Issue 37

P. Bernardi et alii, Frattura ed Integrità Strutturale, 37 (2016) 15-21; DOI: 10.3221/IGF-ESIS.37.03 20 The main mechanical properties of steel and concrete, together with the average free shrinkage strain ε sh and the creep coefficient φ c at the date of testing, are summarized in Tab. 2. Numerical analyses are performed by following the same modeling choices already described in the previous Section. Fig. 3a shows a comparison between numerical and experimental [14] results in terms of bending moment M vs. midspan deflection δ; for both the considered beams. Since initial deflection due to shrinkage was not experimentally measured, also in this case numerical curves are shifted to the origin. w [mm] Figure 4 : Numerical and experimental [14] crack pattern at failure for specimen V-01-13DB. As can be seen from Fig. 3a, the shrunk specimen V-01-13DB is characterized by a reduced cracking load and a larger deflection with respect to sample V-01-13WB. Additional comparisons are provided in Fig. 3b, where numerical and experimental values of cracking moment M cr , deflection δ , average and maximum crack width ( w av and w max ) under serviceability conditions are listed. Finally, a good agreement is also found in terms of crack pattern at failure, as proved by Fig. 4, which reports numerical and experimental results for the shrunk specimen V-01-13DB. C ONCLUSIONS n this paper, a non-linear constitutive model for the analysis of RC structures, named 2D-PARC, is modified so as to include early-age shrinkage effects. The procedure is verified through comparisons with experimental data on RC beams subjected to short-term loadings available in the literature. Satisfactory results are obtained in terms of both global behavior and local member response (i.e. stresses in concrete/steel, crack distribution and width), thus making the model a useful tool both in engineering and research practice. R EFERENCES [1] Gilbert, R.I., Shrinkage, cracking and deflection – the serviceability of concrete structures, EJSE International, 1 (2001) 2-14. [2] Gribniak, V., Kaklauskas, G., Kliukas, R., Jakubovskis R., Shrinkage effect on short-term deformation behavior of reinforced concrete – when it should not be neglected, Mater Design, 51 (2013) 1060-70. doi:10.1016/j.matdes.2013.05.028 [3] Bischoff, P.H., Effects of shrinkage on tension stiffening and cracking in reinforced concrete, Can J Civil Eng, 28 (2001) 363–74. doi: 10.1139/l00-117 [4] Scanlon, A., Bischoff, P.H., Shrinkage restraint and loading history effects on deflections of flexural members, ACI Struct J, 105 (2008) 498–506. [5] Rots, J. G., De Borst R., Analysis of mixed-mode fracture in concrete, J Struct Mech, 113 (1987) 1739-1758. doi:10.1061/(ASCE)0733-9399 [6] Vecchio, F.J., Reinforced concrete membrane element formulations, ASCE J Struct Eng, 116 (1990) 730-50. doi:10.1061/(ASCE)0733-9445 [7] Maekawa, K., Soltani, M., Ishida, T., Itoyama, Y., Time-dependent space-averaged constitutive modeling of cracked reinforced concrete subjected to shrinkage and sustained loads, J Adv Concr Technol, 4 (2006) 193-207. doi:10.3151/jact.4.193 [8] Kaklauskas, G., Gribniak, V., Bacinskas, D., Vainiunas, P., Shrinkage influence on tension stiffening in concrete members, Eng Struct, 31 (2009) 1305-12. doi:10.1016/j.engstruct.2008.10.007 I