Keywords: semi-rigid, reliability analysis, failure probability, component method, response surface function, rotational stiffness.

In conventional design procedures, steel frames are analysed with the assumption that the beam to column joints are either fully rigid or ideally pinned. In reality the joint deforms to some extent, a relative rotation occurs between column and beam in the joint; the joint resists a certain amount of bending moment; the joint behaves partially rigid. Overestimating the joint stiffness causes an underestimation of the lateral sway, the relative story displacement, and the failure probability, while underestimating the joint stiffness causes an underestimation of the internal forces in beams and columns in the joints [1].

In this paper, the reliability analysis of unbraced and eccentrically braced steel frames with semi-rigid and rigid beam to column joints subjected to earthquake loads is studied. The rotational stiffness and moment resistance of the joints are determined according to the component method in Eurocode 3 [2].

The implicit serviceability limit state functions of the unbraced frames are constituted using the Turkish Earthquake Standard [3], and approximated by the response surface method [4]. A first order reliability method is then applied to these functions [5,6]. The values of the reliability index and the failure probability of the frames are determined. The reliability index value of a rigid frame is much higher than that of a semi-rigid frame, while the failure probability of a rigid frame is much lower than that of a semi-rigid frame. However, both reliability index values remain above the indicative value for the target reliability index beta=1.5. Furthermore by writing the ultimate limit state equations for the three plastic collapse mechanisms of the frames, the beta value for each collapse mechanism is obtained by using the first order second moment method. The first-order system failure probabilities of the frames are bounded by their beam mechanisms. It is seen that the panel and combined mechanisms have negligible effect on the failure probability of the frames. For the eccentrically braced frames, the implicit serviceability and ultimate limit state functions are also established considering the Turkish Earthquake Standard. The variation of the reliability index beta is depicted as a function of the link length by using the represented algorithm. According to the Turkish Earthquake Standard, the serviceability limit state criterion is more dominant on the reliability index and the failure probability of the unbraced steel frames, while the ultimate limit state criterion is more dominant on the eccentrically braced steel frames.

1

M.A. Hadianfard, R. Razani, "Effects of Semi-Rigid Behaviour of Connections in the Reliability of Steel Frames", Structural Safety, 25, 123-138, 2003. doi:10.1016/S0167-4730(02)00046-2

2

Eurocode 3: Design of Steel Structures, Part 1-8: Design of Joints, Beuth Verlag GmbH, Berlin, Germany, 2005.

3

Turkish Earthquake Standard, "Design of Buildings in Seismic Zones", 2006.

4

Y.W. Liu, F. Moses, "A Sequential Response Surface Method and its Application in the Reliability Analysis of Aircraft Structural Systems", Structural Safety, 16, 39-46, 1994. doi:10.1016/0167-4730(94)00023-J

5

Y.G. Zhao, T. Ono, "A General Procedure for First/Second-Order Reliability Method (FORM/SORM)", Structural Safety, 21, 95-112, 1999. doi:10.1016/S0167-4730(99)00008-9

6

R. Rackwitz, "Reliability Analysis - A Review and Some Perspectives", Structural Safety, 23, 365-395, 2001. doi:10.1016/S0167-4730(02)00009-7

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