A Comparison of Load Distribution Methods at the Node and Internal Force Analysis of the Lattice Beam Based on the Winkler Foundation Model

Abstract

As a new type of retaining structure, lattice beams with tie-back anchor cables have been increasingly used in slope reinforcement and have achieved improved prevention effects. However, the simplified load distribution method (SLDM) at the node, which is the theoretical basis of internal force analysis for lattice beams, is not perfect at present. An alternative new load distribution method (NLDM) at the node based on the force method for the lattice beam was therefore introduced in this paper. Taking into account the loads acting on other nodes of the beams in both directions and according to the static equilibrium condition and deformation compatibility condition at the nodes, NLDM assigns the loads acting on the nodes to the cross beams and vertical beams, respectively, by constructing and solving a system of linear equations. In order to verify the superiority of NLDM, a case of slope reinforced by a lattice beam was introduced in this paper, and the load distribution of the nodes under the design condition was carried out based on both methods. Then, the deflections at the nodes of the lattice beam resting on the Winkler foundation, loaded with the known loads, were analyzed by the superposition method. The results of the deformation analysis showed that the deflections at the same nodes of the beams in both directions based on NLDM were almost equal, thus demonstrating the superiority of NLDM in terms of deformation compatibility. In addition, a comparative analysis of the theoretical bending moments of the lattice beam under the design and the actual working conditions based on both methods was also carried out. The results of the bending moment analysis showed that the bending moments of the cross beam differed significantly in the middle third of the beam length, while the bending moments of the vertical beams differed significantly at the beam sections where the maximum bending moments are located, and the theoretical bending moments under the actual working condition were in relatively good agreement with the measured values. Consequently, NLDM for the lattice beam was self-consistent in terms of the deformation compatibility at the node, and therefore the introduction of this new method provides an important theoretical basis for the accurate internal force analysis of lattice beams.

A new improved particle swarm algorithm for optimization of anchor lattice beam support structures

“…Meanwhile, the impact of dynamics on the structure is indubitably significant and cannot be disregarded [7], Zhang Jian-Jing et al [8] investigated the seismic behavior of slopes reinforced with anchor cables and lattice beams, recorded seismic waves and artificial seismic waves of varying magnitudes, and conducted large-scale vibration table tests on 1:20 geometric scale slope models. Junwei Fan et al [9] introduced a new method of load distribution for lattice beam nodes based on the force method, considering the load of other nodes in the vertical beam. According to the static equilibrium condition at the nodes, the load on the beam and the vertical beam is tested, to obtain the internal force of the lattice beam.…”

Field Test and Numerical Study of Three Types of Frame Beams Subjected to a 600 kN Anchoring Force

“…For instance, Yuan and Liu [16] established a dynamic simplified model for frame beams with anchor cables to study dynamic response characteristics and the seismic mechanism of the frame beams. Fan et al [17] devised a new load distribution method intended for calculating internal forces for frame beams. Lian et al [18] examined the erosion protection provided by frame beams and their impact on stabilization and load-bearing behavior, conducting an analysis of the critical stability conditions of soil particles in a shallow slope under rainfall infiltration.…”