Method for checking the resistance of the connection between the prefabricated pillar and the cup plinth in the hierarchy.

The verification we want to discuss in this post concerns the connection of the prefabricated pillar and the cup plinth.

The discussion of the subject is carried out by recalling some references of legislation and literature.

Since some assumptions are not supported by bibliographic references, the comparison and in-depth analysis are welcome that allow greater clarity on the topics exposed.

**Height of the socket – depth of insertion of the pillar**

In UNI EN 1992-1-1 (EC2) an indication is given on the minimum height of the glass.

§10.9.6.3 provides the indication l> = 1.2 h, making it clear that this is the minimum height of the socket with which the model of distribution of forces F1, F2, F3 can be considered applicable through the filling of concrete and the corresponding frictional forces.

Figure 16.24a of volume III by Leonhardt (the carry below, is part of §16.3.3.1) shows a joint configuration with rough surfaces, while §16.3.3.2 Smooth surfaces from formwork, shows the indication to enlarge the depth of penetration “t” calculated according to §16.3.3.1 for the factor 1.4.

The calculation of the driving depth is done considering:

- t >= 1.2*d se M/(N*d) <= 0.15
- t >= 2*d if M/(N*d) > 2

it is possible to interpolate for intermediate values. It is not clear whether t = 2 * d is to be understood as the maximum value of the insertion.

We believe it is appropriate to consider values of the insertion depth between 1.2 and 2 times the side of the pillar, depending on the actual flexural stress to which the pillar is subjected along the side considered.

In the event that the bending action derives from a seismic analysis, the stress with which to calculate the depth of insertion is that of the seismic analysis performed, a function of the structure coefficient (q) adopted.

**Resistance of the glass**

The resistance of the cup is verified with the forces F1, F2, F3 suggested by the EC2 verification model. The AICAP book “Guide to the use of Eurocode 2” describes in an exhaustive manner the verification method.

The design stress of the socket, which is considered as a “connection” between the pillar and the foundation, is carried out in accordance with §5.11.2.1.2 of UNI EN 1998-1 (EC8-1), amplifying the bending strength of the pillar for γ_{Rd} =1.2 by average ductility class and γ_{Rd} =1.35 for high ductility class.

**Foundation resistance and geotechnical checks**

In the case of seismic analysis on a dissipative structure, the bending action of verification for the socket is determined according to EC8-1 §4.4.2.6, where M_{d} is determined with M_{Ed}*γ_{Rd}*Ω in which γ_{Rd} =1 to q <= 3 e γ_{Rd} = 1.2 in the other cases, while Ω it is the minimum of relationships M_{Rd}/M_{Ed} in the two main orthogonal directions of the pillars in which the plastic hinges can be formed.

The value of Ω depends on the resisting moment, the stressing moment and the normal stress in the seismic combination, which may differ from pillar to pillar, depending on the real geometry of the building.

The maximum value of Ω is the value of q.

The moment M_{d} = M_{Ed}*γ_{Rd}*Ω in any case it must not be higher than the moment M_{Ed} determined with an elastic analysis (q = 1).

The value γ_{Rd}*Ω may be significantly higher than the value 1.1 for CDB and 1.3 for CDA, suggested by the Ministerial Decree 14/1/2008 Technical Standards for Construction (NTC08) in §7.2.5 which, in this case, is not at all in favor of safety.

In the example below (Hotel for the Paul Biya Stadium in Yaounde, Cameroun) the values of Ω are variable from 1.62 to 2.64 which is, in fact, the value of the structure coefficient adopted.

Lower values would be at the expense of a great differentiation of the pillars, not possible in this case because it is a prefabricated structure in reinforced concrete.