Author details

4. Conclusions

Table 4.

42

Table 3.

Parameters for simulations of lines 13.

Truss and Frames - Recent Advances and New Perspectives

A simple truss-based finite element method was proposed to simulate the load distributions and geometric configurations of assemblies that behave in a catenarylike manner, subject to external, variable loads. The formulation was tailored to the particular problem of log booms (structures that retain logs from reaching the machinery of hydropower plants) under the influence of river streams and the logs they convey. The nonlinear formulation imposes equilibrium between internal and external forces so that an iterative scheme must be numerically solved. The method was verified by comparison against analytical results from a theoretical catenary model: the relative error and uncertainty for the maximum and minimum forces were within 0.2%, while the mesh refinement order of convergence was close to 1. The tool was later validated against experimental model-scale data from the towing tank at the Institute for Technological Research [12] and prototype-scale numerical data from commercial software SIMPACK®, and all the results agree adequately [14]: for the experimental data validation, the numerical method was capable of reproducing the observations of the experiments, and the maximum relative discrepancy observed was about 6%. The differences are invariant to the increase in the assembly length, but they seem sensible to variations of the free stream. Likewise, the prototype-scale validations all show adequate agreement, regardless of the line configurations, and a maximum relative error, considering SIMPACK® as the reference, of less than 8%. These percentages corroborate the adequacy of the method for the purpose by which it was developed: to a have a fast, yet reliable,

Comparison of results between SIMPACK® and the current method—Lines 13.

Line 13A/13B Line 13C/13D SP (kN) FEM (kN) u (%) SP (kN) FEM (kN) u (%) LE RE LE RE uLE uRE LE RE LE RE uLE uRE 1550 1263 1655 1329 6.8 5.2 822 647 876 679 6.6 5.0 934 759 1000 801 7.0 5.5 1501 1318 1607 1401 7.1 6.3 745 618 793 650 6.5 5.2 537 436 572 458 6.5 5.1 577 486 615 512 6.7 5.5 600 525 639 556 6.6 5.9 429 358 455 376 6.0 5.2 209 165 221 173 5.8 4.7 280 234 297 247 6.2 5.4 341 301 361 318 6.0 5.5

VR (m/s) V (m/s) Angle (°) V (m/s) Angle (°) 2.5 < V < 3.5 3.18 54.44 2.11 59.60 2.5 < V < 3.5 2.49 54.81 2.04 42.00 1.0 < V < 3.5 2.14 52.11 1.60 56.26 1.0 < V < 3.5 1.80 49.56 1.33 42.48 1.0 < V < 2.0 1.69 53.06 1.13 61.03 1.0 < V < 2.0 1.36 52.80 1.05 43.53

Line 13A/13B Line 13C/13D

Jose Rodolfo Chreim\* and Joao Lucas Dozzi Dantas Institute for Technological Research, Sao Paulo, Brazil

\*Address all correspondence to: jrchreim@outlook.com

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
