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RE: Bridge Seismic Analysis

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Jorge,

In general I agree with your objections. Nevertheless the described
procedure is quite common in practice since not every office has expensive
non-linear software available. I believe that the superposition of the two
analysis yields a conservative result. Maybe others more familiar with
bridge design in this forum could clarify better this issue.

Javier Encinas, PE
-----Original Message-----
From: Jorge Jimenez [mailto:joraljim(--nospam--at)prtc.net] 
Sent: Thursday, January 15, 2009 5:38 PM
To: seaint(--nospam--at)seaint.org
Subject: Bridge Seismic Analysis

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
 
 
 
 
 
 
 
 



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