NONLINEAR ANALYSIS OF FRAME-SHEAR WALL STRUCTURES

Abstract

The research work reported in the thesis has been conducted in order to develop amethod for predicting com prehensively the nonlinear behaviour of frame-shear wall structures. Acomputational technique has been presented for obtaining the complete nonlinear load deflection response of reinforced concrete frame-shear wall structures subjected to aproportional static, short time loading with a view to study their post elastic behaviour. Nonlinearity in structural response is exhibited mainly in two different forms. The first is material or physical nonlinearity which results in anonlinear force deformation relationship of the structural member due to nonlinearity in the stress-strain relationship of the constitutive materials. The second is geometric nonlinearity which results in nonlinear interaction between axial loads and large deformations due to finite changes in the geometry of the structure. Review of existing work on the behaviour of frame-shear wall structures indicates that the linear aspects of uuch structures have been investigated by anumber of authors but only avery limited amount of research is available regarding their nonlinear behaviour. Some investigators have outlined a procedure for the approximate inelastic analysis of frameshear wall structures by considering an idealised mathematical model comprising of a substitute cantilever connected with ii pin ended rigid links to a shear wall. In these studies an elastic-plastic thrust-moment-curvature relationship has been adopted for the frame members whereas an elastic strain hardening thrust-moment-curvature relationship has been used for the shear wall component. The P-A effect has been incorporated but the instability effects have been neglected in the analysis. The detection of coliuim hinges has been considered as one of the failure criterion. Further the studies have been limited to the determination of the load displacement curve upto the collapse load. Yet another investigator has employed the finite element technique for the nonlinear analysis of the substitute cantilever model already described above. The existing methods of nonlinear analysis of frameshear wall structures are thus based on a number of simplify ing assumptions which are usually adopted for the analysis of such complex structures and their scope is therefore limited. The analytical method developed for the present investigation has been formulated in such a way that it is more comprehensive in approach and reveals the true behaviour of frame-shear wall structures in the post elastic range. The method of analysis employs an idealised mathematical model comprising of a substitute frame connected with pin ended rigid links to a shear wall to represent the frameshear wall structures. Gravity loads acting transversely on girders have thus been accurately accounted for in the analysis. This is a comparatively better mathematical model ill as compared to the one adopted in earlier studies. The proposed analytical method is based on the direct stiffness matrix approach and takes into account both the material and geometric nonlinearities. It is illustrated that the conventional direct stiffness matrix approach can be success fully employod to study the poet elastic behaviour of frameshear wall structures. The method of analysis assumes a perfectly elastic-plastic bilinear thrust-moment-curvature relationship for the frame members. The nonlinearity in the shear wall has been accounted for by using the thrust-momentcurvature relations derived from the stress-strain laws, cross sectional configuration and properties of the materials in the analysis. Thus it will be seen that in the analysis of the shear wall the simplified assumptions regarding the thrust-moment-curvature relations as proposed in earlier studies have not been made in the present work to avoid errors on that account. Large deformations may occur in frame-shear wall structures in the post elastic range and the high axial loads interacting through finite deformations can cause significant instability effects. Therefore axial deformations, joint displacements (the P-A effect) as well as the flexural deformations within members (the beam column effect) which has not been considered in earlier studies have been accommodated in the proposed computational technique. The nonlinear behaviour of the reinforced concrete frame-shear wall structures subjected to a proportional IV vertical and lateral loading has been studied for a range of values of the following parameters: 1. The ratio of shear wall to column stiffness, 1, 10 and 50. 2. The ratio of column to beam stiffness, 1 and 2. 5. The ratio of lateral to vertical loads on the fraBe element, 0.4 and 1. 4. The slenderness ratio of columns, 10, 20 and 30. 5. The percentage of reinforcement, 1% only. The above parameters have been studied using the proposed method of nonlinear analysis on single and double storeyed reinforced concrete plane frame-shear wall systems. It is realised that shear walls are not used in this storey range therefore the parameters chosen have been kept sufficiently wide ranging to reflect the stiffness relationships of taller structures. Limitations of computational facilities and com puter time have restricted the study but still the results of the analyses do give an insight into the nonlinear behav iour of this class of structures. In practice structures are really subjected to nonproportional loads and the lateral loads would be compara tively large if a frame-shear wall structure were to collapse. Therefore, although the proportional loading has been assumed in the analysis the ratios of lateral to vertical loads V adopted in this study are purposely kept high to allow for the possibility of a greater lateral loading on the structure. Two types of shear wall idealisations, a shear wall behaving elastically throughout and a nonlinearly behaving shear wall have been studied with the above parameters in the analysis. The study of frame-shear wall interaction problems in volve a large number of variables with wide ranging values and a quantification of their behaviour is indeed not simple. Earlier studies have brought out or reaffirmed important qualitative assessments of the behaviour of such structures. In particular the load deflection characteristics have been studied in detail. This thesis presents numerical results on such important parameters as plastic hinge rotations, load deflection characteristics, stiffness reductions of the nonlinearly behaving shear walls, force distribution amongst the frames and the shear walls and the interaction between them at different storey levels. In any study involving the post elastic behaviour of a structure the rotations or the inelastic deformations occuring at plastified sections prior to or at collapse are an important factor for consideration, particularly so for reinforced concrete structures. In reinforced concrete structures due to the limited rotation capacity of member sections it is therefore also necessary for the analysis to proyide an estimate of the inelastic deformations taking place in the structure so that the ductility requirements at any stage of the loading process can be assessed. VI -Information on this important aspect has not been reported earlier. As an advancement on existing information, the present computational technique also provides an estimate of the plastic hinge rotations taking place in the structure at any stage of the loading process. It is observed that the inelastic deformations taking place in the frame-shear wall structures do not place any severe ductility demands on the structure until its complete collapse is reached. Nearly all normally designed reinforced concrete sections possess adequate rotation capacity for the complete plastic collapse to take place in such structures. However since the analysis provides an estimate of the plastic hinge rotations taking place in the structure at any stage of the loading process the load factor corresponding to any permissible limited plastic hinge rotation capacity can be obtained from the analysis. Thus a safe value of the load factor corresponding to any available rotation capacity can be obtained although the analysis continues till the collapse of the structure by formation of sufficient number of plastic hinges to transform either the whole or part of the structure into a mechanism. In order to illustrate the versatility of the proposed computational technique to multistorey frame-shear wall structures a method of checking the design of buildings symmetrical in plan and consisting of plane frames and shear walls has also been presented. The procedure has been demonstrated by its application to a typical building Vll of three storeys. Finally based on these studies the conclusions regarding the nonlinear behaviour of frame-shear wall structures have been summarised and recommendations for further research work are suggested.