Research ArticleThe Effects of Construction Techniques and GeometricalProperties on the Dynamic Behavior of Historic TimberMinarets in Sakarya Turkey

M Bilal Bagbancı and Ozlem Koprulu Bagbancı

Architecture Faculty Uludag University 16059 Bursa Turkey

Correspondence should be addressed to M Bilal Bagbancı bilalbagbanciyahoocom

Received 16 May 2018 Revised 20 July 2018 Accepted 31 July 2018 Published 13 September 2018

Academic Editor Daniele Baraldi

Copyright copy 2018 M Bilal Bagbancı and Ozlem Koprulu Bagbancı -is is an open access article distributed under the CreativeCommons Attribution License which permits unrestricted use distribution and reproduction in any medium provided theoriginal work is properly cited

Sakarya City as the host of many civilizations has many historic monuments-e city is in the most active earthquake zone in theregion-eminarets of mosques are the most important structures because they are slender-erefore they are sensitive to lateralloads and earthquakes and strong winds may cause damage to these structures -e highest number of mosque minarets partly ortotally collapsed in the 1999 Kocaeli and Duzce earthquakes that occurred in Turkey-e region is rich in trees so timber has beenused in the construction of different structures in Sakarya City and the vicinity for many years In this study five historic timberminarets in Sakarya City were experimentally and computationally examined to determine the effects of the constructiontechniques and geometrical properties on the dynamic behavior of the minarets Ambient vibration tests of timber minarets wereperformed and the construction techniques and geometrical features were examined the results of these are discussed below Itwas determined that the outer wall construction technique body height slenderness and cross-sectional area play important rolesin the dynamic behavior of timber minarets Finally an empirical formula was derived from the relationships for rapid estimationof the fundamental period of timber minarets

1 Introduction

Minarets are towers that are close to or built into mosquestructures and are used by the muezzin to call out the adhanto indicate that it is time to pray in Islam -e earliestmosques were built without minarets and the muezzinperformed his duty in many other locations such as in frontof or on the roof of the masjid In Islamic architecture thefirst minarets were constructed at the corners of the Mosqueof lsquoAmr at Fustat byMaslama the Governor of Egypt duringthe reign of Mursquoawiya in 673 AD Over time numerousmagnificent minarets have been constructed from differentmaterials and structural systems in various regions of theworld [1]

Minarets which were first built in a square shape werelater built in conical and cylindrical shapes -ey weretypically constructed using stone and brick materials andtimber was rarely used in their construction because it is less

resistant to fire and water than stone and brick As a resultthe use of timber minarets is very limited [2]

Minarets built adjacent to mosques are slender struc-tures that are sensitive to horizontal loads Structural safetyassessments of historic minarets have gained importance inthe last decade because of their weakness under strong windsand intense earthquakes

In this context structural healthmonitoring is importantto determine the dynamic behavior of these structures Fewinvestigations on the seismic and dynamic behavior oftimber minarets exist in the literature as the most com-monly studied minarets are masonry and reinforced con-crete minarets Dogangun et al [3] analyzed historicunreinforcedmasonryminarets that were 20 25 and 30m inheight using two ground motions recorded during the 1999Kocaeli and Duzce earthquakes in Turkey A number of testshave been applied to historical masonry and reinforcedconcrete minarets by Bayraktar et al [4ndash7] In these studies

HindawiShock and VibrationVolume 2018 Article ID 9853896 12 pageshttpsdoiorg10115520189853896

the enhanced frequency domain decomposition (EFDD)and stochastic subspace identification (SSI) methods havebeen used for the structural identification of minarets

Sahin et al [8] studied the dynamic characteristics ofa reinforced concrete minaret through finite elementanalysis and field ambient vibration measurement Digitalsignal processing software SignalCAD was used for ana-lyzing raw measured data obtained from ambient vibrationtesting In the dynamic characteristic identificationModalCAD software developed in MATLAB was usedOliveira et al [9] performed ambient vibration tests todetermine the characteristics of seven minarets with heightsranging from 23m to 67m in Istanbul Turkey Motaal [10]studied to investigate the effects of soil stiffness pile lengthdiameter and arrangement on the minaret and pile dynamicbehavior Reinforced concrete and 60m height El-RahmanEl-Raheem Mosque minaret was selected to carry out thestudy -e most recent study was conducted by Livaogluet al [11] regarding the effect of geometrical features on thedynamic behavior of seven historic masonry minarets inBursa Turkey Ambient vibration tests were performed withthe aim of defining the modal parameters of the minarets

Investigations of the dynamic behavior of tall timberstructures are concentrated on observation towers multi-story timber buildings and traditional timber towers Cheet al [12] studied the dynamic characteristics of a typicalexample of an ancient timber architecture structure theYingxian Wooden Pagoda in Western Shanxi Province byusing microtremor measurements and the finite elementmethod Yu et al [13] studied the structural mechanicscharacteristics of ancient wooden architecture structures inChina -ey studied the mechanical structural and com-putational connection models and static and dynamic testson the structure models and on-site measurements wereperformed to determine the behavior of these structuresGaile [14] aimed at identifying the performance of steel andtimber lightweight observation towers that are open to thepublic in Latvia -e tower structure as well as its technicalconditions dynamic parameters and dynamic response tohuman movement along the tower height were investigated-e main parameter that denoted the response level of thetower to human movement was the tower self-weightFeldman et al [15] evaluated the dynamic properties oftall timber multistory buildings and timber towers underwind-induced vibration -e factors that influenced thedynamic parameters such as the construction type heightand vibration amplitudes were discussed Zhang et al [16]used a prediction method in the frequency domain forpredicting the vibrations in the Buddhist sutra depositary atYangzhou Zhunti Temple by using a double-confirmationanalysis method based on the autospectrum

In this study five historic timber minarets built usingdifferent construction techniques and geometrical propertiesare experimentally and computationally analyzed -eminarets are located close to each other in Sakarya TurkeySakarya City is located in the North Anatolian Fault Zonewhich is one of the most active strike-slip faults in the world-roughout history many devastating earthquakes haveoccurred in this region Damaging earthquakes in this region

include the Sakarya-Hendek earthquake in 1943 (Ms 66)and the Sakarya-Akyazı earthquake in 1967 (Ms 68) aswell as the Kocaeli (Ms 78) and Duzce earthquakes in1999 (Ms 7) [17] each causing numerous deaths Many ofthe historic monuments and minarets in the area weredamaged or demolished as a result of these earthquakes It isimportant to understand the dynamic behavior of thesestructures In this study the authors aimed to understandingthe effects of the construction techniques and geometricalproperties of timber minarets on their dynamic behavior andproposed an empirical formula derived from these re-lationships for rapid estimation of the fundamental period oftimber minarets

2 Construction Techniques and ArchitecturalFeatures of Timber Minarets

-e architectural styles and structural systems of Turkishminarets vary depending on the construction material andavailable techniques as well as the abilities and backgroundof workmen among other factors -erefore contiguous orseparate minarets have been built from stone brick ortimber materials they can be cubic cylindrical or polygonalHowever in Turkish architecture Classical Ottoman min-arets may be assumed to be the final stage of the Turkishminarets with slim cylindrical polygonal shafts and conicalroofs Classical masonry minarets have the following ninesegments a foundation pulpit transition element cylin-drical body balcony upper part spire end ornament andstairs -e foundation is constructed using very thick stoneblocks that are firmly connected In many instances thissegment is connected to the bearing walls of the mosque-epulpit is the top of the bottom part of a minaret which istypically square or less frequently octagonal Minarets fromthe Early Ottoman period have eight- ten- twelve- orsixteen-faced polygonal pulpits Transition elements provideuninterrupted and smooth transitions between the pulpitand the cylindrical or polygonal body -erefore the pulpitand body shapes influence the geometric shape Transitionsbetween polygonal pulpits to a cylindrical body were en-sured using a cut pyramid and an inverted as well as planetriangular element or various systematic Turkish triangular-shaped elements -e purpose of placing the balcony seg-ments above the ground at definite height levels is to helpproject the sound of the muezzin over extended distancesAlthough this purpose has lost its effectiveness in recentyears due to the use of loudspeakers balconies still survivebecause they are aesthetically pleasing Balcony decorationsare vitally important as they contribute to the magnificenceof minarets and artisans exhibited their talents by producingthese decorations Balconies consisting of a slab and parapetsbehave as a cantilever -e upper part of a minaret is thesegment that is located between the last balcony and thespire which generally includes a cylindrical or polygonalbody however different geometric properties were usedduring the Seljuk period

Minaret spires are generally considered to be a roof witha timber structural system and are lead coated -us thespire generally has different structural properties from those

2 Shock and Vibration

of the upper part of the minaret body -e end ornament isa metal device that is generally made of metal on top of theminaret with a symbol at the end Stairs are one of the mainstructural elements of the minarets that provide a means toclimb to the balcony Different structural materials havebeen used such as timber steel and masonry -e restraintconditions of stairs with rungs for the body of the minaretaffect their performance when subjected to lateral loads[1 2]

-ere are differences in the construction of masonry andtimber minarets Timber minarets have no transition seg-ment -e outer wall designs of the cylindrical body andupper part have the same thickness and are built using thesame construction techniques unlike masonry minarets Atimber core is only used in the upper part in masonryminarets but in timberminarets the timber core is one pieceand is continuous from the foundation to the top of theminaret Stairs are arranged between the core and outer wall-e outer walls are constructed with different techniques-e sections of a timber minaret can be seen in Figure 1

3 Studied Timber Minarets

-e studied five timber minarets are located in Sakarya Cityand they are close to each other -e investigated minaretshave different geometrical properties -e height of theminarets and other geometrical properties have variousdimensions Except for the outer wall of the minarets theother sections have similar construction techniques -eouter walls are constructed with different techniques -emost frequent usage is 8sim10times 4sim5 cm wide columns at10sim15 cm intervals in a circular plan and 4times 4sim5times 5 cmhorizontal beams at 75sim200 cm vertical intervals betweenthe columns bracing elements are used with different anglesand at different intervals In the other technique no bracingelements are used between the columns but a 2 cm thickcladding timber material is used on the outside of the timbercolumns (Figure 2)

-e geometric properties construction dates outer wallconstruction techniques weights and positions relative tomosques that are used in construction are presented inTables 1ndash5

4 Experimental and Computational Analysis ofTimber Minarets

-edynamic parameters of the studied timberminarets wereboth experimentally and computationally investigated -eexperimental study was performed in situ using sensitivesensors and a data acquisition system to determine thedynamic structural properties In addition laboratory and insitu ultrasonic tests were performed to find out the materialproperties of timber elements After the experimental ap-proach the structures were analyzed using a finite elementmethod

41 Experimental Approach -e dynamic parameters suchas the fundamental frequency mode shapes and damping

ratios of timber minarets were investigated using non-destructive test methods-is technique is called operationalmodal analysis -e modal parameters were determined bythe frequency-domain decomposition technique -is isoften called the peak-picking technique -e relationshipbetween the input x(t) and output y(t) can be written asfollows [18 19]

[Gyy(w)] [H(w)]lowast[Gxx(w)][H(w)]

T (1)

where Gxx is the power spectral density (PSD) matrix of theinput Gyy is the PSD matrix of the output H is the fre-quency response function (FRF) matrix and lowast and T denotecomplex conjugations and transpositions respectively -eHeaviside partial fraction theorem is used under the as-sumption that the input is random both in time and spacewith a zero mean white noise distribution so that its PSD isa constant matrix -en after mathematical manipulationsthe output PSD can be reduced to a poleresidue form asfollows

End ornament

Cylindricalbody

Foundation

Pulpit

Spire

Upper partof the minaret

Balcony

Figure 1 -e sections of a timber minaret

Shock and Vibration 3

[Gyy(w)] 1113944m

k11113888

Ak1113858 1113859

jwminus λk+

Ak1113858 1113859lowast

jwminus λklowast+

Bk1113858 1113859

minusjwminus λk

+Bk1113858 1113859lowast

minusjwminus λklowast1113889

(2)

where Ak is the k-th residue matrix of the output PSD -eresponse spectral density matrix can be written in the formbelow considering a lightly damped system [19]

[Gyy(w)] 1113944kSub(w)

dkψkψkT

jwminus λk+

dklowastψklowastψkT

jwminus λklowast1113888 1113889 (3)

where dk is a scalar constant and ψk is the k-th mode shapevector -us performing singular value decomposition ofthe output PSD matrix at discrete frequencies w wi thefollowing can be obtained

1113954Gyy jwi( 11138571113960 1113961 UiSiUHi (4)

where matrix Ui is a unitary matrix holding the singularvector uij and Si is a diagonal matrix holding the scalarsingular values sij the superscript H denotes complexconjugation and transposition Near the peak correspondingto the k-th mode in the spectrum only the k-th mode isdominant and the PSD matrix approximates to a rank-onematrix as follows [19]

Ağa Mosque Ali Kuzu Mosque Fethiye Mosque Teşvikiye Mosque Guumllluumlk Mosque

Figure 2 -e studied mosque minarets

Table 1 -e geometric properties and construction techniques of the Tesvikiye Mosque minaret

Body Upper body Spire Construction techniques and the dimensions of thecircular outer wall (cm)

Tesvikiye Mosqueminaret (1953)

Height (m) 792 232 242

55

5

8 10 8 8 8 810 10 10 10 8 10 8 10 8 810

100

100

Outer diameter (m) 116 116 mdashOuter wall thickness (m) 005 005 mdash

Weight (kN) 800 250 240Timber core diameter (m) 030 024minus 020 020minus 010

Location Adjacent to the mosque

4 Shock and Vibration

1113954Gyy jwi( 1113857 siui1uHi1 wi⟶ wk (5)

-e first singular vector at the r-th resonance is an es-timate of the r-th mode shape [19]

1113954ϕr ur1 (6)

In the case of repeated modes the PSD matrix rank isequal to the multiplicity number of the modes -e modalfrequencies can be identified via the peaks of the singularvalue plots while the corresponding singular vectors give themode shapes It is worth noting that natural frequencies andmode shapes can be estimated using such a method since theenhanced frequency-domain decomposition technique al-lows for the estimation of damping ratios [19]

In dynamic tests for very low noise sensors the Sensebox70010203 series is used -is series is an ideal solution forforced vibration dynamic identification shake-table testsmachinery health monitoring and structural health moni-toring of relatively less rigid structures A wide selection ofoptions exists from a plusmn 2 gminus 400 g measurement range and0ndash4000Hz bandwidth -e Dynamic Data AcquisitionStructural Health Monitoring Device Testbox 2010 seriesdata acquisition system has been used for applications instructural monitoring civil engineering earthquake engi-neering and other dynamic applications [20] Modalanalysis tests were performed at the balcony of the minaret-e sensors were placed at the x (north) y (east) and zdirections inside the balcony door -e sensors and theirplacements are shown in Figure 3

Table 2 -e geometric properties and construction techniques of the Gulluk Mosque minaret

Body Upper body Spire Construction techniques and the dimensions of thecircular outer wall (cm)

Gulluk Mosqueminaret (1966)

Height (m) 1335 327 294

55

8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 810

200

Outer diameter (m) 120 120 mdashOuter wall thickness (m) 005 005 mdash

Weight (kN) 1310 402 198Timber core diameter (m) 030 024minus 020 020minus 010

Location Adjacent to the mosque

Table 3 -e geometric properties and construction techniques of the Fethiye Mosque minaret

Body Upperbody Spire

Construction techniques and thedimensions of the circular outer wall

(cm)

Fethiye Mosque minaret (middle of the20th century)

Height (m) 905 325 270

520

05

8 15 8 15 8 15 8 15 8 15 8 815

Outer diameter (m) 106 106 mdashOuter wall thickness

(m) 005 005 mdash

Weight (kN) 703 265 142Timber corediameter (m) 030 020minus 016 016minus 010

Location Adjacent to the mosque

Shock and Vibration 5

-e ambient vibration tests were performed under en-vironmental forces such as traffic and wind-e tests shouldbe long enough to reduce the noise effects and also it isrequired for the accurate damping estimations -ereforethe measurement durations were 30 minutes and the fre-quency span was chosen as 0ndash100Hz -e singular values ofthe spectral densities of all the test setups are shown inFigure 4

Laboratory and in situ ultrasonic tests were performed tofind out the material properties of timber elements used inthe construction of the minarets -e density was measuredaccording to the EN 384 standard [21] Ultrasonic tests wereconducted using a V-meter with cylinder-shaped trans-ducers -e indirect method parallel to the grain and thedirect method perpendicular to the grain were used in thetests (Figure 5)

-e relationship Edin u2 ρ was used in the calculationswhere Edin represents the dynamic modulus of elasticity(Nmm2) u is the propagation velocity of the longitudinalstress waves (msn) and ρ is the density of the specimens(kgm3) [22] -e average results are presented in Table 6

42 Computational Approach -e three-dimensional finiteelement models of the studied five timber minarets wereprepared using the SAP2000 v20 finite element analysisprogram [23] -ey were modeled with the beam elementshaving six degrees of freedom at every node -e finite el-ement model that belongs to one of theminarets investigatedin this study can be seen in Figure 6

-e obtained experimental modes from in situ tests arecontrolled using both modal assurance criteria (MAC) table

Table 4 -e geometric properties and construction techniques of the Ali Kuzu Mosque minaret

Body Upper body Spire Construction techniques and the dimensions of thecircular outer wall (cm)

Ali Kuzu Mosqueminaret (1955)

Height (m) 1286 304 306

8 8 8 8 8 8 8

755

755

755

15 15 15 15 15 15

Outer diameter (m) 134 134 mdashOuter wall thickness (m) 005 005 mdash

Weight (kN) 1473 327 203Timber core diameter (m) 030 022minus 018 018minus 010

Location Adjacent to the mosque

Table 5 -e geometric properties and construction techniques of the Aga Mosque minaret

Body Upper body Spire Construction techniques and the dimensions of thecircular outer wall (cm)

Aga Mosque minaret(1870ndashrestorated2010)

Height (m) 768 262 266

8 15 8 15 8 15 8 15 8 15 8 85

520

015

Outer diameter (m) 146 146 mdashOuter wall thickness (m) 005 005 mdash

Weight (kN) 1604 420 191Timber core diameter (m) 030 024minus 020 020minus 010

Location Adjacent to the mosque

6 Shock and Vibration

and the complexity plots -e linear elastic material modelwas assumed for the minaret analysis because the experi-mental results for the in situ tests were also in the elasticrange After the finite element models were prepared themodal analysis of the minarets was performed -e naturalfrequencies mode shapes and mass participation factorswere obtained from numerical analyses -e boundaryconditions were updated depending on the experimentalresults to represent the real behavior of the minarets -ematerial properties were obtained from the test results andother sources [24 25] -e comparison of the seven modesfrequencies of the studied minarets between the experi-mental and computational approaches is presented in Ta-ble 7 -e first four modes are the bending modes the fifthmode is the torsion mode and the sixth and seventh modesare the bending modes When comparing the experimentaland computational results there is a good harmony amongmode shapes and natural frequencies -e errors betweenthe results ranged up to a minimum of 1 to a maximum of10

-e first seven modes and frequencies of one of thestudied minarets obtained frommodal analysis are shown inFigure 7

5 Discussion

51 Effect of Construction Techniques on Dynamic BehaviorMinaret structural systems are based on a circular plan usinga timber core in the center and timber walls on the exterior-e stairs are arranged between the inner core and outerwalls -e main difference in the construction of timberminarets is in the outer wall design -e builders useddifferent design techniques -e outer walls of the studiedfive minarets were also constructed with different tech-niques which play a role in the dynamic behavior -e mainfactors that affect this behavior are the stiffness-to-mass ratioand damping-e relationship between the stiffness-to-mass

ratio and the frequency is determined with the classicalformula f 12π lowast

(km)

1113968 where f is the frequency and m

and k are the mass and stiffness respectively Comparisonsshow that minarets with high stiffness-to-mass ratios alsohave higher frequencies than minarets with low stiffness-to-mass ratios Figure 8 shows the stiffness-to-mass ratios andfrequencies of the studied minarets represented by theirouter walls

-e minarets of the Tesvikiye Mosque have the higheststiffness-to-mass ratio -e timber columns of the outer wallare arranged at 10 cm intervals and the horizontal beams arearranged between the columns at 100 cm intervals Bracingelements are continuously used throughout the minaretheight Although the only difference between the con-struction techniques of the Tesvikiye Mosque and GullukMosque minarets is the frequency of horizontal beams thestiffness-to-mass ratio of the Tesvikiye Mosque was over 2times than that of the minaret of the Gulluk Mosque -eminaret of the Aga Mosque had the second highest stiffness-to-mass ratio -e outer wall of the Aga Mosque was builtwith timber columns arranged at 15 cm intervals withhorizontal timber beams arranged every 100 cm betweencolumns Additionally a 2 cm thick timber claddingmaterialwas used outside the outer walls -is cladding materialincreased both the stiffness and mass of the structure -eminarets of the Fethiye and Ali Kuzu Mosques had thelowest stiffness-to-mass ratios -e lack of effective usage ofbracing elements and less column usage were the factorsleading to the lowest stiffness-to-mass ratios

-e damping ratio also affects the dynamic behavior-edamping ratios varied between 12 and 20 -e minaret ofthe Aga Mosque had the highest damping ratio of 1967 -eusage of the timber cladding material and steel connectionsled to a high damping ratio however the other minaretshave similar ratios

52 Effect of the Geometrical Properties onDynamic BehaviorMinarets are tall and slender structures therefore theirgeometric properties such as height cross-sectional areaand heightwidth ratio are important regarding the dynamicminaret behavior Minarets behave like cantilevers in whichthe stiffness can be calculated by the formula k 3EIL3where k is the stiffness E is the modulus of elasticity I is themoment of inertia and L is the height In this study withoutnormalization the test results show that the highest minaretshave the lowest frequencies However the effect of height onthe frequency can be seen more clearly by eliminating theother parameters from the frequency Various minarets havesimilar heights therefore the relationship between theheight and frequency can be seen in more detail In Figure 9regression analysis between the height of the minarets andthe normalized frequencies shows that height affects thedynamic minaret behavior

In this study the minaret height-to-width ratios wereinvestigated to determine their effects on the dynamicbehavior minarets have high height-to-width ratios withlow frequencies that are affected by their height andslenderness -e relationship between the normalized

x

yz

Figure 3 -e sensors and their placements on the balcony floor

Shock and Vibration 7

frequencies and slenderness of the studied minarets can beseen in Figure 10

-e cross-sectional area also affects the dynamic prop-erties In the examined minarets the cross-sectional area ofthe Aga Mosque minaret was higher than that of the otherminarets -ese effects are particularly evident and the firstperiod percentage of mass participation was expected to behigher Table 8 shows the mass participation factors thatwere obtained from the numerical analyses It can be seenthat the Aga Mosque minaret has a 75 mass participationfactor in the first mode which is 10 higher than those ofthe other minarets

6 Empirical Formula for Computing theFundamental Frequencies of Minarets

-e construction techniques and the geometrical propertieswere important parameters for understanding the dynamicbehavior of these structures Based on the data collectedfrom the experimental and computational approachesa simple formula was developed to estimate the first fre-quency of vibration

-e fundamental frequency of a minaret is expected to bea function of the moment of inertia the height of theminaret modulus of elasticity cross-sectional area and

ndash60

ndash80

ndash100

ndash120

ndash1400 5 10 15 20 25

f (Hz)

dB |

(lg)2 (H

z)

(a)

0 5 10 15 20 25f (Hz)

ndash60

ndash80

ndash100

ndash120

ndash140

dB |

(lg)2 (H

z)

(b)

0 5 10 15 20 25f (Hz)

ndash60

ndash80

ndash100

ndash120

ndash140

dB |

(lg)2 (H

z)

(c)

0 5 10 15 20 25f (Hz)

ndash60

ndash80

ndash100

ndash120

ndash140

dB |

(lg)2 (H

z)

(d)

0 5 10 15 20 25f (Hz)

ndash60

ndash80

ndash100

ndash120

dB |

(lg)2 (H

z)

(e)

Figure 4-e singular values of the spectral densities of all of the test setups (a) Tesvikiye Mosque minaret (b) Gulluk Mosque minaret (c)Aga Mosque minaret (d) Ali Kuzu Mosque minaret (e) Fethiye Mosque minaret

8 Shock and Vibration

density -e height of the minaret was given by the lengthfrom the top of the pulpit to the base of the spire (body+upper body in Tables 1ndash5) the cross-sectional area and themoment of inertia were calculated by using the base of thebody density and modulus of elasticity which were given bythe data collected from the experimental approaches (Table 6)

Based on the parameters obtained from the experimentaland in situ measurements a new equation was developed fordetermination of the fundamental frequency

f prop middot Hminus32

middot

E middot I

ρ middot A

1113971

(7)

where prop is a constant depending on the constructiontechniques of the outer walls of the minarets H is the heightof the minaret (body + upper body) E is the modulus ofelasticity (parallel to the grain) I is the moment of inertia A

is the cross-sectional area and ρ is the density-e parameter prop was calculated as 015 for the Tesvikiye

and Gulluk Mosque minarets and 010 for the Ali Kuzu Agaand Fethiye Mosque minarets -e Tesvikiye and Gulluk

minarets had similar construction techniques and thedistinctive features of the outer walls were the frequent use ofthe outer columns and the bracing elements (Figure 2Tables 1 and 2) On the contrary the lesser used bracingelements can be seen in the construction of the outer wallsof the Ali Kuzu and Fethiye Mosque minarets (Figure 2Tables 3 and 4) Conversely 2 cm thick timber was used asa cladding material in the construction of the outer walls ofthe Aga Mosque minaret It was observed that the param-eter prop could be taken as 010 as in the Ali Kuzu and FethiyeMosque minarets In Figure 11 the fundamental frequenciesof theminarets obtained from the experimental in situ valuesand Equation (7) were compared with each other -e errorsranged up to a maximum of 9

7 Conclusions

Minarets are sensitive structures that are under lateral forcesand collapse during intense earthquakes and strong winds-ere are few studies regarding the construction techniquesand dynamic behavior of minarets and many studies haveconcentrated on masonry minarets Although reinforcedconcrete minarets are more common than masonry minaretsthey also collapse frequently under lateral forces -ereforethe use of timber in minaret construction has gained im-portance In this study five timber minarets located inSakarya City Turkey were experimentally and computa-tionally investigated to determine the effects of the con-struction techniques and geometric properties of the minaretson their dynamic behavior Ambient vibration tests wereconducted to determine the dynamic characteristics of the

Figure 5 In situ ultrasonic test of timber core (the direct method)

Table 6 -e material properties of the timber elements used in theconstruction of minarets

Mosques

Modulus of elasticity (kNm2)

Unit weight(kNm3)

Parallel tothe grain

Perpendicularto the grain

Indirectmethod Direct method

TesvikiyeMosque 3960000 520000 590

Gulluk Mosque 4520000 530000 583Fethiye Mosque 4010000 450000 587Ali Kuzu Mosque 3520000 420000 592Aga Mosque 5070000 610000 601

Bracingelements

Stairs

Beam

Centercore

Outercolumn

Frameelement

(12 DOF)

Uz UzRz Rz Rx

UxUx

UyUyRyRy

Rx

Figure 6 -e finite element model and DOF system of the GullukMosque minaret

Shock and Vibration 9

minarets Laboratory and in situ ultrasonic tests were per-formed to determine the physical andmaterial properties-efinite element models of the studied five timber minarets wereprepared and modeled with the beam elements having sixdegrees of freedom at every node -e obtained experimentalmodes from in situ tests are controlled using both modalassurance criteria (MAC) table and the complexity plots -elinear elastic material model was assumed forminaret analysisbecause the experimental results for the in situ tests were alsoin the elastic range -e boundary conditions were updateddepending on the experimental results to represent the realbehavior of the minarets Using all data an empirical formulawas derived for the rapid estimation of the fundamental

period of timber minarets -is formula shows that theconstruction technique of the outer wall is as important as thematerial and geometric properties of the minarets -e fre-quent usage of the outer columns at 10 cm intervals andbracing elements in the construction of the outer walls of theGulluk and Tesvikiye Mosques minarets resulted in higherfundamental frequencies than the others On the contrary inthe other minarets the usage of 15 cm outer column intervalsthe usage of timber cladding material in the Aga Mosqueminaret instead of bracing elements and less usage of bracingelements in the Ali Kuzu and FethiyeMosqueminarets are theconstruction differences affecting the dynamic behavior -eformula leads to an upper limit with an error of 9

Y XZ Y XZ Y XZ Y XZ Y XZ Y XZ Y XZ

Mode 1f 118 Hz

Mode 2f 119 Hz

Mode 3f 650 Hz

Mode 4f 651 Hz

Mode 5f 952 Hz

Mode 6f 1466 Hz

Mode 7f 1470 Hz

Figure 7 -e first seven modes and natural frequencies of the Gulluk Mosque minaret

Table 7 First seven modes frequencies (experimental approach versus computational approach)

Mode numberTesvikiye Gulluk Fethiye Ali Kuzu Aga

Exp Comp Exp Comp Exp Comp Exp Comp Exp Comp1 242 246 127 118 093 096 072 078 210 2152 269 247 127 119 105 101 074 079 232 2153 1140 1164 715 650 322 393 371 409 959 10354 1221 1165 724 651 352 396 391 414 969 10455 1370 1375 1030 952 520 502 508 450 1196 11526 2285 2104 1501 1466 815 841 815 794 1213 12587 2307 2121 1502 1470 842 845 842 826 1310 1260Exp experimental approach Comp computational approach

Table 8 -e mass participation factors of the studied minarets

MosquesFirst mode Second mode Sum of first three modes

x y x y x yTesvikiye Mosque 6383 6381 2064 2067 8536 8522Gulluk Mosque 6268 6265 2048 2051 8858 8856Fethiye Mosque 6998 6987 1444 1460 8922 8925Ali Kuzu Mosque 6648 6611 1843 1934 8791 9006Aga Mosque 7507 7478 1193 1222 8730 8820

10 Shock and Vibration

In addition minaret height slenderness and minaretcross-sectional area affect the dynamic behavior of minarets-e frequent usage of horizontal beams in the outer wallconstruction of timber minarets increases the rigidity of thestructure and affects their dynamic behavior -e usage ofsteel connectors provides high damping ratios

In conclusion the construction techniques and geo-metric properties of timber minarets greatly affect theirdynamic behavior Better design criteria development and

retrofitting guideline preparation with a different modelingunder different ground motions and strong winds will helpto ensure better minaret safety

Data Availability

All data generated or analyzed during the study are includedin this paper

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

In this paper the results of a research project carried out bythe authors are utilized supported by Uludag University (noOUAP(MM)-201532)

References

[1] A Dogangun R Acar R Livaoglu and O I Tuluk ldquoPer-formance of masonry minarets against earthquakes and windsin Turkeyrdquo in Proceedings of 1st International Conference on

0

05

1

15

2

25

3

0 50 100 150 200 250

Freq

uenc

y f

Stiffnessmass km

Teşvikiye

Ağa

Guumllluumlk

Fethiye

Ali Kuzu

8 8 8

755

755

755

15 15

520

05

8 15 8 815

55

8 10 8 810

200

8 15 8 8

55

200

15

55

5

8 10 8 810

100

100

Figure 8 -e relationship between the stiffness-to-mass ratios and frequencies

R2 = 0962

0010203040506070809

1

12 13 14 15 16 17 18 19 20

Nor

mal

ized

freq

uenc

y f

Height L

Fethiye

TeşvikiyeAğa

Ali KuzuGuumllluumlk

Figure 9-e relationship between the normalized frequencies andheights

R2=0950

0010203040506070809

1

8 10 12 14 16 18

Nor

mal

ized

freq

uenc

y f

Heightdiameter Ld

Teşvikiye

Ağa

Fethiye

Ali KuzuGuumllluumlk

Figure 10 -e relationship between the normalized frequenciesand heights to diameters

078

191225

096

128

072

21242

093127

000

050

100

150

200

250

300

Ali Kuzu Ağa Teşvikiye Fethiye Guumllluumlk

Firs

t mod

e fre

quen

cy (H

z)

FormulaExperimental

(8)

(9)(7)

(3)(1)

Figure 11 -e fundamental frequencies (formula versus experi-mental results)

Shock and Vibration 11

Restoration of Heritage Masonry Structures P32 pp 1ndash10Cairo Egypt April 2006

[2] K H Kusuzumu ldquoTraditional construction techniques andcurrent restorations of Istanbul minaretsrdquo MSc thesis MimarSinan University Istanbul Turkey 2010 in Turkish

[3] A Dogangun R Acar H Sezen and R Livaoglu ldquoIn-vestigation of dynamic response of masonry minaret struc-turesrdquo Bulletin of Earthquake Engineering vol 6 no 3pp 505ndash517 2008

[4] A Bayraktar A C Altunısık B Sevim T Turker M Akkoseand N Coskun ldquoModal analysis experimental validation andcalibration of a historical masonry minaretrdquo Journal of Testingand Evaluation vol 36 no 6 pp 516ndash524 2008

[5] A Bayraktar B Sevim A C Altunısık and T TurkerldquoAnalytical and operational modal analyses of Turkish stylereinforced concrete minarets for structural identificationrdquoExperimental Techniques vol 33 no 2 pp 65ndash75 2009

[6] A Bayraktar B Sevim A C Altunısık and T TurkerldquoEarthquake analysis of reinforced concrete minarets usingambient vibration test resultsrdquo Structural Design of Tall andSpecial Buildings vol 19 no 3 pp 257ndash273 2010

[7] A Bayraktar A C Altunisik B Sevim and T TurkerldquoSeismic response of a historical masonry minaret usinga finite element model updated with operational modaltestingrdquo Journal of Vibration and Control vol 17 no 1pp 129ndash149 2011

[8] A Sahin A Bayraktar M Ozcan B Sevim A C Altunısıkand T Turker ldquoDynamic field test system identificationand modal validation of a RC minaret pre and postprocessing the wind-induced ambient datardquo Journal ofPerformance of Constructed Facilities vol 25 no 4pp 336ndash556 2011

[9] C S Oliveira E Ccedilaktı D Stengel and M Branco ldquoMinaretbehaviour under earthquake loading the case of historicalIstanbulrdquo Earthquake Engineering amp Structural Dynamicsvol 41 no 1 pp 19ndash39 2012

[10] M A A Motaal ldquoEffect of piles on the seismic response ofmosques minaretsrdquo Ain Shams Engineering Journal vol 5no 1 pp 29ndash40 2014

[11] R Livaoglu M H Basturk A Dogangun and C SerhatogluldquoEffect of geometric properties on dynamic behaviour ofhistoric masonry minaretrdquo KSCE Journal of Civil Engineeringvol 20 no 6 pp 2392ndash2402 2016

[12] A L Che Y He X R Ge T Iwatate and Y Oda ldquoStudy onthe dynamic structural characteristics of an ancient timberYingxian wooden pagodardquo in Proceedings of GeoShanghaiInternational Conference pp 390ndash396 Shanghai China June2006

[13] M Yu Y Oda D Fang and J Zhao ldquoAdvances in structuralmechanics of Chinese ancient architecturesrdquo Frontiers ofArchitecture and Civil Engineering in China vol 2 no 1pp 1ndash25 2008

[14] L Gaile ldquoAnalysis of dynamic parameters of observationtowers in Latviardquo in Proceedings of 9th International Scientificand Practical Conference pp 57ndash62 Rezekne Latvia June2013

[15] A Feldman H Huang W S Chang et al ldquoDynamicproperties of tall timber structures under wind-induced vi-brationrdquo in Proceedings of World Conference on TimberEngineering Vienne Austria August 2016

[16] Y Zhang N Zhang Y Cao andH Xia ldquoA predictionmethodof historical timber buildingsrsquo vibrations induced by trafficloads and its validationrdquo Shock and Vibration vol 2017Article ID 1451483 12 pages 2017

[17] Bogaziccedili University Kandilli Observatory and EarthquakeResearch Institute 2017 httpwwwkoeribounedutrsismo2deprem-bilgileribuyuk-depremler

[18] J S Bendat and A G Piersol Random Data Analysis andMeasurement Procedures Wiley San Francisco CA USA 4thedition 1986

[19] C Raineri G Fabbrocino E Cosenza and G ManfredildquoImplementation of OMA procedures using labview theoryand applicationrdquo in Proceedings of 2nd International Oper-ational Modal Analyses Conference pp 1ndash12 CopenhagenDenmark April-May 2007

[20] OMA Operational Modal Analysis Release 45 StructuralVibration Solution AS Denmark Europe 2016

[21] European Committee for Standardization EN 384-StructuralTimber-Determination of Characteristic Values of MechanicalProperties and Density Office for Official Publications of theEuropean Communities Luxembourg Europe 1995

[22] P B Lourenco A O Feio and J S Machado ldquoChestnut woodin compression perpendicular to the grain non-destructivecorrelations for test results in new and old woodrdquo Con-struction and Building Materials vol 21 no 8 pp 1617ndash16272007

[23] Autodesk Inc Sap 2000 V20 Autodesk Inc San Rafael CAUSA 2017

[24] United States Department of Agriculture Forest ServiceWood Handbook Wood as an Engineering Material UnitedStates Department of Agriculture Forest Service WashingtonDC USA 2010

[25] -ermal expansion coefficients for some common materialsOctober 2017 httpswwwengineeringtoolboxcomlinear-expansion-coefficients-d_95html

12 Shock and Vibration

of the upper part of the minaret body -e end ornament isa metal device that is generally made of metal on top of theminaret with a symbol at the end Stairs are one of the mainstructural elements of the minarets that provide a means toclimb to the balcony Different structural materials havebeen used such as timber steel and masonry -e restraintconditions of stairs with rungs for the body of the minaretaffect their performance when subjected to lateral loads[1 2]

-ere are differences in the construction of masonry andtimber minarets Timber minarets have no transition seg-ment -e outer wall designs of the cylindrical body andupper part have the same thickness and are built using thesame construction techniques unlike masonry minarets Atimber core is only used in the upper part in masonryminarets but in timberminarets the timber core is one pieceand is continuous from the foundation to the top of theminaret Stairs are arranged between the core and outer wall-e outer walls are constructed with different techniques-e sections of a timber minaret can be seen in Figure 1

3 Studied Timber Minarets

-e studied five timber minarets are located in Sakarya Cityand they are close to each other -e investigated minaretshave different geometrical properties -e height of theminarets and other geometrical properties have variousdimensions Except for the outer wall of the minarets theother sections have similar construction techniques -eouter walls are constructed with different techniques -emost frequent usage is 8sim10times 4sim5 cm wide columns at10sim15 cm intervals in a circular plan and 4times 4sim5times 5 cmhorizontal beams at 75sim200 cm vertical intervals betweenthe columns bracing elements are used with different anglesand at different intervals In the other technique no bracingelements are used between the columns but a 2 cm thickcladding timber material is used on the outside of the timbercolumns (Figure 2)

-e geometric properties construction dates outer wallconstruction techniques weights and positions relative tomosques that are used in construction are presented inTables 1ndash5

4 Experimental and Computational Analysis ofTimber Minarets

-edynamic parameters of the studied timberminarets wereboth experimentally and computationally investigated -eexperimental study was performed in situ using sensitivesensors and a data acquisition system to determine thedynamic structural properties In addition laboratory and insitu ultrasonic tests were performed to find out the materialproperties of timber elements After the experimental ap-proach the structures were analyzed using a finite elementmethod

41 Experimental Approach -e dynamic parameters suchas the fundamental frequency mode shapes and damping

ratios of timber minarets were investigated using non-destructive test methods-is technique is called operationalmodal analysis -e modal parameters were determined bythe frequency-domain decomposition technique -is isoften called the peak-picking technique -e relationshipbetween the input x(t) and output y(t) can be written asfollows [18 19]

[Gyy(w)] [H(w)]lowast[Gxx(w)][H(w)]

T (1)

where Gxx is the power spectral density (PSD) matrix of theinput Gyy is the PSD matrix of the output H is the fre-quency response function (FRF) matrix and lowast and T denotecomplex conjugations and transpositions respectively -eHeaviside partial fraction theorem is used under the as-sumption that the input is random both in time and spacewith a zero mean white noise distribution so that its PSD isa constant matrix -en after mathematical manipulationsthe output PSD can be reduced to a poleresidue form asfollows

End ornament

Cylindricalbody

Foundation

Pulpit

Spire

Upper partof the minaret

Balcony

Figure 1 -e sections of a timber minaret

Shock and Vibration 3

[Gyy(w)] 1113944m

k11113888

Ak1113858 1113859

jwminus λk+

Ak1113858 1113859lowast

jwminus λklowast+

Bk1113858 1113859

minusjwminus λk

+Bk1113858 1113859lowast

minusjwminus λklowast1113889

(2)

where Ak is the k-th residue matrix of the output PSD -eresponse spectral density matrix can be written in the formbelow considering a lightly damped system [19]

[Gyy(w)] 1113944kSub(w)

dkψkψkT

jwminus λk+

dklowastψklowastψkT

jwminus λklowast1113888 1113889 (3)

where dk is a scalar constant and ψk is the k-th mode shapevector -us performing singular value decomposition ofthe output PSD matrix at discrete frequencies w wi thefollowing can be obtained

1113954Gyy jwi( 11138571113960 1113961 UiSiUHi (4)

where matrix Ui is a unitary matrix holding the singularvector uij and Si is a diagonal matrix holding the scalarsingular values sij the superscript H denotes complexconjugation and transposition Near the peak correspondingto the k-th mode in the spectrum only the k-th mode isdominant and the PSD matrix approximates to a rank-onematrix as follows [19]

Ağa Mosque Ali Kuzu Mosque Fethiye Mosque Teşvikiye Mosque Guumllluumlk Mosque

Figure 2 -e studied mosque minarets

Table 1 -e geometric properties and construction techniques of the Tesvikiye Mosque minaret

Body Upper body Spire Construction techniques and the dimensions of thecircular outer wall (cm)

Tesvikiye Mosqueminaret (1953)

Height (m) 792 232 242

55

5

8 10 8 8 8 810 10 10 10 8 10 8 10 8 810

100

100

Outer diameter (m) 116 116 mdashOuter wall thickness (m) 005 005 mdash

Weight (kN) 800 250 240Timber core diameter (m) 030 024minus 020 020minus 010

Location Adjacent to the mosque

4 Shock and Vibration

1113954Gyy jwi( 1113857 siui1uHi1 wi⟶ wk (5)

-e first singular vector at the r-th resonance is an es-timate of the r-th mode shape [19]

1113954ϕr ur1 (6)

In the case of repeated modes the PSD matrix rank isequal to the multiplicity number of the modes -e modalfrequencies can be identified via the peaks of the singularvalue plots while the corresponding singular vectors give themode shapes It is worth noting that natural frequencies andmode shapes can be estimated using such a method since theenhanced frequency-domain decomposition technique al-lows for the estimation of damping ratios [19]

In dynamic tests for very low noise sensors the Sensebox70010203 series is used -is series is an ideal solution forforced vibration dynamic identification shake-table testsmachinery health monitoring and structural health moni-toring of relatively less rigid structures A wide selection ofoptions exists from a plusmn 2 gminus 400 g measurement range and0ndash4000Hz bandwidth -e Dynamic Data AcquisitionStructural Health Monitoring Device Testbox 2010 seriesdata acquisition system has been used for applications instructural monitoring civil engineering earthquake engi-neering and other dynamic applications [20] Modalanalysis tests were performed at the balcony of the minaret-e sensors were placed at the x (north) y (east) and zdirections inside the balcony door -e sensors and theirplacements are shown in Figure 3

Table 2 -e geometric properties and construction techniques of the Gulluk Mosque minaret

Body Upper body Spire Construction techniques and the dimensions of thecircular outer wall (cm)

Gulluk Mosqueminaret (1966)

Height (m) 1335 327 294

55

8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 810

200

Outer diameter (m) 120 120 mdashOuter wall thickness (m) 005 005 mdash

Weight (kN) 1310 402 198Timber core diameter (m) 030 024minus 020 020minus 010

Location Adjacent to the mosque

Table 3 -e geometric properties and construction techniques of the Fethiye Mosque minaret

Body Upperbody Spire

Construction techniques and thedimensions of the circular outer wall

(cm)

Fethiye Mosque minaret (middle of the20th century)

Height (m) 905 325 270

520

05

8 15 8 15 8 15 8 15 8 15 8 815

Outer diameter (m) 106 106 mdashOuter wall thickness

(m) 005 005 mdash

Weight (kN) 703 265 142Timber corediameter (m) 030 020minus 016 016minus 010

Location Adjacent to the mosque

Shock and Vibration 5

-e ambient vibration tests were performed under en-vironmental forces such as traffic and wind-e tests shouldbe long enough to reduce the noise effects and also it isrequired for the accurate damping estimations -ereforethe measurement durations were 30 minutes and the fre-quency span was chosen as 0ndash100Hz -e singular values ofthe spectral densities of all the test setups are shown inFigure 4

Laboratory and in situ ultrasonic tests were performed tofind out the material properties of timber elements used inthe construction of the minarets -e density was measuredaccording to the EN 384 standard [21] Ultrasonic tests wereconducted using a V-meter with cylinder-shaped trans-ducers -e indirect method parallel to the grain and thedirect method perpendicular to the grain were used in thetests (Figure 5)

-e relationship Edin u2 ρ was used in the calculationswhere Edin represents the dynamic modulus of elasticity(Nmm2) u is the propagation velocity of the longitudinalstress waves (msn) and ρ is the density of the specimens(kgm3) [22] -e average results are presented in Table 6

42 Computational Approach -e three-dimensional finiteelement models of the studied five timber minarets wereprepared using the SAP2000 v20 finite element analysisprogram [23] -ey were modeled with the beam elementshaving six degrees of freedom at every node -e finite el-ement model that belongs to one of theminarets investigatedin this study can be seen in Figure 6

-e obtained experimental modes from in situ tests arecontrolled using both modal assurance criteria (MAC) table

Table 4 -e geometric properties and construction techniques of the Ali Kuzu Mosque minaret

Body Upper body Spire Construction techniques and the dimensions of thecircular outer wall (cm)

Ali Kuzu Mosqueminaret (1955)

Height (m) 1286 304 306

8 8 8 8 8 8 8

755

755

755

15 15 15 15 15 15

Outer diameter (m) 134 134 mdashOuter wall thickness (m) 005 005 mdash

Weight (kN) 1473 327 203Timber core diameter (m) 030 022minus 018 018minus 010

Location Adjacent to the mosque

Table 5 -e geometric properties and construction techniques of the Aga Mosque minaret

Body Upper body Spire Construction techniques and the dimensions of thecircular outer wall (cm)

Aga Mosque minaret(1870ndashrestorated2010)

Height (m) 768 262 266

8 15 8 15 8 15 8 15 8 15 8 85

520

015

Outer diameter (m) 146 146 mdashOuter wall thickness (m) 005 005 mdash

Weight (kN) 1604 420 191Timber core diameter (m) 030 024minus 020 020minus 010

Location Adjacent to the mosque

6 Shock and Vibration

and the complexity plots -e linear elastic material modelwas assumed for the minaret analysis because the experi-mental results for the in situ tests were also in the elasticrange After the finite element models were prepared themodal analysis of the minarets was performed -e naturalfrequencies mode shapes and mass participation factorswere obtained from numerical analyses -e boundaryconditions were updated depending on the experimentalresults to represent the real behavior of the minarets -ematerial properties were obtained from the test results andother sources [24 25] -e comparison of the seven modesfrequencies of the studied minarets between the experi-mental and computational approaches is presented in Ta-ble 7 -e first four modes are the bending modes the fifthmode is the torsion mode and the sixth and seventh modesare the bending modes When comparing the experimentaland computational results there is a good harmony amongmode shapes and natural frequencies -e errors betweenthe results ranged up to a minimum of 1 to a maximum of10

-e first seven modes and frequencies of one of thestudied minarets obtained frommodal analysis are shown inFigure 7

5 Discussion

51 Effect of Construction Techniques on Dynamic BehaviorMinaret structural systems are based on a circular plan usinga timber core in the center and timber walls on the exterior-e stairs are arranged between the inner core and outerwalls -e main difference in the construction of timberminarets is in the outer wall design -e builders useddifferent design techniques -e outer walls of the studiedfive minarets were also constructed with different tech-niques which play a role in the dynamic behavior -e mainfactors that affect this behavior are the stiffness-to-mass ratioand damping-e relationship between the stiffness-to-mass

ratio and the frequency is determined with the classicalformula f 12π lowast

(km)

1113968 where f is the frequency and m

and k are the mass and stiffness respectively Comparisonsshow that minarets with high stiffness-to-mass ratios alsohave higher frequencies than minarets with low stiffness-to-mass ratios Figure 8 shows the stiffness-to-mass ratios andfrequencies of the studied minarets represented by theirouter walls

-e minarets of the Tesvikiye Mosque have the higheststiffness-to-mass ratio -e timber columns of the outer wallare arranged at 10 cm intervals and the horizontal beams arearranged between the columns at 100 cm intervals Bracingelements are continuously used throughout the minaretheight Although the only difference between the con-struction techniques of the Tesvikiye Mosque and GullukMosque minarets is the frequency of horizontal beams thestiffness-to-mass ratio of the Tesvikiye Mosque was over 2times than that of the minaret of the Gulluk Mosque -eminaret of the Aga Mosque had the second highest stiffness-to-mass ratio -e outer wall of the Aga Mosque was builtwith timber columns arranged at 15 cm intervals withhorizontal timber beams arranged every 100 cm betweencolumns Additionally a 2 cm thick timber claddingmaterialwas used outside the outer walls -is cladding materialincreased both the stiffness and mass of the structure -eminarets of the Fethiye and Ali Kuzu Mosques had thelowest stiffness-to-mass ratios -e lack of effective usage ofbracing elements and less column usage were the factorsleading to the lowest stiffness-to-mass ratios

-e damping ratio also affects the dynamic behavior-edamping ratios varied between 12 and 20 -e minaret ofthe Aga Mosque had the highest damping ratio of 1967 -eusage of the timber cladding material and steel connectionsled to a high damping ratio however the other minaretshave similar ratios

52 Effect of the Geometrical Properties onDynamic BehaviorMinarets are tall and slender structures therefore theirgeometric properties such as height cross-sectional areaand heightwidth ratio are important regarding the dynamicminaret behavior Minarets behave like cantilevers in whichthe stiffness can be calculated by the formula k 3EIL3where k is the stiffness E is the modulus of elasticity I is themoment of inertia and L is the height In this study withoutnormalization the test results show that the highest minaretshave the lowest frequencies However the effect of height onthe frequency can be seen more clearly by eliminating theother parameters from the frequency Various minarets havesimilar heights therefore the relationship between theheight and frequency can be seen in more detail In Figure 9regression analysis between the height of the minarets andthe normalized frequencies shows that height affects thedynamic minaret behavior

In this study the minaret height-to-width ratios wereinvestigated to determine their effects on the dynamicbehavior minarets have high height-to-width ratios withlow frequencies that are affected by their height andslenderness -e relationship between the normalized

x

yz

Figure 3 -e sensors and their placements on the balcony floor

Shock and Vibration 7

frequencies and slenderness of the studied minarets can beseen in Figure 10

-e cross-sectional area also affects the dynamic prop-erties In the examined minarets the cross-sectional area ofthe Aga Mosque minaret was higher than that of the otherminarets -ese effects are particularly evident and the firstperiod percentage of mass participation was expected to behigher Table 8 shows the mass participation factors thatwere obtained from the numerical analyses It can be seenthat the Aga Mosque minaret has a 75 mass participationfactor in the first mode which is 10 higher than those ofthe other minarets

6 Empirical Formula for Computing theFundamental Frequencies of Minarets

-e construction techniques and the geometrical propertieswere important parameters for understanding the dynamicbehavior of these structures Based on the data collectedfrom the experimental and computational approachesa simple formula was developed to estimate the first fre-quency of vibration

-e fundamental frequency of a minaret is expected to bea function of the moment of inertia the height of theminaret modulus of elasticity cross-sectional area and

ndash60

ndash80

ndash100

ndash120

ndash1400 5 10 15 20 25

f (Hz)

dB |

(lg)2 (H

z)

(a)

0 5 10 15 20 25f (Hz)

ndash60

ndash80

ndash100

ndash120

ndash140

dB |

(lg)2 (H

z)

(b)

0 5 10 15 20 25f (Hz)

ndash60

ndash80

ndash100

ndash120

ndash140

dB |

(lg)2 (H

z)

(c)

0 5 10 15 20 25f (Hz)

ndash60

ndash80

ndash100

ndash120

ndash140

dB |

(lg)2 (H

z)

(d)

0 5 10 15 20 25f (Hz)

ndash60

ndash80

ndash100

ndash120

dB |

(lg)2 (H

z)

(e)

Figure 4-e singular values of the spectral densities of all of the test setups (a) Tesvikiye Mosque minaret (b) Gulluk Mosque minaret (c)Aga Mosque minaret (d) Ali Kuzu Mosque minaret (e) Fethiye Mosque minaret

8 Shock and Vibration

density -e height of the minaret was given by the lengthfrom the top of the pulpit to the base of the spire (body+upper body in Tables 1ndash5) the cross-sectional area and themoment of inertia were calculated by using the base of thebody density and modulus of elasticity which were given bythe data collected from the experimental approaches (Table 6)

Based on the parameters obtained from the experimentaland in situ measurements a new equation was developed fordetermination of the fundamental frequency

f prop middot Hminus32

middot

E middot I

ρ middot A

1113971

(7)

where prop is a constant depending on the constructiontechniques of the outer walls of the minarets H is the heightof the minaret (body + upper body) E is the modulus ofelasticity (parallel to the grain) I is the moment of inertia A

is the cross-sectional area and ρ is the density-e parameter prop was calculated as 015 for the Tesvikiye

and Gulluk Mosque minarets and 010 for the Ali Kuzu Agaand Fethiye Mosque minarets -e Tesvikiye and Gulluk

minarets had similar construction techniques and thedistinctive features of the outer walls were the frequent use ofthe outer columns and the bracing elements (Figure 2Tables 1 and 2) On the contrary the lesser used bracingelements can be seen in the construction of the outer wallsof the Ali Kuzu and Fethiye Mosque minarets (Figure 2Tables 3 and 4) Conversely 2 cm thick timber was used asa cladding material in the construction of the outer walls ofthe Aga Mosque minaret It was observed that the param-eter prop could be taken as 010 as in the Ali Kuzu and FethiyeMosque minarets In Figure 11 the fundamental frequenciesof theminarets obtained from the experimental in situ valuesand Equation (7) were compared with each other -e errorsranged up to a maximum of 9

7 Conclusions

Minarets are sensitive structures that are under lateral forcesand collapse during intense earthquakes and strong winds-ere are few studies regarding the construction techniquesand dynamic behavior of minarets and many studies haveconcentrated on masonry minarets Although reinforcedconcrete minarets are more common than masonry minaretsthey also collapse frequently under lateral forces -ereforethe use of timber in minaret construction has gained im-portance In this study five timber minarets located inSakarya City Turkey were experimentally and computa-tionally investigated to determine the effects of the con-struction techniques and geometric properties of the minaretson their dynamic behavior Ambient vibration tests wereconducted to determine the dynamic characteristics of the

Figure 5 In situ ultrasonic test of timber core (the direct method)

Table 6 -e material properties of the timber elements used in theconstruction of minarets

Mosques

Modulus of elasticity (kNm2)

Unit weight(kNm3)

Parallel tothe grain

Perpendicularto the grain

Indirectmethod Direct method

TesvikiyeMosque 3960000 520000 590

Gulluk Mosque 4520000 530000 583Fethiye Mosque 4010000 450000 587Ali Kuzu Mosque 3520000 420000 592Aga Mosque 5070000 610000 601

Bracingelements

Stairs

Beam

Centercore

Outercolumn

Frameelement

(12 DOF)

Uz UzRz Rz Rx

UxUx

UyUyRyRy

Rx

Figure 6 -e finite element model and DOF system of the GullukMosque minaret

Shock and Vibration 9

minarets Laboratory and in situ ultrasonic tests were per-formed to determine the physical andmaterial properties-efinite element models of the studied five timber minarets wereprepared and modeled with the beam elements having sixdegrees of freedom at every node -e obtained experimentalmodes from in situ tests are controlled using both modalassurance criteria (MAC) table and the complexity plots -elinear elastic material model was assumed forminaret analysisbecause the experimental results for the in situ tests were alsoin the elastic range -e boundary conditions were updateddepending on the experimental results to represent the realbehavior of the minarets Using all data an empirical formulawas derived for the rapid estimation of the fundamental

period of timber minarets -is formula shows that theconstruction technique of the outer wall is as important as thematerial and geometric properties of the minarets -e fre-quent usage of the outer columns at 10 cm intervals andbracing elements in the construction of the outer walls of theGulluk and Tesvikiye Mosques minarets resulted in higherfundamental frequencies than the others On the contrary inthe other minarets the usage of 15 cm outer column intervalsthe usage of timber cladding material in the Aga Mosqueminaret instead of bracing elements and less usage of bracingelements in the Ali Kuzu and FethiyeMosqueminarets are theconstruction differences affecting the dynamic behavior -eformula leads to an upper limit with an error of 9

Y XZ Y XZ Y XZ Y XZ Y XZ Y XZ Y XZ

Mode 1f 118 Hz

Mode 2f 119 Hz

Mode 3f 650 Hz

Mode 4f 651 Hz

Mode 5f 952 Hz

Mode 6f 1466 Hz

Mode 7f 1470 Hz

Figure 7 -e first seven modes and natural frequencies of the Gulluk Mosque minaret

Table 7 First seven modes frequencies (experimental approach versus computational approach)

Mode numberTesvikiye Gulluk Fethiye Ali Kuzu Aga

Exp Comp Exp Comp Exp Comp Exp Comp Exp Comp1 242 246 127 118 093 096 072 078 210 2152 269 247 127 119 105 101 074 079 232 2153 1140 1164 715 650 322 393 371 409 959 10354 1221 1165 724 651 352 396 391 414 969 10455 1370 1375 1030 952 520 502 508 450 1196 11526 2285 2104 1501 1466 815 841 815 794 1213 12587 2307 2121 1502 1470 842 845 842 826 1310 1260Exp experimental approach Comp computational approach

Table 8 -e mass participation factors of the studied minarets

MosquesFirst mode Second mode Sum of first three modes

x y x y x yTesvikiye Mosque 6383 6381 2064 2067 8536 8522Gulluk Mosque 6268 6265 2048 2051 8858 8856Fethiye Mosque 6998 6987 1444 1460 8922 8925Ali Kuzu Mosque 6648 6611 1843 1934 8791 9006Aga Mosque 7507 7478 1193 1222 8730 8820

10 Shock and Vibration

In addition minaret height slenderness and minaretcross-sectional area affect the dynamic behavior of minarets-e frequent usage of horizontal beams in the outer wallconstruction of timber minarets increases the rigidity of thestructure and affects their dynamic behavior -e usage ofsteel connectors provides high damping ratios

In conclusion the construction techniques and geo-metric properties of timber minarets greatly affect theirdynamic behavior Better design criteria development and

retrofitting guideline preparation with a different modelingunder different ground motions and strong winds will helpto ensure better minaret safety

Data Availability

All data generated or analyzed during the study are includedin this paper

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

In this paper the results of a research project carried out bythe authors are utilized supported by Uludag University (noOUAP(MM)-201532)

References

[1] A Dogangun R Acar R Livaoglu and O I Tuluk ldquoPer-formance of masonry minarets against earthquakes and windsin Turkeyrdquo in Proceedings of 1st International Conference on

0

05

1

15

2

25

3

0 50 100 150 200 250

Freq

uenc

y f

Stiffnessmass km

Teşvikiye

Ağa

Guumllluumlk

Fethiye

Ali Kuzu

8 8 8

755

755

755

15 15

520

05

8 15 8 815

55

8 10 8 810

200

8 15 8 8

55

200

15

55

5

8 10 8 810

100

100

Figure 8 -e relationship between the stiffness-to-mass ratios and frequencies

R2 = 0962

0010203040506070809

1

12 13 14 15 16 17 18 19 20

Nor

mal

ized

freq

uenc

y f

Height L

Fethiye

TeşvikiyeAğa

Ali KuzuGuumllluumlk

Figure 9-e relationship between the normalized frequencies andheights

R2=0950

0010203040506070809

1

8 10 12 14 16 18

Nor

mal

ized

freq

uenc

y f

Heightdiameter Ld

Teşvikiye

Ağa

Fethiye

Ali KuzuGuumllluumlk

Figure 10 -e relationship between the normalized frequenciesand heights to diameters

078

191225

096

128

072

21242

093127

000

050

100

150

200

250

300

Ali Kuzu Ağa Teşvikiye Fethiye Guumllluumlk

Firs

t mod

e fre

quen

cy (H

z)

FormulaExperimental

(8)

(9)(7)

(3)(1)

Figure 11 -e fundamental frequencies (formula versus experi-mental results)

Shock and Vibration 11

Restoration of Heritage Masonry Structures P32 pp 1ndash10Cairo Egypt April 2006

[2] K H Kusuzumu ldquoTraditional construction techniques andcurrent restorations of Istanbul minaretsrdquo MSc thesis MimarSinan University Istanbul Turkey 2010 in Turkish

[3] A Dogangun R Acar H Sezen and R Livaoglu ldquoIn-vestigation of dynamic response of masonry minaret struc-turesrdquo Bulletin of Earthquake Engineering vol 6 no 3pp 505ndash517 2008

[4] A Bayraktar A C Altunısık B Sevim T Turker M Akkoseand N Coskun ldquoModal analysis experimental validation andcalibration of a historical masonry minaretrdquo Journal of Testingand Evaluation vol 36 no 6 pp 516ndash524 2008

[5] A Bayraktar B Sevim A C Altunısık and T TurkerldquoAnalytical and operational modal analyses of Turkish stylereinforced concrete minarets for structural identificationrdquoExperimental Techniques vol 33 no 2 pp 65ndash75 2009

[6] A Bayraktar B Sevim A C Altunısık and T TurkerldquoEarthquake analysis of reinforced concrete minarets usingambient vibration test resultsrdquo Structural Design of Tall andSpecial Buildings vol 19 no 3 pp 257ndash273 2010

[7] A Bayraktar A C Altunisik B Sevim and T TurkerldquoSeismic response of a historical masonry minaret usinga finite element model updated with operational modaltestingrdquo Journal of Vibration and Control vol 17 no 1pp 129ndash149 2011

[8] A Sahin A Bayraktar M Ozcan B Sevim A C Altunısıkand T Turker ldquoDynamic field test system identificationand modal validation of a RC minaret pre and postprocessing the wind-induced ambient datardquo Journal ofPerformance of Constructed Facilities vol 25 no 4pp 336ndash556 2011

[9] C S Oliveira E Ccedilaktı D Stengel and M Branco ldquoMinaretbehaviour under earthquake loading the case of historicalIstanbulrdquo Earthquake Engineering amp Structural Dynamicsvol 41 no 1 pp 19ndash39 2012

[10] M A A Motaal ldquoEffect of piles on the seismic response ofmosques minaretsrdquo Ain Shams Engineering Journal vol 5no 1 pp 29ndash40 2014

[11] R Livaoglu M H Basturk A Dogangun and C SerhatogluldquoEffect of geometric properties on dynamic behaviour ofhistoric masonry minaretrdquo KSCE Journal of Civil Engineeringvol 20 no 6 pp 2392ndash2402 2016

[12] A L Che Y He X R Ge T Iwatate and Y Oda ldquoStudy onthe dynamic structural characteristics of an ancient timberYingxian wooden pagodardquo in Proceedings of GeoShanghaiInternational Conference pp 390ndash396 Shanghai China June2006

[13] M Yu Y Oda D Fang and J Zhao ldquoAdvances in structuralmechanics of Chinese ancient architecturesrdquo Frontiers ofArchitecture and Civil Engineering in China vol 2 no 1pp 1ndash25 2008

[14] L Gaile ldquoAnalysis of dynamic parameters of observationtowers in Latviardquo in Proceedings of 9th International Scientificand Practical Conference pp 57ndash62 Rezekne Latvia June2013

[15] A Feldman H Huang W S Chang et al ldquoDynamicproperties of tall timber structures under wind-induced vi-brationrdquo in Proceedings of World Conference on TimberEngineering Vienne Austria August 2016

[16] Y Zhang N Zhang Y Cao andH Xia ldquoA predictionmethodof historical timber buildingsrsquo vibrations induced by trafficloads and its validationrdquo Shock and Vibration vol 2017Article ID 1451483 12 pages 2017

[17] Bogaziccedili University Kandilli Observatory and EarthquakeResearch Institute 2017 httpwwwkoeribounedutrsismo2deprem-bilgileribuyuk-depremler

[18] J S Bendat and A G Piersol Random Data Analysis andMeasurement Procedures Wiley San Francisco CA USA 4thedition 1986

[19] C Raineri G Fabbrocino E Cosenza and G ManfredildquoImplementation of OMA procedures using labview theoryand applicationrdquo in Proceedings of 2nd International Oper-ational Modal Analyses Conference pp 1ndash12 CopenhagenDenmark April-May 2007

[20] OMA Operational Modal Analysis Release 45 StructuralVibration Solution AS Denmark Europe 2016

[21] European Committee for Standardization EN 384-StructuralTimber-Determination of Characteristic Values of MechanicalProperties and Density Office for Official Publications of theEuropean Communities Luxembourg Europe 1995

[22] P B Lourenco A O Feio and J S Machado ldquoChestnut woodin compression perpendicular to the grain non-destructivecorrelations for test results in new and old woodrdquo Con-struction and Building Materials vol 21 no 8 pp 1617ndash16272007

[23] Autodesk Inc Sap 2000 V20 Autodesk Inc San Rafael CAUSA 2017

[24] United States Department of Agriculture Forest ServiceWood Handbook Wood as an Engineering Material UnitedStates Department of Agriculture Forest Service WashingtonDC USA 2010

[25] -ermal expansion coefficients for some common materialsOctober 2017 httpswwwengineeringtoolboxcomlinear-expansion-coefficients-d_95html

12 Shock and Vibration

[Gyy(w)] 1113944m

k11113888

Ak1113858 1113859

jwminus λk+

Ak1113858 1113859lowast

jwminus λklowast+

Bk1113858 1113859

minusjwminus λk

+Bk1113858 1113859lowast

minusjwminus λklowast1113889

(2)

where Ak is the k-th residue matrix of the output PSD -eresponse spectral density matrix can be written in the formbelow considering a lightly damped system [19]

[Gyy(w)] 1113944kSub(w)

dkψkψkT

jwminus λk+

dklowastψklowastψkT

jwminus λklowast1113888 1113889 (3)

where dk is a scalar constant and ψk is the k-th mode shapevector -us performing singular value decomposition ofthe output PSD matrix at discrete frequencies w wi thefollowing can be obtained

1113954Gyy jwi( 11138571113960 1113961 UiSiUHi (4)

where matrix Ui is a unitary matrix holding the singularvector uij and Si is a diagonal matrix holding the scalarsingular values sij the superscript H denotes complexconjugation and transposition Near the peak correspondingto the k-th mode in the spectrum only the k-th mode isdominant and the PSD matrix approximates to a rank-onematrix as follows [19]

Ağa Mosque Ali Kuzu Mosque Fethiye Mosque Teşvikiye Mosque Guumllluumlk Mosque

Figure 2 -e studied mosque minarets

Table 1 -e geometric properties and construction techniques of the Tesvikiye Mosque minaret

Body Upper body Spire Construction techniques and the dimensions of thecircular outer wall (cm)

Tesvikiye Mosqueminaret (1953)

Height (m) 792 232 242

55

5

8 10 8 8 8 810 10 10 10 8 10 8 10 8 810

100

100

Outer diameter (m) 116 116 mdashOuter wall thickness (m) 005 005 mdash

Weight (kN) 800 250 240Timber core diameter (m) 030 024minus 020 020minus 010

Location Adjacent to the mosque

4 Shock and Vibration

1113954Gyy jwi( 1113857 siui1uHi1 wi⟶ wk (5)

-e first singular vector at the r-th resonance is an es-timate of the r-th mode shape [19]

1113954ϕr ur1 (6)

In the case of repeated modes the PSD matrix rank isequal to the multiplicity number of the modes -e modalfrequencies can be identified via the peaks of the singularvalue plots while the corresponding singular vectors give themode shapes It is worth noting that natural frequencies andmode shapes can be estimated using such a method since theenhanced frequency-domain decomposition technique al-lows for the estimation of damping ratios [19]

In dynamic tests for very low noise sensors the Sensebox70010203 series is used -is series is an ideal solution forforced vibration dynamic identification shake-table testsmachinery health monitoring and structural health moni-toring of relatively less rigid structures A wide selection ofoptions exists from a plusmn 2 gminus 400 g measurement range and0ndash4000Hz bandwidth -e Dynamic Data AcquisitionStructural Health Monitoring Device Testbox 2010 seriesdata acquisition system has been used for applications instructural monitoring civil engineering earthquake engi-neering and other dynamic applications [20] Modalanalysis tests were performed at the balcony of the minaret-e sensors were placed at the x (north) y (east) and zdirections inside the balcony door -e sensors and theirplacements are shown in Figure 3

Table 2 -e geometric properties and construction techniques of the Gulluk Mosque minaret

Body Upper body Spire Construction techniques and the dimensions of thecircular outer wall (cm)

Gulluk Mosqueminaret (1966)

Height (m) 1335 327 294

55

8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 810

200

Outer diameter (m) 120 120 mdashOuter wall thickness (m) 005 005 mdash

Weight (kN) 1310 402 198Timber core diameter (m) 030 024minus 020 020minus 010

Location Adjacent to the mosque

Table 3 -e geometric properties and construction techniques of the Fethiye Mosque minaret

Body Upperbody Spire

Construction techniques and thedimensions of the circular outer wall

(cm)

Fethiye Mosque minaret (middle of the20th century)

Height (m) 905 325 270

520

05

8 15 8 15 8 15 8 15 8 15 8 815

Outer diameter (m) 106 106 mdashOuter wall thickness

(m) 005 005 mdash

Weight (kN) 703 265 142Timber corediameter (m) 030 020minus 016 016minus 010

Location Adjacent to the mosque

Shock and Vibration 5

-e ambient vibration tests were performed under en-vironmental forces such as traffic and wind-e tests shouldbe long enough to reduce the noise effects and also it isrequired for the accurate damping estimations -ereforethe measurement durations were 30 minutes and the fre-quency span was chosen as 0ndash100Hz -e singular values ofthe spectral densities of all the test setups are shown inFigure 4

Laboratory and in situ ultrasonic tests were performed tofind out the material properties of timber elements used inthe construction of the minarets -e density was measuredaccording to the EN 384 standard [21] Ultrasonic tests wereconducted using a V-meter with cylinder-shaped trans-ducers -e indirect method parallel to the grain and thedirect method perpendicular to the grain were used in thetests (Figure 5)

-e relationship Edin u2 ρ was used in the calculationswhere Edin represents the dynamic modulus of elasticity(Nmm2) u is the propagation velocity of the longitudinalstress waves (msn) and ρ is the density of the specimens(kgm3) [22] -e average results are presented in Table 6

42 Computational Approach -e three-dimensional finiteelement models of the studied five timber minarets wereprepared using the SAP2000 v20 finite element analysisprogram [23] -ey were modeled with the beam elementshaving six degrees of freedom at every node -e finite el-ement model that belongs to one of theminarets investigatedin this study can be seen in Figure 6

-e obtained experimental modes from in situ tests arecontrolled using both modal assurance criteria (MAC) table

Table 4 -e geometric properties and construction techniques of the Ali Kuzu Mosque minaret

Body Upper body Spire Construction techniques and the dimensions of thecircular outer wall (cm)

Ali Kuzu Mosqueminaret (1955)

Height (m) 1286 304 306

8 8 8 8 8 8 8

755

755

755

15 15 15 15 15 15

Outer diameter (m) 134 134 mdashOuter wall thickness (m) 005 005 mdash

Weight (kN) 1473 327 203Timber core diameter (m) 030 022minus 018 018minus 010

Location Adjacent to the mosque

Table 5 -e geometric properties and construction techniques of the Aga Mosque minaret

Body Upper body Spire Construction techniques and the dimensions of thecircular outer wall (cm)

Aga Mosque minaret(1870ndashrestorated2010)

Height (m) 768 262 266

8 15 8 15 8 15 8 15 8 15 8 85

520

015

Outer diameter (m) 146 146 mdashOuter wall thickness (m) 005 005 mdash

Weight (kN) 1604 420 191Timber core diameter (m) 030 024minus 020 020minus 010

Location Adjacent to the mosque

6 Shock and Vibration

and the complexity plots -e linear elastic material modelwas assumed for the minaret analysis because the experi-mental results for the in situ tests were also in the elasticrange After the finite element models were prepared themodal analysis of the minarets was performed -e naturalfrequencies mode shapes and mass participation factorswere obtained from numerical analyses -e boundaryconditions were updated depending on the experimentalresults to represent the real behavior of the minarets -ematerial properties were obtained from the test results andother sources [24 25] -e comparison of the seven modesfrequencies of the studied minarets between the experi-mental and computational approaches is presented in Ta-ble 7 -e first four modes are the bending modes the fifthmode is the torsion mode and the sixth and seventh modesare the bending modes When comparing the experimentaland computational results there is a good harmony amongmode shapes and natural frequencies -e errors betweenthe results ranged up to a minimum of 1 to a maximum of10

-e first seven modes and frequencies of one of thestudied minarets obtained frommodal analysis are shown inFigure 7

5 Discussion

51 Effect of Construction Techniques on Dynamic BehaviorMinaret structural systems are based on a circular plan usinga timber core in the center and timber walls on the exterior-e stairs are arranged between the inner core and outerwalls -e main difference in the construction of timberminarets is in the outer wall design -e builders useddifferent design techniques -e outer walls of the studiedfive minarets were also constructed with different tech-niques which play a role in the dynamic behavior -e mainfactors that affect this behavior are the stiffness-to-mass ratioand damping-e relationship between the stiffness-to-mass

ratio and the frequency is determined with the classicalformula f 12π lowast

(km)

1113968 where f is the frequency and m

and k are the mass and stiffness respectively Comparisonsshow that minarets with high stiffness-to-mass ratios alsohave higher frequencies than minarets with low stiffness-to-mass ratios Figure 8 shows the stiffness-to-mass ratios andfrequencies of the studied minarets represented by theirouter walls

-e minarets of the Tesvikiye Mosque have the higheststiffness-to-mass ratio -e timber columns of the outer wallare arranged at 10 cm intervals and the horizontal beams arearranged between the columns at 100 cm intervals Bracingelements are continuously used throughout the minaretheight Although the only difference between the con-struction techniques of the Tesvikiye Mosque and GullukMosque minarets is the frequency of horizontal beams thestiffness-to-mass ratio of the Tesvikiye Mosque was over 2times than that of the minaret of the Gulluk Mosque -eminaret of the Aga Mosque had the second highest stiffness-to-mass ratio -e outer wall of the Aga Mosque was builtwith timber columns arranged at 15 cm intervals withhorizontal timber beams arranged every 100 cm betweencolumns Additionally a 2 cm thick timber claddingmaterialwas used outside the outer walls -is cladding materialincreased both the stiffness and mass of the structure -eminarets of the Fethiye and Ali Kuzu Mosques had thelowest stiffness-to-mass ratios -e lack of effective usage ofbracing elements and less column usage were the factorsleading to the lowest stiffness-to-mass ratios

-e damping ratio also affects the dynamic behavior-edamping ratios varied between 12 and 20 -e minaret ofthe Aga Mosque had the highest damping ratio of 1967 -eusage of the timber cladding material and steel connectionsled to a high damping ratio however the other minaretshave similar ratios

52 Effect of the Geometrical Properties onDynamic BehaviorMinarets are tall and slender structures therefore theirgeometric properties such as height cross-sectional areaand heightwidth ratio are important regarding the dynamicminaret behavior Minarets behave like cantilevers in whichthe stiffness can be calculated by the formula k 3EIL3where k is the stiffness E is the modulus of elasticity I is themoment of inertia and L is the height In this study withoutnormalization the test results show that the highest minaretshave the lowest frequencies However the effect of height onthe frequency can be seen more clearly by eliminating theother parameters from the frequency Various minarets havesimilar heights therefore the relationship between theheight and frequency can be seen in more detail In Figure 9regression analysis between the height of the minarets andthe normalized frequencies shows that height affects thedynamic minaret behavior

In this study the minaret height-to-width ratios wereinvestigated to determine their effects on the dynamicbehavior minarets have high height-to-width ratios withlow frequencies that are affected by their height andslenderness -e relationship between the normalized

x

yz

Figure 3 -e sensors and their placements on the balcony floor

Shock and Vibration 7

frequencies and slenderness of the studied minarets can beseen in Figure 10

-e cross-sectional area also affects the dynamic prop-erties In the examined minarets the cross-sectional area ofthe Aga Mosque minaret was higher than that of the otherminarets -ese effects are particularly evident and the firstperiod percentage of mass participation was expected to behigher Table 8 shows the mass participation factors thatwere obtained from the numerical analyses It can be seenthat the Aga Mosque minaret has a 75 mass participationfactor in the first mode which is 10 higher than those ofthe other minarets

6 Empirical Formula for Computing theFundamental Frequencies of Minarets

-e construction techniques and the geometrical propertieswere important parameters for understanding the dynamicbehavior of these structures Based on the data collectedfrom the experimental and computational approachesa simple formula was developed to estimate the first fre-quency of vibration

-e fundamental frequency of a minaret is expected to bea function of the moment of inertia the height of theminaret modulus of elasticity cross-sectional area and

ndash60

ndash80

ndash100

ndash120

ndash1400 5 10 15 20 25

f (Hz)

dB |

(lg)2 (H

z)

(a)

0 5 10 15 20 25f (Hz)

ndash60

ndash80

ndash100

ndash120

ndash140

dB |

(lg)2 (H

z)

(b)

0 5 10 15 20 25f (Hz)

ndash60

ndash80

ndash100

ndash120

ndash140

dB |

(lg)2 (H

z)

(c)

0 5 10 15 20 25f (Hz)

ndash60

ndash80

ndash100

ndash120

ndash140

dB |

(lg)2 (H

z)

(d)

0 5 10 15 20 25f (Hz)

ndash60

ndash80

ndash100

ndash120

dB |

(lg)2 (H

z)

(e)

Figure 4-e singular values of the spectral densities of all of the test setups (a) Tesvikiye Mosque minaret (b) Gulluk Mosque minaret (c)Aga Mosque minaret (d) Ali Kuzu Mosque minaret (e) Fethiye Mosque minaret

8 Shock and Vibration

density -e height of the minaret was given by the lengthfrom the top of the pulpit to the base of the spire (body+upper body in Tables 1ndash5) the cross-sectional area and themoment of inertia were calculated by using the base of thebody density and modulus of elasticity which were given bythe data collected from the experimental approaches (Table 6)

Based on the parameters obtained from the experimentaland in situ measurements a new equation was developed fordetermination of the fundamental frequency

f prop middot Hminus32

middot

E middot I

ρ middot A

1113971

(7)

where prop is a constant depending on the constructiontechniques of the outer walls of the minarets H is the heightof the minaret (body + upper body) E is the modulus ofelasticity (parallel to the grain) I is the moment of inertia A

is the cross-sectional area and ρ is the density-e parameter prop was calculated as 015 for the Tesvikiye

and Gulluk Mosque minarets and 010 for the Ali Kuzu Agaand Fethiye Mosque minarets -e Tesvikiye and Gulluk

minarets had similar construction techniques and thedistinctive features of the outer walls were the frequent use ofthe outer columns and the bracing elements (Figure 2Tables 1 and 2) On the contrary the lesser used bracingelements can be seen in the construction of the outer wallsof the Ali Kuzu and Fethiye Mosque minarets (Figure 2Tables 3 and 4) Conversely 2 cm thick timber was used asa cladding material in the construction of the outer walls ofthe Aga Mosque minaret It was observed that the param-eter prop could be taken as 010 as in the Ali Kuzu and FethiyeMosque minarets In Figure 11 the fundamental frequenciesof theminarets obtained from the experimental in situ valuesand Equation (7) were compared with each other -e errorsranged up to a maximum of 9

7 Conclusions

Minarets are sensitive structures that are under lateral forcesand collapse during intense earthquakes and strong winds-ere are few studies regarding the construction techniquesand dynamic behavior of minarets and many studies haveconcentrated on masonry minarets Although reinforcedconcrete minarets are more common than masonry minaretsthey also collapse frequently under lateral forces -ereforethe use of timber in minaret construction has gained im-portance In this study five timber minarets located inSakarya City Turkey were experimentally and computa-tionally investigated to determine the effects of the con-struction techniques and geometric properties of the minaretson their dynamic behavior Ambient vibration tests wereconducted to determine the dynamic characteristics of the

Figure 5 In situ ultrasonic test of timber core (the direct method)

Table 6 -e material properties of the timber elements used in theconstruction of minarets

Mosques

Modulus of elasticity (kNm2)

Unit weight(kNm3)

Parallel tothe grain

Perpendicularto the grain

Indirectmethod Direct method

TesvikiyeMosque 3960000 520000 590

Gulluk Mosque 4520000 530000 583Fethiye Mosque 4010000 450000 587Ali Kuzu Mosque 3520000 420000 592Aga Mosque 5070000 610000 601

Bracingelements

Stairs

Beam

Centercore

Outercolumn

Frameelement

(12 DOF)

Uz UzRz Rz Rx

UxUx

UyUyRyRy

Rx

Figure 6 -e finite element model and DOF system of the GullukMosque minaret

Shock and Vibration 9

minarets Laboratory and in situ ultrasonic tests were per-formed to determine the physical andmaterial properties-efinite element models of the studied five timber minarets wereprepared and modeled with the beam elements having sixdegrees of freedom at every node -e obtained experimentalmodes from in situ tests are controlled using both modalassurance criteria (MAC) table and the complexity plots -elinear elastic material model was assumed forminaret analysisbecause the experimental results for the in situ tests were alsoin the elastic range -e boundary conditions were updateddepending on the experimental results to represent the realbehavior of the minarets Using all data an empirical formulawas derived for the rapid estimation of the fundamental

period of timber minarets -is formula shows that theconstruction technique of the outer wall is as important as thematerial and geometric properties of the minarets -e fre-quent usage of the outer columns at 10 cm intervals andbracing elements in the construction of the outer walls of theGulluk and Tesvikiye Mosques minarets resulted in higherfundamental frequencies than the others On the contrary inthe other minarets the usage of 15 cm outer column intervalsthe usage of timber cladding material in the Aga Mosqueminaret instead of bracing elements and less usage of bracingelements in the Ali Kuzu and FethiyeMosqueminarets are theconstruction differences affecting the dynamic behavior -eformula leads to an upper limit with an error of 9

Y XZ Y XZ Y XZ Y XZ Y XZ Y XZ Y XZ

Mode 1f 118 Hz

Mode 2f 119 Hz

Mode 3f 650 Hz

Mode 4f 651 Hz

Mode 5f 952 Hz

Mode 6f 1466 Hz

Mode 7f 1470 Hz

Figure 7 -e first seven modes and natural frequencies of the Gulluk Mosque minaret

Table 7 First seven modes frequencies (experimental approach versus computational approach)

Mode numberTesvikiye Gulluk Fethiye Ali Kuzu Aga

Exp Comp Exp Comp Exp Comp Exp Comp Exp Comp1 242 246 127 118 093 096 072 078 210 2152 269 247 127 119 105 101 074 079 232 2153 1140 1164 715 650 322 393 371 409 959 10354 1221 1165 724 651 352 396 391 414 969 10455 1370 1375 1030 952 520 502 508 450 1196 11526 2285 2104 1501 1466 815 841 815 794 1213 12587 2307 2121 1502 1470 842 845 842 826 1310 1260Exp experimental approach Comp computational approach

Table 8 -e mass participation factors of the studied minarets

MosquesFirst mode Second mode Sum of first three modes

x y x y x yTesvikiye Mosque 6383 6381 2064 2067 8536 8522Gulluk Mosque 6268 6265 2048 2051 8858 8856Fethiye Mosque 6998 6987 1444 1460 8922 8925Ali Kuzu Mosque 6648 6611 1843 1934 8791 9006Aga Mosque 7507 7478 1193 1222 8730 8820

10 Shock and Vibration

In addition minaret height slenderness and minaretcross-sectional area affect the dynamic behavior of minarets-e frequent usage of horizontal beams in the outer wallconstruction of timber minarets increases the rigidity of thestructure and affects their dynamic behavior -e usage ofsteel connectors provides high damping ratios

In conclusion the construction techniques and geo-metric properties of timber minarets greatly affect theirdynamic behavior Better design criteria development and

retrofitting guideline preparation with a different modelingunder different ground motions and strong winds will helpto ensure better minaret safety

Data Availability

All data generated or analyzed during the study are includedin this paper

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

In this paper the results of a research project carried out bythe authors are utilized supported by Uludag University (noOUAP(MM)-201532)

References

[1] A Dogangun R Acar R Livaoglu and O I Tuluk ldquoPer-formance of masonry minarets against earthquakes and windsin Turkeyrdquo in Proceedings of 1st International Conference on

0

05

1

15

2

25

3

0 50 100 150 200 250

Freq

uenc

y f

Stiffnessmass km

Teşvikiye

Ağa

Guumllluumlk

Fethiye

Ali Kuzu

8 8 8

755

755

755

15 15

520

05

8 15 8 815

55

8 10 8 810

200

8 15 8 8

55

200

15

55

5

8 10 8 810

100

100

Figure 8 -e relationship between the stiffness-to-mass ratios and frequencies

R2 = 0962

0010203040506070809

1

12 13 14 15 16 17 18 19 20

Nor

mal

ized

freq

uenc

y f

Height L

Fethiye

TeşvikiyeAğa

Ali KuzuGuumllluumlk

Figure 9-e relationship between the normalized frequencies andheights

R2=0950

0010203040506070809

1

8 10 12 14 16 18

Nor

mal

ized

freq

uenc

y f

Heightdiameter Ld

Teşvikiye

Ağa

Fethiye

Ali KuzuGuumllluumlk

Figure 10 -e relationship between the normalized frequenciesand heights to diameters

078

191225

096

128

072

21242

093127

000

050

100

150

200

250

300

Ali Kuzu Ağa Teşvikiye Fethiye Guumllluumlk

Firs

t mod

e fre

quen

cy (H

z)

FormulaExperimental

(8)

(9)(7)

(3)(1)

Figure 11 -e fundamental frequencies (formula versus experi-mental results)

Shock and Vibration 11

Restoration of Heritage Masonry Structures P32 pp 1ndash10Cairo Egypt April 2006

[2] K H Kusuzumu ldquoTraditional construction techniques andcurrent restorations of Istanbul minaretsrdquo MSc thesis MimarSinan University Istanbul Turkey 2010 in Turkish

[3] A Dogangun R Acar H Sezen and R Livaoglu ldquoIn-vestigation of dynamic response of masonry minaret struc-turesrdquo Bulletin of Earthquake Engineering vol 6 no 3pp 505ndash517 2008

[4] A Bayraktar A C Altunısık B Sevim T Turker M Akkoseand N Coskun ldquoModal analysis experimental validation andcalibration of a historical masonry minaretrdquo Journal of Testingand Evaluation vol 36 no 6 pp 516ndash524 2008

[5] A Bayraktar B Sevim A C Altunısık and T TurkerldquoAnalytical and operational modal analyses of Turkish stylereinforced concrete minarets for structural identificationrdquoExperimental Techniques vol 33 no 2 pp 65ndash75 2009

[6] A Bayraktar B Sevim A C Altunısık and T TurkerldquoEarthquake analysis of reinforced concrete minarets usingambient vibration test resultsrdquo Structural Design of Tall andSpecial Buildings vol 19 no 3 pp 257ndash273 2010

[7] A Bayraktar A C Altunisik B Sevim and T TurkerldquoSeismic response of a historical masonry minaret usinga finite element model updated with operational modaltestingrdquo Journal of Vibration and Control vol 17 no 1pp 129ndash149 2011

[8] A Sahin A Bayraktar M Ozcan B Sevim A C Altunısıkand T Turker ldquoDynamic field test system identificationand modal validation of a RC minaret pre and postprocessing the wind-induced ambient datardquo Journal ofPerformance of Constructed Facilities vol 25 no 4pp 336ndash556 2011

[9] C S Oliveira E Ccedilaktı D Stengel and M Branco ldquoMinaretbehaviour under earthquake loading the case of historicalIstanbulrdquo Earthquake Engineering amp Structural Dynamicsvol 41 no 1 pp 19ndash39 2012

[10] M A A Motaal ldquoEffect of piles on the seismic response ofmosques minaretsrdquo Ain Shams Engineering Journal vol 5no 1 pp 29ndash40 2014

[11] R Livaoglu M H Basturk A Dogangun and C SerhatogluldquoEffect of geometric properties on dynamic behaviour ofhistoric masonry minaretrdquo KSCE Journal of Civil Engineeringvol 20 no 6 pp 2392ndash2402 2016

[12] A L Che Y He X R Ge T Iwatate and Y Oda ldquoStudy onthe dynamic structural characteristics of an ancient timberYingxian wooden pagodardquo in Proceedings of GeoShanghaiInternational Conference pp 390ndash396 Shanghai China June2006

[13] M Yu Y Oda D Fang and J Zhao ldquoAdvances in structuralmechanics of Chinese ancient architecturesrdquo Frontiers ofArchitecture and Civil Engineering in China vol 2 no 1pp 1ndash25 2008

[14] L Gaile ldquoAnalysis of dynamic parameters of observationtowers in Latviardquo in Proceedings of 9th International Scientificand Practical Conference pp 57ndash62 Rezekne Latvia June2013

[15] A Feldman H Huang W S Chang et al ldquoDynamicproperties of tall timber structures under wind-induced vi-brationrdquo in Proceedings of World Conference on TimberEngineering Vienne Austria August 2016

[16] Y Zhang N Zhang Y Cao andH Xia ldquoA predictionmethodof historical timber buildingsrsquo vibrations induced by trafficloads and its validationrdquo Shock and Vibration vol 2017Article ID 1451483 12 pages 2017

[17] Bogaziccedili University Kandilli Observatory and EarthquakeResearch Institute 2017 httpwwwkoeribounedutrsismo2deprem-bilgileribuyuk-depremler

[18] J S Bendat and A G Piersol Random Data Analysis andMeasurement Procedures Wiley San Francisco CA USA 4thedition 1986

[19] C Raineri G Fabbrocino E Cosenza and G ManfredildquoImplementation of OMA procedures using labview theoryand applicationrdquo in Proceedings of 2nd International Oper-ational Modal Analyses Conference pp 1ndash12 CopenhagenDenmark April-May 2007

[20] OMA Operational Modal Analysis Release 45 StructuralVibration Solution AS Denmark Europe 2016

[21] European Committee for Standardization EN 384-StructuralTimber-Determination of Characteristic Values of MechanicalProperties and Density Office for Official Publications of theEuropean Communities Luxembourg Europe 1995

[22] P B Lourenco A O Feio and J S Machado ldquoChestnut woodin compression perpendicular to the grain non-destructivecorrelations for test results in new and old woodrdquo Con-struction and Building Materials vol 21 no 8 pp 1617ndash16272007

[23] Autodesk Inc Sap 2000 V20 Autodesk Inc San Rafael CAUSA 2017

[24] United States Department of Agriculture Forest ServiceWood Handbook Wood as an Engineering Material UnitedStates Department of Agriculture Forest Service WashingtonDC USA 2010

[25] -ermal expansion coefficients for some common materialsOctober 2017 httpswwwengineeringtoolboxcomlinear-expansion-coefficients-d_95html

12 Shock and Vibration

1113954Gyy jwi( 1113857 siui1uHi1 wi⟶ wk (5)

-e first singular vector at the r-th resonance is an es-timate of the r-th mode shape [19]

1113954ϕr ur1 (6)

In the case of repeated modes the PSD matrix rank isequal to the multiplicity number of the modes -e modalfrequencies can be identified via the peaks of the singularvalue plots while the corresponding singular vectors give themode shapes It is worth noting that natural frequencies andmode shapes can be estimated using such a method since theenhanced frequency-domain decomposition technique al-lows for the estimation of damping ratios [19]

In dynamic tests for very low noise sensors the Sensebox70010203 series is used -is series is an ideal solution forforced vibration dynamic identification shake-table testsmachinery health monitoring and structural health moni-toring of relatively less rigid structures A wide selection ofoptions exists from a plusmn 2 gminus 400 g measurement range and0ndash4000Hz bandwidth -e Dynamic Data AcquisitionStructural Health Monitoring Device Testbox 2010 seriesdata acquisition system has been used for applications instructural monitoring civil engineering earthquake engi-neering and other dynamic applications [20] Modalanalysis tests were performed at the balcony of the minaret-e sensors were placed at the x (north) y (east) and zdirections inside the balcony door -e sensors and theirplacements are shown in Figure 3

Table 2 -e geometric properties and construction techniques of the Gulluk Mosque minaret

Body Upper body Spire Construction techniques and the dimensions of thecircular outer wall (cm)

Gulluk Mosqueminaret (1966)

Height (m) 1335 327 294

55

8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 810

200

Outer diameter (m) 120 120 mdashOuter wall thickness (m) 005 005 mdash

Weight (kN) 1310 402 198Timber core diameter (m) 030 024minus 020 020minus 010

Location Adjacent to the mosque

Table 3 -e geometric properties and construction techniques of the Fethiye Mosque minaret

Body Upperbody Spire

Construction techniques and thedimensions of the circular outer wall

(cm)

Fethiye Mosque minaret (middle of the20th century)

Height (m) 905 325 270

520

05

8 15 8 15 8 15 8 15 8 15 8 815

Outer diameter (m) 106 106 mdashOuter wall thickness

(m) 005 005 mdash

Weight (kN) 703 265 142Timber corediameter (m) 030 020minus 016 016minus 010

Location Adjacent to the mosque

Shock and Vibration 5

-e ambient vibration tests were performed under en-vironmental forces such as traffic and wind-e tests shouldbe long enough to reduce the noise effects and also it isrequired for the accurate damping estimations -ereforethe measurement durations were 30 minutes and the fre-quency span was chosen as 0ndash100Hz -e singular values ofthe spectral densities of all the test setups are shown inFigure 4

Laboratory and in situ ultrasonic tests were performed tofind out the material properties of timber elements used inthe construction of the minarets -e density was measuredaccording to the EN 384 standard [21] Ultrasonic tests wereconducted using a V-meter with cylinder-shaped trans-ducers -e indirect method parallel to the grain and thedirect method perpendicular to the grain were used in thetests (Figure 5)

-e relationship Edin u2 ρ was used in the calculationswhere Edin represents the dynamic modulus of elasticity(Nmm2) u is the propagation velocity of the longitudinalstress waves (msn) and ρ is the density of the specimens(kgm3) [22] -e average results are presented in Table 6

42 Computational Approach -e three-dimensional finiteelement models of the studied five timber minarets wereprepared using the SAP2000 v20 finite element analysisprogram [23] -ey were modeled with the beam elementshaving six degrees of freedom at every node -e finite el-ement model that belongs to one of theminarets investigatedin this study can be seen in Figure 6

-e obtained experimental modes from in situ tests arecontrolled using both modal assurance criteria (MAC) table

Table 4 -e geometric properties and construction techniques of the Ali Kuzu Mosque minaret

Body Upper body Spire Construction techniques and the dimensions of thecircular outer wall (cm)

Ali Kuzu Mosqueminaret (1955)

Height (m) 1286 304 306

8 8 8 8 8 8 8

755

755

755

15 15 15 15 15 15

Outer diameter (m) 134 134 mdashOuter wall thickness (m) 005 005 mdash

Weight (kN) 1473 327 203Timber core diameter (m) 030 022minus 018 018minus 010

Location Adjacent to the mosque

Table 5 -e geometric properties and construction techniques of the Aga Mosque minaret

Body Upper body Spire Construction techniques and the dimensions of thecircular outer wall (cm)

Aga Mosque minaret(1870ndashrestorated2010)

Height (m) 768 262 266

8 15 8 15 8 15 8 15 8 15 8 85

520

015

Outer diameter (m) 146 146 mdashOuter wall thickness (m) 005 005 mdash

Weight (kN) 1604 420 191Timber core diameter (m) 030 024minus 020 020minus 010

Location Adjacent to the mosque

6 Shock and Vibration

and the complexity plots -e linear elastic material modelwas assumed for the minaret analysis because the experi-mental results for the in situ tests were also in the elasticrange After the finite element models were prepared themodal analysis of the minarets was performed -e naturalfrequencies mode shapes and mass participation factorswere obtained from numerical analyses -e boundaryconditions were updated depending on the experimentalresults to represent the real behavior of the minarets -ematerial properties were obtained from the test results andother sources [24 25] -e comparison of the seven modesfrequencies of the studied minarets between the experi-mental and computational approaches is presented in Ta-ble 7 -e first four modes are the bending modes the fifthmode is the torsion mode and the sixth and seventh modesare the bending modes When comparing the experimentaland computational results there is a good harmony amongmode shapes and natural frequencies -e errors betweenthe results ranged up to a minimum of 1 to a maximum of10

-e first seven modes and frequencies of one of thestudied minarets obtained frommodal analysis are shown inFigure 7

5 Discussion

51 Effect of Construction Techniques on Dynamic BehaviorMinaret structural systems are based on a circular plan usinga timber core in the center and timber walls on the exterior-e stairs are arranged between the inner core and outerwalls -e main difference in the construction of timberminarets is in the outer wall design -e builders useddifferent design techniques -e outer walls of the studiedfive minarets were also constructed with different tech-niques which play a role in the dynamic behavior -e mainfactors that affect this behavior are the stiffness-to-mass ratioand damping-e relationship between the stiffness-to-mass

ratio and the frequency is determined with the classicalformula f 12π lowast

(km)

1113968 where f is the frequency and m

and k are the mass and stiffness respectively Comparisonsshow that minarets with high stiffness-to-mass ratios alsohave higher frequencies than minarets with low stiffness-to-mass ratios Figure 8 shows the stiffness-to-mass ratios andfrequencies of the studied minarets represented by theirouter walls

-e minarets of the Tesvikiye Mosque have the higheststiffness-to-mass ratio -e timber columns of the outer wallare arranged at 10 cm intervals and the horizontal beams arearranged between the columns at 100 cm intervals Bracingelements are continuously used throughout the minaretheight Although the only difference between the con-struction techniques of the Tesvikiye Mosque and GullukMosque minarets is the frequency of horizontal beams thestiffness-to-mass ratio of the Tesvikiye Mosque was over 2times than that of the minaret of the Gulluk Mosque -eminaret of the Aga Mosque had the second highest stiffness-to-mass ratio -e outer wall of the Aga Mosque was builtwith timber columns arranged at 15 cm intervals withhorizontal timber beams arranged every 100 cm betweencolumns Additionally a 2 cm thick timber claddingmaterialwas used outside the outer walls -is cladding materialincreased both the stiffness and mass of the structure -eminarets of the Fethiye and Ali Kuzu Mosques had thelowest stiffness-to-mass ratios -e lack of effective usage ofbracing elements and less column usage were the factorsleading to the lowest stiffness-to-mass ratios

-e damping ratio also affects the dynamic behavior-edamping ratios varied between 12 and 20 -e minaret ofthe Aga Mosque had the highest damping ratio of 1967 -eusage of the timber cladding material and steel connectionsled to a high damping ratio however the other minaretshave similar ratios

52 Effect of the Geometrical Properties onDynamic BehaviorMinarets are tall and slender structures therefore theirgeometric properties such as height cross-sectional areaand heightwidth ratio are important regarding the dynamicminaret behavior Minarets behave like cantilevers in whichthe stiffness can be calculated by the formula k 3EIL3where k is the stiffness E is the modulus of elasticity I is themoment of inertia and L is the height In this study withoutnormalization the test results show that the highest minaretshave the lowest frequencies However the effect of height onthe frequency can be seen more clearly by eliminating theother parameters from the frequency Various minarets havesimilar heights therefore the relationship between theheight and frequency can be seen in more detail In Figure 9regression analysis between the height of the minarets andthe normalized frequencies shows that height affects thedynamic minaret behavior

In this study the minaret height-to-width ratios wereinvestigated to determine their effects on the dynamicbehavior minarets have high height-to-width ratios withlow frequencies that are affected by their height andslenderness -e relationship between the normalized

x

yz

Figure 3 -e sensors and their placements on the balcony floor

Shock and Vibration 7

frequencies and slenderness of the studied minarets can beseen in Figure 10

-e cross-sectional area also affects the dynamic prop-erties In the examined minarets the cross-sectional area ofthe Aga Mosque minaret was higher than that of the otherminarets -ese effects are particularly evident and the firstperiod percentage of mass participation was expected to behigher Table 8 shows the mass participation factors thatwere obtained from the numerical analyses It can be seenthat the Aga Mosque minaret has a 75 mass participationfactor in the first mode which is 10 higher than those ofthe other minarets

6 Empirical Formula for Computing theFundamental Frequencies of Minarets

-e construction techniques and the geometrical propertieswere important parameters for understanding the dynamicbehavior of these structures Based on the data collectedfrom the experimental and computational approachesa simple formula was developed to estimate the first fre-quency of vibration

-e fundamental frequency of a minaret is expected to bea function of the moment of inertia the height of theminaret modulus of elasticity cross-sectional area and

ndash60

ndash80

ndash100

ndash120

ndash1400 5 10 15 20 25

f (Hz)

dB |

(lg)2 (H

z)

(a)

0 5 10 15 20 25f (Hz)

ndash60

ndash80

ndash100

ndash120

ndash140

dB |

(lg)2 (H

z)

(b)

0 5 10 15 20 25f (Hz)

ndash60

ndash80

ndash100

ndash120

ndash140

dB |

(lg)2 (H

z)

(c)

0 5 10 15 20 25f (Hz)

ndash60

ndash80

ndash100

ndash120

ndash140

dB |

(lg)2 (H

z)

(d)

0 5 10 15 20 25f (Hz)

ndash60

ndash80

ndash100

ndash120

dB |

(lg)2 (H

z)

(e)

Figure 4-e singular values of the spectral densities of all of the test setups (a) Tesvikiye Mosque minaret (b) Gulluk Mosque minaret (c)Aga Mosque minaret (d) Ali Kuzu Mosque minaret (e) Fethiye Mosque minaret

8 Shock and Vibration

density -e height of the minaret was given by the lengthfrom the top of the pulpit to the base of the spire (body+upper body in Tables 1ndash5) the cross-sectional area and themoment of inertia were calculated by using the base of thebody density and modulus of elasticity which were given bythe data collected from the experimental approaches (Table 6)

Based on the parameters obtained from the experimentaland in situ measurements a new equation was developed fordetermination of the fundamental frequency

f prop middot Hminus32

middot

E middot I

ρ middot A

1113971

(7)

where prop is a constant depending on the constructiontechniques of the outer walls of the minarets H is the heightof the minaret (body + upper body) E is the modulus ofelasticity (parallel to the grain) I is the moment of inertia A

is the cross-sectional area and ρ is the density-e parameter prop was calculated as 015 for the Tesvikiye

and Gulluk Mosque minarets and 010 for the Ali Kuzu Agaand Fethiye Mosque minarets -e Tesvikiye and Gulluk

minarets had similar construction techniques and thedistinctive features of the outer walls were the frequent use ofthe outer columns and the bracing elements (Figure 2Tables 1 and 2) On the contrary the lesser used bracingelements can be seen in the construction of the outer wallsof the Ali Kuzu and Fethiye Mosque minarets (Figure 2Tables 3 and 4) Conversely 2 cm thick timber was used asa cladding material in the construction of the outer walls ofthe Aga Mosque minaret It was observed that the param-eter prop could be taken as 010 as in the Ali Kuzu and FethiyeMosque minarets In Figure 11 the fundamental frequenciesof theminarets obtained from the experimental in situ valuesand Equation (7) were compared with each other -e errorsranged up to a maximum of 9

7 Conclusions

Minarets are sensitive structures that are under lateral forcesand collapse during intense earthquakes and strong winds-ere are few studies regarding the construction techniquesand dynamic behavior of minarets and many studies haveconcentrated on masonry minarets Although reinforcedconcrete minarets are more common than masonry minaretsthey also collapse frequently under lateral forces -ereforethe use of timber in minaret construction has gained im-portance In this study five timber minarets located inSakarya City Turkey were experimentally and computa-tionally investigated to determine the effects of the con-struction techniques and geometric properties of the minaretson their dynamic behavior Ambient vibration tests wereconducted to determine the dynamic characteristics of the

Figure 5 In situ ultrasonic test of timber core (the direct method)

Table 6 -e material properties of the timber elements used in theconstruction of minarets

Mosques

Modulus of elasticity (kNm2)

Unit weight(kNm3)

Parallel tothe grain

Perpendicularto the grain

Indirectmethod Direct method

TesvikiyeMosque 3960000 520000 590

Gulluk Mosque 4520000 530000 583Fethiye Mosque 4010000 450000 587Ali Kuzu Mosque 3520000 420000 592Aga Mosque 5070000 610000 601

Bracingelements

Stairs

Beam

Centercore

Outercolumn

Frameelement

(12 DOF)

Uz UzRz Rz Rx

UxUx

UyUyRyRy

Rx

Figure 6 -e finite element model and DOF system of the GullukMosque minaret

Shock and Vibration 9

minarets Laboratory and in situ ultrasonic tests were per-formed to determine the physical andmaterial properties-efinite element models of the studied five timber minarets wereprepared and modeled with the beam elements having sixdegrees of freedom at every node -e obtained experimentalmodes from in situ tests are controlled using both modalassurance criteria (MAC) table and the complexity plots -elinear elastic material model was assumed forminaret analysisbecause the experimental results for the in situ tests were alsoin the elastic range -e boundary conditions were updateddepending on the experimental results to represent the realbehavior of the minarets Using all data an empirical formulawas derived for the rapid estimation of the fundamental

period of timber minarets -is formula shows that theconstruction technique of the outer wall is as important as thematerial and geometric properties of the minarets -e fre-quent usage of the outer columns at 10 cm intervals andbracing elements in the construction of the outer walls of theGulluk and Tesvikiye Mosques minarets resulted in higherfundamental frequencies than the others On the contrary inthe other minarets the usage of 15 cm outer column intervalsthe usage of timber cladding material in the Aga Mosqueminaret instead of bracing elements and less usage of bracingelements in the Ali Kuzu and FethiyeMosqueminarets are theconstruction differences affecting the dynamic behavior -eformula leads to an upper limit with an error of 9

Y XZ Y XZ Y XZ Y XZ Y XZ Y XZ Y XZ

Mode 1f 118 Hz

Mode 2f 119 Hz

Mode 3f 650 Hz

Mode 4f 651 Hz

Mode 5f 952 Hz

Mode 6f 1466 Hz

Mode 7f 1470 Hz

Figure 7 -e first seven modes and natural frequencies of the Gulluk Mosque minaret

Table 7 First seven modes frequencies (experimental approach versus computational approach)

Mode numberTesvikiye Gulluk Fethiye Ali Kuzu Aga

Exp Comp Exp Comp Exp Comp Exp Comp Exp Comp1 242 246 127 118 093 096 072 078 210 2152 269 247 127 119 105 101 074 079 232 2153 1140 1164 715 650 322 393 371 409 959 10354 1221 1165 724 651 352 396 391 414 969 10455 1370 1375 1030 952 520 502 508 450 1196 11526 2285 2104 1501 1466 815 841 815 794 1213 12587 2307 2121 1502 1470 842 845 842 826 1310 1260Exp experimental approach Comp computational approach

Table 8 -e mass participation factors of the studied minarets

MosquesFirst mode Second mode Sum of first three modes

x y x y x yTesvikiye Mosque 6383 6381 2064 2067 8536 8522Gulluk Mosque 6268 6265 2048 2051 8858 8856Fethiye Mosque 6998 6987 1444 1460 8922 8925Ali Kuzu Mosque 6648 6611 1843 1934 8791 9006Aga Mosque 7507 7478 1193 1222 8730 8820

10 Shock and Vibration

In addition minaret height slenderness and minaretcross-sectional area affect the dynamic behavior of minarets-e frequent usage of horizontal beams in the outer wallconstruction of timber minarets increases the rigidity of thestructure and affects their dynamic behavior -e usage ofsteel connectors provides high damping ratios

In conclusion the construction techniques and geo-metric properties of timber minarets greatly affect theirdynamic behavior Better design criteria development and

retrofitting guideline preparation with a different modelingunder different ground motions and strong winds will helpto ensure better minaret safety

Data Availability

All data generated or analyzed during the study are includedin this paper

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

In this paper the results of a research project carried out bythe authors are utilized supported by Uludag University (noOUAP(MM)-201532)

References

[1] A Dogangun R Acar R Livaoglu and O I Tuluk ldquoPer-formance of masonry minarets against earthquakes and windsin Turkeyrdquo in Proceedings of 1st International Conference on

0

05

1

15

2

25

3

0 50 100 150 200 250

Freq

uenc

y f

Stiffnessmass km

Teşvikiye

Ağa

Guumllluumlk

Fethiye

Ali Kuzu

8 8 8

755

755

755

15 15

520

05

8 15 8 815

55

8 10 8 810

200

8 15 8 8

55

200

15

55

5

8 10 8 810

100

100

Figure 8 -e relationship between the stiffness-to-mass ratios and frequencies

R2 = 0962

0010203040506070809

1

12 13 14 15 16 17 18 19 20

Nor

mal

ized

freq

uenc

y f

Height L

Fethiye

TeşvikiyeAğa

Ali KuzuGuumllluumlk

Figure 9-e relationship between the normalized frequencies andheights

R2=0950

0010203040506070809

1

8 10 12 14 16 18

Nor

mal

ized

freq

uenc

y f

Heightdiameter Ld

Teşvikiye

Ağa

Fethiye

Ali KuzuGuumllluumlk

Figure 10 -e relationship between the normalized frequenciesand heights to diameters

078

191225

096

128

072

21242

093127

000

050

100

150

200

250

300

Ali Kuzu Ağa Teşvikiye Fethiye Guumllluumlk

Firs

t mod

e fre

quen

cy (H

z)

FormulaExperimental

(8)

(9)(7)

(3)(1)

Figure 11 -e fundamental frequencies (formula versus experi-mental results)

Shock and Vibration 11

Restoration of Heritage Masonry Structures P32 pp 1ndash10Cairo Egypt April 2006

[2] K H Kusuzumu ldquoTraditional construction techniques andcurrent restorations of Istanbul minaretsrdquo MSc thesis MimarSinan University Istanbul Turkey 2010 in Turkish

[3] A Dogangun R Acar H Sezen and R Livaoglu ldquoIn-vestigation of dynamic response of masonry minaret struc-turesrdquo Bulletin of Earthquake Engineering vol 6 no 3pp 505ndash517 2008

[4] A Bayraktar A C Altunısık B Sevim T Turker M Akkoseand N Coskun ldquoModal analysis experimental validation andcalibration of a historical masonry minaretrdquo Journal of Testingand Evaluation vol 36 no 6 pp 516ndash524 2008

[5] A Bayraktar B Sevim A C Altunısık and T TurkerldquoAnalytical and operational modal analyses of Turkish stylereinforced concrete minarets for structural identificationrdquoExperimental Techniques vol 33 no 2 pp 65ndash75 2009

[6] A Bayraktar B Sevim A C Altunısık and T TurkerldquoEarthquake analysis of reinforced concrete minarets usingambient vibration test resultsrdquo Structural Design of Tall andSpecial Buildings vol 19 no 3 pp 257ndash273 2010

[7] A Bayraktar A C Altunisik B Sevim and T TurkerldquoSeismic response of a historical masonry minaret usinga finite element model updated with operational modaltestingrdquo Journal of Vibration and Control vol 17 no 1pp 129ndash149 2011

[8] A Sahin A Bayraktar M Ozcan B Sevim A C Altunısıkand T Turker ldquoDynamic field test system identificationand modal validation of a RC minaret pre and postprocessing the wind-induced ambient datardquo Journal ofPerformance of Constructed Facilities vol 25 no 4pp 336ndash556 2011

[9] C S Oliveira E Ccedilaktı D Stengel and M Branco ldquoMinaretbehaviour under earthquake loading the case of historicalIstanbulrdquo Earthquake Engineering amp Structural Dynamicsvol 41 no 1 pp 19ndash39 2012

[10] M A A Motaal ldquoEffect of piles on the seismic response ofmosques minaretsrdquo Ain Shams Engineering Journal vol 5no 1 pp 29ndash40 2014

[11] R Livaoglu M H Basturk A Dogangun and C SerhatogluldquoEffect of geometric properties on dynamic behaviour ofhistoric masonry minaretrdquo KSCE Journal of Civil Engineeringvol 20 no 6 pp 2392ndash2402 2016

[12] A L Che Y He X R Ge T Iwatate and Y Oda ldquoStudy onthe dynamic structural characteristics of an ancient timberYingxian wooden pagodardquo in Proceedings of GeoShanghaiInternational Conference pp 390ndash396 Shanghai China June2006

[13] M Yu Y Oda D Fang and J Zhao ldquoAdvances in structuralmechanics of Chinese ancient architecturesrdquo Frontiers ofArchitecture and Civil Engineering in China vol 2 no 1pp 1ndash25 2008

[14] L Gaile ldquoAnalysis of dynamic parameters of observationtowers in Latviardquo in Proceedings of 9th International Scientificand Practical Conference pp 57ndash62 Rezekne Latvia June2013

[15] A Feldman H Huang W S Chang et al ldquoDynamicproperties of tall timber structures under wind-induced vi-brationrdquo in Proceedings of World Conference on TimberEngineering Vienne Austria August 2016

[16] Y Zhang N Zhang Y Cao andH Xia ldquoA predictionmethodof historical timber buildingsrsquo vibrations induced by trafficloads and its validationrdquo Shock and Vibration vol 2017Article ID 1451483 12 pages 2017

[17] Bogaziccedili University Kandilli Observatory and EarthquakeResearch Institute 2017 httpwwwkoeribounedutrsismo2deprem-bilgileribuyuk-depremler

[18] J S Bendat and A G Piersol Random Data Analysis andMeasurement Procedures Wiley San Francisco CA USA 4thedition 1986

[19] C Raineri G Fabbrocino E Cosenza and G ManfredildquoImplementation of OMA procedures using labview theoryand applicationrdquo in Proceedings of 2nd International Oper-ational Modal Analyses Conference pp 1ndash12 CopenhagenDenmark April-May 2007

[20] OMA Operational Modal Analysis Release 45 StructuralVibration Solution AS Denmark Europe 2016

[21] European Committee for Standardization EN 384-StructuralTimber-Determination of Characteristic Values of MechanicalProperties and Density Office for Official Publications of theEuropean Communities Luxembourg Europe 1995

[22] P B Lourenco A O Feio and J S Machado ldquoChestnut woodin compression perpendicular to the grain non-destructivecorrelations for test results in new and old woodrdquo Con-struction and Building Materials vol 21 no 8 pp 1617ndash16272007

[23] Autodesk Inc Sap 2000 V20 Autodesk Inc San Rafael CAUSA 2017

[24] United States Department of Agriculture Forest ServiceWood Handbook Wood as an Engineering Material UnitedStates Department of Agriculture Forest Service WashingtonDC USA 2010

[25] -ermal expansion coefficients for some common materialsOctober 2017 httpswwwengineeringtoolboxcomlinear-expansion-coefficients-d_95html

12 Shock and Vibration

-e ambient vibration tests were performed under en-vironmental forces such as traffic and wind-e tests shouldbe long enough to reduce the noise effects and also it isrequired for the accurate damping estimations -ereforethe measurement durations were 30 minutes and the fre-quency span was chosen as 0ndash100Hz -e singular values ofthe spectral densities of all the test setups are shown inFigure 4

Laboratory and in situ ultrasonic tests were performed tofind out the material properties of timber elements used inthe construction of the minarets -e density was measuredaccording to the EN 384 standard [21] Ultrasonic tests wereconducted using a V-meter with cylinder-shaped trans-ducers -e indirect method parallel to the grain and thedirect method perpendicular to the grain were used in thetests (Figure 5)

-e relationship Edin u2 ρ was used in the calculationswhere Edin represents the dynamic modulus of elasticity(Nmm2) u is the propagation velocity of the longitudinalstress waves (msn) and ρ is the density of the specimens(kgm3) [22] -e average results are presented in Table 6

42 Computational Approach -e three-dimensional finiteelement models of the studied five timber minarets wereprepared using the SAP2000 v20 finite element analysisprogram [23] -ey were modeled with the beam elementshaving six degrees of freedom at every node -e finite el-ement model that belongs to one of theminarets investigatedin this study can be seen in Figure 6

-e obtained experimental modes from in situ tests arecontrolled using both modal assurance criteria (MAC) table

Table 4 -e geometric properties and construction techniques of the Ali Kuzu Mosque minaret

Body Upper body Spire Construction techniques and the dimensions of thecircular outer wall (cm)

Ali Kuzu Mosqueminaret (1955)

Height (m) 1286 304 306

8 8 8 8 8 8 8

755

755

755

15 15 15 15 15 15

Outer diameter (m) 134 134 mdashOuter wall thickness (m) 005 005 mdash

Weight (kN) 1473 327 203Timber core diameter (m) 030 022minus 018 018minus 010

Location Adjacent to the mosque

Table 5 -e geometric properties and construction techniques of the Aga Mosque minaret

Body Upper body Spire Construction techniques and the dimensions of thecircular outer wall (cm)

Aga Mosque minaret(1870ndashrestorated2010)

Height (m) 768 262 266

8 15 8 15 8 15 8 15 8 15 8 85

520

015

Outer diameter (m) 146 146 mdashOuter wall thickness (m) 005 005 mdash

Weight (kN) 1604 420 191Timber core diameter (m) 030 024minus 020 020minus 010

Location Adjacent to the mosque

6 Shock and Vibration

and the complexity plots -e linear elastic material modelwas assumed for the minaret analysis because the experi-mental results for the in situ tests were also in the elasticrange After the finite element models were prepared themodal analysis of the minarets was performed -e naturalfrequencies mode shapes and mass participation factorswere obtained from numerical analyses -e boundaryconditions were updated depending on the experimentalresults to represent the real behavior of the minarets -ematerial properties were obtained from the test results andother sources [24 25] -e comparison of the seven modesfrequencies of the studied minarets between the experi-mental and computational approaches is presented in Ta-ble 7 -e first four modes are the bending modes the fifthmode is the torsion mode and the sixth and seventh modesare the bending modes When comparing the experimentaland computational results there is a good harmony amongmode shapes and natural frequencies -e errors betweenthe results ranged up to a minimum of 1 to a maximum of10

-e first seven modes and frequencies of one of thestudied minarets obtained frommodal analysis are shown inFigure 7

5 Discussion

51 Effect of Construction Techniques on Dynamic BehaviorMinaret structural systems are based on a circular plan usinga timber core in the center and timber walls on the exterior-e stairs are arranged between the inner core and outerwalls -e main difference in the construction of timberminarets is in the outer wall design -e builders useddifferent design techniques -e outer walls of the studiedfive minarets were also constructed with different tech-niques which play a role in the dynamic behavior -e mainfactors that affect this behavior are the stiffness-to-mass ratioand damping-e relationship between the stiffness-to-mass

ratio and the frequency is determined with the classicalformula f 12π lowast

(km)

1113968 where f is the frequency and m

and k are the mass and stiffness respectively Comparisonsshow that minarets with high stiffness-to-mass ratios alsohave higher frequencies than minarets with low stiffness-to-mass ratios Figure 8 shows the stiffness-to-mass ratios andfrequencies of the studied minarets represented by theirouter walls

-e minarets of the Tesvikiye Mosque have the higheststiffness-to-mass ratio -e timber columns of the outer wallare arranged at 10 cm intervals and the horizontal beams arearranged between the columns at 100 cm intervals Bracingelements are continuously used throughout the minaretheight Although the only difference between the con-struction techniques of the Tesvikiye Mosque and GullukMosque minarets is the frequency of horizontal beams thestiffness-to-mass ratio of the Tesvikiye Mosque was over 2times than that of the minaret of the Gulluk Mosque -eminaret of the Aga Mosque had the second highest stiffness-to-mass ratio -e outer wall of the Aga Mosque was builtwith timber columns arranged at 15 cm intervals withhorizontal timber beams arranged every 100 cm betweencolumns Additionally a 2 cm thick timber claddingmaterialwas used outside the outer walls -is cladding materialincreased both the stiffness and mass of the structure -eminarets of the Fethiye and Ali Kuzu Mosques had thelowest stiffness-to-mass ratios -e lack of effective usage ofbracing elements and less column usage were the factorsleading to the lowest stiffness-to-mass ratios

-e damping ratio also affects the dynamic behavior-edamping ratios varied between 12 and 20 -e minaret ofthe Aga Mosque had the highest damping ratio of 1967 -eusage of the timber cladding material and steel connectionsled to a high damping ratio however the other minaretshave similar ratios

52 Effect of the Geometrical Properties onDynamic BehaviorMinarets are tall and slender structures therefore theirgeometric properties such as height cross-sectional areaand heightwidth ratio are important regarding the dynamicminaret behavior Minarets behave like cantilevers in whichthe stiffness can be calculated by the formula k 3EIL3where k is the stiffness E is the modulus of elasticity I is themoment of inertia and L is the height In this study withoutnormalization the test results show that the highest minaretshave the lowest frequencies However the effect of height onthe frequency can be seen more clearly by eliminating theother parameters from the frequency Various minarets havesimilar heights therefore the relationship between theheight and frequency can be seen in more detail In Figure 9regression analysis between the height of the minarets andthe normalized frequencies shows that height affects thedynamic minaret behavior

In this study the minaret height-to-width ratios wereinvestigated to determine their effects on the dynamicbehavior minarets have high height-to-width ratios withlow frequencies that are affected by their height andslenderness -e relationship between the normalized

x

yz

Figure 3 -e sensors and their placements on the balcony floor

Shock and Vibration 7

frequencies and slenderness of the studied minarets can beseen in Figure 10

-e cross-sectional area also affects the dynamic prop-erties In the examined minarets the cross-sectional area ofthe Aga Mosque minaret was higher than that of the otherminarets -ese effects are particularly evident and the firstperiod percentage of mass participation was expected to behigher Table 8 shows the mass participation factors thatwere obtained from the numerical analyses It can be seenthat the Aga Mosque minaret has a 75 mass participationfactor in the first mode which is 10 higher than those ofthe other minarets

6 Empirical Formula for Computing theFundamental Frequencies of Minarets

-e construction techniques and the geometrical propertieswere important parameters for understanding the dynamicbehavior of these structures Based on the data collectedfrom the experimental and computational approachesa simple formula was developed to estimate the first fre-quency of vibration

-e fundamental frequency of a minaret is expected to bea function of the moment of inertia the height of theminaret modulus of elasticity cross-sectional area and

ndash60

ndash80

ndash100

ndash120

ndash1400 5 10 15 20 25

f (Hz)

dB |

(lg)2 (H

z)

(a)

0 5 10 15 20 25f (Hz)

ndash60

ndash80

ndash100

ndash120

ndash140

dB |

(lg)2 (H

z)

(b)

0 5 10 15 20 25f (Hz)

ndash60

ndash80

ndash100

ndash120

ndash140

dB |

(lg)2 (H

z)

(c)

0 5 10 15 20 25f (Hz)

ndash60

ndash80

ndash100

ndash120

ndash140

dB |

(lg)2 (H

z)

(d)

0 5 10 15 20 25f (Hz)

ndash60

ndash80

ndash100

ndash120

dB |

(lg)2 (H

z)

(e)

Figure 4-e singular values of the spectral densities of all of the test setups (a) Tesvikiye Mosque minaret (b) Gulluk Mosque minaret (c)Aga Mosque minaret (d) Ali Kuzu Mosque minaret (e) Fethiye Mosque minaret

8 Shock and Vibration

density -e height of the minaret was given by the lengthfrom the top of the pulpit to the base of the spire (body+upper body in Tables 1ndash5) the cross-sectional area and themoment of inertia were calculated by using the base of thebody density and modulus of elasticity which were given bythe data collected from the experimental approaches (Table 6)

Based on the parameters obtained from the experimentaland in situ measurements a new equation was developed fordetermination of the fundamental frequency

f prop middot Hminus32

middot

E middot I

ρ middot A

1113971

(7)

where prop is a constant depending on the constructiontechniques of the outer walls of the minarets H is the heightof the minaret (body + upper body) E is the modulus ofelasticity (parallel to the grain) I is the moment of inertia A

is the cross-sectional area and ρ is the density-e parameter prop was calculated as 015 for the Tesvikiye

and Gulluk Mosque minarets and 010 for the Ali Kuzu Agaand Fethiye Mosque minarets -e Tesvikiye and Gulluk

minarets had similar construction techniques and thedistinctive features of the outer walls were the frequent use ofthe outer columns and the bracing elements (Figure 2Tables 1 and 2) On the contrary the lesser used bracingelements can be seen in the construction of the outer wallsof the Ali Kuzu and Fethiye Mosque minarets (Figure 2Tables 3 and 4) Conversely 2 cm thick timber was used asa cladding material in the construction of the outer walls ofthe Aga Mosque minaret It was observed that the param-eter prop could be taken as 010 as in the Ali Kuzu and FethiyeMosque minarets In Figure 11 the fundamental frequenciesof theminarets obtained from the experimental in situ valuesand Equation (7) were compared with each other -e errorsranged up to a maximum of 9

7 Conclusions

Minarets are sensitive structures that are under lateral forcesand collapse during intense earthquakes and strong winds-ere are few studies regarding the construction techniquesand dynamic behavior of minarets and many studies haveconcentrated on masonry minarets Although reinforcedconcrete minarets are more common than masonry minaretsthey also collapse frequently under lateral forces -ereforethe use of timber in minaret construction has gained im-portance In this study five timber minarets located inSakarya City Turkey were experimentally and computa-tionally investigated to determine the effects of the con-struction techniques and geometric properties of the minaretson their dynamic behavior Ambient vibration tests wereconducted to determine the dynamic characteristics of the

Figure 5 In situ ultrasonic test of timber core (the direct method)

Table 6 -e material properties of the timber elements used in theconstruction of minarets

Mosques

Modulus of elasticity (kNm2)

Unit weight(kNm3)

Parallel tothe grain

Perpendicularto the grain

Indirectmethod Direct method

TesvikiyeMosque 3960000 520000 590

Gulluk Mosque 4520000 530000 583Fethiye Mosque 4010000 450000 587Ali Kuzu Mosque 3520000 420000 592Aga Mosque 5070000 610000 601

Bracingelements

Stairs

Beam

Centercore

Outercolumn

Frameelement

(12 DOF)

Uz UzRz Rz Rx

UxUx

UyUyRyRy

Rx

Figure 6 -e finite element model and DOF system of the GullukMosque minaret

Shock and Vibration 9

minarets Laboratory and in situ ultrasonic tests were per-formed to determine the physical andmaterial properties-efinite element models of the studied five timber minarets wereprepared and modeled with the beam elements having sixdegrees of freedom at every node -e obtained experimentalmodes from in situ tests are controlled using both modalassurance criteria (MAC) table and the complexity plots -elinear elastic material model was assumed forminaret analysisbecause the experimental results for the in situ tests were alsoin the elastic range -e boundary conditions were updateddepending on the experimental results to represent the realbehavior of the minarets Using all data an empirical formulawas derived for the rapid estimation of the fundamental

period of timber minarets -is formula shows that theconstruction technique of the outer wall is as important as thematerial and geometric properties of the minarets -e fre-quent usage of the outer columns at 10 cm intervals andbracing elements in the construction of the outer walls of theGulluk and Tesvikiye Mosques minarets resulted in higherfundamental frequencies than the others On the contrary inthe other minarets the usage of 15 cm outer column intervalsthe usage of timber cladding material in the Aga Mosqueminaret instead of bracing elements and less usage of bracingelements in the Ali Kuzu and FethiyeMosqueminarets are theconstruction differences affecting the dynamic behavior -eformula leads to an upper limit with an error of 9

Y XZ Y XZ Y XZ Y XZ Y XZ Y XZ Y XZ

Mode 1f 118 Hz

Mode 2f 119 Hz

Mode 3f 650 Hz

Mode 4f 651 Hz

Mode 5f 952 Hz

Mode 6f 1466 Hz

Mode 7f 1470 Hz

Figure 7 -e first seven modes and natural frequencies of the Gulluk Mosque minaret

Table 7 First seven modes frequencies (experimental approach versus computational approach)

Mode numberTesvikiye Gulluk Fethiye Ali Kuzu Aga

Exp Comp Exp Comp Exp Comp Exp Comp Exp Comp1 242 246 127 118 093 096 072 078 210 2152 269 247 127 119 105 101 074 079 232 2153 1140 1164 715 650 322 393 371 409 959 10354 1221 1165 724 651 352 396 391 414 969 10455 1370 1375 1030 952 520 502 508 450 1196 11526 2285 2104 1501 1466 815 841 815 794 1213 12587 2307 2121 1502 1470 842 845 842 826 1310 1260Exp experimental approach Comp computational approach

Table 8 -e mass participation factors of the studied minarets

MosquesFirst mode Second mode Sum of first three modes

x y x y x yTesvikiye Mosque 6383 6381 2064 2067 8536 8522Gulluk Mosque 6268 6265 2048 2051 8858 8856Fethiye Mosque 6998 6987 1444 1460 8922 8925Ali Kuzu Mosque 6648 6611 1843 1934 8791 9006Aga Mosque 7507 7478 1193 1222 8730 8820

10 Shock and Vibration

In addition minaret height slenderness and minaretcross-sectional area affect the dynamic behavior of minarets-e frequent usage of horizontal beams in the outer wallconstruction of timber minarets increases the rigidity of thestructure and affects their dynamic behavior -e usage ofsteel connectors provides high damping ratios

In conclusion the construction techniques and geo-metric properties of timber minarets greatly affect theirdynamic behavior Better design criteria development and

retrofitting guideline preparation with a different modelingunder different ground motions and strong winds will helpto ensure better minaret safety

Data Availability

All data generated or analyzed during the study are includedin this paper

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

In this paper the results of a research project carried out bythe authors are utilized supported by Uludag University (noOUAP(MM)-201532)

References

[1] A Dogangun R Acar R Livaoglu and O I Tuluk ldquoPer-formance of masonry minarets against earthquakes and windsin Turkeyrdquo in Proceedings of 1st International Conference on

0

05

1

15

2

25

3

0 50 100 150 200 250

Freq

uenc

y f

Stiffnessmass km

Teşvikiye

Ağa

Guumllluumlk

Fethiye

Ali Kuzu

8 8 8

755

755

755

15 15

520

05

8 15 8 815

55

8 10 8 810

200

8 15 8 8

55

200

15

55

5

8 10 8 810

100

100

Figure 8 -e relationship between the stiffness-to-mass ratios and frequencies

R2 = 0962

0010203040506070809

1

12 13 14 15 16 17 18 19 20

Nor

mal

ized

freq

uenc

y f

Height L

Fethiye

TeşvikiyeAğa

Ali KuzuGuumllluumlk

Figure 9-e relationship between the normalized frequencies andheights

R2=0950

0010203040506070809

1

8 10 12 14 16 18

Nor

mal

ized

freq

uenc

y f

Heightdiameter Ld

Teşvikiye

Ağa

Fethiye

Ali KuzuGuumllluumlk

Figure 10 -e relationship between the normalized frequenciesand heights to diameters

078

191225

096

128

072

21242

093127

000

050

100

150

200

250

300

Ali Kuzu Ağa Teşvikiye Fethiye Guumllluumlk

Firs

t mod

e fre

quen

cy (H

z)

FormulaExperimental

(8)

(9)(7)

(3)(1)

Figure 11 -e fundamental frequencies (formula versus experi-mental results)

Shock and Vibration 11

Restoration of Heritage Masonry Structures P32 pp 1ndash10Cairo Egypt April 2006

[2] K H Kusuzumu ldquoTraditional construction techniques andcurrent restorations of Istanbul minaretsrdquo MSc thesis MimarSinan University Istanbul Turkey 2010 in Turkish

[3] A Dogangun R Acar H Sezen and R Livaoglu ldquoIn-vestigation of dynamic response of masonry minaret struc-turesrdquo Bulletin of Earthquake Engineering vol 6 no 3pp 505ndash517 2008

[4] A Bayraktar A C Altunısık B Sevim T Turker M Akkoseand N Coskun ldquoModal analysis experimental validation andcalibration of a historical masonry minaretrdquo Journal of Testingand Evaluation vol 36 no 6 pp 516ndash524 2008

[5] A Bayraktar B Sevim A C Altunısık and T TurkerldquoAnalytical and operational modal analyses of Turkish stylereinforced concrete minarets for structural identificationrdquoExperimental Techniques vol 33 no 2 pp 65ndash75 2009

[6] A Bayraktar B Sevim A C Altunısık and T TurkerldquoEarthquake analysis of reinforced concrete minarets usingambient vibration test resultsrdquo Structural Design of Tall andSpecial Buildings vol 19 no 3 pp 257ndash273 2010

[7] A Bayraktar A C Altunisik B Sevim and T TurkerldquoSeismic response of a historical masonry minaret usinga finite element model updated with operational modaltestingrdquo Journal of Vibration and Control vol 17 no 1pp 129ndash149 2011

[8] A Sahin A Bayraktar M Ozcan B Sevim A C Altunısıkand T Turker ldquoDynamic field test system identificationand modal validation of a RC minaret pre and postprocessing the wind-induced ambient datardquo Journal ofPerformance of Constructed Facilities vol 25 no 4pp 336ndash556 2011

[9] C S Oliveira E Ccedilaktı D Stengel and M Branco ldquoMinaretbehaviour under earthquake loading the case of historicalIstanbulrdquo Earthquake Engineering amp Structural Dynamicsvol 41 no 1 pp 19ndash39 2012

[10] M A A Motaal ldquoEffect of piles on the seismic response ofmosques minaretsrdquo Ain Shams Engineering Journal vol 5no 1 pp 29ndash40 2014

[11] R Livaoglu M H Basturk A Dogangun and C SerhatogluldquoEffect of geometric properties on dynamic behaviour ofhistoric masonry minaretrdquo KSCE Journal of Civil Engineeringvol 20 no 6 pp 2392ndash2402 2016

[12] A L Che Y He X R Ge T Iwatate and Y Oda ldquoStudy onthe dynamic structural characteristics of an ancient timberYingxian wooden pagodardquo in Proceedings of GeoShanghaiInternational Conference pp 390ndash396 Shanghai China June2006

[13] M Yu Y Oda D Fang and J Zhao ldquoAdvances in structuralmechanics of Chinese ancient architecturesrdquo Frontiers ofArchitecture and Civil Engineering in China vol 2 no 1pp 1ndash25 2008

[14] L Gaile ldquoAnalysis of dynamic parameters of observationtowers in Latviardquo in Proceedings of 9th International Scientificand Practical Conference pp 57ndash62 Rezekne Latvia June2013

[15] A Feldman H Huang W S Chang et al ldquoDynamicproperties of tall timber structures under wind-induced vi-brationrdquo in Proceedings of World Conference on TimberEngineering Vienne Austria August 2016

[16] Y Zhang N Zhang Y Cao andH Xia ldquoA predictionmethodof historical timber buildingsrsquo vibrations induced by trafficloads and its validationrdquo Shock and Vibration vol 2017Article ID 1451483 12 pages 2017

[17] Bogaziccedili University Kandilli Observatory and EarthquakeResearch Institute 2017 httpwwwkoeribounedutrsismo2deprem-bilgileribuyuk-depremler

[18] J S Bendat and A G Piersol Random Data Analysis andMeasurement Procedures Wiley San Francisco CA USA 4thedition 1986

[19] C Raineri G Fabbrocino E Cosenza and G ManfredildquoImplementation of OMA procedures using labview theoryand applicationrdquo in Proceedings of 2nd International Oper-ational Modal Analyses Conference pp 1ndash12 CopenhagenDenmark April-May 2007

[20] OMA Operational Modal Analysis Release 45 StructuralVibration Solution AS Denmark Europe 2016

[21] European Committee for Standardization EN 384-StructuralTimber-Determination of Characteristic Values of MechanicalProperties and Density Office for Official Publications of theEuropean Communities Luxembourg Europe 1995

[22] P B Lourenco A O Feio and J S Machado ldquoChestnut woodin compression perpendicular to the grain non-destructivecorrelations for test results in new and old woodrdquo Con-struction and Building Materials vol 21 no 8 pp 1617ndash16272007

[23] Autodesk Inc Sap 2000 V20 Autodesk Inc San Rafael CAUSA 2017

[24] United States Department of Agriculture Forest ServiceWood Handbook Wood as an Engineering Material UnitedStates Department of Agriculture Forest Service WashingtonDC USA 2010

[25] -ermal expansion coefficients for some common materialsOctober 2017 httpswwwengineeringtoolboxcomlinear-expansion-coefficients-d_95html

12 Shock and Vibration

and the complexity plots -e linear elastic material modelwas assumed for the minaret analysis because the experi-mental results for the in situ tests were also in the elasticrange After the finite element models were prepared themodal analysis of the minarets was performed -e naturalfrequencies mode shapes and mass participation factorswere obtained from numerical analyses -e boundaryconditions were updated depending on the experimentalresults to represent the real behavior of the minarets -ematerial properties were obtained from the test results andother sources [24 25] -e comparison of the seven modesfrequencies of the studied minarets between the experi-mental and computational approaches is presented in Ta-ble 7 -e first four modes are the bending modes the fifthmode is the torsion mode and the sixth and seventh modesare the bending modes When comparing the experimentaland computational results there is a good harmony amongmode shapes and natural frequencies -e errors betweenthe results ranged up to a minimum of 1 to a maximum of10

-e first seven modes and frequencies of one of thestudied minarets obtained frommodal analysis are shown inFigure 7

5 Discussion

51 Effect of Construction Techniques on Dynamic BehaviorMinaret structural systems are based on a circular plan usinga timber core in the center and timber walls on the exterior-e stairs are arranged between the inner core and outerwalls -e main difference in the construction of timberminarets is in the outer wall design -e builders useddifferent design techniques -e outer walls of the studiedfive minarets were also constructed with different tech-niques which play a role in the dynamic behavior -e mainfactors that affect this behavior are the stiffness-to-mass ratioand damping-e relationship between the stiffness-to-mass

ratio and the frequency is determined with the classicalformula f 12π lowast

(km)

1113968 where f is the frequency and m

and k are the mass and stiffness respectively Comparisonsshow that minarets with high stiffness-to-mass ratios alsohave higher frequencies than minarets with low stiffness-to-mass ratios Figure 8 shows the stiffness-to-mass ratios andfrequencies of the studied minarets represented by theirouter walls

-e minarets of the Tesvikiye Mosque have the higheststiffness-to-mass ratio -e timber columns of the outer wallare arranged at 10 cm intervals and the horizontal beams arearranged between the columns at 100 cm intervals Bracingelements are continuously used throughout the minaretheight Although the only difference between the con-struction techniques of the Tesvikiye Mosque and GullukMosque minarets is the frequency of horizontal beams thestiffness-to-mass ratio of the Tesvikiye Mosque was over 2times than that of the minaret of the Gulluk Mosque -eminaret of the Aga Mosque had the second highest stiffness-to-mass ratio -e outer wall of the Aga Mosque was builtwith timber columns arranged at 15 cm intervals withhorizontal timber beams arranged every 100 cm betweencolumns Additionally a 2 cm thick timber claddingmaterialwas used outside the outer walls -is cladding materialincreased both the stiffness and mass of the structure -eminarets of the Fethiye and Ali Kuzu Mosques had thelowest stiffness-to-mass ratios -e lack of effective usage ofbracing elements and less column usage were the factorsleading to the lowest stiffness-to-mass ratios

-e damping ratio also affects the dynamic behavior-edamping ratios varied between 12 and 20 -e minaret ofthe Aga Mosque had the highest damping ratio of 1967 -eusage of the timber cladding material and steel connectionsled to a high damping ratio however the other minaretshave similar ratios

52 Effect of the Geometrical Properties onDynamic BehaviorMinarets are tall and slender structures therefore theirgeometric properties such as height cross-sectional areaand heightwidth ratio are important regarding the dynamicminaret behavior Minarets behave like cantilevers in whichthe stiffness can be calculated by the formula k 3EIL3where k is the stiffness E is the modulus of elasticity I is themoment of inertia and L is the height In this study withoutnormalization the test results show that the highest minaretshave the lowest frequencies However the effect of height onthe frequency can be seen more clearly by eliminating theother parameters from the frequency Various minarets havesimilar heights therefore the relationship between theheight and frequency can be seen in more detail In Figure 9regression analysis between the height of the minarets andthe normalized frequencies shows that height affects thedynamic minaret behavior

In this study the minaret height-to-width ratios wereinvestigated to determine their effects on the dynamicbehavior minarets have high height-to-width ratios withlow frequencies that are affected by their height andslenderness -e relationship between the normalized

x

yz

Figure 3 -e sensors and their placements on the balcony floor

Shock and Vibration 7

frequencies and slenderness of the studied minarets can beseen in Figure 10

-e cross-sectional area also affects the dynamic prop-erties In the examined minarets the cross-sectional area ofthe Aga Mosque minaret was higher than that of the otherminarets -ese effects are particularly evident and the firstperiod percentage of mass participation was expected to behigher Table 8 shows the mass participation factors thatwere obtained from the numerical analyses It can be seenthat the Aga Mosque minaret has a 75 mass participationfactor in the first mode which is 10 higher than those ofthe other minarets

6 Empirical Formula for Computing theFundamental Frequencies of Minarets

-e construction techniques and the geometrical propertieswere important parameters for understanding the dynamicbehavior of these structures Based on the data collectedfrom the experimental and computational approachesa simple formula was developed to estimate the first fre-quency of vibration

-e fundamental frequency of a minaret is expected to bea function of the moment of inertia the height of theminaret modulus of elasticity cross-sectional area and

ndash60

ndash80

ndash100

ndash120

ndash1400 5 10 15 20 25

f (Hz)

dB |

(lg)2 (H

z)

(a)

0 5 10 15 20 25f (Hz)

ndash60

ndash80

ndash100

ndash120

ndash140

dB |

(lg)2 (H

z)

(b)

0 5 10 15 20 25f (Hz)

ndash60

ndash80

ndash100

ndash120

ndash140

dB |

(lg)2 (H

z)

(c)

0 5 10 15 20 25f (Hz)

ndash60

ndash80

ndash100

ndash120

ndash140

dB |

(lg)2 (H

z)

(d)

0 5 10 15 20 25f (Hz)

ndash60

ndash80

ndash100

ndash120

dB |

(lg)2 (H

z)

(e)

Figure 4-e singular values of the spectral densities of all of the test setups (a) Tesvikiye Mosque minaret (b) Gulluk Mosque minaret (c)Aga Mosque minaret (d) Ali Kuzu Mosque minaret (e) Fethiye Mosque minaret

8 Shock and Vibration

density -e height of the minaret was given by the lengthfrom the top of the pulpit to the base of the spire (body+upper body in Tables 1ndash5) the cross-sectional area and themoment of inertia were calculated by using the base of thebody density and modulus of elasticity which were given bythe data collected from the experimental approaches (Table 6)

Based on the parameters obtained from the experimentaland in situ measurements a new equation was developed fordetermination of the fundamental frequency

f prop middot Hminus32

middot

E middot I

ρ middot A

1113971

(7)

where prop is a constant depending on the constructiontechniques of the outer walls of the minarets H is the heightof the minaret (body + upper body) E is the modulus ofelasticity (parallel to the grain) I is the moment of inertia A

is the cross-sectional area and ρ is the density-e parameter prop was calculated as 015 for the Tesvikiye

and Gulluk Mosque minarets and 010 for the Ali Kuzu Agaand Fethiye Mosque minarets -e Tesvikiye and Gulluk

minarets had similar construction techniques and thedistinctive features of the outer walls were the frequent use ofthe outer columns and the bracing elements (Figure 2Tables 1 and 2) On the contrary the lesser used bracingelements can be seen in the construction of the outer wallsof the Ali Kuzu and Fethiye Mosque minarets (Figure 2Tables 3 and 4) Conversely 2 cm thick timber was used asa cladding material in the construction of the outer walls ofthe Aga Mosque minaret It was observed that the param-eter prop could be taken as 010 as in the Ali Kuzu and FethiyeMosque minarets In Figure 11 the fundamental frequenciesof theminarets obtained from the experimental in situ valuesand Equation (7) were compared with each other -e errorsranged up to a maximum of 9

7 Conclusions

Minarets are sensitive structures that are under lateral forcesand collapse during intense earthquakes and strong winds-ere are few studies regarding the construction techniquesand dynamic behavior of minarets and many studies haveconcentrated on masonry minarets Although reinforcedconcrete minarets are more common than masonry minaretsthey also collapse frequently under lateral forces -ereforethe use of timber in minaret construction has gained im-portance In this study five timber minarets located inSakarya City Turkey were experimentally and computa-tionally investigated to determine the effects of the con-struction techniques and geometric properties of the minaretson their dynamic behavior Ambient vibration tests wereconducted to determine the dynamic characteristics of the

Figure 5 In situ ultrasonic test of timber core (the direct method)

Table 6 -e material properties of the timber elements used in theconstruction of minarets

Mosques

Modulus of elasticity (kNm2)

Unit weight(kNm3)

Parallel tothe grain

Perpendicularto the grain

Indirectmethod Direct method

TesvikiyeMosque 3960000 520000 590

Gulluk Mosque 4520000 530000 583Fethiye Mosque 4010000 450000 587Ali Kuzu Mosque 3520000 420000 592Aga Mosque 5070000 610000 601

Bracingelements

Stairs

Beam

Centercore

Outercolumn

Frameelement

(12 DOF)

Uz UzRz Rz Rx

UxUx

UyUyRyRy

Rx

Figure 6 -e finite element model and DOF system of the GullukMosque minaret

Shock and Vibration 9

minarets Laboratory and in situ ultrasonic tests were per-formed to determine the physical andmaterial properties-efinite element models of the studied five timber minarets wereprepared and modeled with the beam elements having sixdegrees of freedom at every node -e obtained experimentalmodes from in situ tests are controlled using both modalassurance criteria (MAC) table and the complexity plots -elinear elastic material model was assumed forminaret analysisbecause the experimental results for the in situ tests were alsoin the elastic range -e boundary conditions were updateddepending on the experimental results to represent the realbehavior of the minarets Using all data an empirical formulawas derived for the rapid estimation of the fundamental

period of timber minarets -is formula shows that theconstruction technique of the outer wall is as important as thematerial and geometric properties of the minarets -e fre-quent usage of the outer columns at 10 cm intervals andbracing elements in the construction of the outer walls of theGulluk and Tesvikiye Mosques minarets resulted in higherfundamental frequencies than the others On the contrary inthe other minarets the usage of 15 cm outer column intervalsthe usage of timber cladding material in the Aga Mosqueminaret instead of bracing elements and less usage of bracingelements in the Ali Kuzu and FethiyeMosqueminarets are theconstruction differences affecting the dynamic behavior -eformula leads to an upper limit with an error of 9

Y XZ Y XZ Y XZ Y XZ Y XZ Y XZ Y XZ

Mode 1f 118 Hz

Mode 2f 119 Hz

Mode 3f 650 Hz

Mode 4f 651 Hz

Mode 5f 952 Hz

Mode 6f 1466 Hz

Mode 7f 1470 Hz

Figure 7 -e first seven modes and natural frequencies of the Gulluk Mosque minaret

Table 7 First seven modes frequencies (experimental approach versus computational approach)

Mode numberTesvikiye Gulluk Fethiye Ali Kuzu Aga

Exp Comp Exp Comp Exp Comp Exp Comp Exp Comp1 242 246 127 118 093 096 072 078 210 2152 269 247 127 119 105 101 074 079 232 2153 1140 1164 715 650 322 393 371 409 959 10354 1221 1165 724 651 352 396 391 414 969 10455 1370 1375 1030 952 520 502 508 450 1196 11526 2285 2104 1501 1466 815 841 815 794 1213 12587 2307 2121 1502 1470 842 845 842 826 1310 1260Exp experimental approach Comp computational approach

Table 8 -e mass participation factors of the studied minarets

MosquesFirst mode Second mode Sum of first three modes

x y x y x yTesvikiye Mosque 6383 6381 2064 2067 8536 8522Gulluk Mosque 6268 6265 2048 2051 8858 8856Fethiye Mosque 6998 6987 1444 1460 8922 8925Ali Kuzu Mosque 6648 6611 1843 1934 8791 9006Aga Mosque 7507 7478 1193 1222 8730 8820

10 Shock and Vibration

In addition minaret height slenderness and minaretcross-sectional area affect the dynamic behavior of minarets-e frequent usage of horizontal beams in the outer wallconstruction of timber minarets increases the rigidity of thestructure and affects their dynamic behavior -e usage ofsteel connectors provides high damping ratios

In conclusion the construction techniques and geo-metric properties of timber minarets greatly affect theirdynamic behavior Better design criteria development and

retrofitting guideline preparation with a different modelingunder different ground motions and strong winds will helpto ensure better minaret safety

Data Availability

All data generated or analyzed during the study are includedin this paper

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

In this paper the results of a research project carried out bythe authors are utilized supported by Uludag University (noOUAP(MM)-201532)

References

[1] A Dogangun R Acar R Livaoglu and O I Tuluk ldquoPer-formance of masonry minarets against earthquakes and windsin Turkeyrdquo in Proceedings of 1st International Conference on

0

05

1

15

2

25

3

0 50 100 150 200 250

Freq

uenc

y f

Stiffnessmass km

Teşvikiye

Ağa

Guumllluumlk

Fethiye

Ali Kuzu

8 8 8

755

755

755

15 15

520

05

8 15 8 815

55

8 10 8 810

200

8 15 8 8

55

200

15

55

5

8 10 8 810

100

100

Figure 8 -e relationship between the stiffness-to-mass ratios and frequencies

R2 = 0962

0010203040506070809

1

12 13 14 15 16 17 18 19 20

Nor

mal

ized

freq

uenc

y f

Height L

Fethiye

TeşvikiyeAğa

Ali KuzuGuumllluumlk

Figure 9-e relationship between the normalized frequencies andheights

R2=0950

0010203040506070809

1

8 10 12 14 16 18

Nor

mal

ized

freq

uenc

y f

Heightdiameter Ld

Teşvikiye

Ağa

Fethiye

Ali KuzuGuumllluumlk

Figure 10 -e relationship between the normalized frequenciesand heights to diameters

078

191225

096

128

072

21242

093127

000

050

100

150

200

250

300

Ali Kuzu Ağa Teşvikiye Fethiye Guumllluumlk

Firs

t mod

e fre

quen

cy (H

z)

FormulaExperimental

(8)

(9)(7)

(3)(1)

Figure 11 -e fundamental frequencies (formula versus experi-mental results)

Shock and Vibration 11

Restoration of Heritage Masonry Structures P32 pp 1ndash10Cairo Egypt April 2006

[2] K H Kusuzumu ldquoTraditional construction techniques andcurrent restorations of Istanbul minaretsrdquo MSc thesis MimarSinan University Istanbul Turkey 2010 in Turkish

[3] A Dogangun R Acar H Sezen and R Livaoglu ldquoIn-vestigation of dynamic response of masonry minaret struc-turesrdquo Bulletin of Earthquake Engineering vol 6 no 3pp 505ndash517 2008

[4] A Bayraktar A C Altunısık B Sevim T Turker M Akkoseand N Coskun ldquoModal analysis experimental validation andcalibration of a historical masonry minaretrdquo Journal of Testingand Evaluation vol 36 no 6 pp 516ndash524 2008

[5] A Bayraktar B Sevim A C Altunısık and T TurkerldquoAnalytical and operational modal analyses of Turkish stylereinforced concrete minarets for structural identificationrdquoExperimental Techniques vol 33 no 2 pp 65ndash75 2009

[6] A Bayraktar B Sevim A C Altunısık and T TurkerldquoEarthquake analysis of reinforced concrete minarets usingambient vibration test resultsrdquo Structural Design of Tall andSpecial Buildings vol 19 no 3 pp 257ndash273 2010

[7] A Bayraktar A C Altunisik B Sevim and T TurkerldquoSeismic response of a historical masonry minaret usinga finite element model updated with operational modaltestingrdquo Journal of Vibration and Control vol 17 no 1pp 129ndash149 2011

[8] A Sahin A Bayraktar M Ozcan B Sevim A C Altunısıkand T Turker ldquoDynamic field test system identificationand modal validation of a RC minaret pre and postprocessing the wind-induced ambient datardquo Journal ofPerformance of Constructed Facilities vol 25 no 4pp 336ndash556 2011

[9] C S Oliveira E Ccedilaktı D Stengel and M Branco ldquoMinaretbehaviour under earthquake loading the case of historicalIstanbulrdquo Earthquake Engineering amp Structural Dynamicsvol 41 no 1 pp 19ndash39 2012

[10] M A A Motaal ldquoEffect of piles on the seismic response ofmosques minaretsrdquo Ain Shams Engineering Journal vol 5no 1 pp 29ndash40 2014

[11] R Livaoglu M H Basturk A Dogangun and C SerhatogluldquoEffect of geometric properties on dynamic behaviour ofhistoric masonry minaretrdquo KSCE Journal of Civil Engineeringvol 20 no 6 pp 2392ndash2402 2016

[12] A L Che Y He X R Ge T Iwatate and Y Oda ldquoStudy onthe dynamic structural characteristics of an ancient timberYingxian wooden pagodardquo in Proceedings of GeoShanghaiInternational Conference pp 390ndash396 Shanghai China June2006

[13] M Yu Y Oda D Fang and J Zhao ldquoAdvances in structuralmechanics of Chinese ancient architecturesrdquo Frontiers ofArchitecture and Civil Engineering in China vol 2 no 1pp 1ndash25 2008

[14] L Gaile ldquoAnalysis of dynamic parameters of observationtowers in Latviardquo in Proceedings of 9th International Scientificand Practical Conference pp 57ndash62 Rezekne Latvia June2013

[15] A Feldman H Huang W S Chang et al ldquoDynamicproperties of tall timber structures under wind-induced vi-brationrdquo in Proceedings of World Conference on TimberEngineering Vienne Austria August 2016

[16] Y Zhang N Zhang Y Cao andH Xia ldquoA predictionmethodof historical timber buildingsrsquo vibrations induced by trafficloads and its validationrdquo Shock and Vibration vol 2017Article ID 1451483 12 pages 2017

[17] Bogaziccedili University Kandilli Observatory and EarthquakeResearch Institute 2017 httpwwwkoeribounedutrsismo2deprem-bilgileribuyuk-depremler

[18] J S Bendat and A G Piersol Random Data Analysis andMeasurement Procedures Wiley San Francisco CA USA 4thedition 1986

[19] C Raineri G Fabbrocino E Cosenza and G ManfredildquoImplementation of OMA procedures using labview theoryand applicationrdquo in Proceedings of 2nd International Oper-ational Modal Analyses Conference pp 1ndash12 CopenhagenDenmark April-May 2007

[20] OMA Operational Modal Analysis Release 45 StructuralVibration Solution AS Denmark Europe 2016

[21] European Committee for Standardization EN 384-StructuralTimber-Determination of Characteristic Values of MechanicalProperties and Density Office for Official Publications of theEuropean Communities Luxembourg Europe 1995

[22] P B Lourenco A O Feio and J S Machado ldquoChestnut woodin compression perpendicular to the grain non-destructivecorrelations for test results in new and old woodrdquo Con-struction and Building Materials vol 21 no 8 pp 1617ndash16272007

[23] Autodesk Inc Sap 2000 V20 Autodesk Inc San Rafael CAUSA 2017

[24] United States Department of Agriculture Forest ServiceWood Handbook Wood as an Engineering Material UnitedStates Department of Agriculture Forest Service WashingtonDC USA 2010

[25] -ermal expansion coefficients for some common materialsOctober 2017 httpswwwengineeringtoolboxcomlinear-expansion-coefficients-d_95html

12 Shock and Vibration

frequencies and slenderness of the studied minarets can beseen in Figure 10

-e cross-sectional area also affects the dynamic prop-erties In the examined minarets the cross-sectional area ofthe Aga Mosque minaret was higher than that of the otherminarets -ese effects are particularly evident and the firstperiod percentage of mass participation was expected to behigher Table 8 shows the mass participation factors thatwere obtained from the numerical analyses It can be seenthat the Aga Mosque minaret has a 75 mass participationfactor in the first mode which is 10 higher than those ofthe other minarets

6 Empirical Formula for Computing theFundamental Frequencies of Minarets

-e construction techniques and the geometrical propertieswere important parameters for understanding the dynamicbehavior of these structures Based on the data collectedfrom the experimental and computational approachesa simple formula was developed to estimate the first fre-quency of vibration

-e fundamental frequency of a minaret is expected to bea function of the moment of inertia the height of theminaret modulus of elasticity cross-sectional area and

ndash60

ndash80

ndash100

ndash120

ndash1400 5 10 15 20 25

f (Hz)

dB |

(lg)2 (H

z)

(a)

0 5 10 15 20 25f (Hz)

ndash60

ndash80

ndash100

ndash120

ndash140

dB |

(lg)2 (H

z)

(b)

0 5 10 15 20 25f (Hz)

ndash60

ndash80

ndash100

ndash120

ndash140

dB |

(lg)2 (H

z)

(c)

0 5 10 15 20 25f (Hz)

ndash60

ndash80

ndash100

ndash120

ndash140

dB |

(lg)2 (H

z)

(d)

0 5 10 15 20 25f (Hz)

ndash60

ndash80

ndash100

ndash120

dB |

(lg)2 (H

z)

(e)

Figure 4-e singular values of the spectral densities of all of the test setups (a) Tesvikiye Mosque minaret (b) Gulluk Mosque minaret (c)Aga Mosque minaret (d) Ali Kuzu Mosque minaret (e) Fethiye Mosque minaret

8 Shock and Vibration

density -e height of the minaret was given by the lengthfrom the top of the pulpit to the base of the spire (body+upper body in Tables 1ndash5) the cross-sectional area and themoment of inertia were calculated by using the base of thebody density and modulus of elasticity which were given bythe data collected from the experimental approaches (Table 6)

Based on the parameters obtained from the experimentaland in situ measurements a new equation was developed fordetermination of the fundamental frequency

f prop middot Hminus32

middot

E middot I

ρ middot A

1113971

(7)

where prop is a constant depending on the constructiontechniques of the outer walls of the minarets H is the heightof the minaret (body + upper body) E is the modulus ofelasticity (parallel to the grain) I is the moment of inertia A

is the cross-sectional area and ρ is the density-e parameter prop was calculated as 015 for the Tesvikiye

and Gulluk Mosque minarets and 010 for the Ali Kuzu Agaand Fethiye Mosque minarets -e Tesvikiye and Gulluk

minarets had similar construction techniques and thedistinctive features of the outer walls were the frequent use ofthe outer columns and the bracing elements (Figure 2Tables 1 and 2) On the contrary the lesser used bracingelements can be seen in the construction of the outer wallsof the Ali Kuzu and Fethiye Mosque minarets (Figure 2Tables 3 and 4) Conversely 2 cm thick timber was used asa cladding material in the construction of the outer walls ofthe Aga Mosque minaret It was observed that the param-eter prop could be taken as 010 as in the Ali Kuzu and FethiyeMosque minarets In Figure 11 the fundamental frequenciesof theminarets obtained from the experimental in situ valuesand Equation (7) were compared with each other -e errorsranged up to a maximum of 9

7 Conclusions

Minarets are sensitive structures that are under lateral forcesand collapse during intense earthquakes and strong winds-ere are few studies regarding the construction techniquesand dynamic behavior of minarets and many studies haveconcentrated on masonry minarets Although reinforcedconcrete minarets are more common than masonry minaretsthey also collapse frequently under lateral forces -ereforethe use of timber in minaret construction has gained im-portance In this study five timber minarets located inSakarya City Turkey were experimentally and computa-tionally investigated to determine the effects of the con-struction techniques and geometric properties of the minaretson their dynamic behavior Ambient vibration tests wereconducted to determine the dynamic characteristics of the

Figure 5 In situ ultrasonic test of timber core (the direct method)

Table 6 -e material properties of the timber elements used in theconstruction of minarets

Mosques

Modulus of elasticity (kNm2)

Unit weight(kNm3)

Parallel tothe grain

Perpendicularto the grain

Indirectmethod Direct method

TesvikiyeMosque 3960000 520000 590

Gulluk Mosque 4520000 530000 583Fethiye Mosque 4010000 450000 587Ali Kuzu Mosque 3520000 420000 592Aga Mosque 5070000 610000 601

Bracingelements

Stairs

Beam

Centercore

Outercolumn

Frameelement

(12 DOF)

Uz UzRz Rz Rx

UxUx

UyUyRyRy

Rx

Figure 6 -e finite element model and DOF system of the GullukMosque minaret

Shock and Vibration 9

minarets Laboratory and in situ ultrasonic tests were per-formed to determine the physical andmaterial properties-efinite element models of the studied five timber minarets wereprepared and modeled with the beam elements having sixdegrees of freedom at every node -e obtained experimentalmodes from in situ tests are controlled using both modalassurance criteria (MAC) table and the complexity plots -elinear elastic material model was assumed forminaret analysisbecause the experimental results for the in situ tests were alsoin the elastic range -e boundary conditions were updateddepending on the experimental results to represent the realbehavior of the minarets Using all data an empirical formulawas derived for the rapid estimation of the fundamental

period of timber minarets -is formula shows that theconstruction technique of the outer wall is as important as thematerial and geometric properties of the minarets -e fre-quent usage of the outer columns at 10 cm intervals andbracing elements in the construction of the outer walls of theGulluk and Tesvikiye Mosques minarets resulted in higherfundamental frequencies than the others On the contrary inthe other minarets the usage of 15 cm outer column intervalsthe usage of timber cladding material in the Aga Mosqueminaret instead of bracing elements and less usage of bracingelements in the Ali Kuzu and FethiyeMosqueminarets are theconstruction differences affecting the dynamic behavior -eformula leads to an upper limit with an error of 9

Y XZ Y XZ Y XZ Y XZ Y XZ Y XZ Y XZ

Mode 1f 118 Hz

Mode 2f 119 Hz

Mode 3f 650 Hz

Mode 4f 651 Hz

Mode 5f 952 Hz

Mode 6f 1466 Hz

Mode 7f 1470 Hz

Figure 7 -e first seven modes and natural frequencies of the Gulluk Mosque minaret

Table 7 First seven modes frequencies (experimental approach versus computational approach)

Mode numberTesvikiye Gulluk Fethiye Ali Kuzu Aga

Exp Comp Exp Comp Exp Comp Exp Comp Exp Comp1 242 246 127 118 093 096 072 078 210 2152 269 247 127 119 105 101 074 079 232 2153 1140 1164 715 650 322 393 371 409 959 10354 1221 1165 724 651 352 396 391 414 969 10455 1370 1375 1030 952 520 502 508 450 1196 11526 2285 2104 1501 1466 815 841 815 794 1213 12587 2307 2121 1502 1470 842 845 842 826 1310 1260Exp experimental approach Comp computational approach

Table 8 -e mass participation factors of the studied minarets

MosquesFirst mode Second mode Sum of first three modes

x y x y x yTesvikiye Mosque 6383 6381 2064 2067 8536 8522Gulluk Mosque 6268 6265 2048 2051 8858 8856Fethiye Mosque 6998 6987 1444 1460 8922 8925Ali Kuzu Mosque 6648 6611 1843 1934 8791 9006Aga Mosque 7507 7478 1193 1222 8730 8820

10 Shock and Vibration

In addition minaret height slenderness and minaretcross-sectional area affect the dynamic behavior of minarets-e frequent usage of horizontal beams in the outer wallconstruction of timber minarets increases the rigidity of thestructure and affects their dynamic behavior -e usage ofsteel connectors provides high damping ratios

In conclusion the construction techniques and geo-metric properties of timber minarets greatly affect theirdynamic behavior Better design criteria development and

retrofitting guideline preparation with a different modelingunder different ground motions and strong winds will helpto ensure better minaret safety

Data Availability

All data generated or analyzed during the study are includedin this paper

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

In this paper the results of a research project carried out bythe authors are utilized supported by Uludag University (noOUAP(MM)-201532)

References

[1] A Dogangun R Acar R Livaoglu and O I Tuluk ldquoPer-formance of masonry minarets against earthquakes and windsin Turkeyrdquo in Proceedings of 1st International Conference on

0

05

1

15

2

25

3

0 50 100 150 200 250

Freq

uenc

y f

Stiffnessmass km

Teşvikiye

Ağa

Guumllluumlk

Fethiye

Ali Kuzu

8 8 8

755

755

755

15 15

520

05

8 15 8 815

55

8 10 8 810

200

8 15 8 8

55

200

15

55

5

8 10 8 810

100

100

Figure 8 -e relationship between the stiffness-to-mass ratios and frequencies

R2 = 0962

0010203040506070809

1

12 13 14 15 16 17 18 19 20

Nor

mal

ized

freq

uenc

y f

Height L

Fethiye

TeşvikiyeAğa

Ali KuzuGuumllluumlk

Figure 9-e relationship between the normalized frequencies andheights

R2=0950

0010203040506070809

1

8 10 12 14 16 18

Nor

mal

ized

freq

uenc

y f

Heightdiameter Ld

Teşvikiye

Ağa

Fethiye

Ali KuzuGuumllluumlk

Figure 10 -e relationship between the normalized frequenciesand heights to diameters

078

191225

096

128

072

21242

093127

000

050

100

150

200

250

300

Ali Kuzu Ağa Teşvikiye Fethiye Guumllluumlk

Firs

t mod

e fre

quen

cy (H

z)

FormulaExperimental

(8)

(9)(7)

(3)(1)

Figure 11 -e fundamental frequencies (formula versus experi-mental results)

Shock and Vibration 11

Restoration of Heritage Masonry Structures P32 pp 1ndash10Cairo Egypt April 2006

[2] K H Kusuzumu ldquoTraditional construction techniques andcurrent restorations of Istanbul minaretsrdquo MSc thesis MimarSinan University Istanbul Turkey 2010 in Turkish

[3] A Dogangun R Acar H Sezen and R Livaoglu ldquoIn-vestigation of dynamic response of masonry minaret struc-turesrdquo Bulletin of Earthquake Engineering vol 6 no 3pp 505ndash517 2008

[4] A Bayraktar A C Altunısık B Sevim T Turker M Akkoseand N Coskun ldquoModal analysis experimental validation andcalibration of a historical masonry minaretrdquo Journal of Testingand Evaluation vol 36 no 6 pp 516ndash524 2008

[5] A Bayraktar B Sevim A C Altunısık and T TurkerldquoAnalytical and operational modal analyses of Turkish stylereinforced concrete minarets for structural identificationrdquoExperimental Techniques vol 33 no 2 pp 65ndash75 2009

[6] A Bayraktar B Sevim A C Altunısık and T TurkerldquoEarthquake analysis of reinforced concrete minarets usingambient vibration test resultsrdquo Structural Design of Tall andSpecial Buildings vol 19 no 3 pp 257ndash273 2010

[7] A Bayraktar A C Altunisik B Sevim and T TurkerldquoSeismic response of a historical masonry minaret usinga finite element model updated with operational modaltestingrdquo Journal of Vibration and Control vol 17 no 1pp 129ndash149 2011

[8] A Sahin A Bayraktar M Ozcan B Sevim A C Altunısıkand T Turker ldquoDynamic field test system identificationand modal validation of a RC minaret pre and postprocessing the wind-induced ambient datardquo Journal ofPerformance of Constructed Facilities vol 25 no 4pp 336ndash556 2011

[9] C S Oliveira E Ccedilaktı D Stengel and M Branco ldquoMinaretbehaviour under earthquake loading the case of historicalIstanbulrdquo Earthquake Engineering amp Structural Dynamicsvol 41 no 1 pp 19ndash39 2012

[10] M A A Motaal ldquoEffect of piles on the seismic response ofmosques minaretsrdquo Ain Shams Engineering Journal vol 5no 1 pp 29ndash40 2014

[11] R Livaoglu M H Basturk A Dogangun and C SerhatogluldquoEffect of geometric properties on dynamic behaviour ofhistoric masonry minaretrdquo KSCE Journal of Civil Engineeringvol 20 no 6 pp 2392ndash2402 2016

[12] A L Che Y He X R Ge T Iwatate and Y Oda ldquoStudy onthe dynamic structural characteristics of an ancient timberYingxian wooden pagodardquo in Proceedings of GeoShanghaiInternational Conference pp 390ndash396 Shanghai China June2006

[13] M Yu Y Oda D Fang and J Zhao ldquoAdvances in structuralmechanics of Chinese ancient architecturesrdquo Frontiers ofArchitecture and Civil Engineering in China vol 2 no 1pp 1ndash25 2008

[14] L Gaile ldquoAnalysis of dynamic parameters of observationtowers in Latviardquo in Proceedings of 9th International Scientificand Practical Conference pp 57ndash62 Rezekne Latvia June2013

[15] A Feldman H Huang W S Chang et al ldquoDynamicproperties of tall timber structures under wind-induced vi-brationrdquo in Proceedings of World Conference on TimberEngineering Vienne Austria August 2016

[16] Y Zhang N Zhang Y Cao andH Xia ldquoA predictionmethodof historical timber buildingsrsquo vibrations induced by trafficloads and its validationrdquo Shock and Vibration vol 2017Article ID 1451483 12 pages 2017

[17] Bogaziccedili University Kandilli Observatory and EarthquakeResearch Institute 2017 httpwwwkoeribounedutrsismo2deprem-bilgileribuyuk-depremler

[18] J S Bendat and A G Piersol Random Data Analysis andMeasurement Procedures Wiley San Francisco CA USA 4thedition 1986

[19] C Raineri G Fabbrocino E Cosenza and G ManfredildquoImplementation of OMA procedures using labview theoryand applicationrdquo in Proceedings of 2nd International Oper-ational Modal Analyses Conference pp 1ndash12 CopenhagenDenmark April-May 2007

[20] OMA Operational Modal Analysis Release 45 StructuralVibration Solution AS Denmark Europe 2016

[21] European Committee for Standardization EN 384-StructuralTimber-Determination of Characteristic Values of MechanicalProperties and Density Office for Official Publications of theEuropean Communities Luxembourg Europe 1995

[22] P B Lourenco A O Feio and J S Machado ldquoChestnut woodin compression perpendicular to the grain non-destructivecorrelations for test results in new and old woodrdquo Con-struction and Building Materials vol 21 no 8 pp 1617ndash16272007

[23] Autodesk Inc Sap 2000 V20 Autodesk Inc San Rafael CAUSA 2017

[24] United States Department of Agriculture Forest ServiceWood Handbook Wood as an Engineering Material UnitedStates Department of Agriculture Forest Service WashingtonDC USA 2010

[25] -ermal expansion coefficients for some common materialsOctober 2017 httpswwwengineeringtoolboxcomlinear-expansion-coefficients-d_95html

12 Shock and Vibration

density -e height of the minaret was given by the lengthfrom the top of the pulpit to the base of the spire (body+upper body in Tables 1ndash5) the cross-sectional area and themoment of inertia were calculated by using the base of thebody density and modulus of elasticity which were given bythe data collected from the experimental approaches (Table 6)

Based on the parameters obtained from the experimentaland in situ measurements a new equation was developed fordetermination of the fundamental frequency

f prop middot Hminus32

middot

E middot I

ρ middot A

1113971

(7)

where prop is a constant depending on the constructiontechniques of the outer walls of the minarets H is the heightof the minaret (body + upper body) E is the modulus ofelasticity (parallel to the grain) I is the moment of inertia A

is the cross-sectional area and ρ is the density-e parameter prop was calculated as 015 for the Tesvikiye

and Gulluk Mosque minarets and 010 for the Ali Kuzu Agaand Fethiye Mosque minarets -e Tesvikiye and Gulluk

minarets had similar construction techniques and thedistinctive features of the outer walls were the frequent use ofthe outer columns and the bracing elements (Figure 2Tables 1 and 2) On the contrary the lesser used bracingelements can be seen in the construction of the outer wallsof the Ali Kuzu and Fethiye Mosque minarets (Figure 2Tables 3 and 4) Conversely 2 cm thick timber was used asa cladding material in the construction of the outer walls ofthe Aga Mosque minaret It was observed that the param-eter prop could be taken as 010 as in the Ali Kuzu and FethiyeMosque minarets In Figure 11 the fundamental frequenciesof theminarets obtained from the experimental in situ valuesand Equation (7) were compared with each other -e errorsranged up to a maximum of 9

7 Conclusions

Minarets are sensitive structures that are under lateral forcesand collapse during intense earthquakes and strong winds-ere are few studies regarding the construction techniquesand dynamic behavior of minarets and many studies haveconcentrated on masonry minarets Although reinforcedconcrete minarets are more common than masonry minaretsthey also collapse frequently under lateral forces -ereforethe use of timber in minaret construction has gained im-portance In this study five timber minarets located inSakarya City Turkey were experimentally and computa-tionally investigated to determine the effects of the con-struction techniques and geometric properties of the minaretson their dynamic behavior Ambient vibration tests wereconducted to determine the dynamic characteristics of the

Figure 5 In situ ultrasonic test of timber core (the direct method)

Table 6 -e material properties of the timber elements used in theconstruction of minarets

Mosques

Modulus of elasticity (kNm2)

Unit weight(kNm3)

Parallel tothe grain

Perpendicularto the grain

Indirectmethod Direct method

TesvikiyeMosque 3960000 520000 590

Gulluk Mosque 4520000 530000 583Fethiye Mosque 4010000 450000 587Ali Kuzu Mosque 3520000 420000 592Aga Mosque 5070000 610000 601

Bracingelements

Stairs

Beam

Centercore

Outercolumn

Frameelement

(12 DOF)

Uz UzRz Rz Rx

UxUx

UyUyRyRy

Rx

Figure 6 -e finite element model and DOF system of the GullukMosque minaret

Shock and Vibration 9

minarets Laboratory and in situ ultrasonic tests were per-formed to determine the physical andmaterial properties-efinite element models of the studied five timber minarets wereprepared and modeled with the beam elements having sixdegrees of freedom at every node -e obtained experimentalmodes from in situ tests are controlled using both modalassurance criteria (MAC) table and the complexity plots -elinear elastic material model was assumed forminaret analysisbecause the experimental results for the in situ tests were alsoin the elastic range -e boundary conditions were updateddepending on the experimental results to represent the realbehavior of the minarets Using all data an empirical formulawas derived for the rapid estimation of the fundamental

period of timber minarets -is formula shows that theconstruction technique of the outer wall is as important as thematerial and geometric properties of the minarets -e fre-quent usage of the outer columns at 10 cm intervals andbracing elements in the construction of the outer walls of theGulluk and Tesvikiye Mosques minarets resulted in higherfundamental frequencies than the others On the contrary inthe other minarets the usage of 15 cm outer column intervalsthe usage of timber cladding material in the Aga Mosqueminaret instead of bracing elements and less usage of bracingelements in the Ali Kuzu and FethiyeMosqueminarets are theconstruction differences affecting the dynamic behavior -eformula leads to an upper limit with an error of 9

Y XZ Y XZ Y XZ Y XZ Y XZ Y XZ Y XZ

Mode 1f 118 Hz

Mode 2f 119 Hz

Mode 3f 650 Hz

Mode 4f 651 Hz

Mode 5f 952 Hz

Mode 6f 1466 Hz

Mode 7f 1470 Hz

Figure 7 -e first seven modes and natural frequencies of the Gulluk Mosque minaret

Table 7 First seven modes frequencies (experimental approach versus computational approach)

Mode numberTesvikiye Gulluk Fethiye Ali Kuzu Aga

Exp Comp Exp Comp Exp Comp Exp Comp Exp Comp1 242 246 127 118 093 096 072 078 210 2152 269 247 127 119 105 101 074 079 232 2153 1140 1164 715 650 322 393 371 409 959 10354 1221 1165 724 651 352 396 391 414 969 10455 1370 1375 1030 952 520 502 508 450 1196 11526 2285 2104 1501 1466 815 841 815 794 1213 12587 2307 2121 1502 1470 842 845 842 826 1310 1260Exp experimental approach Comp computational approach

Table 8 -e mass participation factors of the studied minarets

MosquesFirst mode Second mode Sum of first three modes

x y x y x yTesvikiye Mosque 6383 6381 2064 2067 8536 8522Gulluk Mosque 6268 6265 2048 2051 8858 8856Fethiye Mosque 6998 6987 1444 1460 8922 8925Ali Kuzu Mosque 6648 6611 1843 1934 8791 9006Aga Mosque 7507 7478 1193 1222 8730 8820

10 Shock and Vibration

In addition minaret height slenderness and minaretcross-sectional area affect the dynamic behavior of minarets-e frequent usage of horizontal beams in the outer wallconstruction of timber minarets increases the rigidity of thestructure and affects their dynamic behavior -e usage ofsteel connectors provides high damping ratios

In conclusion the construction techniques and geo-metric properties of timber minarets greatly affect theirdynamic behavior Better design criteria development and

retrofitting guideline preparation with a different modelingunder different ground motions and strong winds will helpto ensure better minaret safety

Data Availability

All data generated or analyzed during the study are includedin this paper

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

In this paper the results of a research project carried out bythe authors are utilized supported by Uludag University (noOUAP(MM)-201532)

References

[1] A Dogangun R Acar R Livaoglu and O I Tuluk ldquoPer-formance of masonry minarets against earthquakes and windsin Turkeyrdquo in Proceedings of 1st International Conference on

0

05

1

15

2

25

3

0 50 100 150 200 250

Freq

uenc

y f

Stiffnessmass km

Teşvikiye

Ağa

Guumllluumlk

Fethiye

Ali Kuzu

8 8 8

755

755

755

15 15

520

05

8 15 8 815

55

8 10 8 810

200

8 15 8 8

55

200

15

55

5

8 10 8 810

100

100

Figure 8 -e relationship between the stiffness-to-mass ratios and frequencies

R2 = 0962

0010203040506070809

1

12 13 14 15 16 17 18 19 20

Nor

mal

ized

freq

uenc

y f

Height L

Fethiye

TeşvikiyeAğa

Ali KuzuGuumllluumlk

Figure 9-e relationship between the normalized frequencies andheights

R2=0950

0010203040506070809

1

8 10 12 14 16 18

Nor

mal

ized

freq

uenc

y f

Heightdiameter Ld

Teşvikiye

Ağa

Fethiye

Ali KuzuGuumllluumlk

Figure 10 -e relationship between the normalized frequenciesand heights to diameters

078

191225

096

128

072

21242

093127

000

050

100

150

200

250

300

Ali Kuzu Ağa Teşvikiye Fethiye Guumllluumlk

Firs

t mod

e fre

quen

cy (H

z)

FormulaExperimental

(8)

(9)(7)

(3)(1)

Figure 11 -e fundamental frequencies (formula versus experi-mental results)

Shock and Vibration 11

Restoration of Heritage Masonry Structures P32 pp 1ndash10Cairo Egypt April 2006

[2] K H Kusuzumu ldquoTraditional construction techniques andcurrent restorations of Istanbul minaretsrdquo MSc thesis MimarSinan University Istanbul Turkey 2010 in Turkish

[3] A Dogangun R Acar H Sezen and R Livaoglu ldquoIn-vestigation of dynamic response of masonry minaret struc-turesrdquo Bulletin of Earthquake Engineering vol 6 no 3pp 505ndash517 2008

[4] A Bayraktar A C Altunısık B Sevim T Turker M Akkoseand N Coskun ldquoModal analysis experimental validation andcalibration of a historical masonry minaretrdquo Journal of Testingand Evaluation vol 36 no 6 pp 516ndash524 2008

[5] A Bayraktar B Sevim A C Altunısık and T TurkerldquoAnalytical and operational modal analyses of Turkish stylereinforced concrete minarets for structural identificationrdquoExperimental Techniques vol 33 no 2 pp 65ndash75 2009

[6] A Bayraktar B Sevim A C Altunısık and T TurkerldquoEarthquake analysis of reinforced concrete minarets usingambient vibration test resultsrdquo Structural Design of Tall andSpecial Buildings vol 19 no 3 pp 257ndash273 2010

[7] A Bayraktar A C Altunisik B Sevim and T TurkerldquoSeismic response of a historical masonry minaret usinga finite element model updated with operational modaltestingrdquo Journal of Vibration and Control vol 17 no 1pp 129ndash149 2011

[8] A Sahin A Bayraktar M Ozcan B Sevim A C Altunısıkand T Turker ldquoDynamic field test system identificationand modal validation of a RC minaret pre and postprocessing the wind-induced ambient datardquo Journal ofPerformance of Constructed Facilities vol 25 no 4pp 336ndash556 2011

[9] C S Oliveira E Ccedilaktı D Stengel and M Branco ldquoMinaretbehaviour under earthquake loading the case of historicalIstanbulrdquo Earthquake Engineering amp Structural Dynamicsvol 41 no 1 pp 19ndash39 2012

[10] M A A Motaal ldquoEffect of piles on the seismic response ofmosques minaretsrdquo Ain Shams Engineering Journal vol 5no 1 pp 29ndash40 2014

[11] R Livaoglu M H Basturk A Dogangun and C SerhatogluldquoEffect of geometric properties on dynamic behaviour ofhistoric masonry minaretrdquo KSCE Journal of Civil Engineeringvol 20 no 6 pp 2392ndash2402 2016

[12] A L Che Y He X R Ge T Iwatate and Y Oda ldquoStudy onthe dynamic structural characteristics of an ancient timberYingxian wooden pagodardquo in Proceedings of GeoShanghaiInternational Conference pp 390ndash396 Shanghai China June2006

[13] M Yu Y Oda D Fang and J Zhao ldquoAdvances in structuralmechanics of Chinese ancient architecturesrdquo Frontiers ofArchitecture and Civil Engineering in China vol 2 no 1pp 1ndash25 2008

[14] L Gaile ldquoAnalysis of dynamic parameters of observationtowers in Latviardquo in Proceedings of 9th International Scientificand Practical Conference pp 57ndash62 Rezekne Latvia June2013

[15] A Feldman H Huang W S Chang et al ldquoDynamicproperties of tall timber structures under wind-induced vi-brationrdquo in Proceedings of World Conference on TimberEngineering Vienne Austria August 2016

[16] Y Zhang N Zhang Y Cao andH Xia ldquoA predictionmethodof historical timber buildingsrsquo vibrations induced by trafficloads and its validationrdquo Shock and Vibration vol 2017Article ID 1451483 12 pages 2017

[17] Bogaziccedili University Kandilli Observatory and EarthquakeResearch Institute 2017 httpwwwkoeribounedutrsismo2deprem-bilgileribuyuk-depremler

[18] J S Bendat and A G Piersol Random Data Analysis andMeasurement Procedures Wiley San Francisco CA USA 4thedition 1986

[19] C Raineri G Fabbrocino E Cosenza and G ManfredildquoImplementation of OMA procedures using labview theoryand applicationrdquo in Proceedings of 2nd International Oper-ational Modal Analyses Conference pp 1ndash12 CopenhagenDenmark April-May 2007

[20] OMA Operational Modal Analysis Release 45 StructuralVibration Solution AS Denmark Europe 2016

[21] European Committee for Standardization EN 384-StructuralTimber-Determination of Characteristic Values of MechanicalProperties and Density Office for Official Publications of theEuropean Communities Luxembourg Europe 1995

[22] P B Lourenco A O Feio and J S Machado ldquoChestnut woodin compression perpendicular to the grain non-destructivecorrelations for test results in new and old woodrdquo Con-struction and Building Materials vol 21 no 8 pp 1617ndash16272007

[23] Autodesk Inc Sap 2000 V20 Autodesk Inc San Rafael CAUSA 2017

[24] United States Department of Agriculture Forest ServiceWood Handbook Wood as an Engineering Material UnitedStates Department of Agriculture Forest Service WashingtonDC USA 2010

[25] -ermal expansion coefficients for some common materialsOctober 2017 httpswwwengineeringtoolboxcomlinear-expansion-coefficients-d_95html

12 Shock and Vibration

minarets Laboratory and in situ ultrasonic tests were per-formed to determine the physical andmaterial properties-efinite element models of the studied five timber minarets wereprepared and modeled with the beam elements having sixdegrees of freedom at every node -e obtained experimentalmodes from in situ tests are controlled using both modalassurance criteria (MAC) table and the complexity plots -elinear elastic material model was assumed forminaret analysisbecause the experimental results for the in situ tests were alsoin the elastic range -e boundary conditions were updateddepending on the experimental results to represent the realbehavior of the minarets Using all data an empirical formulawas derived for the rapid estimation of the fundamental

period of timber minarets -is formula shows that theconstruction technique of the outer wall is as important as thematerial and geometric properties of the minarets -e fre-quent usage of the outer columns at 10 cm intervals andbracing elements in the construction of the outer walls of theGulluk and Tesvikiye Mosques minarets resulted in higherfundamental frequencies than the others On the contrary inthe other minarets the usage of 15 cm outer column intervalsthe usage of timber cladding material in the Aga Mosqueminaret instead of bracing elements and less usage of bracingelements in the Ali Kuzu and FethiyeMosqueminarets are theconstruction differences affecting the dynamic behavior -eformula leads to an upper limit with an error of 9

Y XZ Y XZ Y XZ Y XZ Y XZ Y XZ Y XZ

Mode 1f 118 Hz

Mode 2f 119 Hz

Mode 3f 650 Hz

Mode 4f 651 Hz

Mode 5f 952 Hz

Mode 6f 1466 Hz

Mode 7f 1470 Hz

Figure 7 -e first seven modes and natural frequencies of the Gulluk Mosque minaret

Table 7 First seven modes frequencies (experimental approach versus computational approach)

Mode numberTesvikiye Gulluk Fethiye Ali Kuzu Aga

Exp Comp Exp Comp Exp Comp Exp Comp Exp Comp1 242 246 127 118 093 096 072 078 210 2152 269 247 127 119 105 101 074 079 232 2153 1140 1164 715 650 322 393 371 409 959 10354 1221 1165 724 651 352 396 391 414 969 10455 1370 1375 1030 952 520 502 508 450 1196 11526 2285 2104 1501 1466 815 841 815 794 1213 12587 2307 2121 1502 1470 842 845 842 826 1310 1260Exp experimental approach Comp computational approach

Table 8 -e mass participation factors of the studied minarets

MosquesFirst mode Second mode Sum of first three modes

x y x y x yTesvikiye Mosque 6383 6381 2064 2067 8536 8522Gulluk Mosque 6268 6265 2048 2051 8858 8856Fethiye Mosque 6998 6987 1444 1460 8922 8925Ali Kuzu Mosque 6648 6611 1843 1934 8791 9006Aga Mosque 7507 7478 1193 1222 8730 8820

10 Shock and Vibration

In addition minaret height slenderness and minaretcross-sectional area affect the dynamic behavior of minarets-e frequent usage of horizontal beams in the outer wallconstruction of timber minarets increases the rigidity of thestructure and affects their dynamic behavior -e usage ofsteel connectors provides high damping ratios

In conclusion the construction techniques and geo-metric properties of timber minarets greatly affect theirdynamic behavior Better design criteria development and

retrofitting guideline preparation with a different modelingunder different ground motions and strong winds will helpto ensure better minaret safety

Data Availability

All data generated or analyzed during the study are includedin this paper

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

In this paper the results of a research project carried out bythe authors are utilized supported by Uludag University (noOUAP(MM)-201532)

References

[1] A Dogangun R Acar R Livaoglu and O I Tuluk ldquoPer-formance of masonry minarets against earthquakes and windsin Turkeyrdquo in Proceedings of 1st International Conference on

0

05

1

15

2

25

3

0 50 100 150 200 250

Freq

uenc

y f

Stiffnessmass km

Teşvikiye

Ağa

Guumllluumlk

Fethiye

Ali Kuzu

8 8 8

755

755

755

15 15

520

05

8 15 8 815

55

8 10 8 810

200

8 15 8 8

55

200

15

55

5

8 10 8 810

100

100

Figure 8 -e relationship between the stiffness-to-mass ratios and frequencies

R2 = 0962

0010203040506070809

1

12 13 14 15 16 17 18 19 20

Nor

mal

ized

freq

uenc

y f

Height L

Fethiye

TeşvikiyeAğa

Ali KuzuGuumllluumlk

Figure 9-e relationship between the normalized frequencies andheights

R2=0950

0010203040506070809

1

8 10 12 14 16 18

Nor

mal

ized

freq

uenc

y f

Heightdiameter Ld

Teşvikiye

Ağa

Fethiye

Ali KuzuGuumllluumlk

Figure 10 -e relationship between the normalized frequenciesand heights to diameters

078

191225

096

128

072

21242

093127

000

050

100

150

200

250

300

Ali Kuzu Ağa Teşvikiye Fethiye Guumllluumlk

Firs

t mod

e fre

quen

cy (H

z)

FormulaExperimental

(8)

(9)(7)

(3)(1)

Figure 11 -e fundamental frequencies (formula versus experi-mental results)

Shock and Vibration 11

Restoration of Heritage Masonry Structures P32 pp 1ndash10Cairo Egypt April 2006

[2] K H Kusuzumu ldquoTraditional construction techniques andcurrent restorations of Istanbul minaretsrdquo MSc thesis MimarSinan University Istanbul Turkey 2010 in Turkish

[3] A Dogangun R Acar H Sezen and R Livaoglu ldquoIn-vestigation of dynamic response of masonry minaret struc-turesrdquo Bulletin of Earthquake Engineering vol 6 no 3pp 505ndash517 2008

[4] A Bayraktar A C Altunısık B Sevim T Turker M Akkoseand N Coskun ldquoModal analysis experimental validation andcalibration of a historical masonry minaretrdquo Journal of Testingand Evaluation vol 36 no 6 pp 516ndash524 2008

[5] A Bayraktar B Sevim A C Altunısık and T TurkerldquoAnalytical and operational modal analyses of Turkish stylereinforced concrete minarets for structural identificationrdquoExperimental Techniques vol 33 no 2 pp 65ndash75 2009

[6] A Bayraktar B Sevim A C Altunısık and T TurkerldquoEarthquake analysis of reinforced concrete minarets usingambient vibration test resultsrdquo Structural Design of Tall andSpecial Buildings vol 19 no 3 pp 257ndash273 2010

[7] A Bayraktar A C Altunisik B Sevim and T TurkerldquoSeismic response of a historical masonry minaret usinga finite element model updated with operational modaltestingrdquo Journal of Vibration and Control vol 17 no 1pp 129ndash149 2011

[8] A Sahin A Bayraktar M Ozcan B Sevim A C Altunısıkand T Turker ldquoDynamic field test system identificationand modal validation of a RC minaret pre and postprocessing the wind-induced ambient datardquo Journal ofPerformance of Constructed Facilities vol 25 no 4pp 336ndash556 2011

[9] C S Oliveira E Ccedilaktı D Stengel and M Branco ldquoMinaretbehaviour under earthquake loading the case of historicalIstanbulrdquo Earthquake Engineering amp Structural Dynamicsvol 41 no 1 pp 19ndash39 2012

[10] M A A Motaal ldquoEffect of piles on the seismic response ofmosques minaretsrdquo Ain Shams Engineering Journal vol 5no 1 pp 29ndash40 2014

[11] R Livaoglu M H Basturk A Dogangun and C SerhatogluldquoEffect of geometric properties on dynamic behaviour ofhistoric masonry minaretrdquo KSCE Journal of Civil Engineeringvol 20 no 6 pp 2392ndash2402 2016

[12] A L Che Y He X R Ge T Iwatate and Y Oda ldquoStudy onthe dynamic structural characteristics of an ancient timberYingxian wooden pagodardquo in Proceedings of GeoShanghaiInternational Conference pp 390ndash396 Shanghai China June2006

[13] M Yu Y Oda D Fang and J Zhao ldquoAdvances in structuralmechanics of Chinese ancient architecturesrdquo Frontiers ofArchitecture and Civil Engineering in China vol 2 no 1pp 1ndash25 2008

[14] L Gaile ldquoAnalysis of dynamic parameters of observationtowers in Latviardquo in Proceedings of 9th International Scientificand Practical Conference pp 57ndash62 Rezekne Latvia June2013

[15] A Feldman H Huang W S Chang et al ldquoDynamicproperties of tall timber structures under wind-induced vi-brationrdquo in Proceedings of World Conference on TimberEngineering Vienne Austria August 2016

[16] Y Zhang N Zhang Y Cao andH Xia ldquoA predictionmethodof historical timber buildingsrsquo vibrations induced by trafficloads and its validationrdquo Shock and Vibration vol 2017Article ID 1451483 12 pages 2017

[17] Bogaziccedili University Kandilli Observatory and EarthquakeResearch Institute 2017 httpwwwkoeribounedutrsismo2deprem-bilgileribuyuk-depremler

[18] J S Bendat and A G Piersol Random Data Analysis andMeasurement Procedures Wiley San Francisco CA USA 4thedition 1986

[19] C Raineri G Fabbrocino E Cosenza and G ManfredildquoImplementation of OMA procedures using labview theoryand applicationrdquo in Proceedings of 2nd International Oper-ational Modal Analyses Conference pp 1ndash12 CopenhagenDenmark April-May 2007

[20] OMA Operational Modal Analysis Release 45 StructuralVibration Solution AS Denmark Europe 2016

[21] European Committee for Standardization EN 384-StructuralTimber-Determination of Characteristic Values of MechanicalProperties and Density Office for Official Publications of theEuropean Communities Luxembourg Europe 1995

[22] P B Lourenco A O Feio and J S Machado ldquoChestnut woodin compression perpendicular to the grain non-destructivecorrelations for test results in new and old woodrdquo Con-struction and Building Materials vol 21 no 8 pp 1617ndash16272007

[23] Autodesk Inc Sap 2000 V20 Autodesk Inc San Rafael CAUSA 2017

[24] United States Department of Agriculture Forest ServiceWood Handbook Wood as an Engineering Material UnitedStates Department of Agriculture Forest Service WashingtonDC USA 2010

[25] -ermal expansion coefficients for some common materialsOctober 2017 httpswwwengineeringtoolboxcomlinear-expansion-coefficients-d_95html

12 Shock and Vibration

In addition minaret height slenderness and minaretcross-sectional area affect the dynamic behavior of minarets-e frequent usage of horizontal beams in the outer wallconstruction of timber minarets increases the rigidity of thestructure and affects their dynamic behavior -e usage ofsteel connectors provides high damping ratios

In conclusion the construction techniques and geo-metric properties of timber minarets greatly affect theirdynamic behavior Better design criteria development and

retrofitting guideline preparation with a different modelingunder different ground motions and strong winds will helpto ensure better minaret safety

Data Availability

All data generated or analyzed during the study are includedin this paper

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

In this paper the results of a research project carried out bythe authors are utilized supported by Uludag University (noOUAP(MM)-201532)

References

[1] A Dogangun R Acar R Livaoglu and O I Tuluk ldquoPer-formance of masonry minarets against earthquakes and windsin Turkeyrdquo in Proceedings of 1st International Conference on

0

05

1

15

2

25

3

0 50 100 150 200 250

Freq

uenc

y f

Stiffnessmass km

Teşvikiye

Ağa

Guumllluumlk

Fethiye

Ali Kuzu

8 8 8

755

755

755

15 15

520

05

8 15 8 815

55

8 10 8 810

200

8 15 8 8

55

200

15

55

5

8 10 8 810

100

100

Figure 8 -e relationship between the stiffness-to-mass ratios and frequencies

R2 = 0962

0010203040506070809

1

12 13 14 15 16 17 18 19 20

Nor

mal

ized

freq

uenc

y f

Height L

Fethiye

TeşvikiyeAğa

Ali KuzuGuumllluumlk

Figure 9-e relationship between the normalized frequencies andheights

R2=0950

0010203040506070809

1

8 10 12 14 16 18

Nor

mal

ized

freq

uenc

y f

Heightdiameter Ld

Teşvikiye

Ağa

Fethiye

Ali KuzuGuumllluumlk

Figure 10 -e relationship between the normalized frequenciesand heights to diameters

078

191225

096

128

072

21242

093127

000

050

100

150

200

250

300

Ali Kuzu Ağa Teşvikiye Fethiye Guumllluumlk

Firs

t mod

e fre

quen

cy (H

z)

FormulaExperimental

(8)

(9)(7)

(3)(1)

Figure 11 -e fundamental frequencies (formula versus experi-mental results)

Shock and Vibration 11

Restoration of Heritage Masonry Structures P32 pp 1ndash10Cairo Egypt April 2006

[2] K H Kusuzumu ldquoTraditional construction techniques andcurrent restorations of Istanbul minaretsrdquo MSc thesis MimarSinan University Istanbul Turkey 2010 in Turkish

[3] A Dogangun R Acar H Sezen and R Livaoglu ldquoIn-vestigation of dynamic response of masonry minaret struc-turesrdquo Bulletin of Earthquake Engineering vol 6 no 3pp 505ndash517 2008

[4] A Bayraktar A C Altunısık B Sevim T Turker M Akkoseand N Coskun ldquoModal analysis experimental validation andcalibration of a historical masonry minaretrdquo Journal of Testingand Evaluation vol 36 no 6 pp 516ndash524 2008

[5] A Bayraktar B Sevim A C Altunısık and T TurkerldquoAnalytical and operational modal analyses of Turkish stylereinforced concrete minarets for structural identificationrdquoExperimental Techniques vol 33 no 2 pp 65ndash75 2009

[6] A Bayraktar B Sevim A C Altunısık and T TurkerldquoEarthquake analysis of reinforced concrete minarets usingambient vibration test resultsrdquo Structural Design of Tall andSpecial Buildings vol 19 no 3 pp 257ndash273 2010

[7] A Bayraktar A C Altunisik B Sevim and T TurkerldquoSeismic response of a historical masonry minaret usinga finite element model updated with operational modaltestingrdquo Journal of Vibration and Control vol 17 no 1pp 129ndash149 2011

[8] A Sahin A Bayraktar M Ozcan B Sevim A C Altunısıkand T Turker ldquoDynamic field test system identificationand modal validation of a RC minaret pre and postprocessing the wind-induced ambient datardquo Journal ofPerformance of Constructed Facilities vol 25 no 4pp 336ndash556 2011

[9] C S Oliveira E Ccedilaktı D Stengel and M Branco ldquoMinaretbehaviour under earthquake loading the case of historicalIstanbulrdquo Earthquake Engineering amp Structural Dynamicsvol 41 no 1 pp 19ndash39 2012

[10] M A A Motaal ldquoEffect of piles on the seismic response ofmosques minaretsrdquo Ain Shams Engineering Journal vol 5no 1 pp 29ndash40 2014

[11] R Livaoglu M H Basturk A Dogangun and C SerhatogluldquoEffect of geometric properties on dynamic behaviour ofhistoric masonry minaretrdquo KSCE Journal of Civil Engineeringvol 20 no 6 pp 2392ndash2402 2016

[12] A L Che Y He X R Ge T Iwatate and Y Oda ldquoStudy onthe dynamic structural characteristics of an ancient timberYingxian wooden pagodardquo in Proceedings of GeoShanghaiInternational Conference pp 390ndash396 Shanghai China June2006

[13] M Yu Y Oda D Fang and J Zhao ldquoAdvances in structuralmechanics of Chinese ancient architecturesrdquo Frontiers ofArchitecture and Civil Engineering in China vol 2 no 1pp 1ndash25 2008

[14] L Gaile ldquoAnalysis of dynamic parameters of observationtowers in Latviardquo in Proceedings of 9th International Scientificand Practical Conference pp 57ndash62 Rezekne Latvia June2013

[15] A Feldman H Huang W S Chang et al ldquoDynamicproperties of tall timber structures under wind-induced vi-brationrdquo in Proceedings of World Conference on TimberEngineering Vienne Austria August 2016

[16] Y Zhang N Zhang Y Cao andH Xia ldquoA predictionmethodof historical timber buildingsrsquo vibrations induced by trafficloads and its validationrdquo Shock and Vibration vol 2017Article ID 1451483 12 pages 2017

[17] Bogaziccedili University Kandilli Observatory and EarthquakeResearch Institute 2017 httpwwwkoeribounedutrsismo2deprem-bilgileribuyuk-depremler

[18] J S Bendat and A G Piersol Random Data Analysis andMeasurement Procedures Wiley San Francisco CA USA 4thedition 1986

[19] C Raineri G Fabbrocino E Cosenza and G ManfredildquoImplementation of OMA procedures using labview theoryand applicationrdquo in Proceedings of 2nd International Oper-ational Modal Analyses Conference pp 1ndash12 CopenhagenDenmark April-May 2007

[20] OMA Operational Modal Analysis Release 45 StructuralVibration Solution AS Denmark Europe 2016

[21] European Committee for Standardization EN 384-StructuralTimber-Determination of Characteristic Values of MechanicalProperties and Density Office for Official Publications of theEuropean Communities Luxembourg Europe 1995

[22] P B Lourenco A O Feio and J S Machado ldquoChestnut woodin compression perpendicular to the grain non-destructivecorrelations for test results in new and old woodrdquo Con-struction and Building Materials vol 21 no 8 pp 1617ndash16272007

[23] Autodesk Inc Sap 2000 V20 Autodesk Inc San Rafael CAUSA 2017

[24] United States Department of Agriculture Forest ServiceWood Handbook Wood as an Engineering Material UnitedStates Department of Agriculture Forest Service WashingtonDC USA 2010

[25] -ermal expansion coefficients for some common materialsOctober 2017 httpswwwengineeringtoolboxcomlinear-expansion-coefficients-d_95html

12 Shock and Vibration

Restoration of Heritage Masonry Structures P32 pp 1ndash10Cairo Egypt April 2006

[2] K H Kusuzumu ldquoTraditional construction techniques andcurrent restorations of Istanbul minaretsrdquo MSc thesis MimarSinan University Istanbul Turkey 2010 in Turkish

[3] A Dogangun R Acar H Sezen and R Livaoglu ldquoIn-vestigation of dynamic response of masonry minaret struc-turesrdquo Bulletin of Earthquake Engineering vol 6 no 3pp 505ndash517 2008

[4] A Bayraktar A C Altunısık B Sevim T Turker M Akkoseand N Coskun ldquoModal analysis experimental validation andcalibration of a historical masonry minaretrdquo Journal of Testingand Evaluation vol 36 no 6 pp 516ndash524 2008

[5] A Bayraktar B Sevim A C Altunısık and T TurkerldquoAnalytical and operational modal analyses of Turkish stylereinforced concrete minarets for structural identificationrdquoExperimental Techniques vol 33 no 2 pp 65ndash75 2009

[6] A Bayraktar B Sevim A C Altunısık and T TurkerldquoEarthquake analysis of reinforced concrete minarets usingambient vibration test resultsrdquo Structural Design of Tall andSpecial Buildings vol 19 no 3 pp 257ndash273 2010

[7] A Bayraktar A C Altunisik B Sevim and T TurkerldquoSeismic response of a historical masonry minaret usinga finite element model updated with operational modaltestingrdquo Journal of Vibration and Control vol 17 no 1pp 129ndash149 2011

[8] A Sahin A Bayraktar M Ozcan B Sevim A C Altunısıkand T Turker ldquoDynamic field test system identificationand modal validation of a RC minaret pre and postprocessing the wind-induced ambient datardquo Journal ofPerformance of Constructed Facilities vol 25 no 4pp 336ndash556 2011

[9] C S Oliveira E Ccedilaktı D Stengel and M Branco ldquoMinaretbehaviour under earthquake loading the case of historicalIstanbulrdquo Earthquake Engineering amp Structural Dynamicsvol 41 no 1 pp 19ndash39 2012

[10] M A A Motaal ldquoEffect of piles on the seismic response ofmosques minaretsrdquo Ain Shams Engineering Journal vol 5no 1 pp 29ndash40 2014

[11] R Livaoglu M H Basturk A Dogangun and C SerhatogluldquoEffect of geometric properties on dynamic behaviour ofhistoric masonry minaretrdquo KSCE Journal of Civil Engineeringvol 20 no 6 pp 2392ndash2402 2016

[12] A L Che Y He X R Ge T Iwatate and Y Oda ldquoStudy onthe dynamic structural characteristics of an ancient timberYingxian wooden pagodardquo in Proceedings of GeoShanghaiInternational Conference pp 390ndash396 Shanghai China June2006

[13] M Yu Y Oda D Fang and J Zhao ldquoAdvances in structuralmechanics of Chinese ancient architecturesrdquo Frontiers ofArchitecture and Civil Engineering in China vol 2 no 1pp 1ndash25 2008

[14] L Gaile ldquoAnalysis of dynamic parameters of observationtowers in Latviardquo in Proceedings of 9th International Scientificand Practical Conference pp 57ndash62 Rezekne Latvia June2013

[15] A Feldman H Huang W S Chang et al ldquoDynamicproperties of tall timber structures under wind-induced vi-brationrdquo in Proceedings of World Conference on TimberEngineering Vienne Austria August 2016

[16] Y Zhang N Zhang Y Cao andH Xia ldquoA predictionmethodof historical timber buildingsrsquo vibrations induced by trafficloads and its validationrdquo Shock and Vibration vol 2017Article ID 1451483 12 pages 2017

[17] Bogaziccedili University Kandilli Observatory and EarthquakeResearch Institute 2017 httpwwwkoeribounedutrsismo2deprem-bilgileribuyuk-depremler

[18] J S Bendat and A G Piersol Random Data Analysis andMeasurement Procedures Wiley San Francisco CA USA 4thedition 1986

[19] C Raineri G Fabbrocino E Cosenza and G ManfredildquoImplementation of OMA procedures using labview theoryand applicationrdquo in Proceedings of 2nd International Oper-ational Modal Analyses Conference pp 1ndash12 CopenhagenDenmark April-May 2007

[20] OMA Operational Modal Analysis Release 45 StructuralVibration Solution AS Denmark Europe 2016

[21] European Committee for Standardization EN 384-StructuralTimber-Determination of Characteristic Values of MechanicalProperties and Density Office for Official Publications of theEuropean Communities Luxembourg Europe 1995

[22] P B Lourenco A O Feio and J S Machado ldquoChestnut woodin compression perpendicular to the grain non-destructivecorrelations for test results in new and old woodrdquo Con-struction and Building Materials vol 21 no 8 pp 1617ndash16272007

[23] Autodesk Inc Sap 2000 V20 Autodesk Inc San Rafael CAUSA 2017

[24] United States Department of Agriculture Forest ServiceWood Handbook Wood as an Engineering Material UnitedStates Department of Agriculture Forest Service WashingtonDC USA 2010

[25] -ermal expansion coefficients for some common materialsOctober 2017 httpswwwengineeringtoolboxcomlinear-expansion-coefficients-d_95html

12 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

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