POST-CRACKING BEHAVIOUR OF FERROCEMENT PRESTRESSED BOX GIRDER ELEMENTS

Abstract

Ferrocement has been used in many applications like boats, tanks, silos and roofs. The behaviour of ferrocement for roofing purposes has been investigated in the form of thin slabs, channel sections, ribbed slabs, tension ribbon, folded plates, shells of various shapes, circular domes and box sections. Out of the various sections mentioned above, thin slabs, channel sections, ribbed slabs and box sections only provide flat tops and can, therefore, be used for flooring also. Channel sections and ribbed slabs are thin and have small flexural rigidities resulting in large deflections and cracks under service loads. The box sections only, thus, provide an ideal solution for applications to medium spans. In the present study, the behaviour of ferrocement ^M prestressed box sections has been investigated analytically and experimentally by ' testing a few box specimens with aview to their applicability for longer spans. Prakhya and Sai (1987) analysed ferrocement plates for linear and non-linear behaviour by the finite element method using the layered technique. Adegenerated shell element with heterosis shape functions was used. Geometrical and material nonlinearity were considered in their analysis. The predicted load-deflection response was compared with the available test data. Sehgal (1989) analysed ferrocement box girders by finite element method for elastic and post cracking behaviour using rectangular flat shell elements. The layered technique was used in the analysis. Only material nonlinearity due to cracking of mortar, tension-stiffening effect of the cracked mortar and non-linear stress-strain relationships of the constituent materials were considered. Al- Rifaie and Mohammed (1999) analysed circular arch shells for linear and non-linear behaviour by the finite element method. Adegenerated shell element of the layered model with Lagrangian shape functions was used. Perfect bond between steel and mortar was assumed. The compression behaviour of mortar was modelled by both elastic perfectly plastic and strain hardening plasticity approach. The analytical results were compared with published experimental values. The finite element method has been used in the present study to predict the precracking and post-cracking response of the box girders. Because, the conventional methods ofanalysis cannot take into account the change in flexural rigidity at different sections due to the cracking of mortar or the yielding of reinforcement, material anisotropy and local redistribution of stresses due to yielding of reinforcement. A degenerated heterosis shell element of quadratic type, capable of representing membrane action, bending action and membrane-cum-bending action is adopted. The smeared crack concept has been adopted. Layered approach has been used for plate/ shell idealisation to facilitate non-linear analysis. The box sections have large flexural and torsion rigidity resulting in small deflections even in the cracked range. Geometric non-linearity does not significantly affect the analysis of box sections and hence ignored. The element is assumed to consist of a suitable number of mortar and reinforcement layers. The wire mesh and skeletal steel layers of equivalent thickness are such that the total area remains the same and their centroids coincide with that of the wire or bar. Only material non-linearity due to cracking or yielding of mortar, tension-stiffening effect of the cracked mortar and non-linear stress-strain relationship of wire mesh and skeletal steel is considered. Stiffness of the element in the uncracked stage is obtained by adding contributions of each layer in the section. In the cracked range the stiffness is obtained by adding contributions of the uncracked and cracked layers of mortar and yielded or unyielded layers of wire mesh and skeletal steel. A perfect bond between reinforcement and mortar has been assumed. There are various methods like bond-linkage and bond-interface to transfer stress (i.e. prestress) of steel to concrete. Butin the present study a simplified equivalent load of prestressing method has been used. An incremental-iterative procedure taking advantages of the tangent and initial stiffness approach has been adopted in the non-linear analysis. A computer program has been developed on the basis of the proposed finite element model to facilitate computer-aided analysis of presticsscd ferrocement box girders. 111 A mathematical model has been proposed and based upon that a computer program has been prepared for the analytical prediction ofcomplete response ofboth unprestressed and prestressed ferrocement box sections right up to failure/ collapse. The analysis by finite element method has been carried out under dead load, prestressing force effects and monotonically increasing uniformly distributed imposed load. Validation of the proposed mathematical model has been done by comparing the predicted results with the reported experimental/ analytical results of typical test problems, taken from literature and also with the experimental results of the present study. An experimental study has been carried out to investigate the complete response of thin ferrocement flexural elements in the pre-cracking and post-cracking stages. The results of the experimental investigation on unprestressed and prestressed ferrocement box specimens with and without segmental construction have been used for validation purpose. The first specimen was a 230 mm deep single cell box unit of 3300 mm overall length and was unprestressed. The second specimen and the third specimen were of similar cross sectional dimensions as the first specimen, except the thickness of the web elements was 45 mm instead of 25 mm. These two specimens were prestressed to study the effect of prestressing on the response of thin ferrocement box sections. The overall length of second and third specimen was 3300 mm and 4800 mm respectively. The third specimen consisted of three, in-situ epoxy jointed, precast segments to study the feasibility of segmental construction in ferrocement box sections and response of the assembled unit. These segments were prepared as per match cast construction and simply jointed by epoxy. The fourth specimen was dimensionally similar to third specimen except the overall depth was 350 mm. Further, this specimen also consisted of three segments, which were jointed by acast-in-situ mortar joint. The skeletal steel of the adjacent segments was welded and wire meshes were overlapped. Prestressing wires were provided in parabolic profile with zero eccentricity at end and maximum at mid span. IV All the specimens were tested under monotonically increasing 16-point imposed loads, to simulate auniformly distributed imposed load. The load was applied in steps through asingle centrally placed hydraulic jack. The deflections, strains and maximum crack widths were recorded at various load level along with first crack and failure load. The results of the experimental investigations of different box specimens have been primarily used for validation of the proposed mathematical model for predicting analytically the complete response of such structures. The results of the experimental study and the analytically predicted response by and large have been found to be in good agreement. All the specimens were designed for uncracked anchorage zones at the time of prestressing. The experimental investigation shows that the first crack appeared in the anchorage zone and the prestressed specimens failed at about 1.65 to 2.51 times the first crack load. The unprestressed single unit, prestressed single unit as well as the segmental box specimens investigated experimentally have been analysed by the proposed mathematical model using a simplified equivalent load of prestressing method (for prestressed specimens only) has been used to simulate the prestressing effects. The analytical results are found to match the experimental results quite well. The study reveals that prestressing of ferrocement box sections is feasible and effective. The prestressing of ferrocement box sections is useful in extending the applicability ofbox sections to longer spans. The maximum deflections at the penultimate loads were about span/170 and span/234 for the unprestressed and the prestressed box specimens respectively. Therefore, geometric non-linearity can be neglected, as has been done, without any significant error in predicting the complete response ofthe ferrocement box girders. The proposed mathematical model is quite efficient compared to the four noded flat shell element used by earlier investigators for the analysis of box girders. Even with a relatively coarse finite element mesh used for discretization, it can predict the behaviour of unprestressed and prestressed box sections satisfactorily both in the precracking and post-cracking phases. The first crack loads predicted by the computer analysis are 5.6 %lower to 12.0 %higher than the respective experimental first crack loads for all the test specimens. While the failure loads predicted by the analysis are 0to 2.3 %lower than the respective experimental values for all the test specimens. The segmental prestressed box specimen with cast-in-situ mortar joint in which skeletal steel was welded and wire meshes were overlapped for alength of 150 mm with the use of rich cement mortar in the joint, behaved like a monolithic box specimen. Segmental construction of ferrocement prestressed box sections with epoxy joints is not as efficient as that with cast-in-situ mortar joints. The epoxy joints is useful only when the whole cross-section is in compression under full design loads. The discontinuity of reinforcement through the joints resulted in apremature failure of the joint. An analysis of the results shows that the load corresponding to 0.1 mm crack width is smaller than the load inducing maximum deflection of span/250. Hence, the Limit State of serviceability for maximum crack-width corresponding to 0.1 mm governs the design instead ofthe maximum deflection limit (i.e. span/250). Since the proposed numerical method neither determines the spacing between cracks nor maximum crack width, the experimentally obtained maximum crack-widths have been compared with the values predicted by using different semi-empirical cum analytical methods suggested by various researchers. It is found that the maximum crack widths predicted by Logan and Shah equation (1973), based on stresses computed in outermost layer of wire mesh, are relatively in better agreement up to 74 to 85 %of the failure load than the Naaman's (1979) predicted values. VI