Effects of Semi-Rigid Connection on Structural Responses

There are several idealizations in numerical analysis of structures. In the joints and supports, which is usually assumed to be pinned or rigid, semi-rigid connection should be considered to obtain more realistic, reliable and also economical results. In this study, rotational spring stiffness-connection ratio relation is clearly explained and revealed. A finite element program SEMIFEM is developed in FORTRAN language for the numerical analysis. This program provides to define semi-rigid connections in terms of rotational spring stiffness or connection ratio simultaneously. In the numerical applications, rotational spring stiffness connection percentage relation of the semi-rigid connected structural members is submitted. Semi-rigid connections are considered in column-to-foundation connection of a portal frame, beam-to-column connection of a prefabricated structure, steel brace connection to reinforced concrete (RC) frame of a steel X-braced RC frame and truss member connection to joint of a steel truss system. The variation of moment, shear force, axial force, displacement and stress is investigated in a selected axis of the structures. Numerical examples are performed with respect to connection percentage of the related structural members by using finite element method. According to finite element analysis results, the degree of the semi-rigid connection is important as much as its existence in the design phase. This study reveals that the effect of semi-rigid connections on structural systems shows different variations from structure to structure. Electronic Journal of Structural Engineering (10) 2010 23 the connected beam was used in optimal design efforts by various researchers (Xu and Grierson 1993; Xu, et al. 1995; Simoes 1996). Al-Salloum and Almusallam (1995) inspected the optimal design of partially-restrained steel frames by fixing the connection stiffness and performing solution for the member sizes using a predictor-corrector optimization algorithm. In recent years, the numerical analyses of the frames with semi-rigid-connections have mostly been carried out using the defined momentrotation curves (King and Chen 1993; Kishi et al. 1993; Liew et al. 1993; Leon et al. 1996, Sekulovic and Salatic 2001; Lee and Moon 2002). Three dimensional steel tubular braced frames and truss systems including semi-rigid connections were analyzed by Liew et al. (2000). Moment-rotation curves were also used to determine structural behavior of prefabricated structures (Fatema and Islam 2006). Semirigid connections in both steel (Dubina and Zaharia 1996, 1997; Zaharia and Dubina 2000; Fülöp and Iványi 2004) and wood truss systems became another research topic of the investigators (Foschi 1977; Gupta 1990; Riley et al. 1992; Larsen and Jensen 2000; Rittenburg and Kunnath 2003). In addition, different approaches to model semi-rigid connections of metal-plate-connected wood truss joints were developed by the other researchers (Cramer et al. 1993; Dung 2000). Semi-rigid connections in the preceding studies were considered by rotational spring stiffness. However, there is very little study in which the degree of the connection was indicated as proportional. In this study, the effect of semi-rigid connections on the structural behaviors is comprehensively investigated. Finite element analyses are performed considering semi-rigid connections in column-tofoundation connection of the portal frame system, beam-to-column connection of the prefabricated structure system, steel brace connection to RC frame of the steel braced RC building system and truss element connection to joint of the steel truss system. There are numerous studies relevant to semi-rigid connections in the literature. Almost all of these studies were carried out using rotational spring stiffness. However, connection percentage of the used spring stiffness values was scarcely presented in these studies. Because of that reason, a set of equations, which establishes relations with rotational spring stiffness and connection percentage, is clarified and utilized. Four different structural systems including semi-rigid connection are researched. Finite element analyses of these systems are performed by using SEMIFEM program developed in FORTRAN language. The user can easily employ this program either entering rotational spring stiffness or connection ratio for structural element connection to joint. 2 SEMI-RIGID CONNECTIONS Structural elements and joints are modelled considering some idealizations. The joints of idealized frame elements are assumed to be constituted by ideally rigid connections. However, another assumption is that structural members of truss systems have ideally pinned connection at joints. Actually, structural connections should be named according to their moment-rotation curves. These curves are usually derived by fitting suitable curves to the experimental data. Various types of M-θr models have been developed as described by Chen and Lui (1991). As seen from M-θr curves given in Figure 1 the moment (M) is depended on a function of relative rotation between structural members connected to the same joint. The finite element analyses are mostly performed assuming semi-rigid connections as rigid or pinned connections for simply calculation. Figure 1. Structural connections. Electronic Journal of Structural Engineering (10) 2010 24 Connection flexibility is defined by various methods. To obtain an initial opinion on stiffness of rotational springs, use the modulus of elasticity (E), moment of inertia (I) and length (L) of related beam with constant cross-section is very effective and understandable approach. Stiffness matrix of a beam in local coordinates can be written using these attributes of this beam as follows (McGuire et al. 1999).