M ASONRY I NFILLED RC F RAMES
5.4.2 Verification of Improved Analytical Model
Three frames (IF-CT, IF-CM1 and IF-CM2) from the past experimental studies, in which shear failure of columns was reported to be the primary mode of failure, were considered for the verification of the improved modelling technique. Since the nonlinear material property of masonry used in the study were not provided in these studies, the axial hinge definition for the masonry strut was developed using the nonlinear stress-strain model proposed by Kaushik et al. (2007) as shown in Fig. 5.8. As already discussed with the previously tested specimens (IF-FB1and IF-FB2), the prevalent single-strut model was not able to predict the shear failure in any of the considered frames. Therefore, the improved analytical model was used to predict the lateral load response of these frames.
Fig. 5.8. Compressive stress-strain curve for the axial hinge in masonry infill of the three frames (Kaushik et al. 2007).
Comparison of the pushover curves obtained using the improved analytical model and experimental response of the selected infilled frames is shown in Fig. 5.9. It was observed that the global response was aptly simulated by the analytical model. Formation of hinges near the specified locations was found to be quite similar to that observed in the
0 7 14 21 28
0 0.002 0.004 0.006 0.008 0.01
Compressive Stress (MPa)
Compressive Strain IF-CM1
IF-CT
IF-CM2
experiments. In case of IF-CM1 (Al-chaar et al. 2002) and IF-CM2 (Cavaleri and Di Trapani 2014), it was observed that initially masonry strut yielded followed by the yielding of flexural hinges, and shear hinges were developed with further increase in the monitored drift. On the other hand, in case of IF-CT (Mehrabi et al. 1996) model, shear hinges reached their capacity after the yielding of axial strut but prior to the yielding of flexural hinges. The reason for IF-CT to exhibit formation of shear hinges at a lower drift level was that the section had the lowest shear capacity and shear demand was higher due to the frame-infill interaction.
(a) (b) (c)
Fig. 5.9. Comparison of analytical and experimental curves using the improved analytical model for: (a) IF-CT; (b) IF-CM1; and (c) IF-CM2.
In case of IF-CT, the improved analytical model exhibited formation of shear hinge at 0.23% drift (124 kN), whereas, in experimental investigation major shear crack formation was reported at 1.37% drift (224 kN) [Fig. 5.10(a)]. In case of IF-CM1 analytical model, it was observed that the shear hinge was developed at a drift level of 0.20% corresponding to a lateral load of 57 kN; whereas the first major shear crack was reported in the experimental study at 0.4% drift (81 kN) [Fig. 5.10(b)]. No details on the initiation of the shear cracks in the columns were provided in the study. In case of IF- CM2 experimental study, it was reported that initially diagonal cracks were formed at the upper joints of the columns [Fig. 5.10(c)] but the drift corresponding to the initiation of shear cracks was not mentioned, whereas, shear hinge reached its capacity at a drift level 0.13% (98 kN) in the analytical model. From the analytical investigation carried out by D’Ayala et al. (2009) to predict the shear failure of columns, it was also observed that the
shear capacity of the sections in the analytical model was reached at a lower drift level compared to the experimental observation of major shear crack.
(a) (b) (c)
Fig. 5.10. Failure mechanism observed experimentally in: (a) IF-CT (Mehrabi et al. 1996); (b) IF-CM1 (Al-chaar et al. 2002); and (c) IF-CM2 (Cavaleri and Di Trapani 2014).
After the formation of shear hinges and yielding of flexural hinges, capacity of the infill as well the capacity of the infilled frame reached almost simultaneously with further increase in monitored drift. Therefore, from the comparison of the experimental results with the analytical response it can be verified that the global response as well as the local failure mechanism can be captured satisfactorily with the improved analytical model. The nonlinear masonry material model in the analysis of all three frames was developed based on the nonlinear stress-strain model proposed by Kaushik et al. (2007), and it was observed that the results are sensitive to material model as properties of masonry are region specific. A more generic masonry material model needs to be established for accurate estimation of shear demand on the columns.
S
UMMARYAn attempt was made in this chapter to understand the applicability of the current recommendations of some commonly used seismic codes to estimate the shear demand on the columns. The existing equivalent strut macromodelling analogy in estimating the global response of the infilled frame was evaluated and its limiting ability of capturing the internal forces in frame members was highlighted. The existing strut modelling analogy was improved by simulating the effect of infill along the contact length of the column to account for the increased shear demand on the column due to the frame-infill interaction.
The analytical response clearly showed that the improved model was able to capture the local shear failure of columns by forming shear hinges in the column, in addition to
accurately predicting the global response (lateral strength and stiffness) of the frames. The improved modelling technique was further verified using other past experimental results, and it was observed that the improved modelling technique successfully captured both the global response as well as the local component (shear) failure in infilled frames.
The shear failure of the columns could not be prevented even though the shear capacity of the column sections was enhanced significantly as per the current codes of practice. Therefore, it becomes utmost important to accurately predict the shear failure of columns in such frames so that their design can be improved. By utilizing the improved analytical macromodel, some design methodologies will be developed in the next chapter to improve the shear behavior of columns for counteracting the local adverse effect of infill.