THE INFLUENCE OF THE ACTION OF PENDULUM SEISMIC MUFFLER AGAINST

THE BENDING OF BUILDING PROVOKED

BY WIND AND SEISMIC FORCES

the author: Dr Vladimir Radojičić , The Faculty of Technical Sciences, FTN

Abstract: The constant lack of energy, the characteristic of 21th

century, rapidly increases and it

appears te be the topic of at almost all levels of social discourses with neooptimistic prognoses.

Key words: the restorable source of energy; the calculation of wind and seismic force impact ,

the pendulum , the oscillation , the muffler

INTRODUCTION

Kula, the Tower, reinforced concrete building intended for the production of electric energy,

provocative from the technological point of view and economical justification at the time of the actual

energy crisis, became the subject of the author researches.

The realization of this plan for building the reinforced concrete object Kula, 1900 m high, was

one of many imaginers ideas of the famous Serb designer of the 20th century, Đorđe Lazarević.

He wanted to combine and to transform into new energy source the strength of the risen brooks of

the river Vlasina and the wind moving the old beech trees and oak trees. He imagined Kula, the highest

reinforced concrete building, whose purpose was to produce electric energy, by the help of water and

wind.

That would be the restorable source of energy satisfying the highest ecology standards.

In the sublimation of Professor Đorđe Lazarević’s idea and the real possibility for its realization,

the author made mathematical calculations of the influence of the wind and seismic forces, dominant on

the building stability.

By choosing one option for the problem solving on the reducing Kula’s top vibrations, the author

showed the real possibilities for the construction of that object.

It is very important that the vibrations of high objects should be reduced as much as possible.

The top of Kula after a definite time moves several ten centimeters making a psychological negative

impression on the present people in thests of Kula and at hat time. The results of the calculations about

the influence of the wind and seismic in the previous paper were in the allowed limits. The problem of

vibrations reduction and Kula’s movements at the top is the second topic of this paper.

The earthquake or the strong winds provoke the naturel vibrations of the object itself with heigh

frequencies which affect the high geste parts as well as the top of Kula moving to the left and right up to

several tens of centimeters every 38 seconds .

It is very important that the vibrations should be reduced at least possible for many reasons: from

constructive to psychological with the negative effects on the behavior of people which are on the highest

part of Kula or at the very top at that moment.

THE DESCRIPTION OF CONSTRUCTION

The reinforced concrete construction Kula consists of the trunk – cylinder connections, the

platform, the restaurant and so the total high of Kula is 1700 meters.

The circle foundation of Kula is 300 meters in diameter supporting by 32 ringlike cross

section columns; its exterior diameter is 15 meters and its interior diameter is 5 meters. They are

symmetriccaly arranged and realized out of MB 80 (figure 1).

Figure 1. the base and Fair`s sections

Kula`s trunk diameter is changeable. It’s 300 meters at the peak elevation at 0,0 meters

with the tendency of decreasing and 130 meters at the peak elevation at 950,0 meters . From that

peak elevation the diameter continually decresases at the hight of 100 meters and it remains the

same till the peak elevation at 700 meters.

There are some connections along the columns and inside them – antiresonant elements

(figure 2 which take part in the “arrangement” of Kula’s own oscilations created by seismic

actions and by wind.

Figure 2. Connections and additional supports

The middle part of the vertical tunnel (figure 3), diameter 50 meters, occupy upward and

downward lifts: 2 express lifts with capacity of 12 persons and the velocity of 8 m/sec for load

transfer and 2 control stairs with the width of 80 cm. left and right segment are for placing

energetic ducts, hydro installations and pumps.

Figure 3. Review of the base of the communication tunnel

AEROAGREGATES AND HYDROAGREGATES ARE PLACEDIN KULA’ BASE

Electric power would be created in aeroagregates moved by the wind strength. In the case

of the wind lack the water, accumulated in 12 steel tanks with 16 meters diameter, the hight of

100 meters, the capacity of 240000 m3 (figure 4) would fall onto the hydroagregates, making

them start. So the interruptios would be eliminated.

Figure 4. The tank`s appreance

Kula`s columns and the trunk are made of concrete MB 80, metal framework RA

400/500. The fodation and the rest of construction elements: concrete MB 80, metal framework

RA 400/500.

The statics and dynamic construction analysis and the stability estimation of Kula are

made by application of SAP and Tower program on the special model using final elements

method.according to the first and the second order theory the estimation has been made for

constant and useful load and for the action of wind and seismic forces.

Figure 5. The Model of the Construction and the Distorted Model out of overloading

THE ACTION OF WIND ON THE CONSTRUCTION

According to high constructions builders aerodynamic wind action has the dominant

influence on the construction stability.

Parameters used in the estimation of on the construction wind influence are:

1. - the wind blow

- the retroactive period of the projected blow

- topography

- rough ground

- the rigidness of the construction

2. The wind blow which was accepted was 19 meters per second or about 90

kilometers per hour.

0,** bSEASONdirb vCCV

Cdir – the coefficient of the direction is usually 1,0

Cseason – the value of the coefficient of the seasonal action is 1,0

Vb,o – the foundamental value of the basic wind blow

The middle wind blow is got from the formula:

brm VzCzCzV *)(*)()( 0

Cr(z) – accepted roughness coefficient

C0(z) – topography coefficient (if the soil topography doesn’t increase wind blow 5%)

Vb – the basic wind blow

Ground category Z0 Zmin

0 Sea or coast exposed to high sea 0,003 1

I Lakes or plain and horizontal ground with minimal vegetation an

without obstacles

0,01 1

II Ground with low vegetation like grass and isolated obstacles (trees,

buildings) for at least 20 hight of obstacles

0,05 2

III Ground with constant cover of vegetation or buildings or isolated

obstacles for hight of obstacles at the most (like villages, suburbs,

woods)

0,3 5

IV Ground with at least 15% area with buildings whose average hight

is over 15 meters

1,0 10

Table 1

- Ground topography (the construction is in the woods)

- Roughness of ground (position and woods closeness)

Roughness coefficient is got from the formula

minmin

maxmin

0

zz za )()(

z za ln*)(

zCzC

zzz

zKzC

rr

Rr

Z0 – roughness length (table 1)

Zmin – minimal hight (table 1)

Zmax – accepted 200 m

Z0,II = 0,55 m for the second category ground

Kr – ground category

Kr = 0,19

07.0

,0

019,0

II

Rz

zK

- Retroactive period of the projected speed in 50 years (combination of wind and ice on the

construction capacity)

- Rigidness of the concrete part of construction

- Constraction stability (in the case of air whirpool selection)

The greatest movements caused by wind in Kula’s top (according to Evrokod) arearound 54

cm.

Some wind influence estimations have been done according to the English standards and

American regulations for high buildings – everything for the sake of control.

In the case of high buildings it is very important for the movements to be minimized

because big movements at Kula’s top with objects for amusement, restaurants and helicopter

station would have negative influence on human’s behavior.

ESTIMATION OF SEISMIC FORCES ACTIONS

The estimation of seismic forces actions were done by spectral analysis.

The following parameters were used:

- the average time period (retroactive period of 50 years)

- the ninth earthquake intesity degree (according to seismological maps) with the ground

acceleration of ag ≤ 0,40g , g = 9,81m/s2 and the expected acceleration dates – accelograms

(notes about the ground acceleration during earthquake, figure 6 and 7) for the earthquakes

magnitude M = 5,6 maximum is M = 9; epicentral distance R = 74 km and epicentral depth H =

16 km.

Figure 6. Accelerogram

Figure 7. Accelerograms

The intensity of earthquake in the epicenter is defined by formula:

I = 1,5M – 0,5M = 5,6 (magnitude)

The maximum average ground acceleration is defined by formula:

20/654 4,0 Rea M

g

R – epicentral distance (expressed in km)

Maximum ground acceleration Vg (cm/s)

20/*43,4 94,0 ReV M

g

Maximum ground movement dg expressed in cm is:

34,12,1 20/*06,0 Red M

g

Numerical intensity of the earthquake:

341,04,210

34,0/4,2log

g

g

a

aI

According to EC8 the average value at remowing waves VS,30 we define

i

iNi

s

V

hV

,1

30,

30

hi-thicknen expressed in metres

vi- speed of remowing waves

Horizontal component of the seismic action elastic spectrum rersponds S0(t) is defined by:

20

0

0

**5,2*** 4

*5,2***

5,2***

15,2**1** 0

T

TTSaTSSTT

T

TSaTSTTT

SaTSTTT

T

TSaTSTT

DCgD

CgoDC

gCB

B

gB

T- time of vibration of the linear system

ag-projected ground acceleration of the ground type A

gRg aa *1

TB-lower period limit in the area with constant spectrum acceleration (figure 2)

Tc- upper limit with constant spectrum acceleration (figure 2)

TD-period value which defined the beginning of the spectrum area with constant reaction to

the movements in the spectrum (tab. 2)

S-the factor of the ground

-the correction factor of amortization n=1 for viscous amortization of 5%

55,0/10 S

– relative viscous amortization

ground category S (S) (S) (S)

A 1,0 0,15 0,4 2,0

B 1,2 0,15 0,5 2,0

C 1,15 0,20 0,6 2,0

D 1,35 0,20 0,8 2,0

E 1,4 0,15 0,5 2,0

Table 2: the values of parameters which describe the recommended type 1

of elastic spectrum answer

ground category S (S) (S) (S)

A 1,0 0,05 0,25 1,2

B 1,35 0,05 0,25 1,2

C 1,5 0,10 0,25 1,2

D 1,8 0,10 0,3 1,2

E 1,6 0,05 0,25 1,2

Table 2: the values of parameters which describe the recommended

type 2 of elastic spectrum answer

Elastic spectrum forme

ground

category

Description of the geological profile

Parametres

Vs,30

(m/s)

NSPT

(udarci/30cm)

CU

(kPa)

A

A rock or a rocky geological formation including

5 metres of low quality material at the surface.

> 800 - -

B

Deposits at heavy sand gravel or very heavy clay

with diameter of several metres and with increase

of mechanical characteristics concerning depth.

360-800 > 50 > 250

C

Deep deposit of heavy of middle hevy sand,

graver or heavy clay with its diameter of several

tenths metres

180-360 15-50 70-250

D deposits of hardly middle non-cohesion ground

(with or without soft cohesive layers) or from

dominat soft to hard cohesive ground

< 180 < 15 < 70

E ground whose profile consists of layer of Vs for

type C or D and of diameter varying from 5 to 20

meters under which is the hard ground of Vs >

800 m/s

- -

S1 deposits consisting of the 10 metres diameter

clay soft layer at least and the high plastic index

mud (P>40) with high percent of water

< 100 10 - 20

Table 3 is for the groud classification

The value of the projected groun movements dg is as follws:

DCg TTSd ***025,0

The tunnel tube with lifts and the rest of the needed material would hypothetically

influence the movement reducrion of the Kula’s top if the estimation of seismic nfluence

included anti-seismc style conections. In the case the action of seismic forces on the earthquake –

like ground of IX MKS would cause the movement of Kula to agreeable limets.

Resonant danger would probably be beyond registered earthquakes up to now. The

greatest seismic influence would be expected to be in the base layer.

Kula’s construction estimation

According to Eurokod it was carried out from the second type theory for the following

load kinds:

-constant loud

-water weight in tanks

-seismic

-wind

-ice load (accepted as the thickness of ice load s=5cm, ice density ρe =500kg/m3)

THE ACTION OF THE MASSIVE BALL – PENDULUM ON THE REDUCTION OF

VIBRATIONS

The author decided to introduce the massive ball – pendulum into the calculations to

reduce the movements of Kula’s top. That solutions was added to the option of the tanks filled

with rainwater.

The pendulum of diameters 6,0 m were the weight 800 t handed of steel cord on the top

of the Kula on the height 1900 m (increased for 200 m because of the lodging of the pendulum)

reducs the value of the acceleration of the heighgest parts of Kula under gusts of wind mowing at

90 km/h for half of the value obtained without the pendulum.

When Kula swings to one side under the influence of wind, the pendulum starts swinging

to the opposite side what "straightens" the object reducing the vibration amplitudes and Kula

continues to bend less which was the main aim.

The pendulum has the function of the vibrations muffter in this case.

The pendulum influences the reduction of Kula’s top movement .

Nowadays building technology reached a very high level so that even the impossible

thing can be possible .

The pendulum has the function of the vibrations muffter in this case.

According to those equation we get the data for the estimate of pendulum – muffter.

c – the deaden (kg/s)

p – the influence of wind and seismic forces (N)

k – the stiffnes (N) . The necessary force to bend the building for 1 metar

m – Dinamic mass of building

u – Halfamplitude on top of Kula or the dimension of bending of Kula (m)

the speed of bending of top of the Kula (m/s)

– the acceleration of Kula’s top at (m/s2)

Figura 8 The model of Kula Figura 9 The deformed Kula’s model

CONCLUSION

It is possible to build very high construction projects. The statics problems can be solved.

These buildings depending of areas where they are constructed are subjected to plastic

deformations by the influence of wind and seismic forces. After this impact the construction stands some

damages and it needs very big and expensive reconstruction work.

The construction overcomes those impacts and it is flexible enough by applying mufflers in its

construction with adequate dimension and the choice of the material. By seismic and dynamic estimation

the pendulum mass reduces.

- Angle of rotation of the construction at given speed was =1o to admissible limits .

- The movements of the Kula`s top was 1,4 meter .

- The calculation of the construction is made by the application the second order theory .

- The volue of stress according to carried aut control has been 215 kg per 1cm3 = 21,5 MPa

while the calculated of the stress intensity on the edges of reinforced concrete columns

would be 21,5 MPa (due to the constant useful load, wind load and seismics).

With the pendulum , it is obtained :

- The values of the tension and moments of the Kula’s top with the pendulum are reduced . The

tension on maximum load of the part of the Kula’s is 16,7 MPa .

- The speed of bending of the Kula’s top is reduced

- The amplitude of the vibrations of the Kula’s as well as

- The movements of the Kula`s top was 0,74 meter , - The time is reduced at 38/25 sec .

The actual example is the wordls high Tower (508 m) Tapei , which endures earthquakes and

typhoon wind of Taivan area.

The estimation of the influence of the action of impacts, in most cases is equal to the estimation

of action forces depends on the characteristics of the seismic impulses and on the possibility that the

construction could be damaged in the elastic and plastic area.

It is necessary to draw up plans for building to be protected, so that the discipation of energy

couldn’t appear.

Nowodays building technology reached a very high level so that even the impossible

thing can be possible .

Bibliography :

1. T.Radojičić , M.Ivković : Monografija akademika Djordja Lazarevića , Izgradnja , Beograd

,1983.

2. Akademik Djordje Lazarević : Jedna ideja za korišćenje vetra , Beograd , 1984 .

3. Materijali i konstrukcije : Simpozijum Društva gradjevinskih inženjera i tehnićčra , Surdulica ,

2003.

4. Rosman R. : Razvoj nosivih konstrukcija visokih zgrada . Zbornik radova (441-450) HDTK ,

2003

5. Kolaco J : The Mile-High dream , Civil Engineering ASCE , 1986