PSI - Issue 72

Dražan Kozak et al. / Procedia Structural Integrity 72 (2025) 270 – 277

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the stones in question have diameters ranging from 150 mm to 250 mm. For this calculation, it was assumed that the stones were spherical. Based on the available data, the mass of the largest stone that could fall on the pipe is 22.13 kg. The height from which the stone falls onto the pipe is 2000 mm. For safety considerations, it was assumed that only one stone falls on a single pipe and that only the largest stone, with a mass of 22.13 kg, is taken into account. This represents the worst-case loading scenario.

Fig. 2. Consideration of worst-case loading based on the stone's impact point.

It was essential to determine the point where the stone struck the pipe. The pipe is designed to be at a 45º angle, and the stone falls through the center of the channel, as illustrated in Figure 2. One section of the pipe measures 600 mm, while the other section measures 350 mm according to the point where the force is applied, resulting in a total length of 950 mm. The total force exerted by the stone is calculated based on its mass and gravity. However, since the force acts on the pipe at a 45º angle, it is necessary to compute only the component that induces deflection of the pipe, which is 153.5 N. The moment of inertia of the pipe's cross-section is calculated using equation (1). The resulting moment of inertia is 2247619 mm 4 . = 6 4 ( 4 − 4 ) (1) The precise calculation of stresses that occur under impact loads is very complex and cannot be performed using classical strength science methods. This complexity mainly pertains to the stress calculations at the point of impact and the propagation of stress waves. As a result, the calculations are limited to approximations that do not consider stress waves or stresses immediately adjacent to the impact site. An impact load refers to the impact of a mass body on another elastic body. The calculations do not take into account contact stresses near the impact site, stress waves, and their reflections, or energy loss due to internal friction. In many cases, these factors do not significantly affect the accuracy of the calculations. The static deflection was calculated according to equation (2). = ∙ 2 2 3 ∙ 3+ √ 3 + (2) The static deflection is 0.0056 mm. The dynamic deflection caused by the impact of the stone on the pipe was calculated according to equation (3).