348 architectural studies, materials & analysis
TRANSCRIPT
Deformation analysis of joints of a long span
trussed wood arch: experimental tests and
numerical analyses
P. Ronca*, M. Veroli\ A. Franchi*
"Politecnico di Milano, Facolta di Ing., Milano, Italy
Abstract
Trussed wooden beams as well as trussed wooden arches are common
typologies covering long span structures of old monuments. The resulting roof
shapes are either linear saddle roofs or domes with planar different geometries.
Both the cases present common material and structural features, which can
influence the static capacity and deformability of structures under sustained
dead loads. Eccessive midspann deflection like eccessive deformation of the
key or the reins of the arch are quite common pathological aspects shown by
wooden monumental roofs. Structural analysis by numerical elastic procedures
disregarding non linear behavior of particular sections like joints, generally
show non realistic low stress range, even for the most critical load
combinations, and insensitive deformation of the structure.
Therefore knowing the real behavior of the joints, often assembled by
steel nails or bolts keeping together two or more wooden planks, results very
significant [1], [2].
1 Introduction
The research work presented in the paper refers to an experimental and
numerical investigation, conducted at the Department of Civil Engineering of
the University of Brescia, to better understand the influence of the bolted joints
Transactions on the Built Environment vol 15, © 1995 WIT Press, www.witpress.com, ISSN 1743-3509
348 Architectural Studies, Materials & Analysis
on the overall deformed shape of a dome made by a sequence of trussed
wooden arches.
In particular the influence of different tightening forces of the bolts, the
deformation of the holes, local damages in the perforated wood have been
studied by some experimental prototypes for a quantitative estimation of the
parameters necessary to establish the real stiffness of the connections. The
experimental results in terms of P-AI and M-A0, were taken into account as a
constitutive law of the deformable connections and the deformability of the
entire trussed arch has been numerically studied.
The experimental prototype, have been prepared in terms of wood types,
geometrical dimension and construction detailing in a way that they reproduce
an actual case. Experimental and numerical results are checked with real values
surveided on the monument of "Palazzo della Loggia" in the city of Brescia
where the dome, sustained by arches similar to the prototypes tested in the
laboratory, shows remarkable deflection.
Previous studies and tests about the damaged and deformed shape of the
dome and the entire structure, vertical masonry walls, and foundation, have
been performed by the same authors [2]. In [3] the first esperimental results on
the first prototype built and tested in the laboratory of the University are
reported.
Figure 1: The wooden vaulted roof Figure 2: The composite
section of the curved arch
beams.
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Architectural Studies, Materials & Analysis 349
The present paper presents the most significant part of the entire test
procedure and illustrates how esperimental findings have been kept as the basic
input for the accurate numerical non-elastic analyses of the structure. The
complete series of results and comments on them are reported in [4].
It is worthwhile to recall that the structural typology of the experimental
arch prototype reproduced in the laboratory, even if referring to a real structure,
is representative of large case structural typologies of roofs. Therefore the work
and results here presented are representative and usefull for a better
understanding of stuctural behavior of long span monumental historical roofs
commonly used in different parts of Europe over a span of centuries [1],
2 Typology of the actual main arches and the experimental
prototype
The photograph of fig.l shows the actual roof made by a vaulted wooden
structure of important dimensions and reaches in elevation a maximum of 25
meters the shape of the dome and the planar rectangular sides 25,28 and 43,45
meters respectively are shown in fig. 3a). The structural architecture of the
vault consists of principal truss wooden arches and simple secondary arches;
both are connected at the top by a truss made wooden beam [2].
b)
Figure 3: a) The structural overall system of the dome; b) principal arch.
Transactions on the Built Environment vol 15, © 1995 WIT Press, www.witpress.com, ISSN 1743-3509
350 Architectural Studies, Materials & Analysis
The principal arches, as the entire structure, of oak wood, are made, as shown
in fig.l, and fig. 3b) of two longitudinal curved beams (the intradoss and the
extradoss of the arch) connected by diagonal and vertical elements.
The sections of the principal and secondary arches, as well as the top
beam are made by the union of three planks of section 10x30 cm. and length of
about 2 meters, as shown in fig.2. The monolitical behavior is provided by
numerous steelplates and bolts, probably inserted in non calibrated holes.
Originally the transversal continuity of the element was assured by the friction
of the planks, achieved by the tightening of the bolts. Essentially because of
deformations of the holes and the time dependent behaviour of the wood the
bolts lost their tightening. As a consequence, slips and mutual displacements
either among the planks and among the elements of the truss joints have
resulted. The structural overall damage of the vault is evidenced by a
considerable deflection of the longitudinal top beam and the key points of the
connected arches. The aim of the tests on the prototypes, constructed on
purpose in the laboratory, is to give information about local and distributed
deformations during different steps of loads for a significant part of the actual
arch, that has been identified as that part of the curve intradoss beam (or
extradoss beam) between two nodes of the truss, as shown in fig.3 b). As
consequence, two different models have been constructed with the same
section geometry, materials (wood and steel), distribution of bolts as the actual
one, but with two different distributions of planks joints, as it is in the original
beam. (See fig.4 and fig.5)
The same figures show the loading apparatus providing the axial load and
flexural moment on the specimen according to results of an approximate
numerical analysis of the real structure.
3 Test results and comment
The complete description of the test and loading apparatus and of the
relevant phases of the test procedure is given in [4]. Here it is worth recalling
that the specimen, have been tested under different values of the tightening
force of the bolts. The variation of the tightening force is taken as the leading
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Architectural Studies, Materials & Analysis 351
Joint 1
Figure 4: Prototype 1Joint A
Figure 5: Prototype 2
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352 Architectural Studies, Materials & Analysis
parameter of the local deformability of the holes and, as a consequence, on the
overall behaviour of the specimens.
The interaction between the bolts and wood, may influence the non
elastic behaviour of the specimen essentially because of the three different local
damages illusrated in fig.6. The most relevant results obtained by testing the
first specimen, quite lowly stressed by flexural action shows a rather stiff
behavior of the specimen even with no tightening force.
The second specimen, concerning the second fundamental typology of
the intradoss beam, has been loaded by a more severe and complete load
programm, a i.e by complete load cycle, and by three different eccentricities of
the load application point. The first specimen presents losses in the stiffness
essentially in the case of a very low tightening force. The same behaviour has
been more properly confirmed by the second specimen. In fig.7 results of the
axial deformation are reported for different eccentricity and no tightening force.
The significant slip of the bolts is evident, probably due to the first and
second meccanisms outlined in fig.6, even if in some particular point initial
splitting crack (mecchanism in #3) has been observed.
Figure 8 shows the rotation of planks joints A, again for different
eccentricities and no tightening force.
4 Determination of local constitutive laws of the joints for the
numerical analyses and discussion of the results.
On the basis of the experimental findings, the input data for the
numerical analysis have been deduced by assuming:
i) the actual behaviour under sustained loads must be achieved by
assuming, as realistic, results obtained for no tightening force of the bolts;
ii) both the rotations and relative displacements refer to average values
calculated from all the values taken on the dial-gages system distributed along
the length of the specimen.
iii) for the numerical discretization the total number of joints caracterized
by the non linear costitutive law obtained by experimental tests, has been
focused on in every section of two consecutive wooden planks, as shown in
figure 9 A, and numerically described by spring elements, physically visualized
in figure 9 B and C.
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Architectural Studies, Materials & Analysis 353
Figure 6: Local mechanisms hole-bolts.
e = 0 mm ° e = -100 mm e = +100mm
12000
*M 8000 •
3 4000
00 0.0005 0.001 0.0015 0.002 0.0025 0.003
Strain
Figure 7: Experimental displacements of the joint A for different values of theeccentricity "e".
e = 0 mm
iI
e = -100 mm —*— e = +100 mm
1600 T1200800 •400
-0.003 -0.002 -0.002 -0.001 -0.001 -0.000̂ (
-800Rotation
0.001
Figure 8: Experimental rotation of the joint A for different values of theeccentricity "e".
Figure 9: Modelization of the joints: A: effective joints; B: axial springelement; C: flexural spring element.
Transactions on the Built Environment vol 15, © 1995 WIT Press, www.witpress.com, ISSN 1743-3509
354 Architectural Studies, Materials & Analysis
For the sake of brevity, just the two final curves, elaborated from the
overall results of the tests, are here reported in figures 10 and 11, which
numerically model axial and flexural springs respectively. Different numerical
analyses have been performed essentially based on the same numerical
discretization (Finite Element) and procedures (ABAQUS), but on different
parametric curves describing P-A1 and M-Acp laws, to simulate the real
behaviour even due to initial not perfect calibration between bolt and hole.
From a wide in situ survey as well as a historical research regarding the
different phases of construction, it has been clear that initial slip for non
calibrated holes was present, even only for technological reasons.
The parametric curves, taking into account different values of initial slip,
used in the numerical analyses are shown in figure 11 a) and b). The complete
series of numerical results are reported in [4]. Here results of the heaviest
situation are reported in terms of maximum deflexion of the key section (30,25
cm, fig. 12), close to the actual one. Internal actions of the intradoss beam of the
arch for the different parametric analysis are reported in figures 13 a) and b).
The maximum values of flexural moment and axial force lead to very
significant values of internal tension (80 kg/cm̂ ), being partially old damaged
wood.
Figure 12: Undeformed and deformed shape.
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Architectural Studies, Materials & Analysis 355
Displacement [cm]
2.00E+04
2.00E+04
a)
Rotation
5.00E+04
b)Figure 10: Constitutive laws used for the axial spring a) and rotational spring
elements b).
• analysis 4 —°— analysis 5 —•— analysis 6
2.00E+04
l.OOE+04
i O.OOE+00
Jj g- - -8 8- - - 8 -i.ooE+04^ ^ (4 m <:- - -2.00E+04
Displacement [cm]
• analysis 4 —°— analysis 5 —*— analysis 6
a)
Rotation [rad]b)
Figure 11: P-A1 and M-A<|) laws with initial parametric slips.
Transactions on the Built Environment vol 15, © 1995 WIT Press, www.witpress.com, ISSN 1743-3509
356 Architectural Studies, Materials & Analysis
-9000
Arch planar length [m]
' analysis 1
analysis 2
analysis 3analysis 4
analysis 5analysis 6
a)
analysis 1
Arch planar length [m]b)
Figure 13: Numerical analyses: distribution of axial load a) and bendingmoment b) for intradoss beam of the arch.
References
[1] Les Chantiers de la Renaissance-Picard, Paris 1991 (In particular' Architecture de Philibertde L'Orme - Roven 1648' & 'Ouvrages d'ingenieurs ou d'architectes executes a la Philibertentre 1780 et 1830-1850').
[2] Franchi A., Giuriani E., Mezzanotte G., Ronca P. -Indagine sul degrade del Palazzo dellaLoggia di Brescia- Relazione Tecnica Generate - Centro di Studio e Ricerca per laConservazione ed il Recupero dei Beni Architettonici ed Ambientali, Brescia, Nov. 1990.
[3] Ronca P. - Diagnosis of Damage in a Wooden Vaulted Structure- IABSE SYMPOSIUM -Rome 1993.
[4] Passer G., Franchi A., Ronca P., Veroli M. - Modelli Analitici e Prove Sperimentali per laSimulazione Numerica degli Archi in Legno del Palazzo della Loggia di Brescia- InternalReport n°l, 1995- Dipart. di Ing. Civile, Universita di Brescia.
ACKNOWLEDGEMENTS
The authors acknowledge eng. G. Passer for his valuable contribution in the experimental andnumerical phases of the research. The work as been partially supported by the grant Murst 60%1994 of the first author.
Transactions on the Built Environment vol 15, © 1995 WIT Press, www.witpress.com, ISSN 1743-3509