### Abstract

A stochastic model of hierarchical series system type for the
bending strength of spruce beams isdefined from the anticipation
that the bending failure takes place at a cross-section with a
defect cluster formed by knots or grain irregularities. The
parameters of the model are estimated from measurements of the
strengths of a large number of shorttest pieces cut from the beams
such that judgementally each test piece contains only a single
defect cluster. The testpiece is spliced to stronger wood beam
shafts in both ends. Due to the occurrence of a substantial number
of splicefailures in the total test series of 197 tests a special
maximum likelihood estimation procedure is applied to estimate
theparameters. Assuming that the estimated parameters are
applicable in the series system model for the full uncutbeams a
theoretical bending strength distribution function is obtained in
dependence of number of defect clusterswithin the span of constant
bending moment loading. A strong test of the predictional power of
the model is establishedby experiments with 54 long beams from the
same population of beams from which the small test pieces were cut.

Original language | English |
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Title of host publication | Reliability and Optimization of Structural Systems |

Place of Publication | Ann Arbor, USA |

Publisher | University of Michigan |

Publication date | 1998 |

Pages | 129-136 |

Publication status | Published - 1998 |

Event | 8th IFIP WG 7.5 Working Conference on Reliability and
Optimization of Structural Systems - Krakow, Poland Duration: 1 Jan 1998 → … |

### Conference

Conference | 8th IFIP WG 7.5 Working Conference on Reliability and Optimization of Structural Systems |
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City | Krakow, Poland |

Period | 01/01/1998 → … |

## Cite this

Ditlevsen, O. D., & Källsner, B. (1998). System effects influencing the bending strength of timber beams. In

*Reliability and Optimization of Structural Systems*(pp. 129-136). University of Michigan.