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37-7-5 M Ballerini
A new prediction formula for the splitting strength of beams loaded by
dowel type connections
Abstract
The paper presents a new semi-empirical prediction formula for the splitting
strength of beams loaded perpendicular-to-grain by dowel-type connections.
The formula is derived on the basis of the results of the main experimental
research carried out by different authors by means of the analysis
of the influence of different parameters. It takes into account the influence
of both the beams' size and the connections' geometry. The formula is initially
derived for beams loaded by single-dowel connections and then corrected
to cover the case of beams loaded by multiple-dowel connections.
The prediction ability of the formula is illustrated, discussed and compared
with the prediction formulas available from literature which have
been adopted in the new European and German design codes for timber
structures. Finally, a design proposal is derived and compared with experimental
results.
Introduction
Beams loaded on their depth by dowel-type connections can fail by splitting
at load levels which may be considerable lower than the ones of the
connections or of the beams. This is particularly true when the distance
from the loaded edge of the furthest row of fasteners (he) is small compared
to the beam height (h).
Due to this reason such engineering solution for the transmission of
forces should be avoided or adequately designed by means of properly reinforcements.
Nevertheless by the presence of possible reinforcements, the need of a
valid prediction formula for the splitting strength of beams loaded by
dowel-type connections is widely recognised. Unfortunately, the evaluation
of the splitting strength is a difficult task due to the large number of
involved parameters.
The most recent drafts for the new European (EC5) and German (DIN
1052) design codes for timber structures suggest two different design formulae
which take into account the several parameters in a very different
way.
The design formula embodied in the draft of the new EC5 is based on
the work originally developed by Van der Put, on the basis of an energetic
approach in the framework of the Linear Elastic Fracture Mechanics, and
recently put forward again in Paper 35-7-7. Essentially, this formula assumes
a linear relationship with the beam thickness and an influence of the
square root of the distance of the furthest row of fasteners from the loaded
edge of the beam (he). On the contrary, it neglects any influence of the
connection geometry.
The design formula embodied in the draft of new DIN 1052 is an evolution
of the prediction formula derived by Ehlbeck, Görlacher & Werner
(Paper 22-7-2), which was based on both empirical and theoretical considerations.
With respect to the Van der Put formula, it assumes a different
influence of the loaded edge distance (by means of the non-dimensional
parameter α = he/h) and also a different non-linear influence of both the
beam thickness (b) and the beam height (h) as a result of the assumed
Weibull failure theory. Moreover, it explicitly considers the influence of
the joint configuration on the splitting strength.
Both prediction formulae seem to have some correct and some wrong
assumptions.
The formula of Van der Put seems to be able to predict more correctly
the influence of the beam height (and also of the beam thickness), as reported
in the recent experimental and numerical researches of Ballerini
and Yasumura performed on beams loaded by single-dowel connections.
Nevertheless, it doesn't takes into consideration the effect of the joint geometry
which is instead clearly detectable in all the experimental researches:
from the oldest (Möhler & LautenschIäger) to the more recent ones.
On the other side, the formula embodied in the recent draft of the new
German design code for timber structures correctly takes into account the
effect of the joint geometry, however it seems less reliable from the viewpoint
of the influence of beam height and thickness.
In the present paper a new semi-empirical prediction formula is derived
on the basis of theoretical considerations and on the main outcomes of the
different experimental researches. Initially, the formula is derived for the
case of beams loaded by single-dowel connections. Afterwards, the formula
is corrected to cover the case of beams loaded by multiple-dowel connections.
This second step is developed considering initially the effect of
the width of the connection and then the effect of the connection height.
Conclusions
CIB-W18 Timber Structures – A review of meeting 1-43 4 CONNECTIONS page 4.37