348 Architectural Studies, Materials & Analysis

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.


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.



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



Joint 1

Figure 4: Prototype 1Joint A

Figure 5: Prototype 2



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.



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.



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.



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.



-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.


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348 Architectural Studies, Materials & Analysis