Time-Dependent Deflection and Deformation of Reinforced Concrete Flat Slabs-An Experimental Study. Paper by R. I. Gilbert and X. H. Guo/AUTHORS' CLOSURE

Discussion by William L. Gamble

FACI, Professor Emeritus of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign

This paper is a welcome addition to the literature on the deflections of reinforced concrete slabs. The very large timedependent deflections are not new, but this information has not been incorporated into codes and standards. The authors could have cited at least three Australian cases from several decades ago where the ratios of total to initial deflections were between 6.5 and 7.5. References 9 and 10 describe measurements on buildings in the Sydney area. Reference 10 describes a case of a roof slab that was never subjected to any loads beyond the slab self-weight plus a small load from plaster, insulation, and roofing amounting to approximately 5% of the slab weight. Reference 11 describes a slab made with lightweight aggregate concrete that was subjected to a series of loading tests. Time-dependent growth in cracking seemed to be clearly involved in the first two cases.

While the slabs described herein were small, at about halfscale, they were not so small that the thin sections should lead to unexpected or unusual shrinkage behavior. Modeling is always a problem, and the use of smaller reinforcing bars-for example, 6 mm bars-would have led to more representative values of d/h, but availability of small-sized deformed reinforcement is often an unsolvable problem. This comment is not meant to be criticism of the specimen design. Just for the record, what is the area of the Y10 bar? There are two different bars designated as 10 mm bars in North American, with significantly different areas, and considerable confusion can result.

There is a comment that all of the exterior columns developed cracks on the outer surfaces "due to bending in the columns resulting from the applied load and the restraint provided by the columns to shrinkage in the slab." Actually, shortening of the slab would lead to tension on the inside of the columns, with cracking on the inside if shrinkage was the only force or deformation acting. Loading effects would be expected to dominate unless the structure was quite long, or perhaps quite small. Five quarter-scale slabs were tested at the University of Illinois at Urbana-Champaign around 1960, with abbreviated descriptions given in Reference 12. They each had three spans of about 1.5 m in each direction. Two slabs with beams on all column lines were 38 mm thick, three slabs with only edge beam were 44 mm thick. In at least one case, the corner columns lifted off of their supports during the interval between removal of the formwork and initiation of load testing. In this case, the shrinkage induced forces overcame the rather minor self-weight. The slabs were painted immediately after formwork removal to reduce shrinkage, but the step obviously was not adequate.

The measured crack widths in Slabs S4, S6, and S7 suggest that reinforcement over the columns yielded sometime during the tests. Yielding seems the only plausible explanation for Slab S4. The other two cases are complicated by the relative large reinforcement spacing, at over twice the slab thickness.

REFERENCES

9. Taylor, P. J., and Heiman, J. L., "Long-Term Deflections of Reinforced Concrete Flat Slabs and Plates," ACI JOURNAL, Proceedings V. 74, No. 11, Nov. 1977, pp. 556-561.

10. Taylor, P. J., "Initial and Long-Term Deflections of a Reinforced Concrete Flat Plate Structure," Civil Engineering Transactions, Institute of Engineers, Australia, V. CE12, No. 1, Apr. 1970, pp. 14-20.

11. Blakey, F. A., "Deformations of an Experimental Lightweight Flat Plate Structure," Civil Engineering Transactions, Institute of Engineers, Australia, V. CE3, No. 1, Mar. 1961, pp. 18-22.

12. Sozen, M. A., and Siess, C. P., "Investigation of Multiple-Panel Reinforced Concrete Floor Slabs: Design Methods-Their Evolution and Comparison," ACI JOURNAL, Proceedings V. 60, No. 8, Aug. 1963, pp. 999-1028.

AUTHORS' CLOSURE

The authors thank the discusser for his comments and agree that the deflection control provisions in the current codes and standards (including ACI 318) fail to adequately model the time-dependent deflection in reinforced concrete slabs, particularly flat slabs. The discusser refers to a paper by Taylor and Heiman that reports measured deflections of flat slabs in existing structures in the 1960s in the Australia. These were the first of many flat-slab structures in Australia and elsewhere where the actual slab deflections measured in service were several times greater than those calculated using the long-term deflection multipliers contained in the codes. The main problem is that the deflection calculation methods do not account for the loss of stiffness caused by time-dependent cracking resulting primarily from restrain to drying shrinkage.

The cross-sectional area of the 10 mm deformed bars used in the test specimens is nominally 78.5 mm^sup 2^. Measurements of the cross-sectional area of the bars indicated that the area may vary between 77.7 and 78.5 mm^sup 2^. Although reinforcement strains were not measured, it is considered unlikely that the wide cracks recorded over the columns were due to yielding of the top steel as suggested, particularly for Slabs S6 and S7 where the sustained load levels were relatively low. The cracks widened with time due to shrinkage and did not change appreciably when the external load was added or removed. The measured timedependent changes in the reactions at the bases of the columns suggest that the redistribution of internal actions with time was not sufficient to cause the steel stress to approach anything like the yield stress. The final crack width depends on the bond-slip relationship between the steel and the concrete in the regions adjacent to each crack, and the observed crack widths suggest that there is a significant deterioration of bond with time. Wide cracks are not necessarily associated with large local steel strains, if significant slip is occurring between the steel and the concrete. The wide cracks observed on the top surface of these slabs over the interior columns are quite typical of the cracks that occur with time in actual flat-slab buildings designed in accordance with the current codes.

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