Stability Analysis of Single-layer Elliptical Parabolid Latticed Shells With Semi-rigid Joints
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Stability analysis of single-layer elliptical paraboloid latticed shells with semi-rigid joints Huihuan Ma n , Feng Fan, Jie Zhong, Zhenggang Cao Harbin Institute of Technology, 2619#, 202 Haihe Road, Nangang District, Harbin 150090, China a r t i c l e i n f o Article history: Received 3 April 2012 Accepted 25 June 2013 Available online 27 July 2013 Keywords: Socket joints Semi-rigid joints Elliptical paraboloid latticed shells Parametric analysis Critical loads a b s t r a c t Based on the bending stiffness of socket joints obtained through experiments, the nite element models of single -laye r ellipti cal paraboloid latticed shells with the semi-rigid socket joints are established . Parametric analysis of the latticed shells is carried out using ANSYS. The parameters considered are bending stiffness, ratio of rise to span, rotation-stiffness, ball size, asymmetric load distribution, tube sectio n, support condition s and initial imperfection s. The effects of the different paramet ers on the critical loads of the shells are thereby identi ed. Both geometric and material nonlinearity are considered during the analysis. Finally, formulae are derived for the calculation of critical loads of the shells under symme tric and asymmetric loading condit ions. This will be useful for the design and application of single-layer latticed shells with semi-rigid joints. & 2013 Elsevier Ltd. All rights reserved. 1. Introduction The design and analysis of single-layer latticed shells is usually based on the assumption that the connections behave either as pinned or rigid joints. However, the joints in most space structures are semi-ri gid, for example the MERO joint systems [1–3], the aluminum alloy truss connector [4], the ORTZ joint [5–7], the bolt– ball joint systems [8–11], the S14, D14 and D06 joints [12], the T.U. U.-S ball joint [13], the space-truss connector [14] and the socket joint system [15]. Eurocode 3 recommends that the assumptions made for structural analysis should correspond to the real beha- vio r of the con nec tio ns. Hen ce, the ana lys is of lat tic ed she ll s should consider the stiffness of the joints. The behavior of singl e-la yer latti ced shel ls with semi -rig id joints is highly nonlinear and is affected by many factors, such as bending stiffness, ratio of rise to span, rotation-stiffness, ball size, asymmetric load distribution, tube section, support condition and initial imperfection. Many studies of semi-rigidly jointed latticed shells have been undertaken. Fathelbab [1] concluded that con- nection stiffness has a considerable effect on the load –displace- ment behavior of structures. The inuence of the rigidity of a joint on the critical load of a single-layer dome has been studied and the equilibration of different critical loads with different joint rigid- ities has been obtained [5] . A numerical model and experimental tests for single-layer latticed domes with ORTZ joint, widely used in Spa in, demonstra te d the inuen ce of such factors as dome geometry, slenderness of members, joint rigidity and load hypoth- esis on the behavior of sing le-l ayer spheri cal domes [6]. Usin g ANS YS, sing le-l ayer latticed dome s with bolt–ball joints were analyzed considering several different parameters, and the major factors inuencing the critical loads were identi ed [8]. El-Sheikh [16] found that the over al l behavior and failure mode of a structure is inuenced by the bending stiffness of the connections. Most of the previous research focused on the spherical domes. However, the elliptic paraboloid single-layer latticed shells with semi-rigid joints ( Fig. 1) can provide a good solution for small or medium span space structures, because of their rapid construction speed, high fabrication accuracy and beautiful appearance. How- ever, few such shells are actually used because their performance is complex and related studies are limited. Hence, it is worthwhile expl orin g their mechanic al perf orman ce. In this pape r, nite element models of single-layer latticed shells with the semi-rigid sock et join ts are establis hed. Two load distri buti ons have been studied: symmetric and asymmetric. A parametric analysis of the shells is conducted to nd their mechanical behavior with differ- ent geometric parameters and joint rigidities. The inuence of the parameters on buckling loads is investigated and the main factors to be considered in design are identi ed. Finally, formulae which allow designers to estimate the buckling loads of the shells are pres ented . The ef ci ency of the propos ed for mul ae is ver i ed usin g numer ical analyse s. These formulae will be usefu l in the design and application of single-layer latticed shells with semi- rigid joints. 2. The nite element models of elliptic paraboloid single-layer latticed shells with semi-rigid joints Two nite element mode ls of elli ptic parabolo id singl e-lay er latti ced shells with sock et join ts are establis hed ( Fig. 1 models Contents lists available at ScienceDire ct journal homepage: www.elsevier.com/locate/tws Thin-Walled Structures 0263- 823 1/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.tws.2013.06.020 n Corresponding author. Tel.: +86 451 86289080; fax: +86 451 86283098. E-mail addresses: [email protected] .cn, [email protected] (H. Ma). Thin-Walled Structures 72 (2013) 128 –138
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