Restraint Effects in Concrete Bridges: A Study of Cracking due to Thermal Actions and Shrinkage in Portal Frame Bridges

Erik Gottsäter

Research output: ThesisDoctoral Thesis (compilation)

218 Downloads (Pure)


Thermal actions and shrinkage cause volume changes in concrete structures. In structures which are restrained from movements, the restraint effects can cause cracking. However, when cracking occurs, the structure can deform to some extent, which reduces the restraint stresses and thus also the crack widths. As the exact crack development is hard to predict beforehand, the actual restraint and thus also the crack widths are hard to estimate. This makes it difficult to determine the reinforcement required for limiting crack widths to acceptable values. The common design approach does not include the reduction of restraint due to cracking. Combined with an unclear formulation of the thermal load case for temperature differences between structural parts in bridges, the overestimation of restraint effects that this results in can lead to inefficient use of reinforcement.

In this study, temperature differences between structural parts of portal frame bridges were investigated, in order to suggest a more detailed load case to be used in design of this bridge type. Temperature simulations of portal frame bridge cross sections and surrounding soil were carried out using a finite element model. The model was validated by measuring and simulating temperature in a bridge during a one-year period. Thereafter, it was used to determine new load values, using climate data from different locations in Sweden. Also, crack widths due to thermal actions and shrinkage were investigated using a finite element model with a non-linear material behavior of concrete. In these analyses, the reduction of stiffness due to cracking was included. The model used was validated using test results from previous research.

The thermal load case suggested in this study describes the temperature distribution in portal frame bridges in a more detailed way than the current load case. It also presents values both for quasi-permanent and characteristic load cases. In the non-linear analyses, cracking due to the investigated restraint effects was shown to be unlikely in bridge decks of portal frame bridges, but cracks might form both in the top and in the bottom of abutments. The largest cracks were found in the bottom of the abutments, where the effects of the spatial temperature difference and shrinkage were coinciding.

When comparing the non-linear finite element analysis results with results obtained without including the stress reduction due to cracking, significantly smaller reinforcement amounts were needed for crack width limitation in the non-linear analyses. However, the minimum reinforcement amount was insufficient in order to limit crack widths also in the non-linear analyses. As it was also found that the reinforcement amount had a small impact on the crack widths in restraint situations, limiting the initial degree of restraint by e.g. changing the bridge geometry could be a more effective way to reduce the crack widths than to add extra reinforcement.
Translated title of the contributionTvångseffekter i betongbroar : En studie av uppsprickning på grund av temperaturlaster och krympning i plattrambroar
Original languageEnglish
  • Mårtensson, Annika, Supervisor
  • Larsson Ivanov, Oskar, Assistant supervisor
  • Molnar, Miklos, Assistant supervisor
  • Plos, Mario, Assistant supervisor, External person
Award date2019 Nov 29
Place of PublicationLund
ISBN (Print)978-91-87993-14-5
Publication statusPublished - 2019 Oct 25

Bibliographical note

Defence details
Date: 2019-11-29
Time: 13:15
Place: Lecture hall V:B, building V, John Ericssons väg 1, Faculty of Engineering LTH, Lund
External reviewer(s)
Name: Hallgren, Mikael
Title: Adjunct Professor.
Affiliation: KTH, Stockholm.

Subject classification (UKÄ)

  • Infrastructure Engineering

Free keywords

  • Restraint
  • Concrete
  • Cracking
  • Thermal action
  • Portal frame bridge
  • FE-analysis


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