The M2 case study represents a point-supported faỗade panel composed of two t = 10-mm-thick HS glass layers ( Rk = 70 MPa [8]) and a middle tint = 4.52-mm-thick PVB film, with global nominal dimensions B = 2500 mm and L = 1500 mm, in accordance with Figure 3.16, and d = 104 mm.
The panel is subjected to the action of self-weight in the vertical direction as well as to major live loads taking the form of wind pressures q = 1 kN/m2 (with tL = 3 s the conventional load duration) acting in the direction per- pendicular to the surface of glass (Figure 3.16). Mechanical point supports
Figure 3.14 Distribution of maximum tensile stresses (a) in glass and (b) in the PVB film (maximum envelope, in [Pa]) for the M1-3 panel, at first cracking (ABAQUS/Standard).
S. Max. principal envelope (max) (avg: 75%)
+7.048e+07 +6.464e+07 +5.880e+07 +5.296e+07 +4.711e+07 +4.127e+07 +3.543e+07 +2.959e+07 +2.375e+07 +1.790e+07 +1.206e+07 +6.221e+06 +3.796e+05
S. Max. principal (avg: 75%)
+2.607e+05 +2.327e+05 +2.047e+05 +1.768e+05 +1.488e+05 +1.208e+05 +9.282e+04 +6.484e+04 +3.686e+04 +8.885e+03 –1.909e+04 –4.707e+04 –7.505e+04
(a) (b)
Figure 3.15 Stiffness variations for the M1 panels at the attainment of first cracking in glass at T = 30 °C and 60 °C, respectively (ABAQUS/Standard).
250 450 650 850 2000 2500 3000
iSMA (mm) 1.0
1.2 1.4 1.6
K1,i / K1,0 (–)
30° 60°
0 1
2 3
are realized in the form of articulated steel rotules, e.g. point fixings able to provide fully rigid translational restraints but enabling, at the same time, possible rotations.
Differing from the M1 case study, the point-supported panel is charac- terized by maximum stresses in the vicinity of the point restraints and at mid-span, as well as by high deformability, due to the absence of continu- ous supports along the edges. Table 3.6 summarizes the main input data for some of the examined M2-reinforced configurations.
Table 3.6 Reference geometrical configurations for the M2 glass panel.
SMA net Panel geometry Loading condition
SMA iSMA B L T q
(mm) (mm) (mm) (mm) (°C) (kN/m2)
No SMA M1-0 – – 2500 1500 30, 40,
50, 60
1 (3 s) SMA
wires
M1-1 4 450
M1-2 350
M1-3 250
M1-4 150
Figure 3.16 M2 case study. (a) Reference geometrical properties for the conventional unreinforced LG panel and (b) example of a rotule connector (axonometry and transversal cross section, nominal dimensions in [mm]).
d
d Hole t
B
59 67
64 109
M 14 x 1,5
ỉ
L
HS PVB
tint (a)
(b)
Table 3.7 Comparative FE results for the M2 panel subjected short-term wind loads under the effects of temperature variations.
Glass Interlayer
wq,M (mm)
Rw,M (%)
wq,E (mm)
Rw,E (%)
q
(MPa) R (%)
int,q
(MPa)
30° 0 5.93 – 0.661 – 8.08 – 0.009
1 5.87 –1.01 0.605 –8.47 8.13 0.61 0.010
2 5.86 –1.18 0.598 –9.53 8.14 0.74 0.011
3 5.84 –1.52 0.587 –11.20 8.15 0.99 0.011
4 5.82 –1.85 0.586 –11.37 8.15 0.99 0.012
40° 0 6.06 – 0.657 – 8.18 – 0.008
1 6.01 –0.83 0.606 –7.76 8.22 0.48 0.009
2 5.99 –1.16 0.603 –8.21 8.16 –0.25 0.009
3 5.98 –1.29 0.600 –8.68 8.08 –1.22 0.024
4 5.96 –1.65 0.595 –9.44 7.95 –2.81 0.021
50° 0 6.19 – 0.652 – 8.28 – 0.005
1 6.15 –0.64 0.615 –5.67 8.17 –1.32 0.014
2 6.13 –0.97 0.606 –7.05 8.09 –2.29 0.016
3 6.12 –1.13 0.604 –7.36 8.06 –2.66 0.023
4 6.09 –1.62 0.594 –8.90 7.81 –5.68 0.023
60° 0 6.37 – 0.644 – 8.42 – 0.002
1 6.32 –0.78 0.609 –5.43 7.87 –6.53 0.028
2 6.31 –0.94 0.608 –5.59 7.57 –10.09 0.028
3 6.29 –1.32 0.607 –5.75 7.47 –11.28 0.028
4 6.26 –1.73 0.607 –5.75 6.57 –21.97 0.031
3.5.2.1 Short-term Loads and Temperature Variations
The first parametric study was carried out on several SMA geometries (see Table 3.6), by progressively increasing the reference temperature T. The major results are collected in Table 3.7, where the “R” percentage ratios are calculated in accordance with Eq. (3.1).
Figure 3.17 Qualitative distribution of out-of-plane deflections in the M2 panel due to the applied wind pressure (vectorial representation, ABAQUS/Standard).
Glass 2 (g2)
Glass 1 (g1)
X Y wq,E
wq,M
Z
In accordance with Figure 3.17, the maximum deflections due to the applied wind pressure were monitored both at the panel center (wq,M) and along the unrestrained edges (wq,E) due to the presence of point supports only.
As shown in Table 3.7 and Figure 3.18, the presence of SMA wires can strongly improve the overall response of the examined panel at high tem- peratures. Compared to the M1 case, however, the specific geometry and boundary conditions of the M2 panel manifests higher benefits in terms of stress control in the glass panels, rather than decrease of maximum deflections.
An interesting modification in terms of distribution of maximum ten- sile stresses in glass as well as in the PVB foils was in fact generally noticed, due to the interaction occurring between the traditional laminated panel and the embedded wires, once the SMA net is activated. This effect can be clearly seen from some selected configurations proposed in Figure 3.18, where the position of SMA wires within the interlayer film can be clearly distinguished, as well as from Figures 3.19–3.21.
As a primary effect of pre-stressing of SMA wires, a partial introduction of compressive stresses in the glass panes was found, as expected. As in the case of the M1 panel, however, the presence of a shear flexible middle PVB foil typically resulted in a moderate increase of compressive stresses in the vicinity of the wires’ ends only. Some examples of compressive stresses
attained in the glass panes as a consequence of temperature variations and SMA wires activation is shown in Figure 3.20.
Almost negligible effects were noticed in terms of initial compressive stresses in glass due to the SMA wires activations, by varying the inter- spacing iSMA of the wires themselves (Figure 3.21d). A general beneficial contribution – especially in terms of overall maximum stresses in glass – was in any case provided by the activation of the SMA net (Figure 3.21).
In terms of PVB, although the attainment of local peak of stresses in the region of PVB immediately adjacent to the SMA wires (especially the wires ends), almost negligible maximum stresses were generally found in the same PVB films, e.g. in the order of ≈0.5 MPa, hence confirming a fully linear elastic behavior of the PVB foils and the total lack of possible dam- age phenomena.
Figure 3.18 Comparison of (a and b) maximum deflections, (c and d) maximum principal stresses in glass (g1), (e and f) maximum principal stresses in glass (g2), and (g and h) maximum stresses in the PVB foil (ABAQUS/Standard), under the action of wind (q = 1 kN/m2, tL = 3 s, T = 30 °C). Values expressed in [m] and in [Pa].
M2-0 (unreinforced panel) M2-3 (iSMA= 250mm. φSMA= 4mm)
(a) (b)
(c) (d)
(e) (f)
(g) (h)
U. U3
S. Max. in-plane principal envelope (max) (avg: 75%)
+6.614e–04
+5.413e+06 +4.929e+06 +4.445e+06 +3.962e+06 +3.478e+06 +2.994e+06 +2.510e+06 +2.027e+06 +1.543e+06 +1.059e+06 +5.756e+05 +9.194e+04 –3.918e+05
S. Max. in-plane principal envelope (max) (avg: 75%)
+8.071e+06 +7.506e+06 +6.941e+06 +6.375e+06 +5.810e+06 +5.244e+06 +4.679e+06 +4.113e+06 +3.548e+06 +2.983e+06 +2.417e+06 +1.852e+06 +1.286e+06
S. Max. principal (avg: 75%)
+9.495e+03 +4.110e+03 +1.275e+03 –6.660e+03 –1.204e+04 –1.743e+04 –2.281e+04 –2.820e+04 –3.358e+04 –3.897e+04 –4.435e+04 –4.974e+04 –5.512e+04
S. Max. principal (avg: 75%)
+1.165e+04 +6.064e+03 +4.806e+02 –5.102e+03 –1.069e+04 –1.627e+04 –2.185e+04 –2.743e+04 –3.302e+04 –3.386e+04 –4.418e+04 –4.977e+04 –5.535e+04 S. Max. in-plane principal envelope (max) (avg: 75%)
+8.151e+06 +7.573e+06 +6.996e+06 +6.419e+06 +5.842e+06 +5.246e+06 +4.687e+06 +4.110e+06 +3.533e+06 +2.955e+06 +2.378e+06 +1.801e+06 +1.224e+06 S. Max. in-plane principal envelope (max) (avg: 75%)
+4.718e+06 +4.297e+06 +3.875e+06 +3.453e+06 +3.032e+06 +2.610e+06 +2.819e+06 +1.767e+06 +1.345e+06 +9.237e+05 +5.021e+05 +8.049e+04 –3.411e+05 +1.120e–04
–4.374e–04 –9.868e–04 –1.536e–03 –2.086e–03 –2.635e–03 –3.184e–03 –3.734e–03 –4.283e–03 –4.833e–03 –5.382e–03 –5.932e–03
U. U3 +5.969e–04 +6.016e–05 –4.766e–04 –1.013e–03 –1.550e–03 –2.087e–03 –2.624e–03 –3.160e–03 –3.697e–03 –4.234e–03 –4.771e–03 –5.308e–03 –5.844e–03
Figure 3.19 Comparison of (a and b) maximum deflections, (c and d) maximum principal stresses in glass (g1), (e and f) maximum principal stresses in glass (g2), and (g and h) maximum stresses in the PVB foil (ABAQUS/Standard), under the action of wind (q = 1 kN/m2, tL = 3 s, T = 60 °C). Values expressed in [m] and in [Pa].
M2-0 (unreinforced panel) M2-3 (iSMA = 250 mm. φSMA = 4 mm)
(a) (b)
(c) (d)
(e) (f)
(g) (h)
U. U3
S. Max. in-plane principal envelope (max) (avg: 75%)
+6.443e–04 +5.953e–05 –1.110e–03 –5.253e–04 –1.695e–03 –2.280e–03 –2.864e–03 –3.449e–03 –4.034e–03 –4.619e–03 –5.204e–03 –5.789e–03 –6.373e–03
+4.921e+06 +4.490e+06 +4.059e+06 +3.628e+06 +3.197e+06 +2.766e+06 +2.335e+06 +1.904e+06 +1.473e+06 +1.041e+06 +6.103e+05 +1.792e+05 –2.520e+05
S. Max. in-plane principal envelope (max) (avg: 75%)
+8.427e+06 +7.854e+06 +7.282e+06 +6.709e+06 +6.137e+06 +5.564e+06 +4.992e+06 +4.419e+06 +3.846e+06 +3.274e+06 +2.701e+06 +2.129e+06 +1.556e+06
S. Max. principal (avg: 75%)
+1.349e+03 –6.690e+02 –2.687e+03 –4.705e+03 –6.723e+03 –8.742e+03 –1.076e+04 –1.278e+04 –1.480e+04 –1.681e+04 –1.883e+04 –2.085e+04 –2.287e+04
S. Max. principal (avg: 75%)
+2.826e+04 +2.407e+04 +1.988e+04 +1.570e+04 +1.151e+04 +7.325e+03 +3.139e+03 –1.047e+03 –5.233e+03 –9.419e+03 –1.361e+04 –1.779e+04 –2.198e+04 S. Max. in-plane principal envelope (max) (avg: 75%)
+7.471e+06 +6.915e+06 +6.359e+06 +5.803e+06 +5.247e+06 +4.691e+06 +4.135e+06 +3.579e+06 +3.023e+06 +2.467e+06 +1.911e+06 +1.355e+06 +7.955e+05 S. Max. in-plane principal envelope (max) (avg: 75%)
+3.929e+06 +3.562e+06 +3.195e+06 +2.828e+06 +2.460e+06 +2.093e+06 +1.726e+06 +1.359e+06 +9.915e+05 +6.243e+05 +2.571e+05 –1.101e+05 –4.773e+05 U. U3
+6.075e–04 +3.274e–05 –1.117e–03 –5.420e–04 –1.691e–03 –2.266e–03 –2.841e–03 –3.416e–03 –3.990e–03 –4.565e–03 –5.140e–03 –5.714e–03 –6.289e–03