Issue 63

H. A. R. Cruz et alii, Frattura ed Integrità Strutturale, 63 (2023) 271-288; DOI: 10.3221/IGF-ESIS.63.21

The experimental, analytical and numerical results are presented in Tab. 1.

λ (L ef /r)

D ext. (mm)

D int. (mm)

r (mm)

L ef (mm)

A g (mm²) 110.57 110.57 110.57 110.57 110.57 110.57 110.57 110.57 110.57 110.57 110.57 110.57 110.57 110.57

*N exp (kN) 18.62 18.18 17.67 17.05 16.16 15.40 14.44 12.78 11.66

N_NBR¹ (kN)

N_AISC² (kN)

N_EC-3³ (kN)

N_CSA-16 4 (kN)

NUMERICAL ABAQUS (kN)

D/t

38 38 38 38 38 38 38 38 38 38 38 38 38 38

36.1 36.1 36.1 36.1 36.1 36.1 36.1 36.1 36.1 36.1 36.1 36.1 36.1 36.1

40 40 40 40 40 40 40 40 40 40 40 40 40 40

13.1 13.1 13.1 13.1 13.1 13.1

250 400 525 650 800 915

20 30 40 50 60 70 80 90

19.61 19.19 18.70 18.10 17.25 16.51 15.56 14.63 13.26 11.47

20.01 19.23 18.55 17.81 16.81 15.95 14.83 13.71 12.08 10.11

19.72 19.36 18.82 18.09 16.98 14.78 13.62 12.04 10.21 16

19.88 18.85 18.78 18.60 18.18 17.66 16.79 15.35 14.08 12.48 10.00

19.20 18.75 18.23 17.59 16.68 15.89 14.89 13.91 12.69 10.51

13.1 1050 13.1 1175 13.1 1325 13.1 1572 13.1 1834 13.1 2096 13.1 2358 13.1 2620

100 120 140 160 180 200

9.41 7.48 5.77 4.32

8.15 6.61 5.43 4.52

8.39 6.92 5.75 4.82

8.58 6.65 5.25 4.25

--

8.01 6.48 5.32

Table 1: Experimental, analytical and numerical results.

* experimental results of bars under compression; 1, 2, 3, 4 Resistances based on standards: ABNT NBR 16239:2013 [26]; ANSI/AISC 360-16 [27]; Eurocode 3 Part 1.4 [28], and CSA-S16 [29].

In the analysis of the results presented in Tab. 1, the first fact noted is the approximately constant distance between the compressive strength curves of the numerical and analytical front models, specifically in the region of higher slenderness ratios. The difference in resistance load between the curves, taking the normative values ABNT NBR 16239:2013 [26] and ABNT NBR 8800:2008 [31] as a reference, varies between the limits of 16 and 25%. Since the main dimensions and their boundary conditions were applied in an equivalent way in the two proposed approaches, such a difference is attributed to the consideration of residual stresses in the normative formulations and their respective absence in the numerical models. When evaluating the results collected for bars with slenderness ratios lower than 80, it is noted that the characteristic strength of the profiles determined by the criteria of the ABNT NBR 8800:2008 [31] code exceeds that predicted by the numerical tests. In their simulations, the local failure of the flattened ends is demonstrated on the numerical front as a limiting factor to the axial compressive strength load of the bars contained in this range of the spectrum of slenderness ratios. This fact can be graphically recognized by the horizontal portion of the modified P ult – Numerical analysis curve in Fig. 16. The resistance load difference between the numerical and analytical curves reaches percentages of up to 24%, in relation to the reference values predicted by the code. In this way, the limitation of the normative analytical formulations to deal with the case is required, by partial adjustments in the process of designing short and medium slender bars or a broad reformulation of the equations that involves the whole spectrum of slenderness ratios. subjected to compressive loads. From the development of numerical models with the aid of the Abaqus® software, subdivided into a couple of simulation phases with prototypes of slenderness ratios ( λ ) ranging from 20 to 200, two main forms of failure of the bars with flattened ends were observed, namely: the global buckling, characterized by the lateral displacement along the length of the axially compressed profiles; and the local instabilities of the transition zones of cross-sections of the models tested. The first of these was noted in the slenderest prototypes, being the ultimate resistance load of the profiles a function of this same property. Additionally, the short and medium slender models presented the second form of failure listed and converged approximately on a single resistance load value, so that local failure due to excessive deformation of the ends of the bars constituted a limiting threshold of characteristic resistance load. It is noteworthy that, for the prototypes with slenderness W C ONCLUSIONS ith the objective of deepening the understanding of the phenomena of global and local instabilities of three dimensional trusses constituted by end-flattened steel bars and typical bolted connections, this study demonstrated, through a series of numerical models the structural behavior of these elements when individually

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