The 2018 Italian Technical Standards for Construction pay particular attention to the issue of non-structural elements which, if not designed correctly, can generate collapses and reduce the safety of structures.
The infills, being non-structural elements, are subject to the following requirement: “The capacity of the elements […] must be greater than the seismic demand corresponding to each of the limit states to be considered.” [italian NTC18 §7.2.3.]
In particular, the seismic demand is evaluated as follows:
Fa = (Sa * Wa)/qa [7.2.1]
Where:
Fa is the horizontal seismic force distributed or acting in the center of mass of the non-structural element, in the most unfavorable direction, resulting from the distributed forces proportional to the mass;
Sa is the maximum acceleration, dimensionless with respect to that of gravity, that the non-structural element undergoes during the earthquake, corresponding to the limit state under consideration (see § 3.2.1);
Wa is the weight of the element;
qa is the behavior factor of the element.
The assessment of capacity, not made explicit in the NTC 2018, will be explored in the following paragraphs.
1. The arch mechanism
The arch mechanism in a masonry wall is a structural principle that develops in response to lateral loads, such as those that can result from horizontal stresses.
The behavior of such a system must be designed and verified to ensure that the forces developed are balanced by the strength of the material and the supports. In this context, a masonry wall can be designed assuming the development of an arch, which can be horizontal or vertical, within the thickness of the wall itself. For structural analysis, it is possible to adopt the model of the three-hinged arch, where the thrust of the arch on the supports and on the central hinge is assumed to act on a tenth of the thickness of the wall as shown in figure 8.3.
Eurocode 6
The parameters relating to the height of the arch, the maximum thrust of the arch per unit length and the lateral design strength per unit area of the wall are defined within Eurocode 6.
In conclusion, the determination of the capacity of the element is carried out by considering a wall strip with a width of one meter and a height corresponding to the height of the interstorey.
In particular, the following formula is provided for the assessment of capacity:
In the hypothesis of slenderness less than or equal to 20, it is assumed that the deflection of the arc (da) is equal to 0.
Therefore, according to this hypothesis, the wording becomes:
Where:
fd represents the design compressive strength of the infill;
ra represents the height of the arch and is equal to 0.9t-da;
da represents the deflection of the arc;
t represents the thickness of the infill;
la represents the length or height of the infill;
c represents the EC6 improvement factor between 1 and 1.5.
In the case of slenderness greater than 20, it is not possible to apply the simplified wording just described.
2. The arch mechanism, mechanisms of damage to the infills, combined effect of damage in the plane and the consequent degradation of resistance out of plane due to seismic actions
To take into account the degradation of resistance in the arc mechanism, reference can be made to the discussion in the literature; for example, the following figure shows the results obtained from the studies conducted by the University of Padua and CisEdil (now merged into Fornaci Laterizi Danesi) on the resistance of non-structural elements, with particular attention to the arched behavior of the walls.
These studies allow to calibrate the formula present in Eurocode 6, introducing a coefficient that takes into account the damage of the infill in the plane, and the consequent degradation of resistance out of plane due to seismic actions, in relation to the inter-storey drift. Therefore, once the pressure on the infill generated by the seismic action (pA) has been calculated, it must be compared with the resistant pressure of the infill (pR), determined through the formula of the arch mechanism, suitably corrected by a reductive coefficient (βa), defined and calibrated for blocks of Danish Brick Furnaces, which considers the damage in the plane, as a function of displacement.
The reduction factor can be assumed as a function of the inter-floor drift up to the limit drift SLV.
In particular, for drifts between 0 and the SLD limit, the reduction factor βa can be calculated by linear interpolation between 1 for drift = 0 and the value indicated as the maximum reduction factor.
The formula for calculating the resistant pressure that takes into account the degradation of resistance, due to damage in the plane of the infill, is expressed by the relation:
The meaning of the coefficients is defined in the previous paragraph.
3. The importance of wind stress
As reported in the introduction, typically when thinking about the verification of infills we imagine the expulsion due to seismic actions, but also the stresses induced by the wind can be significant, especially for tall buildings that are located in areas with low seismicity. For this type of building, in fact, seismic stresses can be modest, but wind actions can also reach 2 KN/m2. Another relevant aspect to take into consideration is the fact that the safety coefficients on the γM material are more precautionary for checks in non-seismic conditions: below are the values of the partial safety coefficients to be attributed to the infills in the case of static and dynamic analyses, as defined in the Technical Standards for Construction (NTC 2018), in the respective chapters 4 and 7.
4. Verification by actions of linear horizontals
The 2018 Technical Standards for Constructions, in paragraph 3.1.4.3, provide that linear horizontal loads must also be considered for local verifications, not combined with the other actions.
Horizontal actions are applied 120 cm from the walking surface and are typically significant for the design of parapets.
The local checks concern, in relation to the conditions of use, the two-dimensional vertical elements such as partitions, walls and external infills.
It would therefore be necessary to investigate the verification of the expulsion of the infill also for this type of stress, even if it is typically widely verified.
5. Automatic checks on the ejection of the infill
2S.I. develops PRO_ILC, software consisting of 15 modules designed to support professionals in the design of local interventions and construction details. Among the modules included within PRO_ILC, for example, there are those dedicated to the calculation of hoops in walls and floors, the calculation of wooden floors and roofs and those dedicated to the verification of infills.
In particular, among these, PRO_SEC is the module dedicated to the verification of masonry infills, and allows designers to carry out the checks examined in this article.
This module allows you to perform the calculation and ejection verification of infills, analyzing their ability to withstand horizontal stresses due to wind or linear horizontal loads and seismic stresses.
PRO_SEC comes with an intuitive and easy-to-use interface.
The module provides four different verification methods:
- Pressure bending and kinematic design: the capacity of the infills is calculated as provided in paragraph 7.8.2.2.3 and it is possible to select the verification mode (pressure bending with concentrated load, pressure bending with distributed load and/or kinematics with plastic hinges).
- With arch mechanism for Danish Brick Furnace blocks: the calculation is the result of a research project carried out by the University of Padua and CisEdil (now merged into Danish Brick Furnaces).
- Compliance with the requirements of point C7.3.6.2 Circular 7/2019: in this case the software does not carry out the checks as they are not required as per Circular C7.3.6.2:
- “Construction elements without structural function whose damage can cause damage to people, must be verified, together with their connections to the structure, for the seismic action corresponding to each of the limit states considered.” (NTC at §7.2.3)
- “The performance, consisting in avoiding the possible expulsion of the infills under the action of the Fd, can be considered achieved with the insertion of light plaster nets on the two sides of the masonry, connected to each other and to the surrounding structures at a distance of no more than 500 mm both in the horizontal and vertical direction, or with the insertion of horizontal reinforcement elements in the mortar beds, at a distance not exceeding 500 mm”
- With EN 1996-1-1 arch mechanism: Eurocode 6 is applied with a reduction factor for drift damage that can be customised by the user, which must be appropriately justified in relation to the type of infill.
It is then possible to select whether to carry out the checks also for the effect of wind actions and horizontal linear load and assign stress values.
Finally, PRO_SEC allows the automatic generation of the report showing the results of the checks, the calculation hypotheses and the design specifications.
PRO_SEC Tamponature ejection check is free, also included in the free versions of PRO_SAP both Entry, e-Time and Startup, which can be downloaded from this link.
Gennj Venturini (venturini@2si.it), Nicolò Rossetti (rossetti@2si.it)
We thank Ing. Luca Barbieri of Fornaci laterizi Danesi for his valuable support in the development of PRO_SEC and in the revision of this article.