Palermo, Pampanin, and Calvi 2004
This paper presented alternative solutions for precast concrete buildings based on jointed ductile connections, which was an innovative concept in the seismic design of frame and shear wall systems. The controlling rocking concept was first proposed for precast concrete frames, and then extended to steel frames. The aim of the structure was maximum displacement with negligible residual deformation. In this paper, the seismic response of structural systems with controlled rocking and the response of traditional monolithic systems are compared through push-pull and non-linear time-history analyses on both single and multi-degree of freedom bridge systems. First, the system was introduced and previous controlled rocking concept applications and tests in bridge piers were explained. After that, behavior of single bridge pier and transverse seismic response of bridge frame with controlling rocking were presented in terms of numerical model, push pull analysis and time-history analysis.
System Concept
The controlled rocking system at hand is composed of precast elements, PT tendons and mild steel. Pure precast elements are connected though unbonded post-tensioning techniques. Limited damage is expected in the structural elements as they are intended to stay in the elastic range: the inelastic demand is accommodated within the ductile connection. Controlled rocking motion occurs in the connections with the opening of and closing of an existing gap. Unbonded post-tensioning tendons/bars are used for self-centering and mild steels are used to dissipate energy through their yielding.
Controlled rocking and an adequate ratio of self-centering and energy dissipation contributions led to flag-shape hysteresis behavior.
λ = (M_pt + M_N) / M_s
Re-centering and dissipative parts are considered as a fundamental parameter affecting the shape of hysteretic behavior of hybrid connections. The nominator of the above formula was moment capacity due to PT cables/tendons and axial load; and the denominator was moment capacity due to energy dissipative device (mild steel). If λ was higher than 1, self-centering was guaranteed. However, hysteretic dissipation reduced if it was too high.
Numerical Model, Analysis and Results
Lumped plastic models were used for the hybrid connection (controlled rocking) system and monolithic system with a single degree of freedom. A cyclic static analysis was used to investigate their hysteretic characteristics. For the SDOF, there were negligible cracks in the pier element. The complete bridge model used three dimensional modeling with elastic beam elements and inelastic rotational springs. All bridge piers were designed with the same moment capacity. In the analyses, three bridges (A, B, C) with different geometries were investigated with both the hybrid and monolithic systems. Bridge system A had the most regular configuration and the applied hybrid system showed more symmetrical hysteresis behavior than the monolithic system. Bridge B had a non-regular distribution of pier heights. This resulted in the inelastic demand being concentrated in the central pier, which lead to a more emphasized asymmetric behavior of the monolithic system when compared to the self-centering hybrid connection system. Bridge C had a non-symmetrical distribution of pier heights. Residual drifts were negligible even in the case of monolithic connections due to the higher global flexibility of the bridge piers when compared to the previous bridge systems A and B.
Reference
Palermo, A., Pampanin S., and Calvi G.M. (2004). “Use of “Controlled Rocking” in the Seismic Design of Bridges,” Proceedings of the 13th World Conference on Earthquake Engineering, Vancouver, B.C., Canada, August 1-6.