In this article, a new energy-based technique is proposed to eliminate trial and error in finding appropriate gain matrices in linear quadratic regulator (LQR) controllers used in active control of structures. The gain matrix is obtained by considering the energy of the structure. To compare the efficiency of the proposed method, a three-storey building with two active tendons in the first and third floors is considered. The proposed gain selection and other techniques reported in the literature for LQR controllers are used to compare the response of the structure for three accelograms. A comparison of the displacement and control forces illustrates the superiority of the proposed method.

No abstract

1 Introduction and backgroundPrestressed concrete cylinder pipe (PCCP) has been used for large-diameter water transmission and distribution mains in the United States as lined cylinder pipe (LCP) since 1942 and as embedded cylinder pipe (ECP) from 1952 onwards. Many classes of ECP have been standardized by the industry based on their internal fluid pressure capacity and backfill earth pressure capacity. The concrete core and prestressing wire are the main structural components, while the steel cylinder acts primarily as a water barrier. The prestressing wire wraps generate a uniform compressive force in the core that offsets the tensile stresses developed in the concrete due to the internal fluid pressure. A mortar or concrete coating surrounds the prestressing wire, embedding the wraps in an alkaline environment to protect them from external corrosive influences and physical damage such as corrosion. Breakage of prestressing wire wraps is a common occurrence in PCCP and is a result of damage due to corrosion, hydrogen embrittlement, overloading or manufacturing defects. Corrosion in immersed concrete structures can be due to earlyage cracks that leave paths for aggressive media, thus compromising the durability of the element [1], [2]. Corrosion and the subsequent breakage of an individual prestressing wire wrap reduces the strength of the pipe at that location [3]. If corrosion continues, multiple wire wrap breaks may occur in the same region, further reducing the strength of the pipe and leading to failure. Since this wire breakage is the primary cause of the structural deterioration of PCCP water mains, it is important to understand the effect of its length and location. The class of prestressing wire with its corresponding ultimate tensile strength is also an important factor for the overall strength of the pipe. Understanding the behaviour of PCCP under combined internal and external loading has gradually developed since the mid 1950s, and the evolution of the standards has been a direct result of investigations into PCCP failures [4], [5]. Although there have been significant improvements in the design and manufacture of PCCP, understanding damaged PCCP, which is intrinsic to this, is still under investigation. A study performed by Zarghami et al. [6], which compared experimental hydrostatic pressure test results with results from numerical FEM, found that the final failure mode for large-diameter PCCP was caused by increased stress in the prestressing wire wraps rather than crushing of the concrete. Liu et al.[2] presented a constitutive model for concrete hardening which considered the degree of hydration concept. The approach allowed the effects of both age and temperature on hydration to be taken into account simultaneously when modelling the early-age behaviour of underground precast concrete pipes. The study used the proposed numerical model to investigate the influences of mix design, casting scheme and curing conditions on the early-age behaviour of the pipes [2].Ojdrovic et al. [7] used finite ele...

No abstract

No abstract