Calculation of Zero Movement in a continuous bridge

[minorchord2000]

I was reviewing a practice problem in the NCEES study manual about locating the zero movement location along a continuous bridge. The bridge is supported at the ends by expansion bearings at the abutments and by pinned bearings at the two interior piers. The span arrangement is 40'-120'-40'. The problem asks for the horizontal load at the top of each column due to shrinkage at 0.0002 in/in and a temperature drop of 40 deg F. The problem dives Ec, I of the columns and thermal expansion coefficient, and the height of each column. According to the published solution the authors use an tributary length subjected to expansion of only one half of the 120' span length between the piers or 60 feet. I personally think it should be the 40 feet from the abutment to the pier plus one half of the middle span for a total length of 40 + 120/2 = 100 feet. What do others think?

 

[PittEng88]

I agree with their solution, because both abutments are allowed to expand/contract. Therefore, the only restrained portion of the bridge will be between the two piers.

 

[OSUCivlEng]

I agree as well. With that symmetrical span arrangement and those bearing constraints I would treat the bridge as expanding and contracting from the center. That would only leave 60' of the center span as contributing to the expansion/contraction forces.

 

[minorchord2000]

Thank you gentlemen for your responses.