BEHAVIOUR OF FERROCEMENT-REINFORCED CONCRETE COMPOSITE WATER TANKS

Abstract

This thesis aims to study the salient features of large-sized ferrocement tanks subjected to static and dynamic loads and to investigate their suitability and economy over r.c. tanks. These tanks featuring undulated wall are made of ferrocement precast cylindrical panels erected vertically with their apex pointing towards the center of the tank. Under hydrostatic pressure these panels are subjected to compression requiring a thin section to sustain that pressure. The hoop tension is concentrated at the top and bottom ring beams which are made of reinforced concrete. Apart from the base slab and the top cover, a ground water tank typically consists of four elements, like (i) the bottom ring beam, (ii) the top ring beam, (iii) the vertical ribs and (iv) the ferrocement panels. In case of an elevated tank, the staging is the another component to be taken into consideration. In mathematical modelling a ribbed ferrocement tank is idealized as an infilledframe 3D structure containing liquid. The frame members are modelled with three noded beam-column elements considering six degrees of freedom per node. The flat shell elements are used for modelling the ferrocement panels, in which each element consists of eight nodes with six degrees of freedom per node. The displacement based formulation is used for water which is discretized by three dimensional elements. Under earthquake loading the staging of an elevated tank often goes into the inelastic range for which an elasto-plastic model is used. The scope and the objectives of the thesis are outlined as follows: (a) To review the literature covering various aspects of the material properties of ferrocement and reinforced concrete and 2D and 3D nonlinear modelling of the reinforced concrete members. (b) To develop a computer programme for 3D analysis of a ferrocement-reinforced concrete composite tank. (c) To study the static and dynamic response of the ferrocement tank by proper modelling of the 3D r.c. frame, the infill curved panel and the water and to propose a simple design procedure for tanks. (d) To study the nonlinear dynamic response of a ferrocement elevated tank. VIII (0 To perform shake table test of a small sized elevated tank and to validate the analytical results. (g) To propose a simplified and efficient method for performing nonlinear analysis of a ferrocement tank supported on a r.c. staging. (h) To study the suitability of the ferrocement tanks over the r.c. water tanks. The scope of the thesis is outlined below. Review of Literature: The literature review includes (i) the review of the material properties of ferrocement and reinforced concrete, (ii) the finite element analysis and laboratory testing of the different r.c. frame members, and (iii) the performance of several 2D and 3D simplified nonlinear model of the reinforced concrete members. Following conclusions are drawn from the above study: • The cracking characteristics of ferrocement are mainly dependent on a) the ultimate tensile strength and the bond strength of mortar, b) the specific surface and the volume fraction of mesh and c) the modulus of elasticity of the mesh and the mortar. For the flexural member, the spacing of the transverse wires of the uppermost layer of mesh controls the crack spacing of ferrocement. • In case of a reinforced concrete member, strain hardening is observed for an under reinforced section whereas strain softening is expected for the over reinforced section. With the increase of the lateral confinement, the failure mode of a reinforced concrete section changes from brittle to ductile mode. However, at the time of failure, the material property becomes almost a local property depending on the extent of damage and therefore the general plasticity theory cannot simulate the exact failure mode. Structural Modelling: The model consists of beam-column, flat shell and 3D elements, characterized by (i) determination of the impulsive hydrodynamic pressures of the fluid, (ii) determination the elastic stresses in the beam-column and the flat shell elements, (iii) definition of the generalized yield functions for controlling the plastification of the frame members and (iv) elasto-plastic modelling for formulating the tangent stiffness matrix to establish the load-deflection relationship during yielding. The 3D yield surface considering the interaction among P , M M j ux' ux' uy' and M is used in the analysis. IX Ground Water Tank: Aset of fifteen large sized ground water tanks were analyzed and their static and dynamic characteristics are studied. The diameter of these tanks are varied from 30m to 50m at 10 minterval and their height was limited between 2m to 6m. The parametric study reveals that for any particular diameter, the total material weight of these tanks does not vary with the number of the panels. Sectional details of different members are worked out and are presented in the thesis. These tanks are lighter in weight than the conventional r.c. tanks and therefore, in hilly earthquake prone areas they are more suitable than the r.c. tanks. From the cost evaluation it appears that these tanks are approximately 30% cheaper than the r.c. tanks. From frequency analysis it appears that the tanks are not absolutely rigid. A simple empirical expression of the fundamental time period is proposed as, T = 740 • 2 P " r s E ¥ (m sec> ••(!) when, p is the mass density and E is the modulus of elasticity of the r.c. members. Assuming p = 2.4 kN sec2/m4 and E= 25 x 106 kN/m2 the Eqn.(l) can be reduced to the following, h2 T = °-23 T ('n sec) -.(2) which shows a good agreement with the computed results obtained by subspace iteration method. In the above equation d and h are the diameter of the tank and the depth of water in m respectively. The linear time-history analysis has been carried out for the ground water tanks. Simulated earthquake corresponding to the mean response spectra of Uttarkashi earthquake (20th. Oct. 1991) has been used as the input ground motion. The hydrodynamic pressure (impulsive) distribution along the periphery of the tanks are computed at the time of maximum horizontal displacement at top and compared with the stresses obtained from the Housner's(1980) expressions. The computed impulsive pressures are found greater than the other which may be due to the larger flexibility of the tanks. Based on the study, an empirical relationship between the computed impulsive pressure and the Housner's pressure has been established by taking the flexibility of the ferrocement tanks into consideration. From the peripheral distribution of hydrodynamic pressure it is concluded that the overall response is a combination of both cos(e) and cos(0) modes. However the cos(e) mode is much dominant over the other at the time of the maximum horizontal displacement. Shake Table Test of Ferrocement Elevated Tank: The test is performed on a 2.25 kL elevated tank supported on a square staging of 2.31 m high. The tank was made of eight thin precast ferrocement panels. The test has been conducted by filling the tank with moist sand due to which the whole system behaved simply as a single degree of freedom system. From free vibration test, the fundamental frequency was obtained as 2.86 Hz showing a good agreement with the computed value (2.90 Hz). At the end of the shake table test, free vibration test was carried out for the stressed structure and a reduced frequency of 1.57 Hz was obtained. Damping ratio increased from 4.2 % to 10.5 % in course of testing due to nonlinearity. The shake table test has been conducted for control shaking of different magnitude Simulated from the response spectra of Uttarkashi earthquake in three separate test runs R,, R2 and R3. Since the fundamental time period lies within the zone of maximum response of the said spectra, the level of table motion was kept very low. During testing the magnitude of the table motion was increased step-wise from the design Zero Period Acceleration (ZPA) (5% of g) to three times of that value. A reduction of 16.6% of fundamental frequency at the end of R2 (2.25 times of ZPA) indicates the retention of around 70% of the initial stiffness even after flexural yielding. The shear cracks at the beam-column joints appeared at the end of R^ (3.0 times of ZPA) during which the frequency dropped signiflcAntly by 45% Analytical Validation: The response analysis and the analytical validation of the tested tank has been carried out with the computer programme by using, (i) the classical elasto-plastic theory using Chen's yield model for the r.c. frame members and (ii) a proposed simplified method developed by following the work of Darvell (1985). In the elasto-plastic analysis of the r.c. frame members the yield surface specified by the interaction among Pu-Mux-Muy-Muz has been used to develop the elasto- plastic stiffness matrix of the element and other related parameters. The yield surface is assumed unexpandable by considering the hardening parameter H=0. Computer programme coding the elasto-plastic behaviour has been developed to analyze the non linear dynamic response of the ferrocement-reinforced concrete composite elevated tank, which shows good agreement with the experimental results. In the proposed method the yielded zone of a column (or beam) due to the design lateral earthquake load is evaluated from the axial load vs. moment interaction diagram. These yielded zones are considered as separate elements. The elastic modulus of the newly introduced yielded elements have been reduced in such a manner that the analyzed frequency of the yielded structure matches to the experimental frequency. Fundamental frequency at different XI stressed level, is used for the frequency matching. The time history analysis of the new conf.guration of the frame system are in good agreement with the experimental results for different ground excitations.