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Bridge Seismic Analysis
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- Subject: Bridge Seismic Analysis
- From: "Jorge Jimenez" <joraljim(--nospam--at)prtc.net>
- Date: Thu, 15 Jan 2009 21:38:01 -0400
I'm currently working on a bridge design in Puerto Rico, and I am wondering about the validity of the procedure for seismic design used for some local engineers. As an example, consider a two-span bridge with a central pier. The deck composed of AASHTO-Girders. At the ends there are counterfort abutments. There are reinforced elastomeric bearing pads at each support. The bridge superstructure is intended to be designed as continuous beam, and thus having positive moments at central pier. There are 2" gaps between the superstructure and the abutments. There are reinforced concrete shear blocks in the transverse direction, having 1/2" gaps with the girders. Structural computer models are: MODEL 1: A continuous beam and the central pier with springs at superstructure supports representing the neoprene pads. MODEL 2: A continuous beam and the central pier with springs at superstructure supports with 1-spring representing one abutment moving toward backfill and the remaining springs representing elastomeric pads. The procedure for seismic modeling and design consider the following steps: 1. Perform the analysis for the gravitary loads. 2. Design the elastomeric pads. 3. Find the equivalent springs to represent the horizontal and vertical stiffness of the elastomers. The bridge is assumed restrained both longitudinal and transversely by the elastomers only. No anchor bolts or another anchoring device is assumed to be used at supports. 4. Perform a multimodal elastic dynamic analysis (MMEDA) for 'Model 1', considering the elastomers stiffness, both in the horizontal and vertical direction. 5. Since the horizontal displacements in 'Model 1' are greater than the bridge gaps, usually in a proportion of 3 to 5, a second MMEDA is made for 'Model 2'. In this new model, the gap at one of the abutments is assumed closed, and one of the end springs representing the stiffness of the abutment with the soil passive resistance contribution. 6. Design of the bridge components using the more critical forces from both analyses. My objections to the described procedure are: 1. The elastomers were designed only for gravitary loads, but used for seismic loads and not meeting the specifications for seismic isolated bridges. 2. The MMEDA assumes systems having free oscillation. Closing gaps produces collisions disturbing that oscillation and therefore the MMEDA becomes invalid. 3. The MMEDA assumes the combination of the different vibration modes of the system. The maximum modal displacements are not simultaneous and there are some combination procedures (CQC, SRSS and others), to find the total expected displacements with the contribution of the most significant modes. Some time interval of free oscillation and certain number of cycles are required by the system to reach the maximum displacement having a close correlation with the analytical modal combination techniques. With the procedure above, it is possible to have one of the end gaps closed even without the first cycle completion for some modes. 4. Usually the abutments have skew angles respect the bridges longitudinal axis. Therefore, the dynamic equations of movement are coupled. The gaps closing and opening in longitudinal and transverse direction behaves randomly, introducing more non-linearity to the system. 5. A MMEDA is only intended to be used in linear elastic systems. A horizontal force vs. displacement plot is bilinear. The unloading trajectory is also bilinear. Is by definition a non-linear system. For non-linear systems step-by-step analysis or other analyses methods could be used. My questions: 1. Do you agree with my objections for the described procedure? 2. It is possible to analyze a bridge in the example without using a non-linear analysis tool? 3. Any comments? Regards, Jorge Jimenez, PE ******* ****** ******* ******** ******* ******* ******* *** * Read list FAQ at: http://www.seaint.org/list_FAQ.asp * * This email was sent to you via Structural Engineers * Association of Southern California (SEAOSC) server. To * subscribe (no fee) or UnSubscribe, please go to: * * http://www.seaint.org/sealist1.asp * * Questions to seaint-ad(--nospam--at)seaint.org. Remember, any email you * send to the list is public domain and may be re-posted * without your permission. Make sure you visit our web * site at: http://www.seaint.org ******* ****** ****** ****** ******* ****** ****** ********
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