Evaluation of Stress Laminated Bridge Decks Based on Full Scale Tests
Kristian Dahl
PhD-student
Norwegian University of Science and Technology, NTNU
Trondheim, Norway
Nils Ivar Bovim
Assistant Professor
Norwegian University of Life Sciences, UMB
Ås, Norway
Kjell Arne Malo
Professor
Norwegian University of Science and Technology, NTNU
Trondheim, Norway
Summary
Full scale testing of stress laminated timber decks has been conducted in order to evaluate
different design procedures. The decks were made of creosote impregnated Norwegian pine.
The tests were non-destructive and were carried out at different prestress levels to study the
pretension effect. The deflection pattern was observed. Linear elastic material parameters
were determined by means of an optimization procedure with respect to the deformation field.
The experimental and numerical results were compared to available design procedures, and
the agreement was in general fairly good. The results are encouraging for further use of FEM
as a design tool for stress laminated bridge decks of wood.
1.
Introduction
A stress laminated timber deck is made of wood lamellae which are placed side by side, see
Figure 1. Steel rods are passed through a set of predrilled holes along the deck length. By
prestressing the rods, contact stresses between the lamellae is obtained. Bending moments as
well as shear forces can thus be transferred in both longitudinal and transverse direction of the
deck. The prestress level is normally between 0.6 and 1.0 MPa. The rods are oriented
transversely to the deck length, and this is the origin of the term transversely stress laminated
bridge decks.
Mainly due to the difference in elastic properties between the longitudinal and the
tangential/radial direction of timber, the stiffness properties vary considerably between the
longitudinal and transverse orientation of the plate. Hence, the timber deck works
mechanically as an orthogonal anisotropic plate, also called an orthotropic plate.
Consequently, timber decks have considerable
lower bending resistance in the transverse
direction than in the longitudinal direction.
More sophisticated plate design procedures
must thus be taken into consideration to ensure
sufficient behaviour and capacity. In particular,
it is crucial to avoid delamination caused by
insufficient capacity for transverse moment and
shear forces acting between the lamellae.
Figure 1: Prestressing detail in wood deck
A number of design procedures exist for orthotropic plates, and some are developed
especially for stresslaminated timber decks. The latter are simplified procedures based on a
transformation of the plate problem into a beam problem with an equivalent characteristic
width of load distribution. The distribution width is used to predict ultimate strength capacity
and deformation. Such simplified beam methods comprise the procedure suggested by
Australian Guidelines [1], Eurocode 5 [2], M. Ritter [3] and the U.S. Dept. of Transportation
[4]. More general methods are based on the differential equation for an orthotropic plate, and
comprise the orthotropic plate theory by Krug and Stein [5] and the theory by GuyonMassonet [6]. Such analyses require the values of longitudinal and transverse modulus of
elasticity, EX and EY, respectively, and the in plane shear modulus GXY of the plate. These
parameters are also required in finite element method (FEM) analyses.
2.
Background
The concept of stress lamination of timber decks was originally developed in Canada where
the principle was first utilized in the 1970’s for rehabilitation of old bridge decks.
Subsequently, the stresslam technique has been used for rehabilitation as well as construction
of new bridges decks. Major test programs have been undertaken at the USDA Forest
Products Laboratory, the Sydney University of Technology and by the Nordic Timber Council
throughout the 1980’s and 90’s. Design procedures were incorporated in the design codes in
1983 in Canada, in 1991 in the United States of America and in 1997 in Eurocode 5. One of
the newest developments is production of massive prestressed wood elements used for other
applications such as floors, ceilings and wall elements in flats and office buildings. In
Norway, the technique has been utilized in many bridges and building applications over the
last years.
Limiting the plate thickness to approx 220 mm, which is the size of normal grown timber in
Norway, the timber decks can span about 5 meters longitudinally using full highway loading.
However, due to their flexible construction, stresslam decks can be produced with different
cross sections such as multiple T’s and boxes and thus increase the stiffness. Replacing
lamellae with glulam panels offers additional possibilities to increase the stiffness and the
overall strength. By means of lamella butt joints the decks can also be produced with
considerable vertical curvature. This principle was e.g. utilized in the so-called Leonardo da
Vinci’s Bridge, a miniature copy of Leonardo’s bridge designed for “The Golden Horn” at the
Bosporus strait in 1502, built in Ås, Norway in 2001 [7].
3.
Objective and experimental work
The study comprises full scale testing of stresslaminated bridge decks. The objective was to
study the overall behaviour of such decks and to evaluate existing design procedures. The
goal was to study and possibly verify the different methods and their computational suitability
for decks made of Norwegian pine. An important aspect of this was the determination of valid
material parameters required by the respective methods. Special attention was also given to
modelling of stresslam decks by means of the finite element method and the parameters such
analyses require.
The experimental work constituted a part of the Nordic Timber Bridge Project on behalf of
Nordic Wood and the Nordic Timber Council, which also funded the work. The tests were
carried out at the Agricultural University of Norway and reported in [7].
3.1. Materials
The wood lamellae were made of Norwegian pine (Pinus Sylvestris) with cross-sections of 48
mm by 222 mm. They were visually graded to C24 [8]. The lamella length was 5200 mm,
which also was the length of the rectangular tested deck. None of the tested decks had butt
joints. The lamellae, impregnated with
creosote type AB, came from the lot
used in the deck of Tynset Bridge,
Norway, built in 2001. The modulus of
elasticity EL was tested for each lamella
with an average value of 12 005 MPa.
The prestressing rods were of the
commercial type Dywidag 15F with an
effective diameter of 15 mm. The
quality was 900/1100 MPa, referring to
the yield/failure stress, respectively.
The horizontal spacing between the
rods was 600 mm. The predrilled holes
Figure 2: Tynset Bridge, Norway, built for highwere located in the centre of the deck
way traffic load with stress laminated timber deck cross section height.
3.2. Load and pretension
The decks were loaded by means of a stiff steel beam connected to two hydraulic actuators
fastened to the floor on each side of the deck. The actuators were equipped with load cells,
confer Figure 7. Both point and line loads could thereby be applied to the deck. The point load
was arranged as a roller bearing between the plate and the steel beam, see Figure 4. The
loading rate was approximately 500 N per second. The maximum load levels were chosen
near the respective design capacities of the different decks and load cases. This was done in
order to produce a wider basis for assessment of the linear elastic behaviour of the deck. Each
loading sequence lasted between 2 and 6 minutes. Ultimate capacities were not tested.
The pretension was applied by means of a hydraulic jack conventionally used for this purpose.
To obtain a uniform pretension stress, the rods were repeatedly tensioned in several
sequences. Each pretension rod was provided with a load cell measuring the pretension load.
The load cells provided information so that tests could be undertaken at assigned pretension
levels. Furthermore, change in the pretension force due to deck loads could be observed. The
decks were generally tested at a pretension level of 0.6 MPa. To study the pretension effect on
deck behaviour in detail, one deck configuration was also tested at different levels ranging
from 0 to 1.0 MPa.
3.3. Deformation
The deflection field of the decks was observed by means of five displacement transducers
installed on a movable beam using one sampling per second, see Figure 3. By moving the
beam, rectangular and quadratic decks were provided with a total number of 35 and 15
observation points, respectively. Repeated load sequences at the same positions produced
approximately identical load-displacement curves, which indicated acceptable measurement
accuracy. To minimize experimental errors, each loading sequence was generally repeated
and sampled three times at each beam position. Initial deck deflection caused by the dead
weight from deck, steel beam and load cells was neglected. To detect any deformation of the
support itself, deformation near the bearing was observed for all test types.
Figure 3: Displacement
ssstransducers
Figure 4: Point load using
roller bearing
Figure 5: Deck line support
detail
3.4. Rectangular deck configuration
The rectangular deck type was supported by continuous line-supports in the transverse
direction along the two opposite shorter sides. The bearing was arranged as shown on Figure
5, ensuring free rotation. The distance between the line-supports was 5100 mm. The deck
width depended on the prestress level and varied between 3040 mm and 3100 mm. Pointloads
were transferred via a steel plate which measured 200 mm by 600 mm, with neoprene
underneath to simulate a twin wheel on asphalt [7]. The point load was applied at two
different positions in the midspan of the deck, one at the centre point and one near the side
boundary. In addition, a transverse line load applied at midspan with a distribution width of
190 mm and a length equal the deck width, was tested.
Figure 6: Quadratic and rectangular stresslaminated decks used for full scale testing [7]
3.5. Quadratic deck configuration
Testing of the in-plane shear stiffness GXY
was carried out using a quadratic plate test
with side lengths equal to 2.3 m. The test
was set up by fixing one of the deck sides
vertically. One of the two remaining
corners was supported by a hinge allowing
rotation but no vertical translation. In the
fourth corner, a load was applied as a
vertical point load F, see Figure 7. By
means of this arrangement, the deck was
exposed to torsion and bending. Two
quadratic deck configurations were tested.
One had the lamellae oriented normal to
the fixed side, while the other was rotated
ninety degrees so that the lamellae were
oriented parallel to the fixed side.
Figure 7: Testing the in-plane shear stiffness by
means of an eccentric point load [7]
4.
Experimental results
Linear regression analyses on the relation between applied load and corresponding
deformation were carried out for each observation point for each load case and sequence. The
resulting deformation fields were subsequently averaged between the sequences and corrected
for support deformation for each of the positions in the 2D grid system. The corresponding
deflection fields are presented in Figure 8 to 10 with linear interpolation between the
observation points.
Figure 8: Vertical deflection of stresslaminated bridge decks subjected to centric point load.
The results are based on 35 measurement points
Figure 9: Vertical deflection from side point load (left) and centric line load (right). The
results are based on 35 measurement points. The transverse curvature due to transversal
contraction effects is palpable under the line load
Figure 10: Vertical deflection of quadratic decks subjected to eccentric point load. The
results are based on 15 measurement points. Note the difference in lamellae orientation.
5.
Numerical results
5.1. Numerical model
The different deck configurations were modelled in the commercial code ANSYS 9.0 with
300 to 700 four-node orthotropic shell-elements (SHELL43) with six degrees of freedom at
each node: translation in nodal x, y and z directions and rotation about the nodal x, y and zaxes [9]. The longitudinal (L) and radial (R) directions of the wood were chosen as the inplane x and y axis, with the tangential (T) direction as the z-axis pointing vertically out of the
deck plane. Based on [8] and an assumed average density of 420 kg/m3, the following linear
elastic material parameters were used for a set of preliminary FEM analyses:
EX = EL = 11 380 MPa
EY = ER = 780 MPa
EZ = ET = 470 MPa
GXY = GLR = 730 MPa
GYZ = GRT = 50 MPa
GXZ = GLT = 690 MPa
νXY = νLR = 0.39
νYZ = νRT = 0.48
νXZ = νLT = 0.50
The support of the rectangular deck was modelled with contact elements to ensure the ability
of plate uplift in the four deck corners. A friction coefficient of 0.3 between support and wood
was used in the horizontal direction. The quadratic deck was modelled with nodes constrained
against x, y and z translation along the line supported edge and with the vertical direction z
constrained at the opposite corner support node. Point and line loads were in general modelled
as pressure loading. Dead weight from wood was modelled as an external pressure equal to
420 kg/m3 · 0,222 m · 9.81 m/s2 = 915 N/m2.
5.2. Numerical procedure and results
Vertical deformation was calculated for the different deck configurations at the same
locations as the experimental observations. This was done for dead weight only, and for dead
weight plus point or line loads, for all measurement points. The difference in numerical
deformation between the two load cases was stored as UZi where index i denotes
measurement point. The sum squared difference SSD between experimental deformation δi
and numerical deformation UZi was calculated. An optimization procedure in ANSYS 9.0 was
used to minimize the value of SSD by adjusting the values of the material parameters EX, EY
and GXY for each configuration. A First Order Optimization Method with an iteration
tolerance equal to 1% was used, see [9]. Successive iterations resulted in an optimized set of
material parameters for each of the tested configurations. These are presented in Table 1. SSD
and the mean square difference MSD were calculated with n equal 35 and 15 for rectangular
and quadratic decks, respectively.
n
SSD
2
SSD = ∑ ( ∂ i − UZ i )
[1]
MSD =
n
i =1
Table 1: Linear elastic in-plane material parameters based on optimization procedure
MPa
Rect. deck, centric point load
1.0
Rect. deck, centric point load
0.6
Rect. deck, side point load
0.6
Rect. deck, centric line load
0.6
Quadr. deck, corner point load
0.6
Quadr. deck, corner point load
0.6
AVERAGE VALUES for 0.6 MPa pretension
MPa
12 703
11 850
12 119
13 188
11 850
11 848
12 171
MPa
292
214
223
522
214
694
373
EY
GXY
MPa
520
397
389
240
899
608
507
ΜSD
mm
0.52
0.60
1.42
0.68
22.70
2.79
-
δmax
FRACTION of EL = 12 005 MPa
101.4 %
3,1 %
4.2 %
-
-
Configuration
Pretension
EX
mm
12.2
13.4
27.1
9.0
167
222
-
Ideally, the different material parameters from the optimizations should have been identical
between the configurations. As can be seen in Table 1, this is not the case. EX, EY and GXY
vary up to 8%, 86% and 77% from the respective mean values. The parameters are thus
dependent on the configuration. Higher pretension seems to give a stiffer system.
Midspan deflections obtained from numerical analyses based on the values listed in section
5.1 and the average parameters in Table 1 are compared with the experimental values for the
rectangular deck configurations in Figure 11. The curves indicate good agreement between
numerical and experimental values for decks with a minimum pretension level of 0.6 MPa.
Figure 11: Numerical and experimentally based deflections in midspan for rectangular deck
configurations. Numerical calculations are based on parameters in section 5.1 and Table 1
Calculated results according to the different design methods are given in Figure 12 for the
rectangular deck with centric pointload and EX = 12 005 MPa [7]. These are compared to
experimental findings and numerical results based on the average parameters in Table 1. The
quantities MX and MY denote bending moment in longitudinal and transverse direction,
respectively, and VY is interlaminar shear out of the plane [7].
Figure 12: Design method results compared to FEM-results and experimental data for the
rectangular deck with a centric point load equal 100 kN and a pretension level of 0.6 MPa
6.
Concluding remarks
Results from numerical optimization on deck deformation resulted in the following in-plane
linear elastic parameters: EX = 1.014·EL, EY = 0.031·EL, GXY = 0.042·EL. All design codes use
EX = EL, which is close to this result. The EY and GXY values are somewhat higher than most
assignments: Australian guidelines [1] assign EY = 0.014·EL - 0.02·EL, Ritter [3] reports EY =
0.013·EL and Eurocode [2] gives EY = 0.015·EL. Eurocode specifies GXY = 0.06·EL while the
other report GXY = 0.03·EL. The differences from the findings are however not large. Based on
this, it seems reasonable to use in-plane parameters as given by the different codes for decks
made of Norwegian pine. It may be noted that the Norwegian Design Rules [8] assigns EY =
0.033·EL and GXY = 0.063·EL for general structural applications.
Comparison of experimental and numerical results to the different design procedures showed
that the procedure suggested by Ritter [3] in general gives results in good agreement with the
present experiments and simulations. Except for the deflection, the Guyon-Massonet method
[6] also produces results with good agreement. The distribution width calculated according to
the Australian guidelines is obviously too large, resulting in a relatively low MX value.
Eurocode 5 seems on the other hand to be rather conservative.
FEM-calculations with orthotropic shell-elements resulted in values which correspond well
with the experimental deflection and hand calculated quantities. Material parameters found by
inverse modelling show however, to some degree, dependency upon deck and load
configuration. The numerical model used is thus insufficient to fully cover the deck
behaviour. The fact that delamination was observed during testing for moderate loads further
indicates that the FEM model can be improved. An improved numerical model should
probably include the pretension bars and be based on solid 3D elements, contact elements
between the lamellae and a nonlinear material model for wood.
7.
References
[1]
Crews K.: Limit States Design Procedures for Stress Laminated Timber Bridge Decks.
Plate Decks. Part 1 – Code. Code & Commentary. Draft Edition 1.0 June 1994,
University of Technology, Sydney, Australia.
[2]
European Committee for standardization: Eurocode 5, Design of timber structures –
Part 2: Bridges. EN 1995-2, 2004.
[3]
Ritter M.: Timber Bridges: Design, Construction, Inspection and Maintenance, Forest
Service, United States Dept. of Agriculture, chapter 9, 1990/1992. 944 p.
[4]
U.S. Dept. of Transportation: Design, Construction, and Quality Control Guidelines for
Stress Laminated Timber Bridge Decks. FHWA-RD-91-120, 1993.
[5]
Krug S., Stein P.: Einfluβfelder orthogonal anisotroper Platten, 1961.
[6]
Bareš R., Massonnet C.: Analysis of Beam Grids and Orthotropic Plates by the GuyonMassonnet-Bareš Method, Crosby Lockwood & Son Ltd, London, 1968.
[7]
Dahl K.: Stress laminated wood decks. Evaluation of current design procedures based
on full scale testing. Master thesis, Norwegian University of Agriculture, Ås, 190 pp, in
Norwegian, 2002.
[8]
Norges Standardiseringsforbund: Norsk standard NS 3470-1, Design of timber
structures. Design rules. Part 1: Common rules. 5th ed., in Norwegian, 1999.
[9]
ANSYS Inc.: Theory Reference. Release 9.0 Doc., Canonsburg, PA, USA, 2004.