Stress Diagnosis Method Based on the Section Flatness of a Bent Pipe

If ground subsidence or seismic load acts on piping that includes bent pipes, the highest stress often occurs not in a straight section but in a bent section. The author has therefore developed a method of estimating the stress generated by a change in diameter by adding an equation for the diameter change and bending moment to the bent pipe stress calculation equations proposed by Rodabaugh and George. To investigate the validity of this method, two kinds of bent pipe made using typical bent pipe manufacturing methods and having representative section wall thickness distributions were tested to determine the relationship between the diameter change and the stress generated when in-plane bending moment is applied. As a result, it was confirmed that the stress estimated from the diameter change closely agrees with the measured value. Introduction: It is essential to determine the stress generated in pipelines in order to maintain their safety against external forces, and to do so by non-destructive diagnosis for pipelines that are in service. However, the method involves measuring deformation after installing strain gauges, so it is impossible to diagnose stress over time unless strain gauges are installed when the pipelines are laid. One common method is to use pipe deflection indicators[1] to measure pipeline deformation and to enter deformation readings into an FEM program to calculate the stress, but this is not a very precise method. Bent pipes are generally used in pipelines extending across rivers and at the entrances to multipurpose utility tunnels, and the highest stresses often occur not in straight sections but in bent sections. Iimura and Sakai have developed a method of non-destructively measuring stresses occurring in bent pipes using the principle of magnetostriction[2]. The values measured by the magnetic method were regressed to Von Karman’s theoretical stress calculation equation [3] for a bent pipe. From the regression curve obtained, it was possible to obtain only the external force moment that purely applies bending to the pipe. But it has been revealed that if the methods of manufacturing the bent pipes differ, the range where stress can be diagnosed is narrower than that of a straight pipe of the same grade. This means that when the non-destructive diagnosis method developed for welding elbows and for induction pipe bends is applied, the upper limit for application of the former is about 50% of the yield stress. Therefore, a non-destructive stress diagnosis method with a wider range of measurable stress was necessary. If ground subsidence or seismic load acts on piping that includes bent sections, bending moment acts on the bent sections in almost every case, causing section flatness on the bent pipe. Various formulae have been proposed for calculating the stress distribution when bending moment due to an external force acts on a bent pipe, the best known of which is that proposed by Von Karman[3]. However, in this study, the practicality of estimating stress generated based on the section flatness by extending the method proposed by Rodabaugh & George[4] is investigated. Φ Figure 1: Definition of the angle of a bent pipe. Calculating the stress distribution from section flatness: According to Rodabaugh & George, the longitudinal and circumferential stresses σiL, σiC, σoL, σoC when in-plane bending moment Mi and out-of-plane bending moment Mo act on a bent pipe are represented by the following equations.