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.