Bridge Expansion Joint/Bearing Movement Design

[hdb35]

Hello,

I have several questions about Bridge expansion joint/Steel Reinforced Elastomeric bearing design per AASHTO LRFD.

For the expansion joint design (Bridge total movement at expansion pier):

Q1. How do you consider the forces that contribute to movement?
For my case, I am considering Thermal (TU), Shrinkage & Creep (SH & CR), Braking (BR) and Wind (WSsuper, WSsub, and WL).
- For TU, SH and CR, I have calculated the Point of no movement (PNM) considering pier & bearing stiffnesses and calculated the corresponding thermal, shrinkage and creep deformations at the expansion piers wrt to the PNM.
- For Braking and Wind loads, I have distributed the calculated forces based on the relative stiffness of each pier, then calculated a corresponding deflection using delta = Force/stiffness relationship.

Q2. Several jurisdictions seem to ignore the effects of Braking and Wind on the total bridge movement, but I am under the impression that I need to include them. My piers are relatively tall and the inclusion of braking and wind seem to have a significant effect on the total movement calculation. What is the justification for neglecting these forces? Is it because they are transient in nature, and the bridge is expected to return to its initial condition shortly after? I feel like the joint should still be sized to accommodate this movement, as you wouldn't want one part of the structure ever unintendedly hitting the other unit.


Q3. LRFD 3.12.2.3-1 provides an equation for calculating the thermal movement, d = alpha * L * T, where L is the distance from the point of no movement to the expansion joint. This doesn't seem to account for any resistance provided by the support (suggesting this would be the deformation for a perfect roller condition). Howver, per LRFD C14.5.1.2:

"Any horizontal movement of a bridge superstructure will be opposed by the resistance of bridge bearings to movement and the rigidity or flexural resistance of substructure elements. The rolling resistance of rocker and rollers, the shear resistance of elastomeric bearings, or the frictional resistance of bearing sliding surfaces will oppose movement. In addition, the rigidity of abutments and the relative flexibility of piers of various heights and foundation types will affect the magnitude of bearing movement and the bearing forces opposing movement"

Therefore, the actual movement of the superstructure will not be the full deformation calculated by LRFD 3.12.2.3-1, but is reduced due to the stiffness of the support. How do we calculate the actual movement due to thermal (and similarly, creep and shrinkage)? I expect this to limit the actual movement, by transferring some of the force to the substructure. Do I need to consider this ACTUAL movement? Samples seem to just go with the deflection from the perfect roller condition (which is albeit conservative). Is it implied that this conservative estimation of thermal forces is enough to neglect the contribution of any other load?


Similarly, for the Bearing Design:

Q4. What exactly is the maximum shear deformation at the pad,Δs, as referred to in LRFD 14.7.6.3.4?
I am taking this as the the shear deformation from the pad's equilibrium (setting temperature) position. So its the max(total expansion effects, total contraction effects) of the superstructure (WSsub does not cause shear deformation in the bearing)

LRFD 14.7.6.3.4. is clear that these effects shall be reduced as stated similarly in Q3:

The maximum shear deformation of the pad at the service limit state, ΔS , shall be taken as the maximum horizontal superstructure displacement, reduced to account for the pier flexibility and
modified for construction procedures.

Similarly to Q3, I am unsure how to reduce these movements for thermal, creep and shrinkage forces as it pertains to the bearing shear deformation. For Wind and Braking, I took the distributed force at each pier, and simply divided it by the total bearing stiffness of each pier (which is kbrgs = GA/h * number of bearings) [LRFD Eq 14.6.3.1-2] , which ignores the deflection of the columns.
Is this the correct approach?

Q5. At what point do you need to consider adding a low friction sliding surface (PTFE) to the top of the elastomeric bearing?
It seems that I will specify a PTFE slider when either of the following conditions are met:
1) If the shear deformation check of 14.7.6.3.4 does not pass, specifying a slider allows Δs to not be taken larger than deformation corresponding to first slip.
2) If the sliding check fails (LRFD 14.6.3.1). Sliding check fails when the horizontal force due to shear deformation (at strength III state) is less than the friction force.
Now, if I have determined that a sliding type bearing is required, how do I perform my movement calculate to limit my deformation corresponding to first slip?

i. Currently, the bearing and pier stiffnesses are combined to obtain the equivalent stiffness of each support, then the forces are distributed based on their relative stiffness (Distribution Factors). This, however, mathematically results in deformations at the expansion bearings with sliding PTFE that are greater than that which corresponds to first slip. This is incorrect because, the bearing will only deform prior to overcoming friction and will then slide (like a roller). Therefore, these distribution factors are only accurate prior to this point. After this point, the stiffness of the support ≅ 0. How do we account for this?

I apologize for the long post, I just haven't been able to wrap my head around the theory of what seems to be a trivial task in most cases. Perhaps I am missing some fundamental concept that would make everything make sense. I would really appreciate any insight or resources on the matter that you all could provide!

 

[BridgeSmith]

Q1 - Braking and wind forces would not generally be considered in expansion joint design, unless you're expecting significant movement of the fixed substructure due to these loads. You would and factor the forces and calculate the resulting movements and add (or subtract) them to the thermal , shrinkage and creep movements according to the load combinations in Art. 3.4.1.

Q2 - Wind forces longitudinal to the bridge are typically relatively small. Also, for long bridges with expansion joints at the piers, the fixed bearings are typically at the abutments. It's unusual to have 2 expansion joints at piers within a superstructure. It's very difficult to manage the seismic requirements with such a configuration. If your movement from these forces is significant, you should consider it in your design.

Q3 - It's the point of zero movement. If you have piers with elastomeric bearings that produce forces that move the 'fixed' pier, you'll have to calculate where the point of zero movement occurs, based on shear in pads and deflection of the piers.

Gotta go run some errands now. I'll get back to the rest later.

 

[jhnblgr]

check out nysdot mathcad for elastomeric bearings. Thermal load controls and most elastomeric design is controlled by the lateral deflection and required ratios or width to height and stability. The fixed bearings takes the lateral loads via a pin. While lateral loads causing deformation might exist they are negligible in essence. If really interested you could calculate the force required to cause deformation with the shear modulus or model the bridge with spring constants. Now to provide lateral restraint keeper plates can be added parallel to the beams to prevent the sole plate from deflection beyond the elastomer limit.