PSI - Issue 44

Simona Coccia et al. / Procedia Structural Integrity 44 (2023) 1356–1363 Simona Coccia et al. / Structural Integrity Procedia 00 (2022) 000–000

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where the horizontal distance in the deformed configuration between the centre of I and the hinge C 1 is: $ = $ ( $ − $ ) (7) To evaluate the distance O 2 between the center of II and the hinge C 2 we can take into account the similitude existing between the blue and the red triangles of Fig.3. We have # = $ ( $ − $ ) @2 ) ! *"+(- ! '. ! ) ) " *"+(- " '. " ) + 1C (8) The ratio between the virtual rotations dq 1 and dq 2 , given by: ) ! *"+(- ! '. ! ) ) " *"+(- " '. " ) = 0. " 0. ! (9) changes little by increasing the rotation of the segments I and II and can be considered equal to the value evaluated in the undeformed configuration (Eq. (2)). So, we have: # = $ ( $ − $ ) @2 1 $ !" + 1C (10) Further, to obtain the horizontal distance between the point of application of the load Q and the center C 2 we can still take into account the similitude between the blue and red triangles of Fig.3.We get ( = $ ( $ − $ ) @2 ) ! *"+(- ! '. ! ) ) " *"+(- " '. " ) + 2C − 2 # # (11) and considering small the rotation of the segment II, i.e 2 # # ≈ 2 # (12) from i (11) e (12) we have: ( = $ ( $ − $ ) G2 1 $ !" + 2H − 2 # (13)

Fig. 3. Model to evaluate the distance in the deformed configuration of the wall.

Substitution of the distances O 1 , O 2 and O Q given by (7), (10) and (13) into Eq. (6), yields: