear dynamic analyses accurately predict earthquake-induced damage [13,14,15].
Some of the main objectives of this study can be summarized as outlined below: (1) to examine the current and structural status of Sungurlu Clock Tower in line with the project, restitution, survey, restoration reports, and on-site observations, and to present suggestions for interventions to be made; (2) assuming that all architectural and structural problems are eliminated since it is not possible to determine the behavior of the tower under its own weight and live loads experimentally, to prepare a mathematical model and to analyze this model by the finite element method; (3) to find the effects of maximum loading and boundary conditions on deformations, stresses, velocities, accelerations, and reaction forces on the tower and its components and to create graphs; and (4) to evaluate and optimize the behavior of the structure and system with graphs showing displacement, moment, axial forces, natural frequency, mode shape, and damping ratios obtained from finite element analysis of the tower.
The paper is organized as follows. The material and method section presents the history of the Sungurlu Clock Tower, its structural features, existing problems, and calculation parameters (Section 2). Section 3 presents the main results of the advanced numerical simulations performed for the clock tower. In the last section, the main results of the research are reported.

2. Materials and Methods

2.1. Sungurlu Clock Tower

In addition to showing the time, clock towers were used as fire and watchtowers, as direction indicators in foggy and hazy weather, and some of them were built as fountains with the fountains on their pedestals, muvakkithane (the place where prayer times are determined by looking at the sun) with rooms under them, and multifunctional structures with a wind vane that measures weather events. Most clock towers have a pedestal, body, honeycomb, mansion, and roof. Generally, there is a room at the base and a staircase to reach the upper levels. This staircase continues in the body part. There is also a clock mechanism inside the mansion. Most of them have windows to hear the sound comfortably [16].
Sources inform that the Sungurlu clock tower (Figure 1), which has no inscription today, was built in 1891/92 by District Governor Edip Bey to Şakir Usta from Yozgat, who also built Yozgat Clock Tower [17].
The tower has a square prism body and shows an eight-story structure that narrows slightly towards the top. The corners of the square prism are rounded with circular profiled moldings, and the floors are separated by protruding moldings. The moldings are reinforced with iron profiles, which were probably built later. Small windows with round arches are on every floor except the second floor. The tower’s top floor ends with an octagonal wooden mansion with multi-armed star-shaped eaves. Each side of the octagon has gnarled window openings. Under the mansion are quadrangular (originally round) clock dials placed in square slots in four directions, and the original clock mechanism is made of metal inside. Below this floor is a balcony with an iron grid that has yet to fail. At the corners of the balcony are small piers in the form of a polygonal prism made of stone connecting the iron grids. One of these piers is partially intact, one is broken in place, and two have disappeared.
On the ground floor is a doorway with a flat-arched opening with profiled brackets in the center of the north façade. The door, probably made of wood in the past, is now made of metal with a single wing.
The tower’s ground floor has a wooden floor, and there is a wooden staircase in the interior, which the balcony floor can reach. The flooring and the stairs are not original and were wholly renewed during the recent repairs.
On the lowest floor of the tower, a row of cut stone cladding was added in the form of a seat, which was built later to prevent water damage.
The building is constructed of stone. The front faces are molded with a single row of square and rectangular cut block stones. The stones’ front (outer) faces were rubbed, and the back (inner) faces were left rough. Sandstone with local characteristics was used as rock [18].

2.2. Structural Status and Problems

The clock tower has survived to the present day by preserving its structural integrity to a great extent. The corrosive effects of time, tectonic movements, and climatic and environmental factors have caused various types of deterioration of the original building elements and materials.
In the Sungurlu region, according to meteorological data (between 1980 and 2016), it is determined that the temperature varies typically between −5 °C and 31 °C during the year; it is below −13 °C in winter and above 36 °C in summer [19]. In the summer, there are also high temperature differences between day and night (between 15 °C and 36 °C). In addition, fossil fuels and traffic-related exhaust gases, which increase significantly in winter months in the city center, cause air pollution. In addition to these factors, negligence in the use and maintenance of the building and faulty repair interventions have played an accelerating role in the deterioration process.

2.2.1. Deterioration of the Stones

Local sandstones were used as rock types in the construction of the tower. Chemical-physical deterioration such as surface contamination, abrasion, fracture, and loss of fragments are observed in the building stones due to various factors.
  • Part loss (Loss): Losses and ruptures occurring in the integrity of the material. This loss is seen more intensely, especially in the stone blocks in the corner moldings (Figure 2). It is mainly seen in breaking the edges and corners of the stone blocks sitting on each other.
Figure 2. Loss of parts when molding balconies.
Figure 2. Loss of parts when molding balconies.
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  • Destroyed elements: In the balcony part of the monument, one of the small piers in the form of a polygonal prism made of stone at the corners connecting the iron grids is partially intact; one is broken; and the other two are destroyed (Figure 3).
Figure 3. Original (left) and present (right) view of the balcony.
Figure 3. Original (left) and present (right) view of the balcony.
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  • Cracks, splits, and fractures: Capillary and deep cracks of various sizes are observed in the stone structures used in the monument (Figure 4). Temperature changes cause different expansions and contractions in building stones consisting of different minerals, leading to the proliferation of capillary cracks in the stone bodies, which are loosened by heat. If no precautions are taken, the size of the cracks grows over time, accelerates the deterioration process, and may lead to part losses.
Figure 4. Splits and fractures caused by physical impact.
Figure 4. Splits and fractures caused by physical impact.
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  • Abrasion (Erosion): This is the wear and superficial damage that occurs primarily due to the effects of climate and atmosphere (rain, snow, wind, acid rain, etc.). The wetting of surfaces by rain or snow and impacts caused by dust and sand grains brought by the wind cause abrasion (Figure 5). In addition, compounds such as sulfur, carbon, chlorine, and nitrogen emitted from exhausts and housing chimneys are acidified in humid environments and cause the erosion of stones.
Figure 5. Superficial and deep wear.
Figure 5. Superficial and deep wear.
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  • Foliation (Flaking): Due to physical and chemical effects, it is a type of deterioration that causes separation and rupture in the form of thin layers and flaking on the stone surfaces (Figure 6).
Figure 6. Flaking on the stone surface.
Figure 6. Flaking on the stone surface.
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  • Deterioration due to unqualified repair interventions: Recent careless cement interventions, plastic completions in missing parts, repairs with colors and textures incompatible with the original stone surfaces, and carelessly placed lighting elements and electrical cables have led to physical, chemical, and visual contamination (Figure 7).
Figure 7. Unqualified repairs to the stone surface.
Figure 7. Unqualified repairs to the stone surface.
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  • Surface accumulations (Contamination): There is contamination on the stone surfaces due to different factors. These layers of dirt appear at different densities in different regions. Stains caused by rainwater leakage are observed under the profiled wiping on the body (Figure 8).
Figure 8. Surface soiling on the north facade (left) and interior (right).
Figure 8. Surface soiling on the north facade (left) and interior (right).
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  • Bird droppings: Bird (pigeon) droppings are observed on the stone surfaces, more intensely on the balcony part, moldings, and windowsills. These cause abrasion on the material surfaces due to the acidic compounds in their content.

2.2.2. Joint Deterioration

The joint mortars between the stone masonry forming the body of the tower show melting and loss in places (Figure 9).

2.2.3. Wood Deterioration

The wooden elements are not original and were wholly renewed during the recent repairs (Figure 10). The renovated wooden elements are generally sound. Physical deterioration was observed, such as partial abrasion, cracking, darkening of paint/varnish layers, flaking, and contamination. Contamination caused by bird droppings is remarkably intense.

2.2.4. Metal Deterioration

The cast iron clock mechanism in the building is original (Figure 11). The square metal clock dials and the copper dome and eaves covering the mansion part of the tower were renewed in recent repairs. The single-leaf door made of iron is a recent addition. The iron stretchers wrapping the molding layers of the building from the inside and outside were built later for reinforcement purposes. Although the original or later metal elements are generally intact, deterioration is observed in rusting, blackening, abrasion, partial deformation, and paint flaking due to corrosion.

2.3. Calculation Parameters

The tower is located on Alparslan Türkeş Street in Sungurlu District of Çorum Province, on the square without a parcel in front of the Sungurlu Municipality Building located on 150 block 8 parcel and Ulu Mosque located on 150 block 6 parcel.
Sungurlu Clock Tower, allocated to the Ministry of Culture and Tourism, was registered as a Group I building by the Ankara Cultural and Natural Heritage Conservation Board with the decision dated 10.08.2000 and numbered 6493.
The historical clock tower has a square plan measuring approximately 2.60 × 2.60 m at ground level (−1.30). The building, which rises with a constant width until the first-floor level (+1.15 level), has a slightly narrowing structure from the first-floor level to the second-floor level (+3.02 level). At the second-floor level, the plan dimensions of the masonry structure are approximately 2.25 × 2.25 m, and the plan dimensions are constant until the balcony level at the +9.94 level. At the balcony level, the tower, which has dimensions of 2.15 × 2.15 m with 5 cm more retracted on each façade, has plan dimensions of 1.95 × 1.95 m from the +11.94 level where the clock dial is located to the +13.30 level where the masonry system ends.
The masonry structure of the tower has a height of 14.60 m from the −1.30 ground level to the +13.30 level, and the total tower height is 19.00 m with the wooden mansion and the world above it (Figure 12).
The masonry wall thickness of the tower structure is 33 cm from the ground to the first-floor level (+1.15 elevation), and it tapers down to 27 cm from the first-floor level to the second-floor level (+3.02 elevation). The masonry wall thickness between the second-floor and balcony levels (+9.94 elevation) is 22 cm from the balcony level.
Existing restitution, restoration, and conservation reports were utilized to determine the material properties. No earthquake with a magnitude of M > 5 between 1900 and 2022 was found in the area where the building is located in the search made in the Boğaziçi University Kandilli Observatory Earthquake Inquiry System [20]. For dynamic analysis, earthquake parameters (Table 1, Figure 13) were determined with the help of the “Turkey Earthquake Hazard Maps Interactive Web Application” published by the Disaster and Emergency Management Presidency according to the coordinates of 40.162500° latitude and 34.374200° longitude [21].
Assuming that the stone masonry building elements show a single material property together with the mortar, the modulus of elasticity E = 450.000 kN/m2 and the unit weight of the material, 24 kN/m3, were accepted. On the prepared calculation model, constant loads and earthquake loads were applied separately in two principal directions: EQx and EQy loading. For easy evaluation of the results, two separate load components were defined as G+EQx (constant loads + earthquake loading in the x-axis direction) and G+EQy (constant loads + earthquake loading in the y-axis direction). The first 12 modes were considered in the spectral calculation, where earthquake effects were determined.
The finite element model of the clock tower was prepared using 1272 points, 4770 vertices, 168 frames, and 1212 shell elements.
In the Turkish Building Earthquake Code [22], compressive safety stress fem = 0.3 MPa is recommended for stone masonry walls. No reduction was made in the forces obtained due to the calculation (R = 1). The safety stresses were increased by a coefficient of 3. In this case, the bearing stresses for stone walls are (Table 2) as follows:
Compression: fm = 0.3 × 3 = 0.9 Mpa;
Tensile: fm(check) = 0.9 × 0.15 = 0.135 Mpa;
Shear τm = 0.30 + 0.5 (0.9/2) = 0.53 MPa.
Table 2. Accepted safety stresses.
Table 2. Accepted safety stresses.
Material TypeCompression (MPa)Tensile (MPa)Shear (MPa)
Stonewall0.9000.1350.530
As a result of the analyses, mode shapes, natural frequency values, maximum displacement values, and maximum compressive, tensile, and shear stress values of the structures were determined, and the earthquake performances of the historical buildings were evaluated.

3. Results and Discussion

Since it is almost impossible to interpret the drifts, forces, and stresses obtained at all nodes and structural elements by examining them individually, we analyzed the calculation results by considering the most unfavorable values using the color-coded shape and stress maps produced by the SAP2000 program.
The total weight of the tower was calculated as 763.669 kN, the total base shear force under the earthquake effect applied in the x direction was calculated as 246.024 kN, and the total base shear force under the earthquake effect applied in the y direction was calculated as 240.811 kN. According to these results, it is seen that the base shear force to which the structure is exposed corresponds to approximately 32.2% of the total weight in the x direction and approximately 31.5% of the total weight in the y direction.
The maximum displacement values obtained from the analyses according to the earthquake effect are approximately 141 mm in the x direction and 143 mm in the y direction at the top point of the tower (Figure 14).
When the finite element analysis of the structure was performed, the first mode period was determined as 0.815 s, the second mode period as 0.806 s, the third mode period as 0.208 s, and the twelfth mode period as 0.086 s. Considering that the oscillation periods of masonry structures are small, the values obtained are consistent (Table 3 and Figure 15).
S22 and S12 stress values prepared separately according to G+EQx and G+EQy load combinations affecting the behavior of the structure were investigated using stress maps.
The S22 tensile stresses in the tower for G+EQx loading are shown. The marked (blue-colored) regions in the upper figure show the locations where tensile stress is greater than fm(check) = 0.135 MPa. As a result of G+EQx loading, the accepted limit value was not reached at any point of the tower. The marked locations in the figure above show the locations of compressive stresses greater than 0.1 Mpa (Figure 16).
S22 tensile stresses in the tower for G+EQy loading are shown. The marked (blue-colored) regions in the upper figure show the locations where tensile stress is greater than fm(check) = 0.135 MPa (Figure 17).
As a result of G+EQy loading, the accepted limit value was not reached at any point of the tower. The marked locations in the figure above show the locations of compressive stresses greater than 0.1 Mpa.
Shear stresses (S12) resulting from G+EQx and G+EQy loading are shown. The blue-colored regions indicate the locations where shear stresses are greater than τm(shear) = 0.315 MPa since the limit values have not been reached (Figure 18).
Tower, entrance, top, and bottom views of the tower are given in Figure 19.
Tensioners made of steel with the following material properties were used on the lower floors. Load components G+EQx and G+EQy show axial force, shear force, torsion, and moment values according to the stresses on the materials used for tensioning (Table 4). These values are within the regulation limits.

4. Conclusions

Since historical buildings have been constructed with different materials and construction techniques and have undergone various maintenance, repair, and changes until today, they contain many uncertainties [23]. Attempts are made to overcome these uncertainties with assumptions when necessary or sufficient samples cannot be taken from the structure for tests and experiments. The results obtained in this study are based on the theoretical method and assumptions made by using restitution and survey data.
To obtain reliable results using the finite element method, which is accepted as the most effective method in structural analysis, the dimensions, material properties, and acting loads of the structural system elements of the building must be accurately defined. It should not be forgotten that possible material deterioration or material losses in certain parts of the structural elements may affect the behavior of the structure. The structure should be analyzed using nonlinear calculation methods for more accurate results. For this purpose, detailed experimental studies should receive the structure’s material properties. In more detailed studies, the joint work of the relevant professional groups will reveal healthier results [24].
In addition to static analyses, dynamic analyses with the SAP2000 program tested the tower’s design’s robustness and durability. In the analyses, a numerical model representing the undamaged and unintervened condition of the Sungurlu clock tower was prepared, and its performance under static and dynamic loads, especially the possible earthquake load in its current position, was examined by considering the first 12 modes.
With this program, which allows for the preparation of this model, it was concluded that the loads acting on the structure according to the principles of ductility, rigidity, and strength could be safely transferred to the ground without causing damage to the structural system and its elements. This relative displacement indicates that although there are cracks in the walls due to material properties, collapse is a remote possibility. For this reason, the relative displacement value found is within acceptable limits.
According to the results, the tower has a highly resistant structure against earthquakes and other loads. The maximum displacement values obtained from the analyses according to the earthquake effect are approximately 141 mm in the x direction and 143 mm in the y direction at the top point of the tower. Since the height of this point relative to the ground is 14.60 m, the displacement ratio corresponds to a relative value of 0.009795. As a result of the structural analyses, it was observed that the compressive stress values accepted for masonry structures according to the earthquake code were not exceeded in the structural elements of the tower.
On the other hand, it was observed that tensile stresses were exceeded in certain areas. Due to the properties of the elements used and the support conditions, the occurrence of these stresses in horizontal loads is acceptable.
When the results and findings obtained above are evaluated together, according to the accepted calculation principles, it is considered that the earthquake resistance of the tower in its undamaged state is sufficient.
From the deformation, stress, velocity, acceleration, and reaction force graphs obtained, it was understood that the tower exhibited the expected structural behavior under its own weight and live loads.
The tower’s natural frequency, mode shape, and damping ratio graphs show that it can withstand an earthquake expected at the DD2 level with a probability of 10 percent in 50 years taken from the AFAD database for its current location (tower coordinates).
The stress and reaction force graphs showed that the structural materials are adequate for the resistance of the structure and system against the existing loads and possible earthquakes. Determining the material properties precisely through experimental studies by taking samples from the structure and making the model exactly with the real properties will increase the quality and importance of the study.

Author Contributions

Conceptualization, A.G.; Methodology, A.G.; Software, Z.B.; Validation, A.G.; Resources, Z.B.; Writing—original draft, Z.B.; Writing—review & editing, A.G.; Visualization, Z.B. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data presented in this study are available on request from the corresponding author (For legal reasons).

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Sungurlu clock tower.
Figure 1. Sungurlu clock tower.
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Figure 9. Joint discharge and unqualified joint repairs.
Figure 9. Joint discharge and unqualified joint repairs.
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Figure 10. Wooden elements in the structure.
Figure 10. Wooden elements in the structure.
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Figure 11. Original clock, eaves cladding, and metal door.
Figure 11. Original clock, eaves cladding, and metal door.
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Figure 12. Plans, sections, and views (units cm).
Figure 12. Plans, sections, and views (units cm).
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Figure 13. Spectrum curves.
Figure 13. Spectrum curves.
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Figure 14. Resulting translations on G+EQx (left/units mm) and G+EQy (right/units mm).
Figure 14. Resulting translations on G+EQx (left/units mm) and G+EQy (right/units mm).
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Figure 15. Mode shapes and displacements.
Figure 15. Mode shapes and displacements.
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Figure 16. Normal (left/units Mpa), tensile (middle/units kPa), and compressive stresses (right/units kPa) (G+EQx).
Figure 16. Normal (left/units Mpa), tensile (middle/units kPa), and compressive stresses (right/units kPa) (G+EQx).
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Figure 17. Normal (left/units Mpa), tensile (middle/units kPa), and compressive stresses (right/units kPa) (G+EQy).
Figure 17. Normal (left/units Mpa), tensile (middle/units kPa), and compressive stresses (right/units kPa) (G+EQy).
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Figure 18. G+EQx and G+EQy shear stresses (units kPa).
Figure 18. G+EQx and G+EQy shear stresses (units kPa).
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Figure 19. Tower, entrance, top, and bottom views.
Figure 19. Tower, entrance, top, and bottom views.
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Table 1. Local Values.
Table 1. Local Values.
Sungurlu Clock Tower
Earthquake ground motion levelDD-2
Short-period map spectral acceleration coefficient0.501 (unitless)
Map spectral acceleration coefficient for 1.0 s period0.160 (unitless)
Peak Ground Acceleration (P.G.A.)0.216 g (m/s2)
Peak Ground Velocity (P.G.V.)14.099 (cm/s)
Support system response coefficient (Ra)1 (unitless)
Soil classZD (medium density/density sand, gravel, or very stiff clay layers)
Table 3. Mode, period, and mass participation rates.
Table 3. Mode, period, and mass participation rates.
ModePeriod (s)X Direction Mass Participation RateY Direction Mass Participation Rate
10.8149050.0000.500
20.8055720.5030.500
30.2075010.7240.500
40.1986970.7240.754
50.1954610.7810.754
60.1340470.7810.754
70.1194580.7810.754
80.1092430.7950.754
90.1060380.8810.754
100.1009750.8810.864
110.0890600.8830.864
120.0857810.8830.864
Table 4. Base shear forces and axial forces.
Table 4. Base shear forces and axial forces.
Output CaseCase TypeStep TypeGlobal FxGlobal FyGlobal Fz
DeadLinStatic 00763.669
EQxLinRespSpMax246.0240.0076760.00036
EQyLinRespSpMax0.013240.8115.385
G+EQxCombinationMin246.0240.007676763.669
G+EQxCombinationMin−246.024−0.00768763.669
G+EQyCombinationMax0.013240.811769.054
G+EQyCombinationMin−0.013240.811758.284
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Gökdemir, A.; Baki, Z. Structural Analysis of the Historical Sungurlu Clock Tower. Appl. Sci. 2024, 14, 7085. https://doi.org/10.3390/app14167085

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Gökdemir A, Baki Z. Structural Analysis of the Historical Sungurlu Clock Tower. Applied Sciences. 2024; 14(16):7085. https://doi.org/10.3390/app14167085

Chicago/Turabian Style

Gökdemir, Ahmet, and Zülküf Baki. 2024. "Structural Analysis of the Historical Sungurlu Clock Tower" Applied Sciences 14, no. 16: 7085. https://doi.org/10.3390/app14167085

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