Non-Destructive Tests of Modulus of Elasticity for the Glued Laminated Timber Beams

8/12/2019 Non-Destructive Tests of Modulus of Elasticity for the Glued Laminated Timber Beams

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Procedia Engineering 48 ( 2012 ) 409 412

1877-7058 2012 Published by Elsevier Ltd.Selection and/or peer-review under responsibility of the Branch Ofce of Slovak Metallurgical Society atFaculty of Metallurgy and Faculty of Mechanical Engineering, Technical University of Koicedoi: 10.1016/j.proeng.2012.09.533

MMaMS 2012

Non-destructive tests of modulus of elasticity for the glued laminatedtimber beams

Lenka Melzerova*, Petr KuklkbaCTU in Prague, Faculty of Civil Engineering, Thkurova 7, Prague 6, 16629, Czech Republic

Abstract

Twenty real dimensions beams from the glued laminated timber were tested in our previously works. Twenty advanced FE models wcreated precisely according to tested beams. Input files for FE models are lengths of segments and local moduli of elasticity. The segmis part of lamella between two finger joints. Each local modulus of elasticity was obtained via non-destructive penetration test. The outfor comparison between real beam and FE model is displacement in half span. The quality of input data file from experiments is veimportant for the good agreement between real tested beams and FE models. In advanced FE models is described distribution of lomoduli of elasticity via distribution function. The solution is based on the LHS. Accuracy of each distribution function is dependentthe number of measured local moduli of elasticity. In presented work was used probabilistic approach for determination of correspondnumber of penetration tests as function of segments lengths. Results of this analysis will be used in the latter series of bending testsnew real dimensions beams and corresponding advanced FE models. 2012 The Authors. Published by Elsevier Ltd.

Selection and/or peer-review under responsibility of the Branch Office of Slovak Metallurgical Society at Faculty of Metallurgy aFaculty of Mechanical Engineering, Technical University of Koice.

Keywords : Glued laminated timber, Non-destructive tests, FE models

Nomenclature

E modulus of elasticity (MPa)w beam displacement (mm) mean of E standard deviation of E

1. Twenty real tested beams

This article is focused on the twenty beams from the glued laminated timber with the real structure dimensions. Aillustrative example of a glued laminated timber beam appears in Figure 1 (a). In general, such a beam consists of arbitrary number of segments glued together over their entire area to form a layered structure. As seen in Figure 1 (b) tpresent example assumed eight layers (lamellas). Individual layers in the laminated beam are usually not compact but asubdivided into segments each having a random length. This arises from cutting out sections of lamellas containing larknots and other possible flaws to improve the overall quality of the beam. Different parameters were monitored during fou

* Corresponding author. Tel.: +420224355438; fax: +4202-2431-0775. E-mail address: [email protected].

Available online at www.sciencedirect.com

2012 Published by Elsevier Ltd.Selection and/or peer-review under responsibility of the Branch Ofce of Slovak Metallurgical Society at

Faculty of Metallurgy and Faculty of Mechanical Engineering, Technical University of Koice


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410 Lenka Melzerov and Petr Kuklk / Procedia Engineering 48 ( 2012 ) 409 412

point bending tests including relation between displacement of beam and its loading. All beams were tested up to thedestruction. Loading was applied incrementally with step equal to 4kN. Maximal forces prior to failure were in the ranfrom 30 to 60 kN. Uniform maximal loading level for all twenty beams was detected, because for each beam came damain different loading level. This uniform loading level is 24 kN for each from two forces in real bending test and 60 kN/m2D FEM model, because length of loading is 0,4 m (Fig.2) [1, 2].

(a) (b)

Fig. 1. Illustration of glued laminated timber (a) and cross-section of tested beam (b).

Fig. 2. Illustrative example of FEM model.

2. Twenty advanced FE models

The advanced FEM models employ probabilistic simulations performed in the framework of LHS method. In the lightthis, each segment is assigned Youngs modulus with a corresponding probability density function. In all cases the Gaussidistribution with the given mean and standard deviation is assumed as seen in Figure 3.

Fig. 3. Illustration of the input data used in the LHS method.

segment finger joint


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The associated distribution function is then utilized to generate individual samples. In the present study the distributfunction was split into 100 intervals to randomly select a single valuekE as schematically shown in Figure 4 (a). This resultis in accord with the LHS method based on 100 strata. The resulting map of realizations is constructed such as to comwith a statistical independence of elastic moduli from segment to segment. Note that selecting lamellas to form a beamconducted in a totally random manner. Results can be statistically evaluated and fitted to the selected probability denfunction as illustrated in Figure 4 (b) for the Gaussian distribution.

(a) (b)

Fig. 4. Principle of selecting the k-th sample in the LHS method (a) Example of the Gaussian probability density function of deflection for the selectedbeam (b).

3. Comparing results from FEM and experiments

To compare individual approaches (experiment, deterministic and probabilistic modeling) a single value given by taverages obtained from 100 samples will be adopted. It might be, however, expected that a better agreement wexperimental results will be obtained with improved probabilistic data of input parameters conditioned by consideramore measurements in individual segments (recall that only four measurements are presently available for each segmeProbability of not exceeding a certain limit deflection is even more important than a simple mean, although not examin

which might provide further insight in the behavior of such structures. The variations of maximal deflections in Figurshowing the comparison with the averages delivered by the probabilistic analysis. Clearly, when comparing only averathe difference between deterministic and probabilistic modeling is almost negligible [3].

Fig. 5. Comparison of measured and calculated deflections.

4. Non-destructive tests of modulus of elasticity

In our previously articles were demonstrated that modulus of elasticity in fibres directions (Ex) is for beam displacementsignificant, but on the distribution of finger joints is displacement practically independent. For our experiments is necessthe knowledge of distribution of modulus of elasticity in fibre direction as precisely as possible [5]. Measurements ofx

0

0,1

0,2

0,3

0,4

0,5

0,6

1 5

, 2 9

1 5

, 6 4

1 6

, 0 0

1 6

, 3 5

1 6

, 7 1

1 7

, 0 6

1 7

, 4 2

1 7

, 7 7

1 8

, 1 2

1 8

, 4 8

1 8

, 8 3

1 9

, 1 9

1 9

, 5 4

1 9

, 9 0

2 0

, 2 5

2 0

, 6 0

2 0

, 9 6

2 1

, 3 1

2 1

, 6 7

2 2

, 0 2

2 2

, 3 8

D e n s i t y

w (mm)


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were realized for twenty beams in each segment of each lamella on four places. Final file of 1448 values of Ex is forstatistical research sufficient. The rightness of measurement was verified independently via strain gauges and displacemesensors on the several places of each beam during loading tests. The relation between stress and strain from the stain gaugduring the loading tests is linear [4].

For greater accuracy of the advanced FE models with variable modulus of elasticity is necessary to increase the numbof measurement of local E in segments. Presented methodology is independent on the sample size of E, but in our futuwork we will test greater number of local E (1400) in each from small number of GLT beams (3). Measured E will bdistributed regularly in each beam. This approach removes the dependence of measured E accuracy on the segment lengBoth files of E (old and new) will be used together according to Bayesian updating (Fig. 6).

Fig. 5. Bayesian updating of E.

5. Conclusions

The proposed approach is mainly suitable for extreme structures. Extreme structures have large differences betwematerial parameters of timber. The standard design is more conservative when compared to the present approach.

Acknowledgements

This outcome has been achieved with the financial support of the Ministry of Education, Youth and Sports of the CzeRepublic, project No. LD12023 advanced methods for design, strengthening and evaluation of glued laminated timber.

References

[1] Melzerov, L., Kuklk, P., 2010. "Variability of Strength for Beams from the Glued Laminated Timber", Proceedings of the 48th InternationScientific Conference on Experimentalni Analyza Napeti 2010 Experimental Stress Analysis, pp. 257-260. ISBN 978-80-244-2533-7.

[2] Melzerov, L., Kuklk, P., 2010. Statistical Research of Mechanical Properties of Glued Laminated Timber Beams. Metallurgy 49, p. 376-380. IS0543-5846.

[3] Melzerov, L., Kuklk, P., ejnoha, M. 2011. "Variable Local Modulus of Elasticity as Inputs to the FEM Models of Beams from the Glued LaminatTimber", 2nd International Conference on Material Modelling, pp. 213. ISBN 978-2-911256-61-5.

[4] Kuklk, P., Melzerov L., 2011. Kompozitn materily na bzi d eva, esk vysok uen technick v Praze, Praha p.76. ISBN 978-80-01-04958-7.[5] Plach, T., Tesrek, P., Wilczynsk, A., Padevt, P. 2010. "Experiment in Real Conditions: Mechanical Properties of Gypsum Block Determined Using

Non-destructive and Destructive Methods", Proceedings of the 3rd WSEAS International Conference on Engineering Mechanics, StructureEngineering Geology/International Conference on Geography and Geology, pp. 418-423. ISBN 978-960-474-203-5.

Existing file of E File of E for the newbeams

Combination ofboth sets of Eincludingreliability matrix

Non-Destructive Tests of Modulus of Elasticity for the Glued Laminated Timber Beams

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