Stochastic finite element analysis of the load-carrying capacity of laminated wood beam-columns
Creators: name: Folz, Bryan Russell
Publisher: name: University of British Columbia
Year: 2009

description: A relatively simple, yet comprehensive, stochastic finite element model is presented herein for predicting the response variability in the load-carrying capacity of glued-laminated wood columns, beams and beam-columns. In this problem spatial stochasticity occurs in the elastic modulus and the compressive and tensile strengths of the lamination material. Central to this investigation is the calibration of the stochastic material models to actual test data. The finite element model is based on a one-dimensional higher order shear deformation beam theory. Material behaviour is, in general, nonlinear; being perfectly brittle in tension and yielding in compression. Material failure occurs in a lamina or at an end-joint wherever the tensile strength is exceeded. The beam-column model employs a full nonlinear solution strategy, tracing the load-displacement response up to collapse which may result from progressive material failure and/or an overall loss of structural stability. Column analysis is formulated as an eigenvalue problem and yields the critical elastic buckling load. Strength and stiffness properties of the lamination material are modeled as one-dimensional homogeneous stochastic fields using a spectral approach. Realizations of each material property are simulated using a series representation of the stochastic field as a summation of sinusoids, each with a random phase, and weighted according to the spectral density function. The collapse load response statistics of a glued-laminated member are determined through a Monte Carlo simulation, which employs the stochastic finite element model. The stochastic modeling of the elastic modulus of the lamination material was characterized as a one-dimensional nonergodic process and its defining parameters were calibrated against available test data. As an application, the response variability in the elastic buckling load of glued-laminated columns was investigated. It was concluded that this problem did not warrant stochastic modeling of the elastic modulus; a random variable approach was deemed sufficiently accurate. This was followed by a sensitivity study on the response variability in the collapse load of glued-laminated beams. In this investigation both the elastic modulus and the tensile strength of each lamina were modeled as one-dimensional correlated stochastic fields. The material models were not calibrated to experimental data. Rather, the defining parameters of the stochastic material models were varied to determine their influence on the response of the beam. It was observed that the specification of the stochastic tensile strength model was of primary importance in influencing the beam response, whereas the elastic modulus and its cross-correlation with the strength had only a marginal influence. Barrier crossing analysis was used to calibrate the defining parameters of the tensile strength process so that simulated strength profiles reproduced the cumulative distribution of minimum tensile strength obtained from test specimens. This tensile strength model was utilized in the stochastic finite element beam model ULAG: Ultimate Load Analysis of Glulam. The collapse load predictions of ULAG were found to be in good agreement with recent test results on full-scale glued-laminated beams. ULAG was then applied to demonstrating and quantifying the statistical size effect in beam strength. As a final application, ULAG was combined with a reliability assessment procedure to optimize, at the manufacturing stage, the load-carrying capacity of a glued-laminated beam.