Sensitivity Analysis of Cable Profile of Prestressed Concrete Beams

The cable profiles for post-tensioning of concrete beams are usually designed as parabolic curves based on the eccentricity of the midpoint of the duct to the neutral axis of the beam. The end points and the midpoint of a duct are very important and sensitive. Hence, the sensitivity of these influence points is being studied and the most sensitive point(s) is being found out.

The method of computational analysis (matrix method) using STAAD.Pro has been taken into account to find out the sensitivity. The sensitivity has been observed by repositioning the points by 25mm from the standard cable profile in both directions at a time. The tensile and compressive stresses and deflections are then observed in six different locations of each span of the beam and the sensitivity is calculated. The results of different points are then compared to find out the most sensitive point.

The test has been done for four different beam profiles i.e. single-span, two-span, three-span and five-span beam considering a combination of self-weight, live load and post-tension load. This study provides the knowledge of sensitive points of the cable profile of the post-tensioning of concrete beams so that the care can be taken during construction.

K.K. Pathak, Professor, Department of Civil Engineering, IIT (BHU), Varanasi, Rounak De and Sayak Roy, undergraduate students of Department of Civil Engineering, IIEST, Shibpur.

Introduction
Pre-stressing of concrete can be achieved by two different methods namely pre-tensioning and post-tensioning. Pre-tensioning is useful in precast concrete blocks while for the in-situ cast concrete beams post-tensioning is most effective and easy to achieve. In post-tensioning process the ducts are first laid in the form of the actual deflection pattern of the beam profile and the casting of the beam is done first. After the concrete is matured high yield high tensile steel wires as tendons are then inserted through the ducts and the post-tensioned forces are applied equally through both ends of the ducts. In post-tensioning, the whole section of the beam can be used as most of the total cross-section stays in compression. Post-tensioned beam profile has been shown in Fig.1

As the upward force on the beam due to post-tensioning totally depends upon the cable profile so profiling the duct(s) is a very critical job before casting a post-tensioned concrete beam and has to be done carefully and correctly. Padmarajaiah et. al. (2000) has conducted analyses on flexural strength of fibre reinforced concrete. Pathak and Sehgal (2004) conducted an analysis of a prestressed concrete beam using different cable models. Kasat and Varghese, (2012), studied prestressed concrete beams using finite element analysis. The observation of the research is the response of prestressed concrete beams due to transverse loading conditions. Bhargava et. al. (2016) have conducted analysis of single span prestressed beam using analytical, matrix and FEA method. The aim of the study is compare three most popular methods of structural analysis. The effect of pre-stressing force and eccentricity on different cable profile for a single span beam has been analyzed using ANSYS by Dixit & Khurd (2017). They found out the effect in terms of deflection of different cable profiles used in prestressed concrete. The goal of this study is to determine the most sensitive point(s) of a cable profile in terms of deflection and stress variation through a post-tensioned beam. To achieve the goal, four different beam profiles have been analyzed using computational analysis for a combination of self-weight, live load and post-tensioned load.

Sensitivity
To find out the desired results a different sensitivity analysis has been carried out. Sensitivity analyses of tensile and compressive stresses as well as analysis of deflection of beam profiles have been carried out for different cases through structural analysis software, STAAD.Pro. Sensitivity of a parameter can be defined as the ratio of change of that parameter to the change of some other controlling parameter. Here the sensitivity of stress and deflection has been taken into account which can be given as-

S_s=∆σ / ∆e
S_d=∆δ / ∆e

Where ∆σ and ∆δ are the change in stress and deflection in concrete at different locations and ∆e is the change in eccentricity of a particular influence point.