PSI - Issue 11

Cyrille Denis Tetougueni et al. / Procedia Structural Integrity 11 (2018) 452–459 Tetougueni et al./ Structural Integrity Procedia 00 (2018) 000 – 000

455

4

of the four hinge as follows:   , −

 , = 0

(1)

From the principle of Virtual Works, we obtain the equation of the collapse multiplier  :

 ,  ,

∑

 = − =

(2)

∑

3. Statement of the Problem In the present study, the effect of two important geometric parameters of masonry arches in the seismic resistance has been studied. In particular, arches with different abutments height in one part and with different thickness have been analysed under seismic load and the mechanisms developed have been found different from those observed in regular arches. A typical geometry of arches with discontinuous abutment height and different arch thickness are respectively presented in Fig.3 and Fig.5.

Fig. 3. Geometry of arches with different height abutment

Four different cases have been considered in the analysis of the influence of discontinuous arch abutments. The abutment’s slenderness and span to rise ratio are two parameters that have been varied as shown in the Table 1. Two loads situation have been considered. In the first situation A, the seismic acceleration is applied from abutment with greater height toward abutment with lower height while the second situation B consider that the seismic acceleration moves from lower abutment to greater one. The analysis shows that the situation A is less prone to collapse respect to the situation B since the collapse multiplier for different cases of situation A is higher than for cases of situation B (Fig.4).

Table 1. Parameters of the cases analysed

Case:

1

2

3

4

f/L

0,2

0,3

0,2

0,3

S/L

0,1

H/B

2

2

4

4

H L /H

0,8

0,8

0,8

0,8