A powerful and practical software for three dimensional linear elastic finite element analysis of prestressed concrete structures is presented. To account the cable profile realistically, it is modelled by B-spline. For finite element computations, tendon and concrete are modelled by 3 noded bar and 20 noded brick elements respectively. The cable concrete interactions are precisely accounted using vector calculus formulae. Pre-stress loss due to friction is also accounted. The proposed algorithm is coded in FORTRAN language to result in PRECON3D software. Using this software two simply supported beams are successfully analysed and validated with the standard analytical results.
K. K. Pathak, CSPM Group, AMPRI (CSIR), Bhopal, Ahmad Ali Khan, N. Dindorkar, Dept.Civil Engg., MANIT Bhopal, and D. K. Sehgal, Dept. Applied Mechanics, IIT Delhi, New Delhi.
IntroductionPrestressed concrete is one of the most widely used construction materials which can resist tension and compression efficiently. In this, external pre-stressing force is applied on the concrete to reduce or eliminate the tensile stresses and thereby control or eliminate cracking. In this way, a pre-stressed concrete section is considerably stiffer than reinforced concrete section. In curved tendons, upward force is imposed on the concrete which may reduce or eliminate the downward deflection as well. Because of above reasons, prestressed concrete structures has become extremely useful in the construction of liquid retaining structures and nuclear containment structures where absolutely no leakage is acceptable. This technique is of great use in railway sleepers, large span bridges and long span roofs. Prestressed concrete slab overcomes many of the disadvantages of reinforced concrete slab. Deflection, which is almost always the governing factor, is better controlled in post-tension slabs. Therefore, a safe and more slender slab can be obtained.
Because of complex nature of cable concrete interaction, analysis of prestressed concrete structures is a complicated task. For realistic analysis of these structures, advanced computing techniques such as finite element method is employed. Linear finite element analysis (FEA) of prestressed concrete structures have been reported by Pandey et al.1, Buragohian and Mukherjee2, Buragohian and Siddhyae3, Pathak and Sehgal4. Non linear analysis of the same are reported by Povoas and Figueiras5, Kang and Scordelis6, Roca and Mari7, Greunen and Scordelis8, Figueiras and Povoas9, Vanzyl and Scordelis10 and Elwi and Hurdey11. Jirousek et al.12, Buragohian and Mukherjee2 and Buragohian and Siddhyae3 have considered cable as parabolic and cubic curve in shell and semilo of shell elements, whereas Pandey et al.1 considered the cable as parabola in 20 node brick element. Pathak and Sehgal4 considered the cable as cubic spline curve in nine node Lagrangean element. Saleem Akhtar et al.13 modelled cable as B-spline for two dimensional finite element analysis.
Although considerable literatures on prestressed concrete are available, most of them deal with specific aspects namely, realistic modeling of the cable, frictional effects and cable concrete interaction. Since a design engineer needs all these in an integrated environment, he has to resort to separate calculation for each aspect. Also most of the software available on the topic are two dimensional. For accurate analyses, there is need of a three dimensional software to analyse prestressed concrete structures. The proposed software aims to fulfil these lacunas. The main features of this package are: