PSI - Issue 11

P. Bamonte et al. / Procedia Structural Integrity 11 (2018) 322–330 P. Bamonte and A. Taliercio/ Structural Integrity Procedia 00 (2018) 000–000

327

6

The values of E  , E z ,   z , and G  z were evaluated according to the expressions proposed by Taliercio (2014), whereas the expression proposed by Zucchini and Lourenço (2002) was used to compute G r  . The remaining elastic parameters were obtained assuming masonry to be transversely isotropic in the ( r ,  )-plane. The values of E z and   z in Table 2 overestimate the material stiffness experimentally evaluated (Table 1). This might be due to the brick-to mortar bonding, which is unlikely to be perfect as in the micromechanical models underlying the values in Table 2.

Table 2. Mechanical properties of masonry.

E r = E  [MPa]

E z [MPa]

 rz =   z

G rz = G  z [MPa]

G r  [MPa]

 r 

6438

4154

0.02

0.13

1709

3160

Gravity and wind loads were taken into account. Gravity is automatically computed as body force according to the material density (1800 kg/m 3 ). Wind load was modelled as a static pressure, varying both along the height and the circumference of the chimney. The reference value of the wind speed (25 m/s) was evaluated following the Italian standards CNR-DT 207/2008, considering a return period of 50 years. The reference value was corrected by means of different coefficients, taking into account, among others, aeroelastic phenomena (i.e. the wind-structure interaction) and the topography of the site, in order to work out the pressure distribution over the chimney. In addition to the static loads, the structural behavior was studied under the effects of a change in temperature, which was defined by considering the presumable conditions when the chimney was operational. The inner temperature was assumed to vary linearly from 300°C at the bottom to 120°C at the top. The temperature distribution inside the structure was then worked out solving a steady-state heat transfer problem, by accounting for convection between air and structure (coefficient of convection = 10 W/[m 2 · K]), and conduction within the solid elements (thermal conductivity = 0.7 W/[m · K]). Thermal strains were evaluated according to the values of the coefficient of thermal expansion reported in Section 2.2. 4. Numerical results Fig.s 5a and b show the contours of the axial stress under gravity loads and wind, respectively. In both cases, radial and circumferential stresses are negligible. Under gravity loads (Fig. 5a), the highest compressive stress is attained at the bottom of the upper part, where the cross-section changes from circular to octagonal. Below the change in section, the stress first decreases and then increases again, to reach another local maximum at ground level. Stress concentrations occur near the door. The maximum axial stress (   0.5 MPa) is compatible with the presumed strength of masonry, and, to the Authors’ knowledge, is a value typical of masonry chimneys subjected only to gravity loads. In the presence of wind loads (Fig. 5b), the axial stresses are definitely higher than the tensile strength of masonry perpendicular to the bed joints (Sec. 2.2). This is, however, at odds with the surveyed crack pattern, as no horizontal cracks are reported in the base of the chimney (Fig. 3). This leads to the conclusion that either the chimney has never been subjected to wind pressures as high as those prescribed by the current standards, or its tensile strength is much higher than expected. The first hypothesis is definitely more convincing, as the base of the chimney is shielded on three sides by other buildings. As far as the change in temperature across the chimney walls is concerned, Fig.s 6a,b,c and d show the temperature distribution at four different heights. The temperature distribution over the sections is quite different: at z = 0 the thinner internal wall, which is heated and free to expand, behaves in a way completely independent from the external wall, which remains at ambient temperature and does not experience any thermal-induced increase in stress. At z = 20 and 40 m, the vertical and horizontal connections act as thermal bridges, allowing heat to be transferred and temperature to increase also in the external wall, whereas at z = 60 m the temperature distribution is regular, given the absence of geometric discontinuities. The temperature distributions predicted by ABAQUS were compared with those given by a simple rheological model, in which the heat transfer and the temperature values were worked out by modelling each part of the section (internal wall, external wall and vertical ribs), as well as the air layers, by taking into account their thermal transmittance/resistance in steady-state conditions. A typical comparison is shown in Fig. 7a: the agreement between