XXI SYMPOZJUM – VIBRATIONS IN PHYSICAL SYSTEMS – Poznań-Kiekrz 2004

WDOWICKI Jacek, WDOWICKA Elżbieta,

Poznan University of Technology,

ul. Piotrowo 5, 60-965 Poznań, Poland

tel.: [phone], E-mail: [e-mail]

SEISMIC ANALYSIS OF THE SHEAR WALL DOMINANT BUILDING

USING CONTINUOUS-DISCRETE APPROACH

1. INTRODUCTION

In tall buildings the lateral loads that arise from effects of wind and earthquakes are

often resisted by a system of coupled shear walls acting as vertical cantilevers. It is

possible to perform the analysis of shear wall structures using either the discrete method

or the continuous one. In the continuous approach, the horizontal connecting beams,

floor slabs, and vertical joints are substituted by continuous connections. In recent years

the use of continuum models in structural analysis has received considerable attention.

These models offer an attractive, low cost method for analysing large structures and they

represent the useful tool for design analysis.

For the dynamic analysis it is convenient to use a hybrid approach based on the

analysis of an equivalent continuous medium and a discrete lumped mass system

[1,4,7,8]. The coupled shear wall system is represented by either a continuous system or

a discrete system at various stages of analysis. The advantage of using these two ways of

representing of the shear wall system is that the flexibility and mass matrices required

for structural dynamic analysis are easily obtained.

The paper presents results of the seismic analysis based on the above-mentioned

method. The seismic analysis was carried out by means of the response spectrum

technique. Design spectrum for elastic analysis according to Eurocode 8, Draft No.6 [6]

was used.

2. MODEL AND THEORETICAL BACKGROUND OF ANALYSIS

In the analysed building, lateral loads that arise as a result of winds and earthquakes

are resisted by the three-dimensional system of coupled shear walls. A diaphragram

action of all floor slabs is taken into consideration as the effect of their in-plane infinite

rigidity and negligible transverse one. Owing to the height to width ratio of the shear

walls, there is a possibility to treat each wall as an open thin-walled beam, according to

Vlasov theory assumptions.

The static analysis was carried out on the basis of some variant of the continuous

connection method [9]. In this method lintel beams are treated as the equivalent shear

connection medium between shear walls, while the walls are simply regarded as vertical

cantilevers. The technique may be used for both plane and spatial structures, which are

essentially regular in form throughout the height.

Dynamic solutions have been obtained by treating the structure as a lumped parameter

system with discrete masses in the form of rigid floor slabs arbitrary located along the

height [7]. The coupled torsional-flexural vibrations have been considered because

torsional response of buildings during ambient and earthquake response is

significant. For shear wall multi-storey structure it is more natural to determine the

flexibility matrix D than stiffness matrix K. The vibration of a structure is described by the

following relation [3]:

M

D

x

&

& +

C

D

x

& + x =

F

D

(1)

where

D - flexibility matrix,

M - mass matrix,

C - damping matrix,

x - d-element vector of generalised coordinates (d - number of dynamic degrees of

freedom of the calculated structure),

F - d-element vector of generalised excitation forces, corresponding to generalised

coordinates.

Calculations were made using DAMB program (Dynamic Analysis of Multistorey

Buildings), as part of an Integrated System [10], which gives a possibility to perform linear

dynamic analysis of three-dimensional shear wall structures.

The flexibility matrix D is generated from the exact solution of the governing

differential equation for 3-D continuous model. Also mass matrix is generated exactly

according to real distribution of walls, connecting beams and floor slabs and including

flexural and torsional inertia. The seismic response of the structure is estimated using the

response spectrum technique. The involved steps are as follows: 1) determination of

natural frequencies and mode shapes, 2) evaluation of modal participation factors and

calculation of modal loading on the structure (using an appropriate design spectrum),

3) determination of response estimate taking into account the contribution from the given

number of modes for various parameters of interest (using three methods: SRSS – the

square root of the sum of the squares, CQC – the complete quadratic combination, DSC

– the double sum combination [5]).

3. RESULTS OF THE SEISMIC ANALYSIS

The results of static and free vibration analyses were presented in previous papers

[7,9]. As the numerical example of seismic analysis the shear wall dominant building,

analysed in [2] was chosen. The analysed multistorey reinforced concrete structure,

constructed by using a special tunnel form technique, is composed of vertical and

horizontal panels set right angles. The plan of the analysed structure is given in Figure 1.

The building height is 42 m, the storey height – 2.8 m and the height of connecting

beams – 0.7 m. The properties of material are taken to be E = 21.4 GPa and G =

8.92 GPa.

In the analysis the design spectrum for linear analysis according to Eurocode 8 has

been taken. The type 1 spectrum and subsoil class C ( S = 1.35, TB = 0.2, TC = 0.6,

TD = 2.0) have been considered. The value of viscous damping ratio ξ = 5% has been

assumed. The analysis has been carried out for the design ground acceleration

ag = 2.5 m/s2 . The results of the analysis based on the response spectrum technique,

obtained for the seismic wave direction parallel to X-axis, are shown in Figures 1 and 2.

4. CONCLUSIONS

In this study the seismic analysis of shear wall tall building has been carried out

using a continuous-discrete approach and the response spectrum technique. It can be

noted that in the method applied both the preparation of data is easy and the length of

computation time is short. Consequently, the software based on this method, represents

a useful tool for the design analysis.

REFERENCES

1. Aksogan O., Arslan H.M., Choo B.S., Forced vibration analysis of stiffened

coupled shear walls using continuous connection method, Engineering

Structures, 25 (2003) 499-506.

2. Balkaya C., Kalkan E., Estimation of fundamental periods of shear-wall dominant

structures, Earth. Eng. & Struct. Dyn., 32 (2002) 985-998.

3. Clough R.W., Penzien J., Dynamics of Structures, McGraw-Hill, New York 1993.

4. Li G.-Q., Choo B.S., A continuous-discrete approach to the free vibration analysis

of stiffened pierced walls on flexible foundations, Int. J. Solids and Structures., 33

(1996) 249-263.

5. Maison BF., Neuss CF., Kasai K., The comparative performance of seismic

response spectrum combination rules in building analysis, Earth. Eng. & Struct.

Dyn., 11 (1983) 623-647.

6. PrEN 1998-1:200X: Eurocode 8: Design of structures for earthquake resistance.

Part 1: General rules, seismic actions and rules for buildings. DRAFT No 6.

Version for translation (Stage 49). January 2003. CEN, Bruxelles.

7. Wdowicki J., Wdowicka E., Wrześniowski K., Free vibration of unsymmetrical

multistorey shear wall buildings, In: Proc. Third Int. Symp. on "Wall Structures".

CIB, Warsaw, Poland, 1984, vol.II: 339-346.

8. Wdowicki J., Wdowicka E., Integrated system for analysis of three-dimensional

shear wall structures, Comp. Meth. in Civil Engineering, 1 (1991) 53-60.

9. Wdowicki J., Wdowicka E., System of programs for analysis of three-dimensional

shear wall structures, The Structural Design of Tall Buildings, 2 (1993) 295- 305.

10. Wdowicki J., Wdowicka E., Błaszczyński T., Integrated system for analysis of shear

wall tall buildings, In: Proc. of the Fifth World Congress "Habitat and High- Rise:

Tradition and Innovation". Council on Tall Buildings and Urban Habitat,

Amsterdam, 1995, 1309-1324.

Figure 1. Normal stresses at the base of shear wall structure

for the seismic wave direction parallel to X-axis

Figure 2. Horizontal displacements of shear wall structure

for the seismic wave direction parallel to X-axis