Thermal Point of Origin - Locating Fixed Supports

[CalebA]

I am calculating the stiffness of the substructure elements and bearings to determine the thermal point of origin (TPO) on a continuous steel bridge. How do I determine which supports to make fixed supports? Is it just the support closest to the TPO? The supports to the left and right of the TPO? Do I need to adjust the stiffness calcs depending on which support/s I make fixed? Does the TPO just become the location of the fixed support?

 

[CalebA]

For anyone else who comes across this thread, I found the answer:

https://wisconsindot.gov/dtsdmanuals/strct/manuals/bridge/ch27.pdf

When deciding which bearings will be fixed and which will be expansion on a bridge, several
guidelines are commonly considered:
• The bearing layout for a bridge must be developed as a consistent system. Vertical
movements are resisted by all bearings, longitudinal horizontal movements are resisted
by fixed bearings and facilitated in expansion bearings, and rotations are generally
allowed to occur as freely as possible.
• For maintenance purposes, it is generally desirable to minimize the number of deck
joints on a bridge, which can in turn affect the bearing layout.
• The bearing layout must facilitate the anticipated thermal movements, primarily in the
longitudinal direction, but also in the transverse direction for wide bridges.
• It is generally desirable for the superstructure to expand in the uphill direction, wherever
possible.
• If more than one substructure unit is fixed within a single superstructure unit, then
forces will be induced into the fixed substructure units and must be considered during
design. If only one pier is fixed, unbalanced friction forces from expansion bearings will
induce force into the fixed pier.
• For curved bridges, the bearing layout can induce additional stresses into the
superstructure, which must be considered during design.
• Forces are distributed to the bearings based on the superstructure analysis.

 

[BridgeSmith]

Temperature movement will be controlled by the stiffness of the substructure and bearing combination at each support.

The shear stiffness of elastomeric bearings is fairly easy. The stiffness of rocker bearings can typically be assumed to be zero. The stiffness of sliding bearings is simple to calculate, but have a fairly broad range of possible resistance values over their service life.

The stiffness of the substructures is the one that's generally very hard to predict accurately. In most cases, abutments are very stiff relative the bearings, so they can usually be considered rigid. The stiffness of piers or bents can be a particularly prickly problem, if they are significantly different in height or configuration.

If the substructures are symmetrical and similar, the bridge can be assumed to expand and contract about the center of the superstructure. This simplifies the calculations considerably.

 

[CalebA]

How do I determine which equation to use for calculating the stiffness of a hammerhead pier? To get EI, I am treating the hammerhead pier as a wall, using an average value for the width. Then I'm finding that there are two equations for calculating pier stiffness, 3EI/H^3 (pier cap free to rotate) & 12EI/H^3 (pier cap free to translate only). Are these the correct equations and how do I know which one to use? I should note that I have a single fixed pier (DOT requires at least 1 steel bolster for curved bridge). Then the rest of the bearings are either elastomeric or PTFE.

 

[BridgeSmith]

Unless your pier is integral with the superstructure, it's free to rotate at the top, so it's 3EI/H^3. H is the height of the pier from fixity of the foundation. If it's on a spread footing or a pile cap, that's generally assumed to be the top the footing/cap.

The force transferred at the PTFE sliding bearings will be limited to the slip force, but you should account for the change in the coefficient of friction over time. PTFE sliding surfaces start out with a low COF, but it can double during the service life of the bridge due to dirt, etc. getting into the sliding plane.

I recommend you avoid PTFE sliding surfaces, if at all possible. It'll mean taller and possibly larger elastomeric bearings, possibly even designing them per Method B and paying the associated cost premium for the tighter material tolerances, but the design is much more straightforward and it will likely cost about the same.