PSI - Issue 78

Riccardo Maurizio Ambrogio Baltrocchi et al. / Procedia Structural Integrity 78 (2026) 9–16

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crack

yield

failure

crack

yield

failure

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0,00 0,15 0,30 0,45 0,60 0,75 0,90 1,05 1,20 1,35 1,50 3,00

0,00 0,15 0,30 0,45 0,60 0,75 0,90 1,05 1,20 1,35 1,50 3,00

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yield

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crack

yield

failure

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0,00 0,15 0,30 0,45 0,60 0,75 0,90 1,05 1,20 1,35 1,50 3,00

0,00 0,15 0,30 0,45 0,60 0,75 0,90 1,05 1,20 1,35 1,50 3,00

α [g]

α [g]

Fig. 4. NLTHA IDA uncoupled and coupled results: (a) Ondal uncoupled; (b) I-shaped 25 m uncoupled; (c) Ondal coupled; (d) I-shaped 25 m coupled.

The IDA bending moment evolution as a function of acceleration increments is plotted in Figure 4. The starting value is the M Ed calculated from LSA, which then branches out positively and negatively depending on the load. The graphs show a series of black dots, representative of the maximum and minimum moment values for each analysis, from which the average value and the upper and lower standard deviation are calculated. The intersection of the curve with the horizontal dashed lines, representing the EDP values obtained from the sectional analysis, allows the calculation of the vertical acceleration value that leads each section to reach the three selected EDPs. The thick blue and red lines indicate the mean values for sagging and hogging moments, respectively, while the thin blue and red lines close to these curves show the standard deviation. Less dispersion of the results is observed up to cracking, where the effect of non-linearity is not present. The average vertical acceleration values are then plotted for direct comparison of the results. The non-linear dynamic analyses also show that the elements reach cracking in sag, while they yield and fail in hog. In particular, Ondal cracks at 0.40 g, then it yields and fails in hog with vertical acceleration values up to 1.50 g (Figure 4a). It can be seen that there is greater dispersion of results compared to the SRA and that the values obtained, particularly for the Ondal and the I-shaped beam are greater in the NLTHA. As mentioned above, the non-linearity affects the behaviour of the section, leading the elements to collapse for higher acceleration values. The effect of non-linearity on the beam is decreased. Standard deviation increases with rising acceleration, with the highest value at failure in hogging. The beam first cracks in sag at 0.25 g, then it reaches failure in hog approximately at 0.80 g (Figure 4b). As a confirmation of the trend depicted by dynamic linear analysis, the actual coupling of the members appears being detrimental for the roof element, lowering the acceleration-to-failure value to approximately 1.50 g (Figure 4c). The I-shaped beam 25 m, on the other hand, experiences a slight beneficial effect from the coupled condition, with collapse expected at 0.95 g (Figure 4d). 3.5. Comparison A comparison is made for a direct evaluation of the effects of linearity vs non-linearity and uncoupled vs coupled configurations.