Andrew J Deeks

In order to evaluate the bending capacity of laminated bamboo lumber (LBL) beams, material performance tests and beam tests have been carried out. A strain-stress relationship is proposed based on compression and tensile tests conducted parallel to the grain. Two failure modes are identified based on the locations of cracks in the beam specimens. Direction of bending and the location of internal joints are shown to influence the mechanical properties of LBL beams. Internal joints have more influence on specimens under tangential bending (where the culms are bent across their width) than that under radial bending (where the culms are bent across their thickness). Irrespective of the bending direction, the strain across the cross-section of the laminated bamboo beam is shown to be linear throughout the test process, following standard beam theory. Based on this theory and the proposed simplified strain–stress relationship for the beam, calculation approaches for the ultimate bending moment and ultimate bending deflection are proposed for three bending failure modes which give a good agreement with the test results.

Structural damage will cause changes in structural vibration properties such as vibration frequency, mode shape and damping ratio. Therefore the structural vibration properties are commonly used in structural condition monitoring and damage identification by comparing them with the theoretical or numerical vibration properties of the undamaged structures. In practice, owing to variations in workmanship, material properties, and environmental conditions, the structural vibration properties derived from theoretical or numerical model may differ from the actual values. This may lead to the damage being undetectable if the change in vibration properties owing to Structural damage is smaller than the modelling difference. In this study, six continuously supported RC slabs having the same dimensions and support conditions were constructed in the laboratory. Four slabs were tested to failure after the concrete was cured 35 days, and another two left unloaded in the lab for more than a year before load tested to failure. Vibration tests were performed on all the slabs before and during the tests at different loading levels to extract slab vibration frequency, mode shape and damping ratio. The primary objective of the study is to demonstrate and quantify the variations of the vibration properties of the RC slab structures.

This study investigated the flexural performance of 20 laminated bamboo beam specimens. The load-strain and load-displacement relationships were obtained from tests, and the detailed failure modes, bending strength, and elastic modulus for all specimens are reported. The study demonstrates the following points: all the beams displayed an initial elastic phase, non-linear deformation, and then brittle failure initiated by rupture on the tension side of the beam. The elastic moduli for compression and tension of the laminated bamboo were the same, and the strain was distributed linearly across the cross-section of the beams during the testing process. There were no obvious width effects on the ultimate strain or bending strength of the laminated bamboo beam. A tri-linear constitutive model is proposed to represent the behaviour of the laminated bamboo under bending, which is shown to reproduce the load-strain and load-displacement responses of the beams very well. In addition, a calculation formula for the ultimate bending moment is proposed.

This study investigated the mechanical performance of 120 laminated bamboo column specimens under axial compression. Experimental and computational investigations were conducted on axially loaded laminated bamboo columns. The load-deflection and load-strain relationships were obtained from column tests, and the detailed failure modes for all specimens are reported. Squashing or crushing failures were observed for the short columns, and bearing capacity of for the short columns is found to be determined mainly by the compressive strength of the material. However, buckling failures were observed for the longer columns, and the failures involved significant lateral deflection. Deflection caused by initial defects influences the bearing capacity of the specimens more and more obviously as the slenderness ratio increases, and the bigger the slenderness ratio, the bigger the lateral deflection corresponding with the peak load. The variation of ultimate lateral strain and longitudinal strain versus slenderness ratio was also studied. Comparison between the test results, theoretical calculations, and FEM analysis results are reported. An equation for calculating the stability coefficient φ of laminated bamboo columns is proposed. The loading capacities obtained from the equation gives good agreement with the test results.

The influence of eccentricity ratio on the behaviour of 50 parallel bamboo strand lumber (PBSL) column specimens was studied under eccentric compression. The load-strain and load-deflection relationships were obtained from column tests, and the detailed failure modes for all specimens are reported. The eccentricity ratio is the main influencing factor on the bearing capacity of the columns, and the ultimate load values decreased with an increase of the eccentricity ratio. Both the ultimate middle deflection values and the absolute ultimate longitudinal strain values initially increased with the increase of the eccentricity ratio, and then stabilized or decreased slightly when the eccentricity ratio was bigger than approximately 0.8. The absolute ultimate lateral strain values for both face A (bracket side or compression side) and face C (tension side) performed similarly with the increasing of eccentricity ratios, increasing initially and then stabilizing or decreasing slowly. An equation for calculating the eccentricity influencing coefficient of PBSL columns is proposed. The calculation results obtained from the equations agreed well with the test results.

This paper introduces a new technique for solving concentrated load problems in the scaled boundary finite element method (FEM). By employing fundamental solutions for the displacements and the stresses, the solution is computed as summation of a fundamental solution part and a regular part. The singularity at the point of load application is modelled exactly by the fundamental solution, and only the regular part, which enforces the boundary conditions of the domain onto the fundamental solution, needs to be approximated in the solution space of the scaled boundary FEM. Examples are provided illustrating that the new approach is much simpler to implement and more accurate than the method currently used for solving concentrated load problems with the scaled boundary method. In each illustration, solution convergence is examined. The relative error is described in terms of the scalar energy norm of the stress field. Mesh refinement is performed using p-refinement with high order element based on the Lobatto shape functions. The proposed technique is described for two-dimensional problems in this paper, but extension to any linear problem, for which fundamental solutions exist, is straightforward.

The scaled boundary finite element method (SBFEM) is a semi-analytical method, whose versatility, accuracy and efficiency are not only equal to, but potentially better than the finite element method and the boundary element method for certain problems. This paper investigates the possibility of using Fourier shape functions in the SBFEM to form the approximation in the circumferential direction. The shape functions effectively form a Fourier series expansion in the circumferential direction, and are augmented by additional linear shape functions. The proposed method is evaluated by solving three elastostatic and steady-state heat transfer problems. The accuracy and convergence of the proposed method is demonstrated, and the performance is found to be better than using polynomial elements or using an element-free Galerkin approximation for the circumferential approximation in the scaled boundary method.

This paper presents a SBFEM (scaled boundary finite element method) based approach for 2-D steady-state heat transfer analysis with cyclic symmetry. The global coefficient matrices of SBFEM are proved to be block-circulant in a cyclically symmetric system, and the global quadratic eigenproblem is partitioned into a series of smaller independent sub-eigenproblems, reducing its computational cost. Numerical examples are given to illustrate the efficiency of the proposed approach.

Meshless methods are suitable for adaptive analysis, as the nodes are unstructured, and can be added or deleted freely. However, the smooth shape functions may produce spurious oscillation away from the region containing error, which may result in addition of unnecessary nodes. In order to avoid the influence of spurious oscillation on adaptive analysis, a node-based error estimator is presented. The recovered nodal stress value is obtained from a reference solution using a double refinement technique. Numerical tests are presented illustrating the effectiveness of the proposed approach in the terms of the number and distribution of nodes compared with traditional approaches.