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Figure 10. Characteristic curves of pier panel 2.5: (a) positive seismic verse; (b) negative seismic verse.
Figure 11. SAM model walls: (a) regular; (b) irregular height; (c) irregular length; (d) irregular length and height.

4.1.3 Pier panel 2.5

Finally, in this panel as for the first one, the failure occurs for eccentric axial load (Fig. 10) but the reduced height of the panel, due to the horizontal irregularity, influences the value of the bearable shear.

4.2 Application of the SAM method

For this numerical application the same geometrical, mechanical and load models were implemented in an available computer code, called Andilwall (http://www.crsoft.it/andilwall/andilwall.aspx).

In Figure 11, the model views of the four walls are given.

The failure mechanisms ofthe pier panels, performing a non linear static analysis, are shown in Figure 12. The dotted lines indicate the eccentrical axial load failure and the line-point line the shear failure. Observing level 2, it is evident that the mechanisms for panels 2.1 and 2.5 coincide with the RAN method, whilst no failure conditions are detected for the central pier 2.3 in all the four study-cases.

(a)

Figure 12. SAM failure mechanisms: (a) regular; (b) irregular height; (c) irregular length; (d) irregular length and height.

Figure 13. 3MURI model walls: (a) regular; (b) irregular height; (c) irregular length; (d) irregular length and height.

4.3 Application of the 3MURI method

The 3MURI computer code was then used (http:// www.stadata.com). A 2D view of the four walls (Fig. 13) and a selection of the failure mechanisms of the walls are shown (Fig. 14).

The colour green (vertically striped) means that the panel is undamaged, the pink one (diagonally striped) that the plastic limit state for bending and axial load has been reached, the red one (horizontally striped) that the collapse occurred for composed flexural and axial load. The cross panels, in light blue (plane) are not affected by failure mechanisms.

Figure 15. Capacity curves of walls: (a) regular; (b) irregular height; (c) irregular length; (d) irregular length and height.

Figure 14. 3MURI failure mechanisms: (a) regular; (b) irregular height; (c) irregular length; (d) irregular length and height.

5 COMPARISON OF RAN, SAM AND 3MURI

Once the three analyses were completed, a comparison of methodologies has been carried out and discussed as follows.

Obviously, the first difference among procedures is the geometric modelling of the panels. Extensively reported in ยง2, it is opinion of the authors that a pairing of the three methodologies is definitely necessary. RAN method rightly considers the updating of the geometric configuration according to the seismic verse, whilst SAM and 3MURI rightly evaluate the external cross panels dimension.

Regarding mechanical characteristics, the parameters required by 3MURI are practically the same of RAN whilst SAM, being mainly targeted to artificial units, requires a more refined calibration in the perpendicular and parallel directions of load.

Another difference of methods is represented by the collapse mechanisms of pier and spandrel panels. The 3MURI and SAM methods did not detect shear collapse mechanisms in any of the panels, but only mechanisms of flexural-axial load failure or uncracked panels. Conversely, in the application of the RAN method, shear collapse mechanisms influenced the panel pier 2.3 for horizontal irregular wall. The presence of this kind of collapse mechanism revealed by the RAN method for stocky panel appears more consistent with the geometry and load condition of the panel. It has to be admitted that a general disagreement about the failure modes is detected.

Moreover, it can be observed that, whilst SAM and 3MURI, being implemented in computer codes, request the use of a "close" calculus, the RAN method

Figure 15. Capacity curves of walls: (a) regular; (b) irregular height; (c) irregular length; (d) irregular length and height.

allows the application through the use of spreadsheets. This implies a simpler use of the methodology and the possibility of adapting it to specific needs, although it is more time consuming.

Finally, a quantitative comparison of the three methodologies has been performed. Some non-linear static analyses of the whole structure were carried out. For regular walls (Fig. 15.a) the three curves show nearly the same value of shear force at the base. The RAN curve is stiffer than the 3MURI and SAM one. The 3MURI ductile branch is longer than SAM's. Once the vertical irregularity is introduced, RAN method provides an higher shear force and stiffness value than 3MURI and SAM. These latter show the same initial stiffness but can not be compared in terms of peak load and displacement (Fig. 15.b). The same considerations on the regular wall can be made for the horizontal irregular wall (Fig. 15.c). The last irregular wall, which considers both the horizontal and vertical irregularity, shows the same behaviour of the vertical irregular wall (Fig. 15.d).

In all these cases the RAN method does not provide the same ductility value as the other two methods, since the non linear analysis was conducted under force but not displacement control (as SAM and 3MURI).

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