PSI - Issue 44

Mariateresa Guadagnuolo et al. / Procedia Structural Integrity 44 (2023) 766–773 Guadagnuolo et al. / Structural Integrity Procedia 00 (2022) 000–000

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In mechanism M P , the P.V.W. must consider only the overhanging hollow block B of the chimney, using the system Dxy. 3. Seismic assessment of chimney stacks The seismic demand on chimneys must be computed through the floor spectra to consider the filtering effect exerted by the underneath building structure. This requires knowing the relevant vibration modes of the main structure. The vibration periods of the entire Royal Palace of Carditello are largely affected by some degraded or uneven buildings (e.g. without roofing) and are different from the ones of the towers where most chimneys are located. Therefore, a tower was isolated, considering the constraints exerted by the adjacent buildings (Guadagnuolo et al. 2022), to analyze the seismic response of chimneys. A self-weight of 18 kN/m 3 was assumed for brick masonry and the modulus of elasticity equal to 1500 MPa (Guadagnuolo et al. 2020). In the mechanism M S , the compressive strength of the roof structure was assumed equal to 1.00 N/mm 2 , accepting a maximum strain of 0.3%. Such values consider the possibility of glulam planks being compressed orthogonally to the direction of fibers, the effect of moisture in the structure, and the brittleness of the overlying tiles. Table 1 contains the capacity a g , LS in terms of ground acceleration and the safety index ζ E computed as the capacity to demand ratio according to (MIT 2019). The peak ground acceleration (demand) is 0.154 g.

Table 1. Acceleration capacity and safety index.

a g,LS /g LSA 0.055 0.142 0.056 0.038 0.041 0.071

ζ E

Kinematic analysis

Mechanism

LSD 0.028

LSC

LSD 0.35

LSA 0.36 0.92 0.36 0.25 0.27 0.46

LSC

Linear

-

-

MC

Nonlinear

-

0.128

-

0.72

Linear

0.028

-

0.35

-

MS

Nonlinear

-

0.034

-

0.19

Linear

0.021

-

0.26

-

MP

Nonlinear

-

0.062

-

0.35

Table 1 shows, for each of the two types of analysis, small differences between the possible chimney mechanisms, with greater values of the index ζ E in the case of nonlinear analysis. The latter is considered more reliable in assessing the entire rocking response because dynamically-loaded elements can sustain accelerations greater than that corresponding to their quasi-static capacity (Abrams et al. 1996; Casapulla et al. 2017). The force based approach, indeed, evaluates the load multiplier related to the onset of rocking, and the possible reserve capacity of dynamic rocking phenomena is ignored. The difference between the static force and displacement-based approach also depends on the relation between the building fundamental period and the chimney period. The closeness, that occurs in some of the mechanisms under consideration, implies an amplification in the acceleration demand in the static force-based approach, which has not an analogous amplification in terms of displacement demand. The above results also allow assessing the rule of roof strength in the seismic response of chimneys. The mechanism M S considers the actual strength of the roof structure, but, in the displacement-based approach, its contribution in the evaluation of ζ E is considered only when the roof's maximum strength or deformation capacity is reached after the acceleration-displacement curve nullifies. The mechanism M C , on the other hand, considers the roof to be a perfect constraint to translation in the chimney overturning, but, generally, has greater displacement capabilities. The comparison between the two mechanisms highlights that the roof structure has a decisive role in preventing chimney stack overturning, only when has high strength (e.g. r/c structures), and the protruding stack is not very high. It should however be considered that when the protruding stack is high, the mechanism M P might become the most likely, being characterized by a lower seismic capacity. The outcomes can be considered representative of the seismic behavior of many chimney stacks that have geometry similar to the one considered. Mostly, the results confirm that historic chimneys with high protruding stacks could damage and collapse for low peak ground accelerations (in the examined chimneys about 0.15 g).