structural improvements for tall buildings under wind

Research ArticleStructural Improvements for Tall Buildings under Wind LoadsComparative Study

Nicola Longarini1 Luigi Cabras2 Marco Zucca1 Suvash Chapain3 and Aly Mousaad Aly3

1Politecnico di Milano Milan Italy2University of Trento Trento Italy3Louisiana State University Baton Rouge LA USA

Correspondence should be addressed to Aly Mousaad Aly alylsuedu

Received 27 April 2017 Revised 13 September 2017 Accepted 26 September 2017 Published 6 November 2017

Academic Editor Evgeny Petrov

Copyright copy 2017 Nicola Longarini et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The behavior of a very slender building is investigated under wind loads to satisfy both strength and serviceability (comfort) designcriteria To evaluate the wind effects wind tunnel testing and structural analysis were conducted by two different procedures (i)Pressure Integration Method (PIM) with finite element modeling and (ii) High Frequency Force Balance (HFFB) technique Theresults from both approaches are compared with those obtained from Eurocode 1 and the Italian design codes emphasizing theneed to further deepen the understanding of problems related to wind actions on such type of structure with high geometricalslenderness In order to reduce wind induced effects structural and damping solutions are proposed and discussed in a comparativestudyThese solutions include (1) height reduction (2) steel belts (3) tuned mass damper (4) viscous dampers and (5) orientationchange Each solution is studied in detail along with its advantages and limitations and the reductions in the design loads andstructural displacements and acceleration are quantifiedThe study shows the potential of damping enhancement in the building tomitigate vibrations and reduce design loads andhence provide an optimal balance among resilience serviceability and sustainabilityrequirements

1 Introduction

11 Background The increased population in urban societiesand the constant pressure of limited land area with expensiveprices have caused the evolution of high-rise buildings High-rise buildings may be considered as a symbol of developmentand civilization From structural point of view these arebuildings of which height will be affected by lateral forcesresulting from earthquake and wind loads to the extent thatsuch forces will play a major role in the design process[1] High-rise building construction is a challenging projectundertaken by experts and engineers To build a tall buildingone should think of a construction project whose designdepends totally on analytical analysis and scaled modeling

As high-rise buildings are receiving more global emi-nence their impact on society and economy has becomepronouncedworldwide Over time new frontiers in high-riseconstruction complement emerging needs for performance

efficacy and economic design Designers are concernedabout choosing structural systems that can carry lateralloads as well as ascertained serviceability and occupant com-fort requirements The economic viability of tall buildingsdepends strongly upon serviceability and occupant comfortas prerequisites In general tall buildings are built to sustainextreme wind loads within an expected long lifespan Theprobability of catastrophic failure is small however studieson wind induced motion and effects on high-rise buildingsare essential from a serviceability and economic point ofviewThe design of buildings with a slenderness ratio (aspectratio = heightwidth) greater than five is usually governed byserviceability more than safety [2] The serviceability of tallbuildings under wind is typically measured by the amount oflateral displacements and acceleration Excessive lateral dis-placements can cause structural and nonstructural damagewhile excessive acceleration can lead to unpleasantness to thebuilding occupants [3]

HindawiShock and VibrationVolume 2017 Article ID 2031248 19 pageshttpsdoiorg10115520172031248

2 Shock and Vibration

An additional challenge is the uncertainty in the amountof structural damping early in the planning phase [4] Toalleviate this issue structural control is a potentialmethod forstructural tuning and damping enhancementThe purpose ofstructural control in civil engineering structures is to reducevibrations produced by external stressors such as earthquakeand wind loads by different techniques such as modifyingstiffness mass damping or shape Structural control meth-ods are typically classified as active passive and semiactivetechniques Passive systems use supplemental devices whichrespond to the vibrations of the structure by dissipatingthe energy triggered by strong dynamic loads without theneed for an external energy supply A variety of passivecontrol mechanisms have been suggested by researchers andengineers including tuned mass dampers viscous dampersfriction dampers and tuned water dampers

An external power source is needed for an active controlsystem to control actuators that apply prescribed forces to astructurebuilding to injectdissipate energy and hence min-imize certain optimization objectives The command signalsto the actuator depend on the measured system response(feed-back control) However active control systems can beunstable and they need bulky power transformers andconsume significant amount of energy which may not beavailable especially immediately after natural disasters suchas earthquakes and high winds For this purpose passivecontrol systems remain the most reliable and practical tech-nique for structural control Some passive control systems arepresented as follows

12 Tuned Mass Dampers (TMDs) A vibration absorber or aTMDconsists of springmass and a damping device installedon a primary system to lessen the dynamic response Themain concept in the TMD is that the frequency of the damperis tuned to resonate out of phase with the vibration of theprimary structure leading to significant energy dissipationNumerous studies are focused on the performance of theTMD and its capability to suppress vibrations especiallydue to wind loads The concept of vibration suppression bya TMD dates back to 1909 when the vibration absorberwas invented by Farham making it as one of the earliestcontrol devices [5] Following this invention numerousstudies were conducted to validate the application as wellas to enhance the performance of the device with differentstructural configurationsThe concept of using a robust TMDwas proposed recently in which an approach was devel-oped to determine the optimal parameters under structuraluncertainties Significant reductions in the response can berealized by the optimum selection of the mass ratio andtuning frequency ratio [6] In high-rise buildings when theinherent sutural damping is low the TMD is proved to bevery effective in reducing the responses [7] TMDs are usedas controlling devices in high-rise buildings in Japan HongKong United States Australia and some other countriesThe Hancock Tower in Boston 244m as mentioned in [8]has two TMDs installed at the opposite ends of the 58thfloor with each unit weighting 300 tons However there areseveral limitations on the practical application of TMDS forexample being tuned to a single vibrational mode is limited

to narrow band of operation frequencies [9] The limitationsof the TMD can be significant when dealing with buildingsexcited at higher modes of vibration for example underearthquake loadsAlso TMDs are sensitive to uncertainties inthe structural parameters Structural parameters may changedue to damage material degradation or even environmentalvariations Such changes can lead to a detuned TMD withreduced effectiveness [10]

13 Tuned Liquid Dampers Tuned liquid dampers (TLDs)gained increased popularity due to their effectiveness inabsorbing low-frequency vibrations induced by wind beingcost effective requiring less maintenance and being easilyimplementable [11] TLDs are energy dissipation devicessuggested for vibration suppression under different dynamicloads A typical TLD consists of a container with liquidwaterto reduce vibrations of a primary structure This allows sig-nificant energy dissipation and hence reduced structuralresponses [12] The fundamental principle of vibration con-trol in structures using TLDs is based on sloshing and wavebreaking for energy dissipation [11] For efficient energy dissi-pation the fundamental frequency of liquid in a TLD shouldbe close to that of the primary structure Several researchstudies have been conducted onTLDs in the past fewdecadesThe research conducted by Bauer in 1984 [13] proposed adamping device to control vibrations where a rectangularcontainer filled with two immiscible liquids was utilized inwhich the interface motion dissipated the energy effectivelyRecently TLDs have been shown to be effective in lateralvibration control of high-rise buildings The Hobert Towerin Tasmania (Australia) with a height of 105m is equippedwith 80 TLDs Similarly in Kagawa (Japan) 16 units of TLDsare installed in the Gold Tower which has a height of 158mThe installation of TLDs is found to suppress vibrations ofbuildings underwind loads by one-third to half of the originalresponses [8]

14 Viscous Dampers Damping is an important mechanismthat dissipates energy and hence permits a structure toachieve high performance under dynamic loads such asearthquake strong wind or blast Numerous fluid dampingdevices with practical applications have been proposed overthe past few decades The use of damping devices filled withviscoelastic liquid to dissipate energy was studied extensivelyboth analytically and experimentally [14] When a VD issubjected to an external load friction forces develop amongdifferent elements Friction forces are developed among themolecules of the dampingmedium shaft andmedium pistonand medium and so on All these actions combine togetherto form a damping force which acts 90 degree out of phasewith the displacement driven force in a primary structure[15 16] Previous uses of viscous dampers (VDs) in militaryapplications include the attenuation of weapon grade shockaircraft ship vibration and underwater detonation

Viscous dampers that were used in military applicationsduring the cold war have been adopted for civil engineeringstructural applications [17] A number of countries are prac-ticing the use of VDs in tall building including Hong KongChina Japan and United States The Sato Building (1992)

Shock and Vibration 3

and Shimura Dormitory (1993) in Japan are vivid examplesof application [8] These devices are of a prime interest incivil engineering because they possess certain characteristicssuch as (1) compactness (2) temperature insensitivity and(3) linear viscous response over a range of frequencies [15]In 1991 a cooperative effort between NCEER and TaylorDevices Inc began to adopt this defense technology forhazard mitigation in buildings [18]

Various theoretical and experimental works are con-ducted on the effective usage of VDs in high-rise buildingsA study conducted on a 39-story building shows that theapplication of VDs reduced the wind induced accelerationof the building by 35 [19] The imperial building in India(10 story) was studied two-thirds of the energy induced bywind and small earthquakes realized to be dissipated by VDs[20] A super tall 62-story building (Xiamen city of southeastChina) with 24575m height was studied for wind inducedresponse reduction by VDs there was a significant reductionin displacement and acceleration [21]

15 Belt Trusses and Outriggers In general moment resistingframes and shear walls are efficient and economical structuralsystems for low- and medium-rise buildings But when theheight of a building goes up these systems may not besufficient enough to resist load induced by the wind andearthquakes Belt truss systems are effectively used to controlexcessive drift due to lateral loads and also to enhance thestiffness of tall buildings [22] The outrigger and belt trusssystems are dynamic load resisting systems in tall buildingswhere external columns control core walls with very stiffstructuralmechanical elements at one or more levels Thefunctional difference between belt trusses and outriggers isthat belt trusses tie the peripheral columns of a buildingwhile the later engages them with the central core Externallyinduced moments are resisted by the core and axial internalloads developed in outer columns that are connected to anoutrigger [23] Belt trusses are used as ldquovirtual outriggersrdquobecause they can transfer the load without the need fora connection between an outrigger system and the core[24] The Plaza Rakyat Tower (located in Kuala Lumpur)employs ldquovirtual outriggerrdquo systems consisting of belt walls(reinforced concrete building) [8] The challenges associatedwith this type of mitigation include the loss of space in build-ings in addition to accompanying structural complexities[25]

16 Paper Layout The current study addresses the appli-cation of different response lessening mechanisms in a tallbuilding subjected to wind loads Five independent responsereduction methods are employed to control vibrations underwind loads Section 2 presents the design criteria set bystandard codes for buildings with high slenderness ratiosconcerning both strength and serviceability requirements InSection 3 the building characteristics wind loads and windtunnel experiments are presented In Sections 4 and 5 thewind induced responses (basemoments base shear drift andacceleration) are evaluated using wind tunnel test data andfinite element model (FEM) Specifically Section 4 presents

the pressure integration method whereas Section 5 intro-duces the high frequency force balance method Section 6focuses on the comparison of the wind induced responsesobtained in Sections 4 and 5 with the design limits providedin standard codes (the Eurocode 1 (EC1) [26] and the ItalianCNR DT2072008 (CNR) code [27]) Since the responsevalues evaluated exceeded the design limits provided by stan-dard codes there was a need to propose structural improve-ments Five different solutions (improvements) are presentedin detail to bring those values under the prescribed limitsTheimprovements explained in Section 7 are height reductionuse of belt trusses installation of dampers and orientationchange In the first improvement about 125 of the totalheight of the building was reduced to check its sensitivity towind In the second improvement internal belt trusses areintroduced at different levels for two and four alignmentsalong the horizontal 119909 axis Again as third and fourthimprovements installation of a TMD at the top and VDsup to the 20th floors are considered separately to investigatetheir effectiveness Rotation of the building to an optimumangle for reduced wind effects is the fifth improvement Allthe improvements mentioned above are studied separatelyindependent of each other Finally the conclusions drawn aresummarized in Section 8

2 Design Criteria

21 Resistance and Comfort Criteria An accurate analysisof the structural system is necessary to build a high-risebuilding that can withstand the complex wind loads Thereare two important design criteria that should be consideredwhile designing high-rise building the first one is UltimateLimit State (ULS) which deals with strength requirements ofstructure and the second is Serviceability Limit State (SLS)that deals with comfort of occupants in the building TheULS criteria are employed to guarantee that the buildingwill not fail under maximum design loads Similarly theSLS criteria are used to ascertain that the building willremain operational and functional by satisfying serviceability(usually comfort) conditions Purpose of SLS requirements isto address the response of people and objects to the behaviorof the structure under the load These criteria have to befulfilled to yield adequate structural robustness as well asto provide required comfort satisfaction to occupants Thecomfort criterion can be fulfilled by limiting peak flooracceleration to predefined values provided in standard codes[28ndash32] Moreover considering the SLS design criterionit is fundamental to investigate the serviceability behavior(in terms of interstory displacements) of the secondarybuilding elements like finishes and system elements [33 34]Generally the response effects of the structure (also calledthe stress effects) have to be evaluated and compared withthe resistant effects the stress effects are the actions on thestructural elements (in terms of shear bending axial andtorsional stresses) in addition to the response (displacementand acceleration) of the structural primary and secondaryelements All stress effects can be evaluated by an appropriateFEM The following are the notations that will be used inFEM model for stress effects 119864Sd for the actions 120575Sd for the


Table 1 Reference values of the acceleration

Building usage Design values Notes[ms2] [g1000]

Residential 0039sim0082 403sim843 Up to 0049ms2 themotion is imperceptible

Office 0196sim0245 20sim25 The motion is perceptibleand irksomeness is

subjective up to 05ms2serious physical problems

Table 2 Resistant displacements (120575Sd is top displacements 120575Sid isinter-story displacements119867 is building height and ℎ119894 is inter-storyheight)

120575Rd values 120575Rid values119867600 le 120575Sd le 119867500 120575Sid le ℎ119894600displacements and 119886Sd for the acceleration Similarly 119864Rd120575Rd and 119886Rd are symbols for the actions displacements andacceleration for the resistant effects respectively

The resistance effects in building can be determined byusing standard codes The international codes can be con-sulted to determine the resistant shear the resistant bendingmoment and the resistant axial load for the ULS Howeverresistant displacements 120575Rd and the resistant acceleration 119886Rdin many cases are not specified in the codes and their valuesmay change either for the characteristics of the finishes orfor the use of the building In most of cases the resistantdisplacements 120575Rd and in particular the resistant acceleration119886Rd are not specified in standard codes and their valuesmay change depending on the use of the building Thus thevalued stress effects and the resistant effects must satisfy thefollowing relations

119864Sd le 119864Rd119886Sd le 119886Rd120575Sd le 120575Rd(1)

The acceleration in (1) refers to the response (accelera-tion) of the building at its top to satisfy the serviceabilityrequirements (SLS) for 10-year return period (119879R = 10 years)Comfort limits 119886Rd shown in Table 1 are set to avoid healthproblems like vertigos sickness and so on in the occupantsMoreover the top displacements (120575Sd) and the interstorydisplacements (120575Sid) calculated for the SLS can be comparedto the resistant values (120575Rd and 120575Rid) shown in Table 2

22 Slenderness Ratio The aspect ratio or the slendernessratio can significantly govern the behavior of high-risebuildings under wind As the building grows taller responselevel to the dynamic load changes Therefore proportions ofheight and length need to be considered carefully The windanalysis has to be even more accurate if the tall building ischaracterized by an unusual shape or by large geometricalslenderness (120582 = 119867119897) defined by its aspect ratio (buildingheight (119867)shortest side of its plan (119871)) Usually up to120582 ge 8ndash11

some comfort problems could exist [27] if the structure doesnot have enough stiffness or it is not equipped with dampingdevices In fact problems affect the comforts in everydayuse in some tall buildings and numerous skyscrapers all thelevels cannot be exploited for the same intended use of thelower floors Very often for the presence of spire or for veryspindly parts at the top the total height reduction (Δℎtot) isobserved in many constructions The reduction of height isthe difference between the top height (119867) and the height ofthe ultimate occupied floor (119867119891) having the same intendeduse of the lower floors Some examples are Burj Khalifa inDubai Δℎtot = 2445m (119867 = 829m 119867119891 = 5845m) forWillis tower in Chicago Δℎtot = 114m (119867 = 527m 119867119891 =413m) for Taipei 101 in Taiwan Δℎtot = 70m (119867 = 508m119867119891 = 438m) for Trump tower in Chicago Δℎtot = 82m(119867 = 423m 119867119891 = 341m) and for Unicredit tower in MilanΔℎtot = 82m (119867 = 231m 119867119891 = 144m)

Nevertheless in order to reach symbolic constructionsfame many tall buildings have a value of 120582 around thementioned limit as these are characterized by streamlinedshapes with a spire at the top [35] Among these are the StGilus Circus in London (119867 = 13610m 119897 = 2805m 120582 =750) the Pirelli building in Milan (119867 = 125m 119897 = 1870m120582 = 668) the Marina City buildings in Chicago (119867 = 180m119897 = 3332m 120582 = 540) the Standard Bank building inJohannesburg (119867 = 139m 119897 = 1417m 120582 = 981) the TrumpTower in NY (119867 = 202m 119897 = 3504m 120582 = 576) and theBond Center in Hong Kong (119867 = 19150m 119897 = 3270m120582 = 585)

Furthermore 120582 close to 8 represents a border betweena very slender tall building and a stubby chimney (someexamples of stubby chimneys in Italy are the Enel chimneyin Porto Tolle (119867 = 24380m 119897 = 2601m 120582 = 934) and theEnel chimney in ldquoTorre Valdaligardquo (119867 = 243m 119897 = 2870m120582 = 847))

In case of high geometrical slenderness 120582 [36] the classicproblems due to the wind load could add up to those causedby dynamic effects like the galloping due to the vortex shed-ding In tall buildings these effects are particularly dangeroussince they concern the resistance of both the main structuralelements and the elements supported by the main structure(eg the steel connections of the facades)

3 Structural and Wind Load Modeling

31 Characteristics of the Building The tall building studiedin this paper is located in north Italy and is optimized foroffice use The building is characterized by a high valueof slenderness 120582 The main features of the structure are asfollows

(i) Total height 119867 = 225m and rectangular floor plan(Figure 1) has sides 1198971 cong 64m in 119909-direction (alongwind) and 1198972 cong 23m in 119910-direction (across wind) thegeometric slenderness ratio is 120582 cong 10

(ii) Circular columns and cores of the building are madewith High Strength Concrete (HSC with 119877ck cong75MPa) but floor deck ismadewithNormal Strength


CoresElevator steel structure

x

y

Along-wind direction

Acro

ss-w

ind

dire

ctio

n

Figure 1 Typical floor plan

Z

f1 = 014 （Ｔ f2 = 015 （Ｔ f3 = 026 （Ｔ

Y

X

Figure 2 First second and third mode shapes of the building

Concrete (NSC with 119877ck cong 45MPa) slab is postten-sion reinforced in the two main directions

(iii) Slab foundation is in NSC with normal and postten-sion reinforcement in the two main directions

The wind resistant structural elements cores of thebuilding are located at the opposite sides of the typical floorplan The thickness of their walls is tapered along the verticaldevelopment of the building Thickness in the basementis 120m from the ground level to the fifth floor is 100mfrom the fifth to the twenty-seventh floor is 070m and fromthe twenty-seventh to the top of the building is 050m Theinner layout optimized for the office use shows four linesof circular columns along the longest side two of which arelocated along the facades and the other two are close to thecentral horizontal axis of the floor plan The structures of theelevators are made of S355 steel and structural glass these are

joined to the main concrete structure and do not contributewith the bracing system Figure 1 shows the floor plan

In the FEM the columns and the beams are representedby beam elements the cores and the decks are represented byplates The eigenvalue analysis is carried out to calculate thenatural frequencies for the first three modes Frequencies forI II and III vibration modes are 119891I = 014Hz (bending in 119909-axis direction) 119891II = 015Hz (bending in 119910-axis direction)and 119891III = 026Hz (torsional around 119911-axis) Figure 2 showsthemode shapes alongwith the dominant structural frequen-cies

32 Aerodynamic Loads High-rise buildings are wind sensi-tive structures so lateral wind load imposed on building is agoverning factor in their structural design Situation becomeseven more complicated if the frequency of oncoming windresonates with natural frequency of building which depends


0 45 90 135 180 225 270 315 36015

20

25

30

35

40

Angle (∘)

Win

d ve

loci

ty

(mＭ

2)

T２ = 100 years

T２ = 10 yearsT２ = 50 years

(a)

oy

x

0∘

45∘

90∘

135∘

180∘

225∘

270∘

315∘

TA

(b)

Figure 3 (a) Wind velocity as a function of the direction angle 120572 (b) Angle 120572 relative to the position of the building

on structural properties of building Pattern in which windflows around the building is distorted by flow separation andwakes developments Combination of these affects results inaerodynamic pressures on the structural system that imposesfluctuating forces and the building tends to respond in thelateral directions as well as in torsion [37]

The response in the along-wind consists of fluctuatingandmean components and the average wind speed is usuallyused to directly evaluate mean load and responses based onpressure and load coefficients The fluctuating componentof response and loads depend dominantly on (1) turbu-lence intensity (2) size reduction effects and (3) dynamicamplification (resonance) The ldquogust factorrdquo approach canbe employed to predicted the along-wind response with areasonable accuracy when the interference effects are notsignificant [37]

Crosswind oscillations can be excessive if building haslow damping Cross wind excitation is closely related to ldquovor-tex sheddingrdquo [38] The building acts as bluff body that sep-arates the flow from surface of structure causing asymmetricpressure distribution around the cross-section of structureThere can be a situation of resonance if vortex shedding fre-quency and natural frequency of building coincide causingexcessive oscillation in transverse direction or even failure

Possible aerodynamic coupling in various degrees offreedom is responsible for torsional motion of building Ifthe resultant wind load coincides with center of mass at eachfloor an eccentric loading can be expected which excites thetorsional mode of vibration Torsional responses are sensitiveto ratio of transverse to torsional frequencies [39] Thus itis fundamental to perform the wind tunnel test for preciseevaluation of along-wind crosswind and torsional responsesin this tall building

33 Wind Tunnel Testing It is critical to determine thewind loads for the specific mean recurrence interval anduncertainties associated with these loads Wind loads andloads factors are prescribed by analytical method given incodes for ordinary building But in case of tall buildings thesemethods lack precision and may not accurately account forimportant phenomena such as crosswind loads aerodynamic

instability vortex shedding and aerodynamic interactionbetween adjacent building [40] Thus to get more preciseproject specific information regarding wind loads and build-ing motion wind tunnel simulation of a scaled model isrequired

For the present case in this tall building the windtunnel tests are fundamental to investigate the effects of thewind like vortex shedding phenomenon (in relation to thedangerous structural behaviors like the galloping) For theaerodynamic tests it is essential to obtain wind velocities inthe site of construction There are different approaches forthe definition of the wind speed which are described as fol-lows

Approach 1 Directional velocities values are consideredbased on estimated wind speed in the site

Approach 2 Directional velocities values are considered onlywhen these values are higher than the velocities prescribedin the codes otherwise velocity prescribed in the codes isconsidered

Approach 3 The values are set by the codes with relation tothe buildings plan these values are the same in the two maindirections

Particularly in this case ldquoApproach 1rdquo is followed and thesite directional velocities come out from an in-depth study ofthe location site [41] The different velocities are reproducedin the wind tunnel on a rigid scale models (1 100) [36 42]The tests have investigated two different layouts with urbancontest and without the urban contest The present analysisrefers to the layout ldquobuilding with the urban contestrdquo whichhas given higher stress values The maximum wind velocitycomes from the north-west direction (270∘ndash300∘ in Figure 3)For return period 119879R = 100 years the maximum velocity isVmax = 38ms this value is higher than the nondirectionalvalue Vcode = 33ms indicated in the Italian code (DM 2008)for the same119879RWind velocities as a function of the directionidentified by the angle 120572 are shown in Figure 3

The forces 119865 and the moments 119872 at the base of thescale models during the wind tests for each of the 16 wind


directions are recorded as a function of the time These areexpressed by the following dimensionless coefficients

119862119865119883 = 119865119883119902119861119867119862119865119884 = 119865119884119902119861119867119862119865119885 = 119865119885119902119861119867119862119872119883 = 1198721198831199021198611198672 119862119872119884 = 1198721198841199021198611198672 119862119872119885 = 1198721198851199021198611198672

(2)

where 119902 = 05 sdot 120588 sdot V2ref is the dynamic pressure 120588 is airdensity Vref = V(119911ref ) refers to the average wind speed at areference point 119911ref = 100m and119861 represents the longest side(top view) of a building with the height 119867 Time historiesof pressures on the surface of the models are measured inabout 400 pressure meters (ldquoTAPsrdquo) for the same 16 winddirections

4 Pressure Integration Method (PIM)

In thismethod finite elementmodel of the full scale structurewas employed to predict the behavior of the real buildingThismethod has the great potential to estimate thewind loadsbecause it can address the limitations of the conventionalforce balance technique while maintaining the advantage ofthat technique [43] 400 TAPs were distributed on the outersurfaces (for thewind tunnel experiment)The distribution ofTAPs is such that number of TAPs per unit area is increasingas it goes upward as shown in Figure 4 Pressure value on eachTAP of the model is calculated as119901TAP (119905 119911ref) = 119888119901 (119905) 119902119881 (119911ref) (3)

where 119888119901(119905) is dimensionless time history of pressure coef-ficient and 119902 is dynamic pressure Once the time history ofpressure on surface is determined external force acting oneach TAP surface can be calculated as

119891TAP (119905 119911ref) = 119901TAP119860TAP (4)

where 119860TAP is the area of each TAP which is evaluated byThiessen polygon method In order to estimate forces 119865 andmoments119872 at floor levels the part of 119891TAP corresponding toeach floor has been identified For each 119896-floor the surfaces119860119896 are identified the generic119860119896 is given by the space betweentwo floors (product of the horizontal length of the floor andthe interstory distance) as shown in Figure 5(a) Then thesurfaces 119860119896119894 (Figure 5(c)) are considered by the intersectionof the ldquoarea of influencerdquo of the 119896-floor 119860119896 (Figure 5(a)) andthe area of influence of the 119894-TAP 119860TAP119894 (Figure 5(b))

For each wind direction 120572 the generic wind force 119865119896 andmoment 119872119896 in the generic 119896-floor implemented in the FEMare given by

119865119896 = [(119901TAP11198601198961 + 119901TAP21198601198962 + sdot sdot sdot + 119901TAP119899119860119896119899)(1198601198961 + 1198601198962 + sdot sdot sdot + 119860119896119899) ] 119872119896= (119901TAP111986011989611198971198961 + 119901TAP211986011989621198971198962 + sdot sdot sdot + 119901TAP119899119860119896119899119897119896119899)

(5)

where 119897119896119894 (119894 = 1 119899) represents the eccentricity betweencenter of gravity and the centroid of the area 119860119896119894 Thecorresponding 119865119896 and 119872119896 were applied in the barycenter ofeach FEMrsquos 119896-floor

By the linear time history analysis (Figure 6) consideringthe first 10mode shapes and different coefficients of structuraldamping (120585 = 1ndash4) the acceleration at the top of thebuilding (119886Sd) was obtained All acceleration is calculated bycombing the two translational values (119909- and 119910-directions)with the torsional value (around 119911-axis) For 120585 = 1 thevalue of 119886Sd at top of building is 045ms2 (Figure 6) which ishigher than the comfort limit value 119886Rd = 020ms2 in Table 1However when the damping in the building is increasedup to 4 the maximum acceleration is about 025ms2which is still higher than the comfort limit value It impliesthat damping should be increased beyond 4 to get thedesired value of acceleration (ie below 020ms2)This valueof damping in the structure can be achieved by installingdamping devices (TMD or VDs) which is studied in thesubsequent sections

5 High Frequency ForceBalance Method (HFFB)

The HFFB technique is widely used to measure wind forceson buildings by wind tunnel testing replicating the full scalescenario High accuracy force sensors are employed to mea-sure wind induced loads at the baseThe generalized loads arecorrelated to measured loads if the building has uncoupledlinear translational and uniform mode shapes [44]

HFFB procedure defines the global wind stress action onthe building as the summation of the static and dynamiccontributions [45ndash48] The dynamic contribution is charac-terized by the background and the resonant part Thus thegeneric action for example the total moment tot at the baseof the building is given by

tot = 119872 + 119872dyn = 119872 + 119892119861 sdot 120590119872119861 + 119892119877 sdot 120590119872119877 (6)

where

(i) tot is total stress moment (static and dynamic con-tributions)

(ii) 119872 is static contribution of the stress moment(iii) 119872dyn is dynamic contribution of the stress moment(iv) 119892119861 sdot 120590119872119861 is background part of the dynamic contribu-

tion(v) 119892119877 sdot 120590119872119877 is resonant part of the dynamic contribution


1 floor2 floor3 floor4 floor5 floor6 floor7 floor8 floor9 floor

10 floor11 floor12 floor13 floor14 floor15 floor16 floor17 floor18 floor19 floor20 floor21 floor22 floor23 floor24 floor25 floor26 floor27 floor28 floor29 floor30 floor31 floor32 floor33 floor34 floor35 floor36 floor37 floor38 floor39 floor40 floor41 floor42 floor43 floor44 floor45 floor46 floor47 floor48 floor49 floor50 floor51 floor

52 floor (roof)

Ground floor

(a) (b)

Figure 4 Pressure tap layout (a) facade East and (b) facade North


ℎℎ

i minus 1 i i + 1

Ak

Floor k + 1

Floor k

Floor k minus 1

lki

lp2

(a)

i minus 1 i i + 1A４０iminus1 A４０i A４０i+1

lp2

(b)

i minus 1 i i + 1Akiminus1 Aki Aki+1

lp2

(c)

Figure 5 (a) Area of influence of the 119896-floor 119860119896 (b) Area of influence of the 119894-TAP 119860TAP119894 (c) Area 119860119896119894 obtained by the intersection of 119860119896and 119860TAP119894

045

Time (s)300 400 500 600 700 800 900 1000 1100 1200

050040030020010000

minus010minus020minus030minus040minus050

a３＞

(mＭ

2)

(a)

Time (s)

025

300 400 500 600 700 800 900 1000 1100 1200

025020015010005000


030

minus030

a３＞

(mＭ

2)

(b)

Figure 6 Time history of the acceleration (in 119910-direction) (a) for 120585 = 1 and (b) for 120585 = 40

In (6) it is possible to distinguish

(i) the extreme Gumbel value

= 119872 + 119892119861 sdot 120590119872119861 (7)

(ii) the resonant value

dyn119877 = 119892119877 sdot 120590119872119877= (radic2 ln (119891119894 sdot 119879) + 05772radic2 ln (119891119894 sdot 119879))

sdot radic 1205874 sdot 120585119891119894 sdot 119878119872 (119891)(8)

in which

(i) 119879 refers to the time period (for the evaluation of themaximum value of the stress action (600 s))

(ii) 119891119894 is the building natural frequency associated withthe direction in which the moment is valued (in

this case the first the second and the third naturalfrequencies are considered by a modal analysis usingFEM)

(iii) 119878119872(119891) refers to the PSD (power spectral density)of the base moments (measured by a dynamometricbalance)

(iv) 120585 is the structural damping

The Gumbel forces and moments coefficients values (foreach time history and for all thewind directions) are obtainedstarting from the Fisher Tippet II probability density function[49] and the fully probabilistic method [50] ensuring theprobabilities of occurrence related to the Gumbel coefficientsvalues and the wind velocities are the sameThe resonant partof the dynamic contribution is used to evaluate the forces119865eq(119911) and the resonant moment 119872eq(119911)

119865eq (119911) = dyn119877119898(119911) 120593119894 (119911)int119867

119900120593119894 (119911) 119911119898 (119911) 119889119911

119872eq (119911) = dyn119877120601119894 (119911) 119868 (119911)int119867

119900120601119894 (119911) 119868 (119911) 119911 119889119911

(9)


minus7000

minus6000

minus5000

minus4000

minus3000

minus2000

minus1000

0

1000

2000

3000

4000

5000

6000

7000

0 45 90 135 180 225 270 315 360

Mx

(kN

m)

Angle

MMMＮＩＮ for = 1

MＮＩＮ for = 2MＮＩＮ for = 4

times103

(a)

0

10

20

30

40

50

0 45 90 135 180 225 270 315 360Angle

minus10

minus20

minus30

minus40

minus50

times103

FFFＮＩＮ for = 1

FＮＩＮ for = 2FＮＩＮ for = 4

Fy

(kN

)

(b)

Figure 7 Base loads (a) base moment in 119909 direction (119872119909) and (b) base shear in 119910-direction

in which 119898(119911) designates the distributed mass of the towerand 119868(119911) refers to the second moment of area while 120601119894(119911)refers to the first eigenvector associated with the directionin which the force is valued From 119865eq(119911) and 119872eq(119911)the translational and rotational acceleration are calculatedin

119886119909 (119911) = int119867119900

120593I (119911) 119865eq (119911) 119889119911int119867119900

1205932I (119911)119898 (119911) 119889119911 120593I (119911) 119886119911 (119911) = int119867

119900119872eq (119911) 120593III (119911) 119889119911int119867119900

1205932III (119911)119872 (119911) 119889119911 120593III (119911) 119886119910 (119911) = int119867

119900119865eq (119911) 120593II (119911) 119889119911int119867119900

1205932II (119911)119898 (119911) 119889119911 120593II (119911) (10)

To take the effect of nonsimultaneousness into account thecontributions in 119909- 119910- and 119911-directions have to be combinedby specific coefficients [29] With the HFFB procedure it ispossible to point out the dynamic effects Base shear bendingmoment and the acceleration response are calculated asfunction of the direction angle 120572 for several damping ratios120585 (10 20 and 40) (Figures 7 and 8) For each winddirection 120572 it is possible to see the static and dynamiccontribution of the wind effects particularly for the sectoraround 292∘ there are maximum values of the actions The

differences between the static part and the dynamic part areunderlinedThe acceleration is calculated at the corner of thebuilding combing acceleration 119886119909 and 119886119910 respectively withthe contribution of the torsional acceleration 119886119911 In Figure 9point 119875 represents a generic point on the building floor 119889119909and 119889119910 are the distances of 119875 from the centroid in 119909- and 119910-direction respectively The maximum design acceleration atpoint 119875 is given by 119886Sd119909 = 119886119909 + 119889119910119886119911 and 119886Sd119910 = 119886119910 + 1198891199091198861199116 Design Limits

The stress forces and the acceleration calculated by the PIMand the HFFB procedures show the dynamic effects due tothe geometrical slenderness and shape of the building Thevalue of shear force (119865) and the moment (119872) at the baseof building and top acceleration (119886Sd) are evaluated by twoprocedures described above which are different from thoseprescribed in the international codes The codes used forthe comparisons are the Eurocode 1 (EC1) and the ItalianCNR DT2072008 (CNR) indicated in the Italian code (DM2008)

For the stress forces comparison is carried out consid-ering the base shear force for 119879R = 100 years (ULS) In thecodes (EC1 DM 2008 and CNR) the base shear force along-wind direction (design value) is very similar to that evaluatedby the HFFB but it is different for the across-wind directionUsing the wind velocities estimated for the site [41] the baseshear force (1198650) is shown in Table 3


135 180 225 270 315 360

035

010

015

005

020

000

025

030

Angle

0 45 90

a３＞

(mＭ

2)

(a)

135 180 225 270 315 360

050

010

015

005

020

000

025

030

045

040

035

Angle

0 45 90

a３＞

(mＭ

2)

(b)

Figure 8 Acceleration response for different damping ratios 120585 (a) in 119909-direction and (b) in 119910-direction (the torsional component isconsidered)

X

Y

O

Pax

ay

azdy

dx

Figure 9 Representation of a point 119875 for acceleration estimation

Among the applicable codes in Italy the across-windeffects can be evaluated only by the CNR but in theirevaluation the CNR does not consider the maximum windvelocity (38ms for 120572 = 2925∘) since it takes in accountonly the wind speed in correspondence to the main axes ofthe building Using the CNR the structure does not appearafflicted by the vortex shedding actually realized in windtunnel testing which causes high value of stress effects inacross-wind direction From the codes evaluating the vortexshedding critical velocity Vcr and comparing it with thereference velocity Vref it results that the vortex shedding doesnot exist in the present building case In fact for Vcr = 50ms(119879R = 10 years) the following relations are satisfied

Vcr lt 125Vref 997888rarr 50ms lt 3968ms (= 125 sdot 3175ms) (valid for EC1) Vcr lt Vref 997888rarr 50ms lt 3190ms (valid for CNR) (11)

In the estimation of Vcr structural damping is not natu-rally set but in case of reinforced concrete structure it rangesbetween 120585 = 08 and 2 (for the SLS it would be moreadvantageous to use an high values of 120585) In this buildingnatural structural damping is taken as 1The comparison interms of acceleration in 119910-direction is shown in the Table 4for 119879R = 10 years (SLS) and for two different damping ratios(120585 = 1 and 120585 = 4)

From Table 4 one can see that in the CNR code thedynamic effects of the wind are taken into account evenif these are overestimated In Table 5 the displacementsobtained by wind tunnel tests as well as with PIM are list-ed

7 Improvements

From above two procedures applied in wind tunnel test(HFFB and APTH) wind induced responses in the buildingare determined In order to reduce those responses up to theacceptable limit prescribed in standard code there needs tobe some improvements in the buildingThe improvements inthe building are analyzed in terms of (i) reduction of height(ii) changing internal structural configuration by putting belttruss in different level (iii) installation of damping devices(TMD and VD) and (iv) changing the orientation of build-ing Before analyzing those improvements it is necessary toclarify some questions about the wind velocity (Section 71)


Table 3 Shear design value at the base of the building

Winddirection Vref [ms] Shear

direction1198650 [kN]

CNR (EC1)1198650 [kN]HFFB

0∘ndash180∘ 344 Along-wind 12211 (10392) 10816Across-wind 10079 33863


2925∘ 38 119909 mdash 27955119910 mdash 46052

Table 4 Stress design acceleration

PIM HFFB CNR EC1119886max (120585 = 1 - 119879R = 10years) [ms2] 045 047 053 019

119886max (120585 = 4 - 119879R = 10years) [ms2] 025 024 mdash mdash

Table 5 Stress design displacements

Wind tunnel tests PIM120575max (120585 = 1 - 119879 = 10 anni)[m] 045 041

120575max (120585 = 4 - 119879R = 10 anni)[m] 025 022

71WindVelocity and the Building Orientation To determinethe site wind velocity it is necessary to take in account twocoefficients the missing data correction coefficient 1198881 [51]and the directional coefficient 1198882 [52] If 1198882 was estimatedby Kasperski in place of Cook [53] referring to [51] themaximum value of the site wind velocity could be decreasedFor the north-west sector (270∘ndash360∘) the wind site study setsthe reference velocity Vref = 285ms (for 119879R = 100 yearsand quote 119911 = 100m) Tacking in account the missing datacoefficient 1198881 = 114 and the directional correction coefficient1198882 = 115 (by Cook) the reference velocity increases tothe new value of Vref = 373ms As mentioned beforeconsidering Kasperski [52] 1198882 decreases to 1198882 = 111 obtaininga new value Vref = 3606ms This last value is lower thanthe first one but always higher than the code no-directionalvelocity estimated by the Italian regulation Vref = 3325ms(119879R = 100 years at 100m) Keeping in mind the fact thatthe wind velocity is changed with the direction one canfind an optimal ordination for the building that can resultin minimized overall loads and responses The effect of winddirectionality on the responses will be investigated later inthis study (Section 75)

72 Height Reduction It is obvious that higher the buildingthe higher the flexibility for the same footage Here the studyfocuses on how sensitive the wind induced responses areto change in the building height In the first design phasethe building height was 225m a reduction in the height inthe order of 125 was considered to check the responsesensitivity The reduction in the height was considered to

Table 6 Percentages of increase in the dominant frequencies

Vibrational mode shape Δ119891 []I (flexural along 119909) 19II (flexural along 119910) 18III (torsional around 119911) 19

understand its effect as an alternative to installing a TMD ormodifying the layout of the building by creating belt internaltrusses

The reduction in the height was achieved by eliminatingthe top five floors Apparently the reduction involves the lossof five floors but if we consider the fact that the structuresupporting the TMD needs three floors the reduction ofheight actually leads to a loss of two floors saving costs andexecution time Consequently the slenderness decreases to120582 cong 850 leading to (i) a reduction of the displacementat the top (ii) a reduction of base forces and momentsand (iii) an increase in the structural stiffness with rigidityimprovement If we consider a simplified cantilever beammodel for the same bending stiffness (EI) of the cross-sectionand the same distributed load (119901) along the height (119867) theinitial displacement (120575119894) and the reduced displacement (120575119903)are given by (per unit load)

120575119894 = (1199011198671198944)(8EI) 120575119903 = (1199011198671199034)(8EI) = 059 times (1199011198671199034)(8EI)

(12)

Thus the reduction in the displacement at the top is aboutΔ120575 cong 41 Considering that the base shear is proportional tothe height of the building and the basemoment is a quadraticfunction of the building height (under the same load 119901) thereduction in the base shear is Δ119865 cong 125 and the reductionin the bending moment is Δ119872 cong 23 The initial stiffness ofthe building 119896119894 = 8EI1198671198943 is increased to 119896119903 = 8EI1198671199033 =149 times 8EI1198671198943 under the same load Thus the increment isabout Δ119896 cong 49 An estimate of the main frequencies couldbe obtained by the following simplified relation

119891 = (119896119898)122120587 (13)

where 119896 is estimated stiffness and119898 is mass Due to reductionin height totalmass of building is decreased by (Δ119898 = 555)which ultimately increased the natural frequencies (Δ119891) aslisted in Table 6 (about 20 increase) Combining the reduc-tion in both wind speed and building height improvementsin terms of base shear reduction (Δ119865119910) moment (Δ119872119909) andtop floor acceleration (Δ119886max) reductions are listed in Table 7All the improvements are verified by the HFFB method

While Table 7 lists the combined effects of the reductionin the building height and the wind speed the sole reductionin the responses due to the reduced building height issignificant The reductions in the base shear force are in theorder of 13 the reduction in the base bending moment isabout 26 and the reduction in the acceleration is about 21


Table 7 Structural improvements for different velocities and heights reductions in the base shear and bendingmoments and the accelerationresponse of the top floor

Configuration 119867 [m] V [ms] Δ119865119910 [] Δ119872119909 [] Δ119886max []Initial 225 38 (Directional velocity) mdash mdash mdashInitial 225 33 (Directional velocity) 198 186 90Initial 225 33 (No-directional velocity) 174 11 77Proposed 199 38 (Directional velocity) 13 26 21Proposed 199 36 (Directional velocity) 195 384 22Proposed 199 33 (Directional velocity) 326 406 294Proposed 199 33 (No-directional velocity) 282 383 153

73 Structural Configuration To save the internal layout ofthe structure from significant changes that could result fromincrease of thickness different structural configurations areconsidered Introduction of an internal belt truss system ora beam-wall increases the stiffness of structure This systemconsists of main cores linked with outer columns by stiffmembers which can be about one ormore story depth Underlateral wind loads the internal moments are resisted by bothcore and tensioncompression developed in outer columnsThus the effectiveness of the building to carry bendingis enhanced [23] The configurations are characterized bybeams height one or two interstory distance It is possible torealize the beams in concrete (beam-wall case) or in S355 steel(belt truss case)

In both cases the belt truss could span along two or fourhorizontal alignment with a depth of one or more storiesas shown in Figure 10 In case of two alignments the belttruss can be placed either along the central axes or along thefacades

The analysis discussed in this paragraph is related to thebuilding with a height of 225m The beam-wall or belt trusselements work as a stiffening bracing system along the axis 119909The response reduction was investigated by using a belt trusssystem in the building at different levelsThree different casesare studied and configurations of each case are explainedbelow

Case 1 Two horizontal alignments of belt trusses with fourinterstory depths are considered The configurations of theproposed bracing system for Case 1 over the buildingrsquos heightare (i) at 12 and top (ii) at 12 and 34 (iii) at 14 and 12 (iv)at 12 and (v) at top as shown in Figure 11 (see also Table 8)

Case 2 Four horizontal alignments of the belt trusses withtwo interstory depth are considered where the belt trussesare located (i) at 12 and (ii) at the top of the building (seeTable 9)

Case 3 Four horizontal alignments of the belt truss with oneinterstory height are considered and belt trusses are intro-duced at 14 12 and 34 of building height (see Table 10)

The comparisons between the original and the modi-fied configurations are carried out in terms of decrease inbase moment Δ119872119910 [] increase in the first vibrationalmode (along the axis 119909) Δ1198911 [] and decrease of the top

Table 8 Comparisons between the original building and thesolution proposed in Case 1 n 4 interstories in height and n 2 linesin horizontal length Case 1

Belt trussesquotes Δ119872119910 Δ120575 Δ1198911 Note

12 and top 158 458 257Number 2 belt trussesndash height number 2

interstory

12 and 34 210 500 289Number 2 belt trussesndash height number 2

interstory


interstory

12 190 437 244Number 2 belt trussesndash height number 4

interstory

Top 60 271 136Number 2 belt trussesndash height number 4

interstory

Table 9 Comparison between the original building and the solutionproposed in Case 2 n 2 interstory in height and n 4 lines inhorizontal length Case 2


at 12 188 458 257Number 4 belt trussesndash height number 2

interstories


interstories

displacement in 119909-direction Δ120575 [] The improvements forall the cases are shown in Tables 8ndash10 If one looks at thegeneral pattern from Tables 8 9 and 10 it can be observedthat the best solution to improve the structural behaviorunder wind load is to place the belt trusses at half height ofthe building rather than at the top as confirmed in Table 11Although there ismaximum reduction of displacement (Δ120575 =50) in Case 1 when the belt trusses are at 12 and 34 thereduction in base moment is small as compared to the otherconfigurations (14 and 12) Thus among all configurationsand best improvements in the base moment (Δ119872119910 = 289)


Cores

Axis 2

Axis 1

Beams connected thetwo parts of the core

Belt trusses positioning

(a)

Cores

Axis 2

Axis 1

Axis 4

Axis 3



Extension of wallsof the core

(b)

Figure 10 Schematic representation of the location of the built trusses in the top view (a) two alignments and (b) four alignments

Table 10 Percentages of response reduction achieved by thesolution proposed in Case 3 n 1 interstory in height and n 4 linesin horizontal length Case 3


12 14 and34 184 354 198

Number 3 belt trussesndash height number 1

interstory

the displacement (Δ120575 = 479) and the natural frequency(Δ1198911 = 269) are achieved in Case 1 when the belt trussesare at 14 and 12 (Table 8)

The significant improvement in terms of natural fre-quency (Δ1198911 = 289 this value determines some dynamiceffects related to the wind action) is represented by two belt

Table 11 Effects of belt-truss location of the response


top 42 202 94Number 2 belt trusses ndash

height number 2interstories

12 140 326 186Number 2 belt trusses ndash


trusses with two interstory height located at 12 and 34 butthe base moment is reduced significantly when belt trussesare at 14 and 12 Clearly the solution with belt trusses withfour interstory heights is more invasive for the layout of thebuilding


(a) 12 and top (b) 12 and 34 (c) 14 and 12 (d) 12 (double) (e) Top (double)

Figure 11 Schematic representation of the position of the belt trusses for Case 1 see Table 8

Therefore structural improvements related to some dif-ferent structural configurations are illustrated Each configu-ration is characterized by the insertion of concrete beam-wallor steel belt truss to increase the stiffness of the building Theconcrete beam-wall seems easier to realize in comparison tothe belt truss but the presence of the necessary openings inthe longitudinal beam-walls is negative for the strut and tiebehavior (thus only few openings could be realized) Con-versely the configurations with steel belt trusses guaranteethe strut and tie behavior but their positioning could bepainstaking

74 Installation ofDampers To improve the structural behav-ior some active or passive mass dumpers solutions couldbe considered [6 54ndash56] In the present case a solutionrepresented by TMD is taken into account The damper isrepresented by a nodal mass linked to center of gravity of topfloor by a linear spring-damper element The mass damperis implemented in the FEM of building as well as the HFFBprocedure The TMD stiffness ratio and the coefficient ofdamping are evaluated according to [55] The TMD wasassumed to be installed at top of the tower making useof the top three stories which has increased the structuraldamping from 1 to 4 Response reduction is analyzed interms of reduction in base shear for different wind directionangles Significant reduction in base shear is achieved byinstallation of TMD as listed on Table 12 It can be observedfrom Table 12 that the base shear is considerably reduced ineach wind direction angle however the highest reduction(Δ119865 = 4346) is obtained along the119909-axis at a damping ratio120585 of 40 when the wind angle is 2925∘

Another solution represented by VDs is implemented inthe FEmodel as shown in Figure 12Thedampers are installedtransversely in the cores from the base up to the 20th floorThe installation includes problems due to the openings in thewalls of the cores to pass from the elevator areas to the inner

Table 12 Improvements by the TMD

Winddirection Base shear direction

1198650 [kN]HFFB ndash Vsite120585 = 10


0∘ndash180∘ Along-wind 10816 8338Across-wind 33863 19847


2925∘ 119909-axis 27955 15803119910-axis 46052 35697

areas By installing viscous dampers base shear is reducedby Δ1198790 = 45 (at ULS) peak acceleration in 119909-directionis reduced by Δ119886119909 = 25 (at SLS) and displacement at thetop of building is reduced by Δ120575 = 33 (at ULS) Althoughviscous dampers are effective in reducing displacement andbase shear they are not that effective in reducing peakacceleration of building Despite the installation of viscousdampers the peak acceleration obtained is 032ms2 whichis greater than the comfort limit of 02ms2 (for office usage)In order to get compatible value of acceleration (smaller than020ms2) installation of viscous damper should be extendedup to 35th story

75 Global Layout Thewind direction angle and interferenceeffects are two important factors that should be carefullystudied early in the design phase Wind loads and responsesin high-rise buildings depend on wind direction angle andinterference of existing building in that area Since theapproaching wind flowmay have different mean wind speedswhen it reaches the building from different directions andconsidering the fact that along-wind and the cross windresponses are different it is feasible to rotate original building


X

Y

Figure 12 FEMwith the viscous dampers implemented in the cores

Table 13 Percentages of response reduction for two proposedorientations

TA rotation Δ119886Sd119910 Δ120575Sd11991045∘ 13 1165∘ 28 24

layout in such a way that the wind induced responses arereduced [57]

From the dynamic procedures and the tests in the windtunnel it is possible to understand the most correct layoutfor building especially if other tall buildings will rise upnearby [58] The decrease of the stress effects in 119910-directionis obtained by 45∘ clockwise rotation of building from theinitial layout (Figure 13) When the building is rotated by 45∘there was only slight reduction of responses but in case of65∘ clockwise rotation the highest reductions of accelerationand the displacement at the top are obtained (Table 13 wheresymbol of acceleration is 119886Sd119910 and the displacement is 120575Sd119910)

Acceleration in 119910-direction is decreased by 2727 (119886Sd119910is reduced from 088ms2 to 064ms2) and displacementin 119910-direction is also reduced by 25 (120575Sd119910 is decreasedfrom 120m to 090m)Despite thementioned improvementsin 119910-direction the 65∘ clockwise rotation of building fromthe original layout has increased the acceleration (119886Sd119909) andthe displacement (120575Sd119909) in 119909-direction In the 119909-directionacceleration is increased by 9 and displacement is increasedby 35 (119886Sd119909 is changed from 053ms2 to 058ms2 and 120575Sd119909is changed from 085m to 088m) Since wind effects in the119909-direction are low compared to 119910-direction slight increaseof responses in 119909-direction could be acceptable as comparedto large reduction of responses in 119910-direction

This reduction in responses is achieved without addingany structural element or component in the primary buildinghence no additional cost on the building This confirms the

oy

x

0∘

45∘

90∘

135∘

180∘

225∘

270∘

315∘

TA

2925∘

y

x

Figure 13 Representation of the orientation change

advantage of rotating the building to the suggested orienta-tion It also explores the significance of response predictionin high-rise building during preliminary design stage

8 Conclusions

In this paper some limits of available design standards(Eurocode 1 amp the Italian design code) to evaluate windactions on high-rise buildings (displacements and accelera-tion responses) are presented pointing themout in a compar-ison to a more sophisticated methods (ie the use of the PIMwith FEM of the building and the HFFB technique) Theselimits are highlighted by the fact that the detailed analysismethod resulted in higher base shear and moment valuesthan those provided by the design standards and that wasstrongly influenced by the high aspect ratio of the building Infact vortex shedding effects were realized in the current studyin both results obtained by the PIM and the HFFB methodsand such phenomenonwas greatly dependent on the buildinggeometry which is not fully addressed in the codes

Structural improvements are proposed which resultedin considerable response reductions without significantlyalerting the architectural shape of the original buildingThesesolutions include (i) height reduction (ii) steel belts (iii)tunedmass damper (iv) viscous dampers and (v) orientationchange A reduction in the apparent height in the order of125 was considered to check the response sensitivity Thereduction in the height was considered to understand itseffect as an alternative to installing a TMD The reductionin the height was achieved by eliminating the top five floorsApparently the reduction involves the loss of five floorsbut if we consider that the structure supporting the TMDneeds three floors the reduction of height actually leads toa loss of only two floors This height lessening led to reducedbase shear force in the order of 13 reduced base bendingmoment (26) and reduced acceleration (21)

Belt truss systems with different structural configurationsare studied and compared in terms of their capability to


bring reduction to the base bending moment reductionof displacement at the top and the increase of naturalfrequenciesThe optimal numbers and location of belt trussesare determined by comparing three different cases for themaximum reduction of wind induced responses In eachcase it is observed that the performance of the belt trusssystems is at its maximum level when they are placed athalf height of the building rather than at the top It can alsobe concluded that two horizontal alignments of belt trussesalong the major axis of the building are more effective thanfour alignments considering same number of belt trussesNevertheless two horizontal alignments of belt trusses withtwo interstory depths located at 14 and 12 the height ofthe building (Case 1) are efficient in reducing the responseswhere the displacement at the top is reduced by about 48and the bending moment is reduced by 29

Vibration suppression by the installation of a TMD isevaluated by reductions in the base shear and bendingmoments as well as displacement and acceleration Resultsshow considerable reduction in base shear in each winddirection angle however a maximum reduction in base shear(435) is achieved by an equivalent damping ratio of 40when the wind direction angle is 2925∘ The TMD appearsto be a valid technical solution but in order to implementit the loss of the top three floors has to be consideredwhich is necessary to build the structure supporting theTMD

Another improvement is presented by viscous damperswhere the dampers are installed transversely in the coresfrom the base up to the 20th floor VDs were installed toexamine their potential to reducing the base loads peakacceleration and the maximum displacement Substantialimprovements are achieved using viscous dampers baseshear is reduced by 45 peak acceleration is lessened by25 and the displacement is reduced by 33 Althoughthe installation of viscous dampers up to the 20th floor iseffective in reducing displacement and base shear it is notenough to reduce the peak acceleration to the prescribedlimits Thus the installation of VDs up to the 35th floor wassuggested

Finally the importance of the global positioning of thebuilding (orientation change) was examined consideringits rotation with respect to an original layout The rotationof the building by 65∘ from the initial layout resulted inthe highest reduction in displacement and acceleration Thereduction in the acceleration is 27whereas the displacementis reduced by 25 This reduction in responses is achievedwithout adding any structural elements or components tothe primary building hence no additional cost This revealsthe advantage of rotating the building to the suggestedorientation and highlights the significance of response pre-diction in high-rise buildings during the preliminary designstage

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

Partial support received from the Louisiana Board of Regents(BoR) (Research Competitiveness Subprogram [RCS]) isacknowledged

References

[1] A Farouk High Rise Buildings and How They Affect CountriesProgression Department of Architecture Engineering CairoUniversity 2011 httpswwwg-casacomconferenceszagrebpapersAkram1-HighRisepdf

[2] H Y O S Park and C L I M Park ldquoDrift control of high-risebuildings with unit load methodrdquo vol 6 pp 23ndash35 1997

[3] H S Park H G Sohn I S Kim and J H Park ldquoApplication ofGPS to monitoring of wind-induced responses of high-risebuildingsrdquo The Structural Design of Tall and Special Buildingsvol 17 no 1 pp 117ndash132 2008

[4] T Kijewski ldquoFull-scale study of the behavior of tall buildingsunder windsrdquo Proc SPIE vol 4337 no 219 pp 441ndash450 2001

[5] R Rana and T T Soong ldquoParametric study and simplifieddesign of tuned mass dampersrdquo Engineering Structures vol 20no 3 pp 193ndash204 1998

[6] A M Aly ldquoVibration control of high-rise buildings for wind Arobust passive and active tuned mass damperrdquo Smart Structuresand Systems vol 13 no 3 pp 473ndash500 2014

[7] Y-M Kim K-P You andH-Y Kim ldquoWind-induced excitationcontrol of a tall building with tuned mass dampersrdquo TheStructural Design of Tall and Special Buildings vol 17 no 3 pp669ndash682 2008

[8] A Kareem T Kijewski andY Tamura ldquoMitigation ofMotion ofTall Buildings with Specific Examples of Recent ApplicationsrdquoWind Struct vol 2 no 3 pp 201ndash251 2007

[9] K A OrsquoConnor J D Johnson S E Hammack et al ldquoInescap-able shock induces resistance to the effects of dexamethasonerdquoPsychoneuroendocrinology vol 28 no 4 pp 481ndash500 2003

[10] S Nagarajaiah and B Basu ldquoOutput only modal identificationand structural damage detection using time frequency wavelettechniquesrdquo Earthquake Engineering and Engineering Vibrationvol 8 no 4 pp 583ndash605 2009

[11] Y Fujino L Sun B M Pacheco and P Chaiseri ldquoTuned liquiddamper (TLD) for suppressing horizontalmotion of structuresrdquoJournal of EngineeringMechanics vol 118 no 10 pp 2017ndash20301992

[12] M J F Silva and A C Costa ldquoExperimental Studies On TheCharacteristics Of Tuned Liquid Dampers For Reducing Vibra-tion In Structuresrdquo in Proceedings of the 14th World ConferenceEarthquake China 2008

[13] H F Bauer ldquoOscillations of immiscible liquids in a rectangularcontainer A new damper for excited structuresrdquo Journal ofSound and Vibration vol 93 no 1 pp 117ndash133 1984

[14] N Makris M C Constantinou and G F Dargush ldquoAnalyticalmodel of viscoelastic fluid dampersrdquo Journal of StructuralEngineering vol 119 no 11 pp 3310ndash3325 1994

[15] M C Constantinou and M D Symans ldquoSeismic response ofstructures with supplemental dampingrdquo The Structural Designof Tall and Special Buildings vol 2 no 2 pp 77ndash92 1993

[16] C Prabha and L Mathew ldquoEffect of Fluid Viscous Dampers inMulti-Storeyed Buildingsrdquo International Journal of Research inEngineering and Technology vol 2 no 9 pp 59ndash64 2014


[17] D P Taylor Using Modern Technology for the Reduction ofEarthquake Damage in Buildings Taylor Devices Inc NorthTonawanda NY USA 2012 httptaylordevicescompdf2013-dampersChange2012pdf

[18] M Constantinou ldquoApplication of fluid viscous dampers toearthquake resistant designrdquo in Report on Research Accomplish-ments 1986ndash1994 pp 73ndash80 National Center for EarthquakeEngineering and Research Buffalo NY USA 1994 httpcid-bimenadesastreshnpdfengdoc8169doc8169-contenidopdf

[19] R J McNamara D P Taylor and P Duflot ldquoFluid Vis-cous Dampers to Reduce Wind-Induced Vibrations in TallBuildingsrdquo Tech Rep Taylor Devices Europe Brussels 2005httpwwwtaylordeviceseupdfstall-building 1pdf

[20] P S Kumar M V Naidu S M Mohan and S S Reddy ldquoAppli-cation of Fluid Viscous Dampers In Multi-Story BuildingsrdquoApplication of Fluid Viscous Dampers In Multi-Story Buildingspp 17064ndash17069 2016

[21] K Ding X Zhao Y Yang and L Ye ldquoApplication of viscousdampers for super tall residential buildings in high-windstrong-seismic areardquo in Proceedings of the 2016 World Congresson Advances in Civil Environmental and Materials Research(ACEM16) Jeju Island South Korea August 2016

[22] A Khanorkar S V Denge and S P Raut ldquoBelt truss as lateralload resisting structural system for tall building a reviewrdquo IJSTE- International Journal of Science Technology amp Engineering vol2 no 10 pp 658ndash662 2016

[23] B M Simantini and M Manjunath ldquoAn analysis of outriggerbelt truss system in high-rise buildingsrdquo IUP Journal of Struc-tural Engineering vol 8 no 3 pp 16ndash25 2015

[24] R S Nair ldquoBelt Trusses and Basements as ldquoVirtualrdquo Outriggersfor Tall Buildingsrdquo Engineering Journal vol 35 no 4 pp 140ndash146 1998

[25] P S Kian ldquoThe use of outrigger and belt truss system for high-rise concrete buildingsrdquo Civil Engineering Dimension vol 3 no1 pp 36ndash41 2001

[26] Eurocode ldquoEurocode 1 Actions on Structures Part 1-4 GeneralActionsWind actionsrdquo prEN 1991-1-4 European Standard 2004

[27] CNR ldquoIstruzioni per la valutazione delle azioni e degli effettidel vento sulle costruzionirdquo in Proceedings of the CNR ndash Com-missione di studio per la predisposizione e lrsquoanalisi di norme tec-niche relative alle costruzioni CNR-DT 2072008 2009 (Italian)httppeoplediceaunifiitgiannibartolinormativeCNRDT207 2008pdf

[28] R McNamara A Kareem and T Kijewski ldquoAsk the expertsPerception of motion criteria for tall buildings subjected towind a panel discussionrdquo in Proceedings of the 2002 StructuresCongress Reston Va USA 2002

[29] K C S Kwok P AHitchcock andMD Burton ldquoPerception ofvibration and occupant comfort in wind-excited tall buildingsrdquoJournal of Wind Engineering amp Industrial Aerodynamics vol 97no 7-8 pp 368ndash380 2009

[30] M D Burton K C S Kwok and A Abdelrazaq ldquoWind-Induced Motion of Tall Buildings Designing for OccupantComfortrdquoThe International Journal of High-Rise Buildings vol4 no 1 pp 1ndash8 2015

[31] A W Irwin ldquoHuman response to dynamic motion of struc-turesrdquo Structural Engineering vol 56 no 9 1978

[32] T Goto T Ohkuma Y Tamura and O Nakamura ldquoGuidelinesfor the evaluation of habitability to building vibration PartII AIJ recommendationsrdquo in Proceedings of the StructuresCongressrsquo 92 vol 92 pp 484ndash487 1991

[33] L G Griffis ldquoServiceability limit states under wind loadrdquo Engi-neering Journal vol 30 no 1 pp 1ndash16 1993

[34] M Huang C Chan and K C Kwok ldquoOccupant comfort eval-uation and wind-induced serviceability design optimization oftall buildingsrdquo Wind and Structures An International Journalvol 14 no 6 pp 559ndash582 2011

[35] M Belloli L Rosa and A Zasso ldquoWind loads on a high slendertower Numerical and experimental comparisonrdquo EngineeringStructures vol 68 pp 24ndash32 2014

[36] L Rosa G Tomasini A Zasso and A M Aly ldquoWind-induceddynamics and loads in a prismatic slender building A modalapproach based on unsteady pressure measurementsrdquo JournalofWindEngineeringamp Industrial Aerodynamics vol 107-108 pp118ndash130 2012

[37] PMendis T Ngo N Haritos A Hira B Samali and J CheungldquoWind loading on tall buildingsrdquo EJSE Special Issue Loading onStructures vol 3 pp 41ndash54 2007

[38] S O Hansen ldquoVortex-induced vibrations of structuresrdquo in Pro-ceedings of the Structural Engineers World Congress BangaloreIndia November 2007 httpciteseerxistpsueduviewdocdownloaddoi=10115474368amprep=rep1amptype=pdf

[39] A Kareem ldquoWind induced torsional loads on structuresrdquoEngineering Structures vol 3 no 2 pp 85-86 1981

[40] P Irwin R Denoon and D Scott Wind Tunnel Testing ofHigh-Rise Buildings An output of the CTBUHWind EngineeringWorking Group Council on Tall Buildings and Urban Habi-tat Chicago USA 2013 httpsstorectbuhorgPDF PreviewsBooks2013 WindTunnelGuide Previewpdf

[41] M P Repetto G Solari F Tubino and A Freda ldquoAnalisi delvento di progetto presso il quartiere storico dellarea della Fieradi Milanordquo SGS PRE VEN SPC 002(B) Genova 2006

[42] A Zasso A M Aly L Rosa and G Tomasini ldquoWind induceddynamics of a prismatic slender building with 1 3 rectangularsectionrdquo in Proceedings of the VI International Colloquium onBluff Bodies Aerodynamics Applications Milan Italy 2008

[43] A M Aly ldquoPressure integration technique for predicting wind-induced response in high-rise buildingsrdquo Alexandria Engineer-ing Journal vol 52 no 4 pp 717ndash731 2013

[44] M F Huang Q Li and W Lou ldquoUncertainty quantificationsin HFFB dynamic analyses of a complex tall buildingrdquo inProceedings of the 2016 World Congress on Advances in CivilEnvironmental and Materials Research (ACEM16) Jeju IslandSouth Korea August 2016

[45] X Chen and A Kareem ldquoValidity of wind load distributionbased on high frequency force balance measurementsrdquo Journalof Structural Engineering vol 131 no 6 pp 984ndash987 2005

[46] T Tschanz and A G Davenport ldquoThe base balance techniquefor the determination of dynamic wind loadsrdquo Journal of WindEngineering and Industrial Aerodynamics vol 13 no 1 pp 429ndash439 1983

[47] N Lin C Letchford Y Tamura B Liang and O NakamuraldquoCharacteristics of wind forces acting on tall buildingsrdquo Journalof Wind Engineering amp Industrial Aerodynamics vol 93 no 3pp 217ndash242 2005

[48] S Pasto L Facchini L Procino and P Spinelli ldquoEquivalentstatic wind loads on tall buildingsrdquo in Proceedings of theVI Inter-national Colloquium on Bluff Bodies Aerodynamics Applicationspp 20ndash24 Milan Italy 2008

[49] J A Peterka and J E Cermak ldquoWind pressures on buildings-probability densitiesrdquo Journal of the Structural Division vol 101no 6 pp 1255ndash1267 1975


[50] N J Cook ldquoCalibration of the quasi-static and peak-factorapproaches to the assessment of wind loads against the methodof Cook and Maynerdquo Journal of Wind Engineering amp IndustrialAerodynamics vol 10 no 3 pp 315ndash341 1982

[51] M P Repetto G Solari andM Tizzi ldquoIl ruolo dei datimancantinella statistica dei venti estremirdquo in XI Convegno Nazionale diIngegneria 2010

[52] M Kasperski ldquoDesign wind loads for a low-rise building takinginto account directional effectsrdquo Journal of Wind Engineering ampIndustrial Aerodynamics vol 95 no 9-11 pp 1125ndash1144 2007

[53] N J Cook ldquoNote on directional and seasonal assessment ofextreme winds for designrdquo Journal of Wind Engineering ampIndustrial Aerodynamics vol 12 no 3 pp 365ndash372 1983

[54] S M Zahrai and S Abbasi ldquoStudy on Possibility of UsingTuned Liquid Dampers (TLD) in High Frequency Structuresrdquoin International Conference on Technological advancements inCivil engineering (ICTACE 2012) 2012

[55] T T Soong andM C Costantinou Passive and active structuralvibration control in civil engineering vol 345 Springer 2014

[56] A M Aly Sayed Ahmed A Zasso and F Resta ldquoProposedconfigurations for the use of smart dampers with bracings intall buildingsrdquo Smart Materials Research vol 2012 Article ID251543 16 pages 2012

[57] A M Aly and S Abburu ldquoOn the design of high-rise buildingsfor multihazard fundamental differences between wind andearthquake demandrdquo Shock and Vibration vol 2015 Article ID148681 22 pages 2015

[58] A M Aly ldquoInfluence of turbulence orientation and siteconfiguration on the response of buildings to extreme windrdquoThe Scientific World Journal vol 2014 Article ID 178465 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of


International Journal of

RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



An additional challenge is the uncertainty in the amountof structural damping early in the planning phase [4] Toalleviate this issue structural control is a potentialmethod forstructural tuning and damping enhancementThe purpose ofstructural control in civil engineering structures is to reducevibrations produced by external stressors such as earthquakeand wind loads by different techniques such as modifyingstiffness mass damping or shape Structural control meth-ods are typically classified as active passive and semiactivetechniques Passive systems use supplemental devices whichrespond to the vibrations of the structure by dissipatingthe energy triggered by strong dynamic loads without theneed for an external energy supply A variety of passivecontrol mechanisms have been suggested by researchers andengineers including tuned mass dampers viscous dampersfriction dampers and tuned water dampers

An external power source is needed for an active controlsystem to control actuators that apply prescribed forces to astructurebuilding to injectdissipate energy and hence min-imize certain optimization objectives The command signalsto the actuator depend on the measured system response(feed-back control) However active control systems can beunstable and they need bulky power transformers andconsume significant amount of energy which may not beavailable especially immediately after natural disasters suchas earthquakes and high winds For this purpose passivecontrol systems remain the most reliable and practical tech-nique for structural control Some passive control systems arepresented as follows

12 Tuned Mass Dampers (TMDs) A vibration absorber or aTMDconsists of springmass and a damping device installedon a primary system to lessen the dynamic response Themain concept in the TMD is that the frequency of the damperis tuned to resonate out of phase with the vibration of theprimary structure leading to significant energy dissipationNumerous studies are focused on the performance of theTMD and its capability to suppress vibrations especiallydue to wind loads The concept of vibration suppression bya TMD dates back to 1909 when the vibration absorberwas invented by Farham making it as one of the earliestcontrol devices [5] Following this invention numerousstudies were conducted to validate the application as wellas to enhance the performance of the device with differentstructural configurationsThe concept of using a robust TMDwas proposed recently in which an approach was devel-oped to determine the optimal parameters under structuraluncertainties Significant reductions in the response can berealized by the optimum selection of the mass ratio andtuning frequency ratio [6] In high-rise buildings when theinherent sutural damping is low the TMD is proved to bevery effective in reducing the responses [7] TMDs are usedas controlling devices in high-rise buildings in Japan HongKong United States Australia and some other countriesThe Hancock Tower in Boston 244m as mentioned in [8]has two TMDs installed at the opposite ends of the 58thfloor with each unit weighting 300 tons However there areseveral limitations on the practical application of TMDS forexample being tuned to a single vibrational mode is limited

to narrow band of operation frequencies [9] The limitationsof the TMD can be significant when dealing with buildingsexcited at higher modes of vibration for example underearthquake loadsAlso TMDs are sensitive to uncertainties inthe structural parameters Structural parameters may changedue to damage material degradation or even environmentalvariations Such changes can lead to a detuned TMD withreduced effectiveness [10]

13 Tuned Liquid Dampers Tuned liquid dampers (TLDs)gained increased popularity due to their effectiveness inabsorbing low-frequency vibrations induced by wind beingcost effective requiring less maintenance and being easilyimplementable [11] TLDs are energy dissipation devicessuggested for vibration suppression under different dynamicloads A typical TLD consists of a container with liquidwaterto reduce vibrations of a primary structure This allows sig-nificant energy dissipation and hence reduced structuralresponses [12] The fundamental principle of vibration con-trol in structures using TLDs is based on sloshing and wavebreaking for energy dissipation [11] For efficient energy dissi-pation the fundamental frequency of liquid in a TLD shouldbe close to that of the primary structure Several researchstudies have been conducted onTLDs in the past fewdecadesThe research conducted by Bauer in 1984 [13] proposed adamping device to control vibrations where a rectangularcontainer filled with two immiscible liquids was utilized inwhich the interface motion dissipated the energy effectivelyRecently TLDs have been shown to be effective in lateralvibration control of high-rise buildings The Hobert Towerin Tasmania (Australia) with a height of 105m is equippedwith 80 TLDs Similarly in Kagawa (Japan) 16 units of TLDsare installed in the Gold Tower which has a height of 158mThe installation of TLDs is found to suppress vibrations ofbuildings underwind loads by one-third to half of the originalresponses [8]

14 Viscous Dampers Damping is an important mechanismthat dissipates energy and hence permits a structure toachieve high performance under dynamic loads such asearthquake strong wind or blast Numerous fluid dampingdevices with practical applications have been proposed overthe past few decades The use of damping devices filled withviscoelastic liquid to dissipate energy was studied extensivelyboth analytically and experimentally [14] When a VD issubjected to an external load friction forces develop amongdifferent elements Friction forces are developed among themolecules of the dampingmedium shaft andmedium pistonand medium and so on All these actions combine togetherto form a damping force which acts 90 degree out of phasewith the displacement driven force in a primary structure[15 16] Previous uses of viscous dampers (VDs) in militaryapplications include the attenuation of weapon grade shockaircraft ship vibration and underwater detonation

Viscous dampers that were used in military applicationsduring the cold war have been adopted for civil engineeringstructural applications [17] A number of countries are prac-ticing the use of VDs in tall building including Hong KongChina Japan and United States The Sato Building (1992)







2 Design Criteria
























x

y


Acro

ss-w

ind

dire

ctio

n


Z

f1 = 014 （Ｔ f2 = 015 （Ｔ f3 = 026 （Ｔ

Y

X









0 45 90 135 180 225 270 315 36015

20

25

30

35

40

Angle (∘)

Win

d ve

loci

ty

(mＭ

2)

T２ = 100 years


(a)

oy

x

0∘

45∘

90∘

135∘

180∘

225∘

270∘

315∘

TA

(b)
















119862119865119883 = 119865119883119902119861119867119862119865119884 = 119865119884119902119861119867119862119865119885 = 119865119885119902119861119867119862119872119883 = 1198721198831199021198611198672 119862119872119884 = 1198721198841199021198611198672 119862119872119885 = 1198721198851199021198611198672

(2)





119891TAP (119905 119911ref) = 119901TAP119860TAP (4)




(5)






tot = 119872 + 119872dyn = 119872 + 119892119861 sdot 120590119872119861 + 119892119877 sdot 120590119872119877 (6)

where







52 floor (roof)

Ground floor

(a) (b)



ℎℎ

i minus 1 i i + 1

Ak

Floor k + 1

Floor k

Floor k minus 1

lki

lp2

(a)


lp2

(b)


lp2

(c)


045

Time (s)300 400 500 600 700 800 900 1000 1100 1200

050040030020010000


a３＞

(mＭ

2)

(a)

Time (s)

025

300 400 500 600 700 800 900 1000 1100 1200

025020015010005000


030

minus030

a３＞

(mＭ

2)

(b)




= 119872 + 119892119861 sdot 120590119872119861 (7)




in which







119865eq (119911) = dyn119877119898(119911) 120593119894 (119911)int119867

119900120593119894 (119911) 119911119898 (119911) 119889119911

119872eq (119911) = dyn119877120601119894 (119911) 119868 (119911)int119867

119900120601119894 (119911) 119868 (119911) 119911 119889119911

(9)


minus7000

minus6000

minus5000

minus4000

minus3000

minus2000

minus1000

0

1000

2000

3000

4000

5000

6000

7000

0 45 90 135 180 225 270 315 360

Mx

(kN

m)

Angle



times103

(a)

0

10

20

30

40

50

0 45 90 135 180 225 270 315 360Angle

minus10

minus20

minus30

minus40

minus50

times103



Fy

(kN

)

(b)



119886119909 (119911) = int119867119900

120593I (119911) 119865eq (119911) 119889119911int119867119900

1205932I (119911)119898 (119911) 119889119911 120593I (119911) 119886119911 (119911) = int119867

119900119872eq (119911) 120593III (119911) 119889119911int119867119900

1205932III (119911)119872 (119911) 119889119911 120593III (119911) 119886119910 (119911) = int119867

119900119865eq (119911) 120593II (119911) 119889119911int119867119900

1205932II (119911)119898 (119911) 119889119911 120593II (119911) (10)






135 180 225 270 315 360

035

010

015

005

020

000

025

030

Angle

0 45 90

a３＞

(mＭ

2)

(a)

135 180 225 270 315 360

050

010

015

005

020

000

025

030

045

040

035

Angle

0 45 90

a３＞

(mＭ

2)

(b)


X

Y

O

Pax

ay

azdy

dx






7 Improvements









2925∘ 38 119909 mdash 27955119910 mdash 46052






120575max (120585 = 4 - 119879R = 10 anni)[m] 025 022







120575119894 = (1199011198671198944)(8EI) 120575119903 = (1199011198671199034)(8EI) = 059 times (1199011198671199034)(8EI)

(12)


119891 = (119896119898)122120587 (13)
















interstory


interstory


interstory


interstory


interstory




interstories


interstories



Cores

Axis 2

Axis 1



(a)

Cores

Axis 2

Axis 1

Axis 4

Axis 3




(b)




12 14 and34 184 354 198


interstory






















2925∘ 119909-axis 27955 15803119910-axis 46052 35697




X

Y








oy

x

0∘

45∘

90∘

135∘

180∘

225∘

270∘

315∘

TA

2925∘

y

x



8 Conclusions











Acknowledgments


References





























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















2 Design Criteria
























x

y


Acro

ss-w

ind

dire

ctio

n


Z

f1 = 014 （Ｔ f2 = 015 （Ｔ f3 = 026 （Ｔ

Y

X









0 45 90 135 180 225 270 315 36015

20

25

30

35

40

Angle (∘)

Win

d ve

loci

ty

(mＭ

2)

T２ = 100 years


(a)

oy

x

0∘

45∘

90∘

135∘

180∘

225∘

270∘

315∘

TA

(b)
















119862119865119883 = 119865119883119902119861119867119862119865119884 = 119865119884119902119861119867119862119865119885 = 119865119885119902119861119867119862119872119883 = 1198721198831199021198611198672 119862119872119884 = 1198721198841199021198611198672 119862119872119885 = 1198721198851199021198611198672

(2)





119891TAP (119905 119911ref) = 119901TAP119860TAP (4)




(5)






tot = 119872 + 119872dyn = 119872 + 119892119861 sdot 120590119872119861 + 119892119877 sdot 120590119872119877 (6)

where







52 floor (roof)

Ground floor

(a) (b)



ℎℎ

i minus 1 i i + 1

Ak

Floor k + 1

Floor k

Floor k minus 1

lki

lp2

(a)


lp2

(b)


lp2

(c)


045

Time (s)300 400 500 600 700 800 900 1000 1100 1200

050040030020010000


a３＞

(mＭ

2)

(a)

Time (s)

025

300 400 500 600 700 800 900 1000 1100 1200

025020015010005000


030

minus030

a３＞

(mＭ

2)

(b)




= 119872 + 119892119861 sdot 120590119872119861 (7)




in which







119865eq (119911) = dyn119877119898(119911) 120593119894 (119911)int119867

119900120593119894 (119911) 119911119898 (119911) 119889119911

119872eq (119911) = dyn119877120601119894 (119911) 119868 (119911)int119867

119900120601119894 (119911) 119868 (119911) 119911 119889119911

(9)


minus7000

minus6000

minus5000

minus4000

minus3000

minus2000

minus1000

0

1000

2000

3000

4000

5000

6000

7000

0 45 90 135 180 225 270 315 360

Mx

(kN

m)

Angle



times103

(a)

0

10

20

30

40

50

0 45 90 135 180 225 270 315 360Angle

minus10

minus20

minus30

minus40

minus50

times103



Fy

(kN

)

(b)



119886119909 (119911) = int119867119900

120593I (119911) 119865eq (119911) 119889119911int119867119900

1205932I (119911)119898 (119911) 119889119911 120593I (119911) 119886119911 (119911) = int119867

119900119872eq (119911) 120593III (119911) 119889119911int119867119900

1205932III (119911)119872 (119911) 119889119911 120593III (119911) 119886119910 (119911) = int119867

119900119865eq (119911) 120593II (119911) 119889119911int119867119900

1205932II (119911)119898 (119911) 119889119911 120593II (119911) (10)






135 180 225 270 315 360

035

010

015

005

020

000

025

030

Angle

0 45 90

a３＞

(mＭ

2)

(a)

135 180 225 270 315 360

050

010

015

005

020

000

025

030

045

040

035

Angle

0 45 90

a３＞

(mＭ

2)

(b)


X

Y

O

Pax

ay

azdy

dx






7 Improvements









2925∘ 38 119909 mdash 27955119910 mdash 46052






120575max (120585 = 4 - 119879R = 10 anni)[m] 025 022







120575119894 = (1199011198671198944)(8EI) 120575119903 = (1199011198671199034)(8EI) = 059 times (1199011198671199034)(8EI)

(12)


119891 = (119896119898)122120587 (13)
















interstory


interstory


interstory


interstory


interstory




interstories


interstories



Cores

Axis 2

Axis 1



(a)

Cores

Axis 2

Axis 1

Axis 4

Axis 3




(b)




12 14 and34 184 354 198


interstory






















2925∘ 119909-axis 27955 15803119910-axis 46052 35697




X

Y








oy

x

0∘

45∘

90∘

135∘

180∘

225∘

270∘

315∘

TA

2925∘

y

x



8 Conclusions











Acknowledgments


References





























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation































x

y


Acro

ss-w

ind

dire

ctio

n


Z

f1 = 014 （Ｔ f2 = 015 （Ｔ f3 = 026 （Ｔ

Y

X









0 45 90 135 180 225 270 315 36015

20

25

30

35

40

Angle (∘)

Win

d ve

loci

ty

(mＭ

2)

T２ = 100 years


(a)

oy

x

0∘

45∘

90∘

135∘

180∘

225∘

270∘

315∘

TA

(b)
















119862119865119883 = 119865119883119902119861119867119862119865119884 = 119865119884119902119861119867119862119865119885 = 119865119885119902119861119867119862119872119883 = 1198721198831199021198611198672 119862119872119884 = 1198721198841199021198611198672 119862119872119885 = 1198721198851199021198611198672

(2)





119891TAP (119905 119911ref) = 119901TAP119860TAP (4)




(5)






tot = 119872 + 119872dyn = 119872 + 119892119861 sdot 120590119872119861 + 119892119877 sdot 120590119872119877 (6)

where







52 floor (roof)

Ground floor

(a) (b)



ℎℎ

i minus 1 i i + 1

Ak

Floor k + 1

Floor k

Floor k minus 1

lki

lp2

(a)


lp2

(b)


lp2

(c)


045

Time (s)300 400 500 600 700 800 900 1000 1100 1200

050040030020010000


a３＞

(mＭ

2)

(a)

Time (s)

025

300 400 500 600 700 800 900 1000 1100 1200

025020015010005000


030

minus030

a３＞

(mＭ

2)

(b)




= 119872 + 119892119861 sdot 120590119872119861 (7)




in which







119865eq (119911) = dyn119877119898(119911) 120593119894 (119911)int119867

119900120593119894 (119911) 119911119898 (119911) 119889119911

119872eq (119911) = dyn119877120601119894 (119911) 119868 (119911)int119867

119900120601119894 (119911) 119868 (119911) 119911 119889119911

(9)


minus7000

minus6000

minus5000

minus4000

minus3000

minus2000

minus1000

0

1000

2000

3000

4000

5000

6000

7000

0 45 90 135 180 225 270 315 360

Mx

(kN

m)

Angle



times103

(a)

0

10

20

30

40

50

0 45 90 135 180 225 270 315 360Angle

minus10

minus20

minus30

minus40

minus50

times103



Fy

(kN

)

(b)



119886119909 (119911) = int119867119900

120593I (119911) 119865eq (119911) 119889119911int119867119900

1205932I (119911)119898 (119911) 119889119911 120593I (119911) 119886119911 (119911) = int119867

119900119872eq (119911) 120593III (119911) 119889119911int119867119900

1205932III (119911)119872 (119911) 119889119911 120593III (119911) 119886119910 (119911) = int119867

119900119865eq (119911) 120593II (119911) 119889119911int119867119900

1205932II (119911)119898 (119911) 119889119911 120593II (119911) (10)






135 180 225 270 315 360

035

010

015

005

020

000

025

030

Angle

0 45 90

a３＞

(mＭ

2)

(a)

135 180 225 270 315 360

050

010

015

005

020

000

025

030

045

040

035

Angle

0 45 90

a３＞

(mＭ

2)

(b)


X

Y

O

Pax

ay

azdy

dx






7 Improvements









2925∘ 38 119909 mdash 27955119910 mdash 46052






120575max (120585 = 4 - 119879R = 10 anni)[m] 025 022







120575119894 = (1199011198671198944)(8EI) 120575119903 = (1199011198671199034)(8EI) = 059 times (1199011198671199034)(8EI)

(12)


119891 = (119896119898)122120587 (13)
















interstory


interstory


interstory


interstory


interstory




interstories


interstories



Cores

Axis 2

Axis 1



(a)

Cores

Axis 2

Axis 1

Axis 4

Axis 3




(b)




12 14 and34 184 354 198


interstory






















2925∘ 119909-axis 27955 15803119910-axis 46052 35697




X

Y








oy

x

0∘

45∘

90∘

135∘

180∘

225∘

270∘

315∘

TA

2925∘

y

x



8 Conclusions











Acknowledgments


References





























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 45 90 135 180 225 270 315 36015

20

25

30

35

40

Angle (∘)

Win

d ve

loci

ty

(mＭ

2)

T２ = 100 years


(a)

oy

x

0∘

45∘

90∘

135∘

180∘

225∘

270∘

315∘

TA

(b)
















119862119865119883 = 119865119883119902119861119867119862119865119884 = 119865119884119902119861119867119862119865119885 = 119865119885119902119861119867119862119872119883 = 1198721198831199021198611198672 119862119872119884 = 1198721198841199021198611198672 119862119872119885 = 1198721198851199021198611198672

(2)





119891TAP (119905 119911ref) = 119901TAP119860TAP (4)




(5)






tot = 119872 + 119872dyn = 119872 + 119892119861 sdot 120590119872119861 + 119892119877 sdot 120590119872119877 (6)

where







52 floor (roof)

Ground floor

(a) (b)



ℎℎ

i minus 1 i i + 1

Ak

Floor k + 1

Floor k

Floor k minus 1

lki

lp2

(a)


lp2

(b)


lp2

(c)


045

Time (s)300 400 500 600 700 800 900 1000 1100 1200

050040030020010000


a３＞

(mＭ

2)

(a)

Time (s)

025

300 400 500 600 700 800 900 1000 1100 1200

025020015010005000


030

minus030

a３＞

(mＭ

2)

(b)




= 119872 + 119892119861 sdot 120590119872119861 (7)




in which







119865eq (119911) = dyn119877119898(119911) 120593119894 (119911)int119867

119900120593119894 (119911) 119911119898 (119911) 119889119911

119872eq (119911) = dyn119877120601119894 (119911) 119868 (119911)int119867

119900120601119894 (119911) 119868 (119911) 119911 119889119911

(9)


minus7000

minus6000

minus5000

minus4000

minus3000

minus2000

minus1000

0

1000

2000

3000

4000

5000

6000

7000

0 45 90 135 180 225 270 315 360

Mx

(kN

m)

Angle



times103

(a)

0

10

20

30

40

50

0 45 90 135 180 225 270 315 360Angle

minus10

minus20

minus30

minus40

minus50

times103



Fy

(kN

)

(b)



119886119909 (119911) = int119867119900

120593I (119911) 119865eq (119911) 119889119911int119867119900

1205932I (119911)119898 (119911) 119889119911 120593I (119911) 119886119911 (119911) = int119867

119900119872eq (119911) 120593III (119911) 119889119911int119867119900

1205932III (119911)119872 (119911) 119889119911 120593III (119911) 119886119910 (119911) = int119867

119900119865eq (119911) 120593II (119911) 119889119911int119867119900

1205932II (119911)119898 (119911) 119889119911 120593II (119911) (10)






135 180 225 270 315 360

035

010

015

005

020

000

025

030

Angle

0 45 90

a３＞

(mＭ

2)

(a)

135 180 225 270 315 360

050

010

015

005

020

000

025

030

045

040

035

Angle

0 45 90

a３＞

(mＭ

2)

(b)


X

Y

O

Pax

ay

azdy

dx






7 Improvements









2925∘ 38 119909 mdash 27955119910 mdash 46052






120575max (120585 = 4 - 119879R = 10 anni)[m] 025 022







120575119894 = (1199011198671198944)(8EI) 120575119903 = (1199011198671199034)(8EI) = 059 times (1199011198671199034)(8EI)

(12)


119891 = (119896119898)122120587 (13)
















interstory


interstory


interstory


interstory


interstory




interstories


interstories



Cores

Axis 2

Axis 1



(a)

Cores

Axis 2

Axis 1

Axis 4

Axis 3




(b)




12 14 and34 184 354 198


interstory






















2925∘ 119909-axis 27955 15803119910-axis 46052 35697




X

Y








oy

x

0∘

45∘

90∘

135∘

180∘

225∘

270∘

315∘

TA

2925∘

y

x



8 Conclusions











Acknowledgments


References





























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119862119865119883 = 119865119883119902119861119867119862119865119884 = 119865119884119902119861119867119862119865119885 = 119865119885119902119861119867119862119872119883 = 1198721198831199021198611198672 119862119872119884 = 1198721198841199021198611198672 119862119872119885 = 1198721198851199021198611198672

(2)





119891TAP (119905 119911ref) = 119901TAP119860TAP (4)




(5)






tot = 119872 + 119872dyn = 119872 + 119892119861 sdot 120590119872119861 + 119892119877 sdot 120590119872119877 (6)

where







52 floor (roof)

Ground floor

(a) (b)



ℎℎ

i minus 1 i i + 1

Ak

Floor k + 1

Floor k

Floor k minus 1

lki

lp2

(a)


lp2

(b)


lp2

(c)


045

Time (s)300 400 500 600 700 800 900 1000 1100 1200

050040030020010000


a３＞

(mＭ

2)

(a)

Time (s)

025

300 400 500 600 700 800 900 1000 1100 1200

025020015010005000


030

minus030

a３＞

(mＭ

2)

(b)




= 119872 + 119892119861 sdot 120590119872119861 (7)




in which







119865eq (119911) = dyn119877119898(119911) 120593119894 (119911)int119867

119900120593119894 (119911) 119911119898 (119911) 119889119911

119872eq (119911) = dyn119877120601119894 (119911) 119868 (119911)int119867

119900120601119894 (119911) 119868 (119911) 119911 119889119911

(9)


minus7000

minus6000

minus5000

minus4000

minus3000

minus2000

minus1000

0

1000

2000

3000

4000

5000

6000

7000

0 45 90 135 180 225 270 315 360

Mx

(kN

m)

Angle



times103

(a)

0

10

20

30

40

50

0 45 90 135 180 225 270 315 360Angle

minus10

minus20

minus30

minus40

minus50

times103



Fy

(kN

)

(b)



119886119909 (119911) = int119867119900

120593I (119911) 119865eq (119911) 119889119911int119867119900

1205932I (119911)119898 (119911) 119889119911 120593I (119911) 119886119911 (119911) = int119867

119900119872eq (119911) 120593III (119911) 119889119911int119867119900

1205932III (119911)119872 (119911) 119889119911 120593III (119911) 119886119910 (119911) = int119867

119900119865eq (119911) 120593II (119911) 119889119911int119867119900

1205932II (119911)119898 (119911) 119889119911 120593II (119911) (10)






135 180 225 270 315 360

035

010

015

005

020

000

025

030

Angle

0 45 90

a３＞

(mＭ

2)

(a)

135 180 225 270 315 360

050

010

015

005

020

000

025

030

045

040

035

Angle

0 45 90

a３＞

(mＭ

2)

(b)


X

Y

O

Pax

ay

azdy

dx






7 Improvements









2925∘ 38 119909 mdash 27955119910 mdash 46052






120575max (120585 = 4 - 119879R = 10 anni)[m] 025 022







120575119894 = (1199011198671198944)(8EI) 120575119903 = (1199011198671199034)(8EI) = 059 times (1199011198671199034)(8EI)

(12)


119891 = (119896119898)122120587 (13)
















interstory


interstory


interstory


interstory


interstory




interstories


interstories



Cores

Axis 2

Axis 1



(a)

Cores

Axis 2

Axis 1

Axis 4

Axis 3




(b)




12 14 and34 184 354 198


interstory






















2925∘ 119909-axis 27955 15803119910-axis 46052 35697




X

Y








oy

x

0∘

45∘

90∘

135∘

180∘

225∘

270∘

315∘

TA

2925∘

y

x



8 Conclusions











Acknowledgments


References





























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












52 floor (roof)

Ground floor

(a) (b)



ℎℎ

i minus 1 i i + 1

Ak

Floor k + 1

Floor k

Floor k minus 1

lki

lp2

(a)


lp2

(b)


lp2

(c)


045

Time (s)300 400 500 600 700 800 900 1000 1100 1200

050040030020010000


a３＞

(mＭ

2)

(a)

Time (s)

025

300 400 500 600 700 800 900 1000 1100 1200

025020015010005000


030

minus030

a３＞

(mＭ

2)

(b)




= 119872 + 119892119861 sdot 120590119872119861 (7)




in which







119865eq (119911) = dyn119877119898(119911) 120593119894 (119911)int119867

119900120593119894 (119911) 119911119898 (119911) 119889119911

119872eq (119911) = dyn119877120601119894 (119911) 119868 (119911)int119867

119900120601119894 (119911) 119868 (119911) 119911 119889119911

(9)


minus7000

minus6000

minus5000

minus4000

minus3000

minus2000

minus1000

0

1000

2000

3000

4000

5000

6000

7000

0 45 90 135 180 225 270 315 360

Mx

(kN

m)

Angle



times103

(a)

0

10

20

30

40

50

0 45 90 135 180 225 270 315 360Angle

minus10

minus20

minus30

minus40

minus50

times103



Fy

(kN

)

(b)



119886119909 (119911) = int119867119900

120593I (119911) 119865eq (119911) 119889119911int119867119900

1205932I (119911)119898 (119911) 119889119911 120593I (119911) 119886119911 (119911) = int119867

119900119872eq (119911) 120593III (119911) 119889119911int119867119900

1205932III (119911)119872 (119911) 119889119911 120593III (119911) 119886119910 (119911) = int119867

119900119865eq (119911) 120593II (119911) 119889119911int119867119900

1205932II (119911)119898 (119911) 119889119911 120593II (119911) (10)






135 180 225 270 315 360

035

010

015

005

020

000

025

030

Angle

0 45 90

a３＞

(mＭ

2)

(a)

135 180 225 270 315 360

050

010

015

005

020

000

025

030

045

040

035

Angle

0 45 90

a３＞

(mＭ

2)

(b)


X

Y

O

Pax

ay

azdy

dx






7 Improvements









2925∘ 38 119909 mdash 27955119910 mdash 46052






120575max (120585 = 4 - 119879R = 10 anni)[m] 025 022







120575119894 = (1199011198671198944)(8EI) 120575119903 = (1199011198671199034)(8EI) = 059 times (1199011198671199034)(8EI)

(12)


119891 = (119896119898)122120587 (13)
















interstory


interstory


interstory


interstory


interstory




interstories


interstories



Cores

Axis 2

Axis 1



(a)

Cores

Axis 2

Axis 1

Axis 4

Axis 3




(b)




12 14 and34 184 354 198


interstory






















2925∘ 119909-axis 27955 15803119910-axis 46052 35697




X

Y








oy

x

0∘

45∘

90∘

135∘

180∘

225∘

270∘

315∘

TA

2925∘

y

x



8 Conclusions











Acknowledgments


References





























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










ℎℎ

i minus 1 i i + 1

Ak

Floor k + 1

Floor k

Floor k minus 1

lki

lp2

(a)


lp2

(b)


lp2

(c)


045

Time (s)300 400 500 600 700 800 900 1000 1100 1200

050040030020010000


a３＞

(mＭ

2)

(a)

Time (s)

025

300 400 500 600 700 800 900 1000 1100 1200

025020015010005000


030

minus030

a３＞

(mＭ

2)

(b)




= 119872 + 119892119861 sdot 120590119872119861 (7)




in which







119865eq (119911) = dyn119877119898(119911) 120593119894 (119911)int119867

119900120593119894 (119911) 119911119898 (119911) 119889119911

119872eq (119911) = dyn119877120601119894 (119911) 119868 (119911)int119867

119900120601119894 (119911) 119868 (119911) 119911 119889119911

(9)


minus7000

minus6000

minus5000

minus4000

minus3000

minus2000

minus1000

0

1000

2000

3000

4000

5000

6000

7000

0 45 90 135 180 225 270 315 360

Mx

(kN

m)

Angle



times103

(a)

0

10

20

30

40

50

0 45 90 135 180 225 270 315 360Angle

minus10

minus20

minus30

minus40

minus50

times103



Fy

(kN

)

(b)



119886119909 (119911) = int119867119900

120593I (119911) 119865eq (119911) 119889119911int119867119900

1205932I (119911)119898 (119911) 119889119911 120593I (119911) 119886119911 (119911) = int119867

119900119872eq (119911) 120593III (119911) 119889119911int119867119900

1205932III (119911)119872 (119911) 119889119911 120593III (119911) 119886119910 (119911) = int119867

119900119865eq (119911) 120593II (119911) 119889119911int119867119900

1205932II (119911)119898 (119911) 119889119911 120593II (119911) (10)






135 180 225 270 315 360

035

010

015

005

020

000

025

030

Angle

0 45 90

a３＞

(mＭ

2)

(a)

135 180 225 270 315 360

050

010

015

005

020

000

025

030

045

040

035

Angle

0 45 90

a３＞

(mＭ

2)

(b)


X

Y

O

Pax

ay

azdy

dx






7 Improvements









2925∘ 38 119909 mdash 27955119910 mdash 46052






120575max (120585 = 4 - 119879R = 10 anni)[m] 025 022







120575119894 = (1199011198671198944)(8EI) 120575119903 = (1199011198671199034)(8EI) = 059 times (1199011198671199034)(8EI)

(12)


119891 = (119896119898)122120587 (13)
















interstory


interstory


interstory


interstory


interstory




interstories


interstories



Cores

Axis 2

Axis 1



(a)

Cores

Axis 2

Axis 1

Axis 4

Axis 3




(b)




12 14 and34 184 354 198


interstory






















2925∘ 119909-axis 27955 15803119910-axis 46052 35697




X

Y








oy

x

0∘

45∘

90∘

135∘

180∘

225∘

270∘

315∘

TA

2925∘

y

x



8 Conclusions











Acknowledgments


References





























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










minus7000

minus6000

minus5000

minus4000

minus3000

minus2000

minus1000

0

1000

2000

3000

4000

5000

6000

7000

0 45 90 135 180 225 270 315 360

Mx

(kN

m)

Angle



times103

(a)

0

10

20

30

40

50

0 45 90 135 180 225 270 315 360Angle

minus10

minus20

minus30

minus40

minus50

times103



Fy

(kN

)

(b)



119886119909 (119911) = int119867119900

120593I (119911) 119865eq (119911) 119889119911int119867119900

1205932I (119911)119898 (119911) 119889119911 120593I (119911) 119886119911 (119911) = int119867

119900119872eq (119911) 120593III (119911) 119889119911int119867119900

1205932III (119911)119872 (119911) 119889119911 120593III (119911) 119886119910 (119911) = int119867

119900119865eq (119911) 120593II (119911) 119889119911int119867119900

1205932II (119911)119898 (119911) 119889119911 120593II (119911) (10)






135 180 225 270 315 360

035

010

015

005

020

000

025

030

Angle

0 45 90

a３＞

(mＭ

2)

(a)

135 180 225 270 315 360

050

010

015

005

020

000

025

030

045

040

035

Angle

0 45 90

a３＞

(mＭ

2)

(b)


X

Y

O

Pax

ay

azdy

dx






7 Improvements









2925∘ 38 119909 mdash 27955119910 mdash 46052






120575max (120585 = 4 - 119879R = 10 anni)[m] 025 022







120575119894 = (1199011198671198944)(8EI) 120575119903 = (1199011198671199034)(8EI) = 059 times (1199011198671199034)(8EI)

(12)


119891 = (119896119898)122120587 (13)
















interstory


interstory


interstory


interstory


interstory




interstories


interstories



Cores

Axis 2

Axis 1



(a)

Cores

Axis 2

Axis 1

Axis 4

Axis 3




(b)




12 14 and34 184 354 198


interstory






















2925∘ 119909-axis 27955 15803119910-axis 46052 35697




X

Y








oy

x

0∘

45∘

90∘

135∘

180∘

225∘

270∘

315∘

TA

2925∘

y

x



8 Conclusions











Acknowledgments


References





























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










135 180 225 270 315 360

035

010

015

005

020

000

025

030

Angle

0 45 90

a３＞

(mＭ

2)

(a)

135 180 225 270 315 360

050

010

015

005

020

000

025

030

045

040

035

Angle

0 45 90

a３＞

(mＭ

2)

(b)


X

Y

O

Pax

ay

azdy

dx






7 Improvements









2925∘ 38 119909 mdash 27955119910 mdash 46052






120575max (120585 = 4 - 119879R = 10 anni)[m] 025 022







120575119894 = (1199011198671198944)(8EI) 120575119903 = (1199011198671199034)(8EI) = 059 times (1199011198671199034)(8EI)

(12)


119891 = (119896119898)122120587 (13)
















interstory


interstory


interstory


interstory


interstory




interstories


interstories



Cores

Axis 2

Axis 1



(a)

Cores

Axis 2

Axis 1

Axis 4

Axis 3




(b)




12 14 and34 184 354 198


interstory






















2925∘ 119909-axis 27955 15803119910-axis 46052 35697




X

Y








oy

x

0∘

45∘

90∘

135∘

180∘

225∘

270∘

315∘

TA

2925∘

y

x



8 Conclusions











Acknowledgments


References





























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















2925∘ 38 119909 mdash 27955119910 mdash 46052






120575max (120585 = 4 - 119879R = 10 anni)[m] 025 022







120575119894 = (1199011198671198944)(8EI) 120575119903 = (1199011198671199034)(8EI) = 059 times (1199011198671199034)(8EI)

(12)


119891 = (119896119898)122120587 (13)
















interstory


interstory


interstory


interstory


interstory




interstories


interstories



Cores

Axis 2

Axis 1



(a)

Cores

Axis 2

Axis 1

Axis 4

Axis 3




(b)




12 14 and34 184 354 198


interstory






















2925∘ 119909-axis 27955 15803119910-axis 46052 35697




X

Y








oy

x

0∘

45∘

90∘

135∘

180∘

225∘

270∘

315∘

TA

2925∘

y

x



8 Conclusions











Acknowledgments


References





























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation






















interstory


interstory


interstory


interstory


interstory




interstories


interstories



Cores

Axis 2

Axis 1



(a)

Cores

Axis 2

Axis 1

Axis 4

Axis 3




(b)




12 14 and34 184 354 198


interstory






















2925∘ 119909-axis 27955 15803119910-axis 46052 35697




X

Y








oy

x

0∘

45∘

90∘

135∘

180∘

225∘

270∘

315∘

TA

2925∘

y

x



8 Conclusions











Acknowledgments


References





























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Cores

Axis 2

Axis 1



(a)

Cores

Axis 2

Axis 1

Axis 4

Axis 3




(b)




12 14 and34 184 354 198


interstory






















2925∘ 119909-axis 27955 15803119910-axis 46052 35697




X

Y








oy

x

0∘

45∘

90∘

135∘

180∘

225∘

270∘

315∘

TA

2925∘

y

x



8 Conclusions











Acknowledgments


References





























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation





















2925∘ 119909-axis 27955 15803119910-axis 46052 35697




X

Y








oy

x

0∘

45∘

90∘

135∘

180∘

225∘

270∘

315∘

TA

2925∘

y

x



8 Conclusions











Acknowledgments


References





























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










X

Y








oy

x

0∘

45∘

90∘

135∘

180∘

225∘

270∘

315∘

TA

2925∘

y

x



8 Conclusions











Acknowledgments


References





























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















Acknowledgments


References





























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation





















































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









structural improvements for tall buildings under wind

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