DUCTILITY BEHAVIOUR OF FRAMED STRUCTURES

Abstract

Ductility signifies the ability of a structure or a member to undergo inelastic deflections beyond the point of first yield under static/dynamic loading while maintaining a certain maximum load carrying capacity. It is well known that during strong motion earthquake, a large amount of energy is absorbed by the structure through its nonlinear deformations before failure. Therefore, an important consideration in the design of earthquake resistant structures is provision of ductility in addition to the usual strength criteria to ensure that in the extreme event of a structure being loaded to failure, it has the capacity to dissipate large energy through ductile deformations. Studies on nonlinear dynamic behaviour of single and multiple degree of freedom system have strongly influenced new design concepts in earthquake engineering. In practice, however, application of these ideas to frames presents problems. In single or multiple degree of freedom system, only the idealised springs are assumed to be non linear and ductility is generally defined with respect to an assumed yield deflection of the spring. In the case of a portal frame, the nonlinearity or plastic hinge formation may occur either in the column and or beam depending on the size,material and the load. Because of this it is necessary to identify the parameters which may describe the behaviour of frames in more realistic fashion. Several definitions of 'ductility are in use based on deflection, curvature, rotation, and strain. The commonly used among these is corresponding to deflection which also has been interpreted differently by various Ill (14,l5,90,91,93,99>Several codes(91'130) also recommended investigators ductility factor of the order of 3 to 5 for ductile reinforced concrete and structural steel frames. The role, nature, and extent of ductility particularly in reinforced concrete structures is however not yet fully understood, and therefore aconsiderable difficulty is faced in deciding the level of ductility for the design of the members. Also very little attempt has so far been made to determine whether such a structure can actually achieve this ductility and further, whether the strains in steel and concrete in the section of the members are within allowable limits at this value of ductility. A review of literature shows that the deflection ductility (29) factor of the order of 5 would generally be difficult to achieve and that it depends on a number of parameters viz. material variables, geometric variables and loading variables etc. Inelastic analyses of reinforced concrete frames have been carried cut by various investi gators. However, none has yet developed an analytical model to study the lateral load-deflection characteristics of a reinforced concrete frame subjected to combined vertical and lateral load with due consideration to confinement cf concrete. Also very little experi mental work has been done to study the lateral load-deflection behaviour of the frames subjected to combined horizontal and vertical loading. Most of the investigators have performed the experiment either by applying horizontal load only or by varying vertical load and keeping horizontal load constant. Very few have attempted studies involving horizontal as well as vertical load on the columns and these too en steel frames. The present investigations therefore are devoted to study the IV lateral load-deflection behaviour of frames subjected to constant vertical load and varying lateral load. The research work has been carried out with the following objectives: 1. Identification of a realistic analytical model to study the behaviour upto ultimate lateral load and ductility demand of reinforced concrete frames. 2. A simplified definition of ductility factor. 3. An exhaustive study of the main variables affecting ductility. 4. Verification of the developed analytical model by comparing the analytical results by performing the experimental tests on models. In the work reported herein, a preliminary analytical study on single storeyed steel frames is carried out followed by a detailed and exhaustive study on reinforced concrete frames for ultimate load behaviour* The nonlinear behaviour of single bay-single storey steel frames is studied by considering an analytical model as suggested by Anderson and Bertero^ ;. The properties of the frames studied have been varied such that they cover a reasonable range from strong column-weak beam at one end to weak column-strong beam at the other. The influence of residual stresses, vertical loads and rate of strain hardening has also been examined. Ductility factor is defined in two different ways: (1; based on the formation of first plastic hinge and (2> based on the intersection of tangents drawn to load-deflection curve at initial and ultimate condition and are used in the present study. V The study reveals that deflection ductility factor is gene rally large when defined with respect to strain as compared to those obtained corresponding to an arbitrary yield point with respect to deflection.Relative stiffnesses of beams and columns strongly influence deflection ductility factors. A strong column-weak beam type frame gives the best results for ductility and load carrying capacity. The research work on reinforced concrete frames is classified into four groups: 1. Development of an analytical model, ?. Suggesting a suitable definition of ductility factor, 3. Study of the main variables affecting ductility,and 4. Development of an experimental set up and testing of reinforced concrete frames. The analytical model for nonlinear analysis of reinforced concrete frames subjected to combined vertical and lateral loads includes both material and geometrical non-linearities. This analysis also considers the effect of confinement through the steel binders. The frame elements are discretized into small segments for the purpose of analysis. The yielded portion at the ends of amember is assumed to be limited to approximately l/5th of the member length. The lateral load-deflection curve of areinforced concrete frame is obtained in gradual steps of lateral loads upto collapse. The influence of relative stiffness of column and beam, grades of longitudinal and transverse reinforcements, quantity of longitudinal steel, diameter and spacing of transverse confining reinforcement on the ductility factors and lateral load capacity was studied in great detail. For this purpose the study was restricted to single bay-single storey, double bay-single storey and single vi bay-double storey reinforced concrete frames. Tests on single storey reinforced concrete frames were carried out under constant vertical load on each column and variable lateral load applied at the top end of the columns and lateral load-deflection behaviour of the frame was observed. The loading arrangement for applying vertical load was specially designed so that this load remained vertical and axial on the columns throughout the test while the frame got deflected due to application of a gradually increasing lateral load. Existing instrumentation techniques were adopted to record loads, strains, lateral deflection and free vibration of the test frames. Five reinforced concrete strong column-weak beam frames designed for vertical load only were chosen for experimental study. All the frames had the same size, dimensions, concrete and longitudinal reinforcement except that four portal frames consisted of four columns in each and one was a plane frame. The influence of spacing of lateral reinforcement was mainly studied to observe the ductility behaviour of the frames. Various definitions of ductility factor have been examined in the present studies and a simplified definition cf ductility factor which will be conveniently usable by structural analysts and designers, has been proposed. It has been observed that strong column-weak beam frames are better suited for the design of earthquake resistant structures compared to other types of frames.