Journal of Constructional Steel Research 62 (2006) 116–120 www.elsevier.com/locate/jcsr Optimum strengthening of a column-supported oil pipeline by a tubular truss J. Farkas, K. Jármai ∗ Faculty of Mechanical Engineering, University of Miskolc, H-3515 Miskolc, Hungary Received 16 November 2004; accepted 13 April 2005 Abstract In the case of a statically indeterminate structure, a systematic optimum design procedure should be performed, since the forces in structural parts depend on their dimensions, and the cost function to be minimized is rather complicated. This is so in the case of a column- supported oil pipeline when it is strengthened by a tubular truss. The internal forces in the tubular truss are derived on the basis of a deflection equation. The strengthening tubular truss is optimized to fulfil the design constraints and minimize the cost. Design constraints relate to the stress in the original pipe and in the truss members, as well as to the strength and geometry of the truss joints. The cost function includes the material cost, as well as the costs of cutting of struts, assembly, welding and painting. © 2005 Published by Elsevier Ltd Keywords: Oil pipeline; Tubular truss; Structural optimization; Minimum cost design; Fabrication cost; Welded structures 1. Introduction In places where the distance between supporting columns is larger than normal, a strengthening of the pipe is necessary. This strengthening can be realized by prestressed cables, or by an upper or lower truss welded to the main transporting pipe. It is assumed that this distance is not too large and therefore a special supporting bridge is not needed. The aim of our study is to design a lower strengthening tubular truss (Fig. 1). This simple truss consists of two diagonals and a vertical member. The diagonals are loaded in tension and have the same cross-sectional area. The vertical member is loaded in compression and bending, and is designed against overall buckling. This complex structural system is statically indetermi- nate, and the unknown force in the column (vertical member) is calculated by the force method using a deflection equation. The symmetric truss geometry has one unknown, the height H . This unknown, as well as the dimensions of truss mem- bers, are calculated from the condition that the material and ∗ Corresponding author. Tel.: +36 46 565111; fax: +36 46 563399. E-mail address: altjar@uni-miskolc.hu (K. Jármai). 0143-974X/$ - see front matter © 2005 Published by Elsevier Ltd doi:10.1016/j.jcsr.2005.04.011 fabrication costs of the strengthening tubular truss should be minimum. Constraints on local buckling of circular hollow-section truss members as well as on the strength and geometry of the node are also considered. The advanced cost function, used in our previous study [1,2], includes the material and fabrication costs. The fabrication costs relate to the cutting of strut ends, assembly, welding and painting. For minimization of the constrained function, an efficient mathematical computer method is used to obtain available circular hollow sections. This is based on Rosenbrock’s hill-climb algorithm, complemented by a discretization procedure [1]. 2. Derivation of the column force The structure of the strengthened pipe is statically undetermined. The unknown column force X 1 can be derived from a deflection equation. The deflection at mid- span of simply supported pipe without strengthening from the distributed load p is (Fig. 1) w p = 5 pL 4 384 EI x (1)