外文翻譯--對于鋼筋混凝土框架結(jié)構(gòu)地震響應(yīng)的分析過程 （英文）

1、Analytical procedures in the study of seismic response of reinforced concrete frames Maria Gabriella Mulas Politecnico di Milano, Milan, haly Filip C. Filippou Unicersity of California, Berkeley, CA 94720 USA (Receiv

2、ed October 1988) The inelastic response of reinforced concrete (RC) plane frames sub- jected to strong ground motions is studied from an analytical stand- point. Two different problems are addressed, namely the modelli

3、ng of elements and the development of efficient numerical techniques in nonlinear dynamic analyses. In this work a new girder model based on the nonlinear beam element proposed by Soleimani is presented; the problem of

4、 inserting such a model in a step-by-step nonlinear dynamic analysis algorithm is solved; and the algorithm efficiency, both in terms of computation time and response precision, is investigated as a function of parame

5、ters such as step length, number of iterations and tolerance. Keywords: seismic response, reinforced concrete frames, dynamic analysis Most modern codes concerning seismic-resistant design allow the dissipation of ene

6、rgy input in the structure by a strong earthquake through inelastic deformations in critical regions. The study of nonlinear structural behaviour both from an analytical and an experimental standpoint then becomes ve

7、ry important. Experimental dynamic testing results, however, in high costs and presents practical problems; a strategy based on experi- ments under quasi-static cyclic loads, which allows the derivation of nonlinear

8、structural models, seems to be more effective. In fact, the numerical analysis of struc- tural response can provide very useful information on seismic design forces and on design criteria which ensure the overall sat

9、isfactory behaviour of structural elements during severe earthquake excitations. Much research effort has been devoted in the last 30 years to developing models of hysteretic behaviour of reinforced concrete (RC) bea

10、ms based on data from experimental investiga- tions and on-field observations of structures damaged by earthquakes. The very first inelastic beam model was proposed by Clough et al. t'2 in 1965. This model, known a

11、s the two-component model, is composed of two parallel ele- ments, one linear elastic and the other elastic-perfectly plastic. Inelastic deformations are concentrated in plastic hinges at the ends of the elasto-plast

12、ic element; the 0141-0296/90/010037- ! 2/$03.00 ~) 1990 Butterworth this model is composed of two parallel deformable elements, one linearly elastic and the other nonlinear, two nonlinear springs at the ends of these

13、 elements, and two rigid links outside the springs. The two rigid links represent the beam-column joint region, while the two nonlinear springs model the fixed-end rotations due to slippage of the reinforcement insid

14、e the beam-column Eng. Struct. 1990, Vol. 12, January 37 Seismic response of reinforced concrete frames: M.G. Mulas and F.C. Filippou Joint C L Reduced effective ~.tiffness i (Elastic stiffness kE=EI~ i i Rotational

15、 springs length zero ~Rigid link ? I.~ ~F__Elasti c zone~l~l ~ ~i “-Inelastic zones -/ ! I Rigid link Figure 1 Proposed girder element and two inelastic zones at the ends. The length of the inelastic zones is c

16、omputed on the basis of the moment diagram. A detailed description of Soleimani's model can be found elsewhere6; for the sake of completeness the main features of the model will be summarized in the following. To

17、 avoid the definition of beam shape functions after the onset of steel yielding, a flexibility approach is adopted in the determination of the beam stiffness ma- trix. The beam flexibility matrix is derived through an

18、 approximate integration of curvatures along the Icngth of the beam under the assumption era linear distribution of bending moments. To determine accurately the tangent flexibility matrix fb it is necessary to trace th

19、e loading history of several sections inside the inelastic zone. This requires, however, a considerable amount of computation time and the storage of a large amount of data. To avoid this two key assumptions arc made

20、 in Soleimani's model: ? every section of the inelastic zone is in the same state (unloading, strain-hardening or stiffness degrading) as the end section. The behaviour of the end section, therefore, controls the b

21、ehaviour of the entire inelastic zone; ? the inelastic zone has an average tangent stiffness t i ? k E (Figure 2) determined as a function of the stiffness of the end section. Joint~~l ~ii C't“ M y M÷

22、I'~ “ * - ~ ~ r ~ BL “ C~ /, / ~s~.kE D F Figure 3 Model for the determination of the flexibility matrix of Soleimani's beam element (from Ref. 6) The flcxural behaviour of each end section is described

23、 by thc nonlinear hystcrctic M-~p (moment-curvature) relation proposed by Clough z° and modified by the authors (Figure 3). The primary curve in this model is bilincar: the first part up to the yield moment M~ i

24、s clastic with slope kr. = El; the second part has a slope p.k E, p being thc strain-hardening ratio. E is Young's modulus of concrete and 1 is the average betwccn lp and I,, where lp and 1, arc the moments of in

25、ertia of t.he cracked section for positive and negative moments, re- spectively, iflp and I, vary along the beam length, I is the average between the values at the opposite ends of the beam. By contrast, different yi

26、eld moment values M~ and M~ arc considered for positive and negative mo- ments, respectively. Unloading takes place with a slope equal to kr; partial unloading followed by reloading is represented by segment HIJ in F

27、igure 3. Stiffness degra- dation is present during reloading, the amount of degra- dation being determined by the last point of complete unloading and thc largest excursion into the inelastic range in the opposite di

28、rection; the reloading slope is equal to s.kE, with s ~< 1 (segment DE). The factor t which describes the average stiffness of the inelastic zone can be defined for the following cases. ~ix~ t.k tik kE=EI ~ - Inel

29、astic ~ Inelastic I_ =1“ E,astic .= .I Figure 2 Clough's model ? Unloading or first loading: all sections are elastic, therefore t, = t~ = ! (1) ? Reloading with stiffness degradation: since the end section

30、, having stiffness si“ kE, will experience maxi- mum stiffness reduction while the section at the inter- face between the elastic zone and the inelastic zone will be still elastic, an average degrading stiffness can