PSI - Issue 44

Vanni Nicoletti et al. / Procedia Structural Integrity 44 (2023) 371–377

376

6

Vanni Nicoletti et al. / Structural Integrity Procedia 00 (2022) 000 – 000

Approach 2

τ [MPa]

Approach 1

C35/45

16 14 12 10

= 0.002 = 0.006 = 0.010 = 0.014 = 0.018 = 0.022 = 0.026 = 0.030 = 0.034 = 0.038 = 0

= 0.022

= 0.018

= 0.014

8 6 4 2

= 0.010

I

= 0.006

E

E I

= 0.002

σ [MPa]

16

14

12

10

8

6

4

2

0

2

4

6

8

10

12

14

16

Fig. 1. Example of nomogram for the B-CJ assessment (concrete grade C35/45, steel characteristic yield stress f yk = 450 MPa). 5. By reversing the reinforcement ratio formulae it is possible to calculate the hoop area ℎ , assuming the B-CJ geometry as known (it is worth remembering that a preliminary sizing is provided at the beginning of the design process). The procedure is performed on the right and left side of the nomogram, leading to two hoop areas that satisfy Approach 1 and 2, respectively. The designer can decide the hoop area amount to use, because the EC8 foresees that at least one of the two approaches must be satisfied. If the steel area cannot be turned into a reasonable hoop amount for the considered B-CJ (in terms of hoop spacing and leg numbers that do not cause congestion troubles during the concrete pouring), then the B-CJ must be re-sized, the model updated and the overall procedure repeated. In addition, the same approach must be adopted considering the orthogonal direction of the joint. Finally, the hoop amount must be harmonized between the two directions, since the hoop diameter and spacing must be unique within the same joint. Examples of nomogram uses are reported in (Nicoletti et al. (2022)), where three B-CJs belonging to the same structure and representing different typologies (interior and exterior joints, drop and flat beams, different beam rebar amounts, etc.), are pre-dimensioned adopting the proposed graphical tool. Furthermore, in the same work, many nomograms referring to different concrete grade, are proposed. 4. Conclusions In this paper, a graphical and simple-to-use tool for the B-CJs sizing is proposed; the tool, in the form of nomograms, can be used since the initial stages of the design process of RC buildings, making it possible to estimate the amount of reinforcements and the suitability of the node dimensions from the early design stages, avoiding the need of modifying the overall design of the building (sometimes including architectural aspects) at the end of the capacity design process. The proposed nomogram is built following the EC8 prescriptions regarding the B-CJ verifications, but it has been shown that it can be used also considering prescriptions of the Italian technical code (NTC18). Nomograms have the great advantage to be dimensionless and usable for all type of joints (interior and exterior) with any dimensions. The use of nomograms is advantageous because it rapidly leads to obtain the dimensions and the hoop amount that satisfy the code joint verifications and, hence, if the joint can be constructed or not due to hoops and bars congestions. Furthermore, all formulas necessary to create nomograms are reported in the paper so as a user can build tailor-made nomograms according to its needs.