PSI - Issue 64

Margherita Autiero et al. / Procedia Structural Integrity 64 (2024) 1798–1805 Author name / Structural Integrity Procedia 00 (2019) 000–000

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resistance axial force at different exposure times was calculated with both capacity methods (the actual EC3 part 1-5 and the new EC3). For this reason, the first step was the evaluation of the effective cross-sectional area, Table1 shows the comparison between the area for the coupled C150x50x15mm and 2mm thickness and the effective cross-area calculated with the effective width method, according to both capacity methods. Table 1 Effective cross-sectional area for the coupled C section 150x50x15x2mm according to the two capacity methods. A A eff, actual EC3 A eff, new EC3 reduction reduction [mm 2 ] [mm 2 ] [mm 2 ] 1080 842 562 48% 22% Once the A eff is known it was possible to evaluate the design buckling resistance at different exposure times by using the Eq1 and Eq2. The results are shown in the following Fig.3c in comparison with the axial force provided by SAFIR, where a positive axial load indicates compression in the beam element. This comparison confirms that the critical element is the selected transversal beam, the thermal action has induced an increment of the initial compression load which corresponds to an expansion of the beam, after 3 minutes the load starts to decrease, and the beam starts to deflect inward, at this point the section has reached a temperature equal to 400°C more or less and so the steel resistance starts to decrease. The load decreases until 5.6 minutes with an inward deflection for a tension load, with a little catenary effect, for the beam. Moreover, it is possible to see that the two capacity methods provide different results within the first 2 minutes, with lower values obtained with the new EC expressions, while after this time the results are very similar to each other.

1200

100 150 200

θ [°C]

NEd,fi Nb,Rd,fi - Actual EC Nb,Rd,fi - New EC

N Rd,fi , N Ed,fi [KN]

1000 1200 1400

Natural fire curve web flange and lip

CFAST LOCAFI z = 4.8m LOCAFI z = 6.1m LOCAFI z = 6.7m

θ °C

1000

800

t collapse = 5.6 min

-200 -150 -100 -50 0 50

0 200 400 600 800

600

0

1

2

3

4

5

6

7

400

200

0

time [min]

0 5 1015202530354045505560

0 5 1015202530

time [min]

time [min]

(a) (c) Fig. 3. (a) temperature distribution within cross section over time (b) temperature distributions along the 1st level of the upright, comparison between LOCAFI and CFAST ones (c) comparison between stress and resistance. The thermo-mechanical analysis has shown that the collapse time for this type of structure is of the order of a few minutes, and to study the collapse it is essential not only to carry out advanced analyses but also to refine them as much as possible, for example to investigate the achievement of the capacity of the beam in terms of compression resistance axial force, the non-uniform temperature distribution had to be considered, combined with the assessment of the effective width to consider the local instabil ity, and the assessment of χ coefficient to consider the global instability in compression. Moreover, the analysis stopped at the achievement of the capacity of the most stressed elements. For this reason, it was not possible to analyse the global collapse and the correct collapse time. This is due to the type of analysis that SAFIR allows to implement, which is dynamic analysis, but it is an implicit analysis, which stops when convergence problems are reached. All these aspects lead to affirm that to correctly estimate the collapse times and the shape of the global mechanism, it could be necessary to go beyond the time provided by SAFIR, manually eliminating the elements that gradually fail. Starting from the analysis carried out with the zone model, since it was demonstrated that the element that led the analysis to stop was the horizontal beams of the 2 nd level, another structural model was built by removing this element and applying the internal forces as times changes, that the previous thermos-mechanical analysis had provided. The following figures show the results of this analysis without the beam of the 2 nd load level. In particular, Fig.4a show the comparison among the axial force provided by SAFIR in the beam element and the buckling resistances calculated with both capacity methods. The first thing that it is possible to appreciate is the fact that the last step of the analysis increased from 5.8 to 7.8 minutes, in this way, the beam of the 3 rd level has continued its heating corresponding to an increase of the horizontal displacements, and the axial load in compression, until 7 minutes when the load starts to decrease, and the beam starts to deflect inward, at this point the (b)