Keywords: shrinkage, expansion, non-linear finite element analysis, bond, deformations, reinforced concrete frames.

The effect of restrained shrinkage or expansion is often neglected in the design of small-span reinforced concrete frames [1]. The restrain provided by supports, adjacent elements, and steel reinforcement bonded to the concrete requires elaborate numerical modeling to represent actual response of the structural elements [2].

In this research, the effect of shrinkage and expansion are assessed for a group of typical one-story multi-bay frames. Two finite element models are used to represent the frames; the first uses the linear elastic assumption to model the reinforced concrete elements [3], whereas the second model incorporates the non-linear stress- strain behavior of concrete and considers the effect of cracking on the inertia, detailing of reinforcement, as well as the effect of bond between concrete and the steel reinforcement [4].

Deformations and stresses for one-bay, four-bay, and seven-bay one story frames, with a 6.0m span for each bay are investigated.

The loading procedure for the linear analysis considered the sum of own weight, superimposed dead load and live load, as well as the effect of shrinkage or expansion. For the nonlinear analysis, the following load staging was considered:

• Self weight, this case includes the effect of self weight of concrete elements on the deformation and stresses.
• Shrinkage or expansion, this case includes the effect of shrinkage or expansion on the concrete elements following the application of own weight, and recording the changes in deformation and stresses.
• Superimposed dead load and live load, this case includes the effect of the full load on the structure following the application of own weight and shrinkage or expansion, and studying the changes in deformation and stresses.

Results of the detailed analyses are compared with simplified models in order to assess the effect of shrinkage or expansion on displacements and redistribution of stresses [5]. A significant difference was observed between the various modeling approaches, and between the linear and non-linear frame models. Based on the comparison between linear and non-linear models, it may be concluded that:

• Considering the nonlinear behavior of reinforcement concrete elements while assessing shrinkage result in an increase in vertical deformations and a reduction in the horizontal displacement.
• The linear shell models resulted in deformations in agreement with the non-linear models, whereas the linear frame models resulted sometimes in misleading values.
• The total stresses in the nonlinear model (stresses in concrete in addition to stresses in steel reinforcement) resulted in values comparable to the linear shell model.

The effect of considering shrinkage or expansion in computing stresses and deformations for the set of frames under investigation indicated that:

• At zones of mid span of frames, the change in stresses is significant in case of seven bays frame. The stresses increased by 15% to 18% in case of shrinkage and decreased by 19% to 28% in case of expansion.
• At zones near the supports of the frames, the change in stresses is significant in case of four spans and seven spans frames. The stresses decreased by 14% to 21% in case shrinkage and increased by 17% to 32% in case of expansion.
• At zones of mid span of frames, the change in vertical displacement is significant in case of non-linear analysis of four and seven bays frames. The displacement increased by 18% to 28% in case of shrinkage and decreased by 13% in case of expansion of seven bays frame only.
• At zones near the supports of frames, the change in vertical displacement is significant in case of one, four and seven bays frames. The displacement increased by 26% to 43% in case of shrinkage and decreased by 39% to 60% in case of expansion.
• At all zones of all types of frames, the change in the horizontal displacement was significant. Detailed analysis should be considered if the horizontal displacement is deemed critical in the design of building.

1

Gilbert, R.I., "Shrinkage, Cracking and Deflection for The Serviceability of Concrete Structures", Electronic Journal of Structural Engineering, January 2001.

2

ACI Committee 209, "Prediction of Creep, Shrinkage and Temperature Effects in Concrete Structures", ACI Manual of Concrete Practice, Detroit, 1997.

3

Wilson, E., "SAP2000 Integrated Finite Element Analysis and Design of Structures", Computers and Structures, Inc., Berkeley, U.S.A., 1995.

4

Cervenka, V., Eligehausen, R., "SBETA Computer Program for Nonlinear Finite Element Analysis of Concrete Structures", Mitteilungen IWB., Stuttgart University, 1990.

5

ACI Committee 318, "Building Code Requirements for Reinforced Concrete", American Concrete Institute, Detroit, 1999.

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