Mechanics of stress-laminated timber bridges with butt end joints

Mats EKEVAD Ph.D. Professor Luleå University of Technology

Skellefteå Sweden

mats.ekevad@ltu.se

Focus is on finite element simulations of wood material and engineered wood products behaviour during loading.

Johannes A. J. HUBER M.Sc. Ph.D. student Luleå University of Technology

Skellefteå Sweden

johannes.huber@ltu.se

Focus on engineered wood and timber structures.

Peter JACOBSSON M.Sc. R&D Manager Martinsons Träbroar AB Skellefteå

Sweden

peter.jacobsson@martinso ns.se

Focus is on increasing competiveness for timber structures and especially bridges.

Summary

A number of variants of single span and three-span stress-laminated timber bridge decks have been studied via finite element simulations and experiments. Glulam beams in the decks were in general shorter than the total length of span which means that there were butt end joints in the decks. The butt end of each beam in a joint was not connected to the other beam which means that each butt end joint reduced the strength and stiffness of the whole of the deck. Results for deflection and stresses were examined for the studied variants in the form of reduction factors for strength and stiffness relative to a deck without butt end joints.

Factors are shown in diagrams as function of ratio butt end distance/beam width and also butt end distance/span width. Comparison of achieved results with existing Eurocode rules shows that Eurocode rules are not totally appropriate.

Keywords: timber bridges, stress laminated, butt end joints, finite element simulations, Eurocode.

1. Introduction

Stress laminated timber bridge decks are made up of glulam beams which are held together side by side by pre-stressed steel bars, see [1] for general information of this timber bridge type. If the decks are longer than the length of single beams the beams are simply put together in length

direction and this is called butt jointing. The butt joints have no joining mechanism such as glue and

the butt joints are distributed all over the deck.

Today there are three criteria in Eurocode [2] which provide the minimum requirements for the necessary butt end distance between butt joints of two neighbouring beams. The assumption is that a butt joint in the same lengthwise position in a deck is allowed only for every fourth beam. For a group of 4 neighbouring beams the distance between butt end joints must be sufficiently large. For the fifth beam a butt end joint is allowed in the same lengthwise position as the first beam. The smallest allowed butt end distance is one out of 2d, 30t and 1.2 m where d is the lengthwise distance between prestressing bars and t is the beam width. Reasonably, the most conservative of these 3 conditions should be chosen although this is not stated clearly in the text. As an example, for d=0.9 m and t=90 mm, the three conditions give 1.8 m, 2.7 m and 1.2 m. From these values 2.7 m should be chosen since this gives the most conservative design for this example. The requirements may be used together with a reduction factor of 0.75 for strength according to Eurocode. No reduction factor for stiffness is specified. For the design of a bridge deck the correction factor plays a vital role. A more refined description of the reduction factor is therefore desired to reduce uncertainty.

The goal of this paper is to investigate the relationship between butt end distance and strength and stiffness of a bridge deck. A short butt end distance is expected to yield a greater reduction of stiffness and strength than a long butt end distance. The method used in this paper was to model stress laminated bridge decks with different spans, widths and thicknesses with the finite element software ABAQUS [3]. The decks were modelled as glulam beams which were held together by lateral pre-stress and resulting friction between neighbouring beams. The individual beams which build up the bridge decks were shorter than the total deck span widths. Therefore, the decks contained butt joints which were distributed in a specific pattern in the deck. The butt joints were not considered to transfer longitudinal forces between the beams.

In a first step simulations of three variants of the bridge decks (named F22, F25, F28) were

conducted in order to validate the calculation method by comparing to existing experimental results.

Then, FEM (finite element method) simulations of several deck variants were performed and the results were analysed without comparisons to experimental results. In [4], [5] and [6] descriptions of FEM models for bridge simulations are described and discussed.

2. Material and Methods

The simulated deck variants are listed in Table 1. First, the variants F22, F25 and F28 which were taken from an experimental study [7] were simulated to calibrate and verify the calculation method.

In the next step variants 1-5 were calculated. These variants were 3-span decks with two different butt end distances and two different beam widths. Three-span decks are usually manufactured with butt joints and the chosen dimensions for the variants are common in industry. Variant 1 was a deck without butt joints and was thus taken as a reference case. Variants 6 and 7 with twice the span widths of variants 1-5 were calculated in a next step in order to get a clearer relationship between reduction factors and ratio butt end distance/beam width. The rest of the variants Ext1A to Ext4B were similar to variants 1-5 but with other butt end distances.

Reduction factors for stiffness were calculated as ratio between maximum deflections for variants divided by maximum deflection for reference variant. Reduction factors for strength were

calculated as ratio between maximum stresses for variants divided by maximum stress for reference

variant. Stresses in positions in the middle of spans and above supports were considered.

Table 1: Variants of bridge decks

Name # Spans

Span- width (m)

Thick- ness (mm)

Beam width (mm)

# Beams

Deck width (m)

Butt end dist- ance (m)

Pre- stress (MPa)

Dist / Beam width

F22 1 5.2 270 90 9 0.81 0.9 0.3 10.0

F25 1 5.2 270 42 19 0.798 0.9 0.3 21.4

F28 1 5.2 270 90 9 0.81 1.35 0.3 15.0

1 (ref) 3 8-10-8 495 90 40 3.6 - 0.35 -

2 3 8-10-8 495 90 40 3.6 1.2 0.35 13.3

3 3 8-10-8 495 90 40 3.6 2.7 0.35 30.0

4 3 8-10-8 495 180 20 3.6 1.2 0.35 6.7

5 3 8-10-8 495 180 20 3.6 2.7 0.35 15.0

6 3 16-20-16 495 180 20 3.6 2.7 0.35 15.0

7 (ref) 3 16-20-16 495 180 20 3.6 - 0.35 -

Ext1A 3 8-10-8 495 180 20 3.6 1.8 0.35 10.0

Ext1B 3 8-10-8 495 90 40 3.6 1.8 0.35 20.0

Ext2A 3 8-10-8 495 180 20 3.6 3.6 0.35 20.0

Ext2B 3 8-10-8 495 90 40 3.6 3.6 0.35 40.0

Ext3A 3 8-10-8 495 180 20 3.6 0.9 0.35 5.0

Ext3B 3 8-10-8 495 90 40 3.6 0.9 0.35 10.0

Ext4A 3 8-10-8 495 180 20 3.6 3.2 0.35 17.8

Ext4B 3 8-10-8 495 90 40 3.6 3.2 0.35 35.6

The calculation method required solutions of contact problems between the beams as sliding with friction occurred locally or on large surfaces. See [4], [5] and [6] for descriptions of methods for simulating contact and slip between beams. The calculations were performed in the FEM software ABAQUS 6.14, [3], with 3-dimensional elements. The material data used was following

recommendations in Eurocode, [2]. Material was assumed linearly elastic and orthotropic with elastic moduli 12000 MPa in longitudinal direction along fibres and 240 MPa in cross directions.

Shear moduli for two shear planes (bending shear and inplane shear) were assumed to be 720 MPa and shear modulus for rolling shear was assumed to be 72 MPa. All Poisson’s rations were set to 0.

The coefficients of frictions were assumed to be 0.29 and 0.34 in longitudinal direction and

transverse direction, respectively. The used elements were parabolic (i.e. of quadratic order) and

examples of mesh density are visible in Figs. 2 and 3. Contact between beams was described by an

exponential pressure-overclosure model with pressure 0.35 MPa and clearance 0.01 mm. Prestress

on side edges of the deck was modelled by a constant distributed load on surfaces 0.27m x 0.20m at

every position of the prestress bars (every 900 mm) for variants F22, F25, F28, 1, 2 and 3. This

resulted in the average prestress indicated in Table 1 but with locally varying pressure close to the

edge beams. The prestress on all other variants was modelled with a constant distributed load on the

side edges of the deck corresponding to the average prestress because of small differences in the

results compared to using discrete prestress locations. Loading and unloading were applied in three

steps; first the prestress was applied, followed by the vertical net load and finally the removal of the

net load. The vertical displacement of the support surfaces under the deck was assumed to be zero

or was modelled by contact conditions against a fixed support.

For the other variants, a distributed vertical load on the entire upper bridge deck surface was

applied. The distributed load was specified as a load per length in the lengthwise, span direction and is visible in figures. Loading was stopped if instability developed or if the deformations became considerably large. Self-weight of the bridge deck was disregarded. The models of the bridge decks were not perfectly symmetrical due to the distribution of the butt joints. However, symmetry in both longitudinal and transversal direction was assumed for all variants except for F22, F25 and F28.

3. Results

3.1 F22, F25 and F28

Load-deflection curve, stress along fibres, contact pressure and displacements for variant F25 is shown in Fig. 1, Fig. 2 and Fig. 3, respectively. Results for F22 and F28 are not shown here but their curves show a similar behaviour as variant F25.

Fig. 1: Load versus deflection for variant F25

3.2 Variants 1-7 and Ext1A to Ext4B

Variant 1 and 7 were references, i.e. they had no butt joints. Variants were loaded up to 200 kN/m

and then unloaded. However, loading was stopped for variant Ext3A at 150 kN/m due to instability

(collapse). Variants 6 and 7 which had larger span lengths than variants 1-5 were loaded up to 100

kN/m and then unloaded. Figs. 5-8 show examples of how deformations and stresses looked like in

the models.

Fig. 2: Variant F25; load 125 kN, stress S33 along fibres, max 31 MPa. Scale factor 20 for deformation.

Fig. 3: Variant F25; load 135 kN, contact pressure on every fourth beam, max 1.19 MPa. Scale

factor 20 for deformation.

Fig. 5: Deformation and stress along fibres for variant 2 at 200 kN/m. Scale factor 45, maximum fibre stress 20 MPa.

Fig. 6: Deformation and lateral normal stress (average is prestress -0.35 MPa) for variant 2 at 200 kN/m. Scale factor 45.

Fig. 7: Deformation and stress along fibres for variant Ext3A at 150 kN/m. Scale factor of 45, max stress 16 MPa.

Fig. 8: Deformation for variant 6 at 100 kN/m. Scale factor 45, max vertical deformation 138 mm.

divided by beam width. The reduction factors were calculated by recording the maximum deflection and maximum stresses along the fibres and dividing by the corresponding values for the reference cases without butt joints. Results at two load levels are shown in order to show influence of nonlinear slip effects.

Fig. 9: Reduction factor for stiffness as a function of ratio butt end distance/ beam width.

Calculated from the deflections measured at two load levels.

Fig. 10: Reduction factor for strength as a function of butt end distance/ beam width. Calculated from the maximum stresses along the fibres measured at two load levels.

Fig. 11 and Fig. 12 show another way of presenting the reduction factor as a function of butt end length divided by span width.

4. Discussion

4.1 F22, F25, F28

The simulation model worked well compared to the physical tests regarding the load-deflection curve (Fig. 1). Certain deviations exist but are negligible and corrections of the models were thus not deemed necessary. Sliding started at relatively low loading and yielded a non-linear loading curve and a differing curve at unloading, i.e. hysteresis occured. In variant F25 (Fig.1) the

hysteresis in the model was less pronounced than in the physical tests. However, in F22 and F28 the

modelled and the physical hysteresis were more alike. Fig. 2 and Fig. 3 show displacements, stresses along fibres and contact pressure which all seem to be realistic.

Fig. 11: Reduction factor for stiffness as a function of butt end distance/ span width. Calculated from the deflections measured at two load levels.

Fig. 12: Reduction factor for strength as a function of butt end distance/ span width. Calculated from the stresses along the fibres measured at two load levels.

4.2 Variants 1-7 and Ext1A to Ext4B

Since variant 1 and 7 were references, i.e. they did not incorporate any butt joints, they resulted in linear loading curves without hysteresis. All other variants resulted in varying degrees of sliding between beams and therefore hysteresis appeared when unloading. Variant Ext3A with a short butt end (0.9 m) and wide beams (180 mm) gave considerably large sliding and simulation was stopped at 150 kN/m due to instability (collapse). Sliding between beams in vertical direction was largest close to the butt joints. Sliding vertically was also large close to regions of large bending moments (middle of span width and above supports). Sliding also occurred in horizontal direction due to torsional moment in the deck.

Reduction factors shown in Figs. 9 and 10 do not give a satisfying picture of the results since curves

are not very smooth. Using butt end distance/span width as a descripting variable instead gave a

wider beams. Larger span widths (variants 6 and 7) gave different results than smaller span widths.

Reduction factors for stiffness and strength were not the same and were lower for strength.

Reduction factor for strength was lower when judging stress in middle of span than when judging stress above supports. Reduction factors for both stiffness and strength were slightly lower when using a higher load level (due to increased slip at high load level).

Eurocode specifies a minimum threshold value of 30 for butt end distance/beam width and specifies a reduction factor of 0.75 for strength. Here, from Fig. 10 the reduction value was roughly 0.70 for butt end length/beam widths greater than 20. The reduction factor for stiffness was higher according to Fig. 9, about 0.85 for butt end length/beam widths greater than 20.

5. Conclusions

- Finite element simulations worked well and gave realistic behaviours which correspond well to the experimental results.

- Calculations of reduction factors as a function of only one variable, e.g. as in Eurocode butt end distance/beam width, did not give a comprehensive picture probably because other variables were involved such as span width and/or deck width.

- Confining butt end distance/beam widths > 20 resulted in reduction factors closer to each other for simulated variants, than for butt end distance/beam widths < 20.

- The reduction factors for stiffness and strength were not the same. The factor was higher for stiffness than for strength.

6. References

[1] Ritter, M. A. (2005). Timber bridges: design, construction, inspection and maintenance (Part one). University Press of the Pacific, ISBN1410221911.

[2] Anonymous, Eurocode 5: Design of timber structures-Part 2: Bridges. SS-EN 1995-2:2004.

[3] Anonymous, Abaqus 6.14 (2014) Users manual. Dassault Systemes Simulia Corp. Rising Sun Mills, 166 Valley Street, Providence, RI 02909-2499, USA. 2011.

[4] Ekevad M.; Jacobsson P.; Forsberg G.. ”Slip between glulam beams in stress-laminated timber bridges: finite element model and full-scale destructive test”. ASCE Journal of Bridge Engineering 16:188-196. 2011.

[5] Ekholm K.; Ekevad M.; Kliger R. (2014). Modelling slip in stress-laminated timber bridges:

comparison of two FEM approaches and test values. ASCE Journal of Bridge Engineering 19(9) 04014029.

[6] Ekevad M.; Jacobsson P.; Kliger R. (2013). Stress-Laminated Timber Bridge Decks: Non- linear Effects in Ultimate and Serviceability Limit States. International Conference on Timber Bridges 2013 (ICTB2013). Arranged by USDA Forest Products Laboratory. Las Vegas, USA, September 30-October 2, 2013.

[7] Vertikalt glidbrott och stumskarvars inverkan på tvärspända träplattor. Provningsrapport (in

Swedish). Kristoffer Ekholm, Chalmers Tekniska Högskola, Konstruktionsteknik, Rapport

2012:06.