The paper analyzes the structural response of a highlevel air blast loaded cablesupported façade. Since the glass panels and the cables present a typical brittle behavior and are subjected to elevated tensile stresses when a highlevel explosion occurs, multiple dissipative devices are simultaneously introduced in the conventional glazing system to mitigate the maximum effects of the design blast wave. Dynamic analyses are performed using a sophisticated FEmodel to describe accurately the response of the façade equipped by dissipative devices. Based on numerical results of previous contributions, viscoelastic spider connectors (VESCs) are introduced in the points of connection between glass panels and pretensioned cables, to replace “rigid” spider connectors commonly used in practice. At the same time, rigidplastic frictional devices (RPDs) are installed at the top of the bearing cables to mitigate furthermore the bracing system. As a result, due to the combined use of VESCs and RPDs opportunely calibrated, the maximum tensile stresses in the glass panels and in the cables appear strongly reduced. In addition, the proposed devices do not trouble the aesthetics of such transparent structural systems. At last, simple design rules are presented to predict the response of cablesupported façades subjected to highlevel dynamic loads and to preliminary estimate the mechanical parameters of combined VESCs and RPDs.
The effects of air blast loads on the dynamic behaviour of glazing façades constitute a topic of great interest and actuality. Because of this reason, numerous authors recently focused on the typical behaviour of simply supported glass plates subjected to explosions, providing interesting analytical formulations [
Teich et al. [
As highlighted also in [
Based on numerical results of previous contributions [
The studied façade consists in 1.55 m × 3.00 m, 10/4.52/10 mm laminated glass panels, obtained by assembling two fully tempered glass sheets and a middle PVBfilm [
Schematic view of the studied cablesupported façade.
Each laminated glass panel is sixpoint fixed, by means of fourhole (corners) and twohole
Fourhole rigid spider connector. Crosssection detail of point support.
Commonly, as in the studied example, fourhole spider connectors are introduced at the corners of glass panels, so that four panels could be contemporarily constrained (Figure
When subjected to highlevel air blast loads, a similar facade undergoes large deflection and is affected by elevated tensile stresses in the glass panels as well as in the bearing pretensioned cables [
The primary characteristic and the main effectiveness of the proposed viscoelastic system consists in the partly absorption/dissipation of the incoming energy due to explosions and in the mitigation of the main components of the curtain wall, especially the glass panes. A similar effect can be achieved by introducing viscoelastic devices in substitution of conventional “rigid” spider connectors [
Crosssection of a possible fourhole VESC (detail of point support with viscoelastic device).
The efficiency of a similar mechanism directly depends on the dissipative capabilities of the used viscoelastic layer. Polymers, glassy materials, natural rubber, or rubbers with additives able to dissipate energy if subjected to shear deformations are largely used in engineering applications. Generally, the effectiveness of a viscoelastic device is expressed in terms of stiffness
In these hypotheses, an optimal calibration of the rigidity
As highlighted in [
The second typology of dissipative devices consists in a frictional system to be installed at the top (or at the bottom) of pretensioned cables [
Frictional device and working scheme (crosssection).
If the external axial load is higher than
A numerical code developed at University of Trieste was used to describe the time varyingpressure blast wave characterizing a highlevel (LevelD of GSA) air blast load [
Blast loading timevarying pressure functions (Level DGSA [
According with the schematic layout proposed in Figure
FEmodel (a) and detail of half fourhole VESC (ABAQUS) (b).
Laminated glass panels were described by means of 410 fournode threelayer
Material properties (ABAQUS).
Young’s modulus  Poisson’s ratio  Density  Behaviour  

[N/m^{2}]  [—]  [kg/m^{3}]  [—]  
Glass panes 

0.23  2490  Linear elastic 
PVB 

0.50  1100  Elastoplastic 
Harmonic steel (cables) 

0.32  7300  Linear elastic 
Stainless steel (connectors and devices) 

0.32  7300  Linear elastic 
The pretensioned cables were modelled in the form of truss elements (T3D2, 12 elements) having a crosssection area equal to half the nominal one. The initial pretension force was applied by imposing a vertical displacement at the base of the cables. Only
Each
All the connector nodes were opportunely constrained, in accordance with the expected behaviour of the single façademodule; therefore, only
The modelled spiders allow the glass panels interacting with the vertical cables by means of
Finally, although negligible, a total damping ratio
Numerical analyses were performed on the FEmodel of the facademodule equipped by VESCs and RPDs to study the behavioural trends of the glazing system subjected to a Level DGSA blast load and to highlight the structural benefits involved by the use of multiple devices. All the analyses had a total duration of 1.1 s. The initial instants (
Numerical results of dynamic analyses (ABAQUS). Level DGSA.
Devices  Glass tensile stress (L1)  Glass tensile stress (L2)  Glass tensile stress (L3)  Cable deflection 




 
[MPa]  [MPa]  [MPa]  [m]  
No devices  138.18  89.30  83.40  0.44 
VESCs  85.73  58.18  47.94  0.41 
VESCs + RPDs  88.60  35.15  49.15  0.44 
Numerical results of dynamic analyses (ABAQUS). Level DGSA.
Devices  Cable axial force (max.)  Cable axial force (min.)  VESCs displacement  VESCs shear strain  RPDs sliding 





 
[kN]  [kN]  [m]  [—]  [m]  
No devices  858  302  —  —  — 
VESCs  798  306  0.0450  2.25  — 
VESCs + RPDs  658  115  0.0415  2.08  0.0165 
Tensile stresses in the middle glass panel, as a function of time (ABAQUS). Location L1.
Tensile stresses in the middle glass panel, as a function of time (ABAQUS). Location L2.
Tensile stresses in the middle glass panel as a function of time (ABAQUS). Location L3.
Maximum axial force in the cables as a function of time (ABAQUS).
Midspan cable deflection as a function of time (ABAQUS).
VESCs manifest their structural effectiveness in the capability of introducing additional deformability/dissipative capabilities in the studied curtain wall [
Numerical simulations allowed to notice that the simultaneous introduction in the studied façade module of VESCs and RPDs can improve significantly the dynamic response of the glazing system, strongly mitigating the effects of a highlevel air blast load. Undoubtedly, as highlighted in the previous sections, RPDs can activate only if the maximum axial forces occurring in them are higher than the sliding force
As proposed in Figures
As proposed in Figure
In conclusion, the glass panels can be strongly mitigate due to VESCs, whereas the bearing cables can be protected from elevated axial forces by RPDs, an in minor part by VESCs.
Due to the introduction of VESCs and RPDs, also the energy balance of the studied façade module strongly modifies. As it would be expected, if the façade module is not equipped by devices, the maximum elastic energy is stored by the bearing cables (Figure
Energy terms for the façademodule not equipped by devices (ABAQUS).
When VESCs are introduced in the glazing system to replace the conventional spider connectors, an important improvement of the damping capabilities of the façade module can be noticed (Figure
Energy terms for the façademodule equipped by VESCs (ABAQUS).
Energy terms for the façademodule equipped by multiple devices (VESCs and RPDs, ABAQUS).
The maximum effects on the studied façade due to the design air blast load can be estimated by simplifying the multidegreeoffreedom (MDOF) cablesupported façade with an equivalent singledegreeoffreedom system (SDOF) [
Let us consider the dynamic parameters of a SDOF system equivalent to the examined cablesupported façade module. The equivalent mass
In (
As result, to properly estimate
Numerical and analytical comparisons summarized in Table
Comparison of numerical and analytical results for the façademodule not equipped by devices.
No devices  Highlevel blast load (DGSA)  

ABAQUS M01 FEmodel  Analytical procedure 


Fundamental period 
0.26  0.28 ( 
1.08 
Max. displacement 
0.44  0.44 ( 
1.00 
Max. velocity 
13.96  17.58 ( 
1.26 
Max. pretension 
858  951 ( 
1.11 
The façade module equipped by VESCs can be assimilated to an equivalent SDOF system having mass
where
the total stiffness provided by the series of VESCs,
Based on (
At the same time, the total damping coefficient of the SDOF system equipped by VESCs is
represents the damping ratio of the conventional façade module (
In addition
represents the total damping ratio
In these hypotheses, once the equivalent dynamic parameters of the SDOF system are known, it is possible to estimate the maximum effects of a given explosion on the studied glazing system with VESCs. However, a further iterative procedure should be performed. The maximum deflection
It is important to notice that
Consider
To avoid the cracking of the viscoelastic layer due to explosion,
Based on (
therefore, it is possible to assert that the total impulse
In these hypotheses, a third iterative procedure should be carried out to estimate the maximum cable deflection and the final pretension due to the “effective” explosion of impulse
Comparison of numerical and analytical results for the façademodule with VESCs.
VESCs  Highlevel blast load (DGSA)  

ABAQUS FEmodel  Analytical procedure 


Max. displacement 
0.41  0.39 ( 
0.95 
Max. velocity 
11.17  14.35 ( 
1.28 
Max. increment of pretension 
498  510 ( 
1.02 
Max. total pretension 
798  810 ( 
1.02 
Max. sliding of VESCs 
0.0450  0.0452 ( 
1.00 
Max. shear strain ratio of VESCs 
2.25  2.26  1.00 
If RPDs are used in combination with VESCs, an additional frictional dissipation capability is introduced in the conventional glazing system. The effectiveness of RPDs directly depends on the amount of their sliding. The amount of plastic energy dissipated by friction is in fact as follows:
where
Nevertheless, the optimal solution should be identified by taking into account the loss of initial pretension in the bearing cables typically associated with the effectiveness of the proposed frictional mechanism. In general, the maximum sliding of RPDs should not exceed the limit [
which represents the sliding associated to the complete loss of pretension in the cables. At the same time, the optimal value for the sliding force
Therefore
In the studied example, as previously asserted, a value of
As result, the maximum sliding of RPDs due to the effective blast load results approximately equal to
Comparison of numerical and analytical results for the façademodule with VESCs and RPDs.
VESCs + RPDs  Highlevel blast load (DGSA)  

ABAQUS FEmodel  Analytical procedure 


Max. sliding of RPDs 
0.0165  0.0159  0.97 
Max. increment of pretension 
358  350  0.98 
Max. total pretension 
658  650 (design load 
0.98 
Residual pretension 
115  120 ( 
1.05 
Max. displacement 
0.44  0.43 ( 
0.97 
which is in good agreement with numerical results (Table
The plastic energy
At last, due to the combined interaction of optimally designed VESCs and RPDs, the maximum deflection
Based on the assumptions proposed in the previous sections, the following steps could help designers to optimize the effectiveness of VESCs and RPDs and the dynamic response of the studied cablesupported façade.
Preliminary design of the façade module and first estimation of maximum blast effects.
Choice of the design air blast load (definition of the total impulse
preliminary design of the façademodule (cables diameter, initial pretension, and glass thickness), and
simplified dynamic analysis of the façademodule without devices (
Introduction of VESCs as follows.
Choice of appropriate values of rigidity
evaluation of the dynamic parameters of the equivalent SODF system with VESCs (
estimation of the total cable deflection
calculation of the maximum elastic energy
estimation of the effective impulse
evaluation of the maximum effects due to
Introduction of RPDs.
Estimation of the limit sliding
choice of the optimal value of sliding force
Check the maximum sliding of frictional devices
FE modelling of the façademodule with VESCs and RPDs.
Verification of the glazing system.
Certainly, a similar design procedure depends on the variability of the design blast loading and the mechanical parameters characterizing the dynamic behaviour of the presented VESCs and RPDs. In addition, once the RPDs are introduced at the cable ends and used in combination with VESCs, no analytical formulations can be used to predict the “effective” response of the façademodule equipped by multiple devices. Consequently, additional numerical simulations should be performed. In any case, as proposed in this work, it should not be ignored that the use of multiple devices allows strongly improving the dynamic response of a cablesupported façade. In addition, the proposed design approach provides analytical results that are in good agreement with numerical predictions as proposed in previous sections.
The criticalities of a cablesupported façade subjected to highlevel blast wave pressures were investigated by means of a sophisticated numerical model. Since the glass panels and the bearing cables present typical brittleelastic behaviour, the occurring in them of elevated tensile stresses should be avoided to preserve the stability of the curtain wall. At the same time, the maximum deflection of the façade should be limited to safeguard the integrity of the pointsupported glass sheets. Because of these reasons, based on numerical results of previous efforts, the effects of multiple dissipative devices were analyzed numerically. The proposed devices consist in viscoelastic spider connectors (VESCs) introduced in the points of connection between the glass panels and the bearing cables and in additional rigidplastic frictional devices (RPDs) installed at the top or bottom of the pretensioned cables. As shown in the paper, numerical simulations have been discussed to highlight the structural advantages and energydissipation capabilities due to the combined use of multiple dissipative devices. In particular, VESCs cut down the maximum tensile stresses in glass panes due to air blast and reduce axial forces and deflections in the cables. At the same time, the joined use of RPDs allow to furthermore control and limit the maximum pretension forces occurring in the bearing cables, improving the structural effectiveness of single VESCs. At last, simple design rules derived from energy considerations were proposed for a first estimation of the maximum effects of a highlevel air blast load and for a preliminary design of the proposed multiple devices.