Computational Methods

Out-of-plane modes of masonry walls can be studied through dynamic models of rigid-like blocks according to the Housner’s equation of motion [1]. The wall becomes a single-degree-of-freedom model that can be free to rotate or restrained. The restrained model was presented in [2] to simulate the dynamic response of walls restrained by steel-tie-rods as concentrated horizontal restraints. In the model, other contributions and parameters can be accounted for: additional loads (roof, arches, vaults, etc.), roof thrust, diverse geometries (e.g. simple rectangular walls or corner mechanisms [3]) [4]. Their modelling translates into a modification of the terms of the equation of motion.
The further introduction of LICORD as innovative anti-seismic devices expects to include a specific term in the equation of motion considering its stiffness and damping. Moreover, the number of degrees of freedom of the whole system increases to two. The modified model is capable of predicting the dynamic response of the wall for all the earthquakes, in form of acceleration time-histories, to consider for the LICORD’s design.



[1] Housner GW. The behavior of inverted pendulum structures during earthquakes. Bull Seismol Soc Am. 1963;53(2):403–417.

[2] L. Giresini, M. Fragiacomo, P.B. Lourenço (2015). Comparison between rocking analysis and kinematic analysis for the dynamic out-of-plane behavior of masonry walls, Earthquake Engineering & Structural Dynamics, 44(13) 2359-2376. DOI: 10.1002/eqe.2592.

[3] L. Giresini, F. Solarino, O. Paganelli, D. V. Oliveira, M. Froli (2019) One-Sided rocking analysis of corner mechanisms in masonry structures: Influence of geometry, energy dissipation, boundary conditions. Soil Dynamics and Earthquake Engineering, 123, 357-370, DOI: 10.1016/j.soildyn.2019.05.012.

[4] L. Giresini, M. Fragiacomo, M. Sassu (2016). Rocking analysis of masonry walls interacting with roofs, Engineering Structures, 116, 107-120. DOI: 10.1016/j.engstruct.2016.02.041.