LIMIT STATE BEHAVIOUR OF FERROCEMENT FLEXURAL ELEMENTS

Abstract

Housing shortage in developing countries, including India, is colossal in nature requiring a major effort, in genuity in construction techniques and large financial and material resources to overcome the present short-fall and the further needs of the continuously growing population. Pre fabricated construction in ferrocement is one promising solution widely accepted for the immediate future. The use of ferrocement for prefabrication in building construction offers numerous advantages. Ferrocement elements are light, and can be handled manually or using light machinery. Ferro cement construction is simple and rapid and is labour intensive allowing part mechanization in factory or at site to achieve better economy. Ferrocement provides a durable material requiring little maintenance. For purpose of low cost housing with relatively light design loads, the ferrocement roofing and flooring elements are usually thin. With the present emphasis on limit state concepts of design, these elements must be designed for the limit states of collapse and serviceability. The present study is an investigation directed towards the prediction of the behaviour of ferrocement flexural elements in the pre and post-cracking phases till failure. The elements chosen for the study are one way flexural elements comprising beams, lintels and slabs simply supported or restrained at edges for moderate spans, two-way flexural roofing/flooring slab elements simply supported or restrained at the edges under moderate live loads upto 2.5 KN/m , ribbed roofing units for large spans for live loads upto 1.5 to 2.0 KN/m2 and grid floors for public and industrial buildings for live loads upto 5 KN/m2. The primary objective of the analytical and experimental investigation is to study the effect of variables like type and geometry of wire meshes, number of layers, volume content, specific surface ratio of the mesh, flexural rigidity and edge conditions on the limit state behaviour of the chosen ferro cement elements. An attempt is made to develop expressions for cracking and limit loads, deflections, curvatures, crack width and crack spacing. The theoretical results are compared with the experimental results of 160 ferrocement specimens cast and tested in the laboratory, and a close agreement is shown to exist between the two. The various flexural and plated elements chosen for investigation have been analysed at the cracking,the yielding of steel and the ultimate l«ad stages using simplifying assumptions valid for composite materials. The analysis of ferrocement one way bending elements has been done using transformed area concept. Slabs have been analysed as isotropic or orthotropic plates depending upon the distribution of reinforcement in the two orthogonal directions. In case of grid and ribbed slabs, an equivalent orthotropic deflections at the cracking, the yield of steel and post yield stages. Analysis of two-way ferrocement thin slabs under uniform loads have been carried out at the three stages. Elastic plate theory, assuming small deflections, is used in the pre-cracking phase. For the second stage of analysis, Johansen's yield-line theory has been used. At the ultimate load stage, Johansen's theory including membrane action has been proposed. In the pre-cracking stage, classical orthotropic plate theory has been used for analysis and for this flexural rigidi ties are obtained in the two directions. Expression for maximum deflection is also developed. For Johansen's yield line analysis., expressions for yield moments are developed for ferrocement material, and these are used to obtain central deflection and the corresponding load. At ultimate load stage, the enhancement of loads due to inclusion of membrane action beyond Johansen's yield moment is significant in thin ferrocement slabs. Expressions for membrane forces, the load enhancement factor, the collapse load and deflections have been developed. The ribbed or the grid slab has been replaced by an equivalent plate and the analysis in the pre-cracking stage has been carried out based upon equivalent orthotropic plate theory. Appropriate expressions for flexural rigidities,moments, loads, deflections, and curvatures have been developed. Analysis of plate has been proposed for analysis. Johansen's yield line theory has been adopted for analysis and the effect of membrane forces has also been included. For one-way bending elements, the analysis at different stages has been done. In the pre-cracking phase, the crosssection of the element is transformed by replacing both skeletal and mesh steels by equivalent mortar areas. For a given crosssection, the expression for neutral axis depth, X„ is aquadratic a and the value of X« is easily determined. In order to determine the end of the pre-cracking phase, it is necessary to define the cracking stress, o . This has been done on the basis of OX experimental results. Expressions for deflection at any section has been obtained by first determining the distribution of curvature along the span in the pre-cracking phase and inte grating the same. With an increase in the outermost layer of mesh/skeletal reinforcement in the tension zone yields first. In this case, expressions for the neutral axis depth, X and the yield moment of resistance, M have been obtained neglecting mortar in the tension zone. The ultimate load stage is characterised by the mortar reaching a specified maximum compressive strain. Using compati bility and equilibrium equations, the neutral axis depth, Xu and the moment of resistance, Mu are obtained. The expression for deflection at any section has been obtained by summing up equivalent orthotropic plate in the post-cracking range has been carried out in a similar manner as described for two-way lending elements. For safety against excessive deflections and cracking, accurate prediction of crack-spacing and crack-width is an important aspect of limit state design. A survey of published literature indicates that expressions for crack-width and crackspacing for one-way bending elements are available. On the other hand, very little published work is available for prediction of crack-width and crack-spacing for two-way bending elements. In the present study expressions for average crack-spacing, 1 ,and maximum crack width Wmax, for one-way and two-way bending elements have been proposed based on experimental results. The expressions indicate that the average crack spacing and maximum crack width depends on the properties of the mortar, the mesh steel, the skeletal steel, the spacing of wires in the outer most layer on the tension side and the volume fraction of the mesh. The test results have been used to define constants introduced in the expressions. To study functional and limit state behaviour and to validitate mathematical modelling, about 160-one-way and two-way ferrocement bending elements have been fabricated, cast and tested up to failure. The test specimens include 36 two-way slabs, 24 ribbed specimens, 24 grid slabs and 76" one-way bending elements along with a large number of control specimens of plain mortar, cubes, cylinders and beams. The meshes used have been classified as A, B, C, D and E depending upon the mesh geometry. Ordinary Portland cement and Badarpur sand have been used in 1 i 3 proportions for the mortar design with water to cement ratio of 0.5. Mortar cubes and cylinders have been cast as control specimens to determine compressive strength and modulus of elasticity. A sufficient number of plain mortar beams have also been cast to determine modulus of rupture of the mortar. Locally available galvanised woven wire meshes of mild steel and high tensile steel of different size, geometry and wire gauge are used. Skeletal steel consisted of 5 mm diameter mild steel bars and 6 mm diameter high yield deformed bars. One-way bending elements have been tested under third point loading with simple roller supports at the ends or with their ends firmly fixed into brick masonry walls. In case of •simply supported and restrained two-way slabs, 16 point load arrangement with roller supports has been used to simulate uniform load. The restrained slabs have been tested with all edges firmly clamped. Dial gauges have been used for measuring deflections. Huggenberger's demountable deformators have been fabricated having gauge lengths of 25, 50, 100 and 200 mm to obtain strain profiles. A precision crack-width detector with 0.02 mm least-count has been used to measure the crack widths at all critical stages of loading. To obtain strains in critical regions and various load stages, electrical resistance strain gauges have also been used. The crack-spacing and propagation of cracks have been carefully monitored and the extent of cracking marked on the tension faces of the slabs at suitable load interval-. The large amount of data collected during experimental investigations has been presented in the form of tables and curves. The experimental results have been used to define some pertinent parameters describing characteristics of ferrocement. Comparison with analytical results has been made to establish the accuracy of proposed mathematical expressions. As a result of experimental investigations, it has been possible to establish the importance of type and geometry of mesh reinforcement, effect of skeletal reinforcement, number of mesh layers, spacing of skeletal steel, mesh mortar parameter, specific surface ratio, the volume fraction of the mesh, support conditions, flexural rigidities, L/d ratios and the number of stiffening ribs in the orthogonal directions on the behaviour of ferrocement elements. From the experimental and theoretical investigations,the following conclusions are drawn within the range of parameters used in the investigation. 1. The expressions proposed for deflection, loads, curvatures and flexural rigidities at critical stages of behaviour and based upon orthotropic plate theory using transformed section concept, predict the behaviour of ferrocement plate structures reinforced, with square meshes better and more precisely than for structures with hexagonal meshes. 2. The average load factor defined as the ratio of the load at failure to the first cracking load, is about 2.5, thereby indicating a sufficiently high degree of ductile behaviour for ferrocement elements. High ductility is also indicated by the ratio of ultimate curvature to the curvature at yield, varying between 8 and 12 in the present study. 3. Maximum deflections lie within the limiting value of span/ 250 in all types of ferrocement elements tested. The deflection at first cracking decreases with the increase in the flexural rigidity of the uncracked section and the ultimate deflections increase significantly with the increase in the volume content of the wire meshes. 4. The average crack spacing at ultimate load varies with the spacing of transverse wires in the outermost regions of tension zone. The transverse wires of the outermost layer of mesh in the tension zone are the preferred locations for these cracks. 5* The theoretical and the experimental results show that maximum crack width is primarily a function of tensile strains in steel in the orthogonal directions, flexural rigidity of the critical section and the size of the mesh opening in the outer most layer in the tension zone. 6. The theoretical expressions predict maximum crack width and crack spacing reasonably accurately, underestimating crack width by only 5 to 10 percent.