Figure 6.25

Figure 6.25 Comparison of the efficiency of various design proposals through the utili- sation values

several thousand iterations does not mean much. The problem occurs when the algorithm is so heavy, a single iteration takes a second or even more to complete. It is then that the user is left with hours upon hours of waiting time for a single optimisation procedure.

While already a significant problem, this is only the beginning. The bridge, as it is represented in the Karamba analysis, consists of 200 elements. This means that the evolutionary solver would either have 200 input values for cross-section height to optimise, or beam sets with constant heights would need to be created (similar to what is shown in Figure 6.25). However, this means that these would need to be defined as parameters that would need to be optimised as well. Add to this the variations in bridge width for the cross-sections of every elements or set of elements, and the complexity rises by several more levels.

Suppose than, that after an excessive amount of time, the optimal cross-section pro- gression along the bridge is achieved. It is only the optimal solution for the load combi- nation that was deemed the critical one at the starting bridge configuration. Needless to say, the evolutionary solving on an algorithm of this scale was pointless to develop any further and was consequently dropped.

6.4.5 Joint locations and prefabricated elements

The next step of the bridge design was the definition of the optimal joint locations.

These are influenced by several parameters. The design cross-section that was used for this analysis was the top one in Figure 6.25 with a constant cross-section.

• The most influential parameter are the building services. The dimensions of the prefabricated segments are primarily limited by the manufacturing, transport, and assembly logistics. While these were not investigated in detail, it was determined that sections of up to 30 m in length would not cause logistic problems.

• Secondly, they need to be positioned where they will encounter the least un- favourable internal section forces and moments. In order to determine such po- sitions, the most critical load combinations need to be combined into envelope diagrams of the dominant actions. In this case, it was the M_y bending moment, followed by theM_x twisting moment, and the V_z shear force.

• Once the best position regarding the dominant action is defined, the other actions will determine what type of support should be used.

• Additionally, in case of variations in cross-section sizes along the bridge, there will be more and less ideal sections for joining the elements.

Creating the M_y bending and the M_x twisting moment envelope was somewhat of a laborious manual process. Because the model can only show the moment diagram of a single load combination, these had to be stored and assembled manually. During the analysis performed up to this point, it was determined that load combination ULS₂yields the largest cross-section forces and moments, which is why it was used to create the two envelopes shown in Figure 6.26, according to the variations in loaded sections.

The displayed joint positions were obtained from the listed considerations. All of them are rotational joints, which release the M_y bending moment. In order to obtain design values of loads on the joints, however, the accompanying actions needed to be examined. Since a joint is located between the start and end cross-section of the two adjoining members, the action values between them needed to be averaged. In Figure 6.27, the design values of actions are shown for joint locations between elements: B13-B14, B52-B53, and D7-D8, according to element identifications from Section 6.3.1.

Figure 6.26Moment diagram envelope forM_y andM_X with the proposed joint locations

Figure 6.27 Design values of actions on joints according to the ULS₂ load combination

6.4.6 Results of the chosen bridge configuration

Before moving to the next stage of the bridge design, an overview of the results of the chosen configuration are presented, while more detailed results can be found in Appendix D.

• For geometry of the model, refer to the top image with the constant cross-section in Figure 6.25.

• In Figure 6.28, a graphic output of the computational model along with utilisation curves based on the critical ULS₂ and SLS_3C combination are presented - these are updated to include joints.

• Figure 6.29 shows the first three corresponding natural frequencies of the model.

• For joint and support locations refer to Figure 6.26. The actions at the joint lo- cations, are seen in Figure 6.27, while the same output for internal cross-section forces/moments at the supports locations is presented in Figure 6.30.

Figure 6.28 ULS and SLS utilisation results of the proposed solution

Figure 6.29 The first three natural frequencies and the modes of the proposed solution Since the bridge analysis is somewhat simplified, the design was chosen with ample over-dimensioning. Looking at the utilisation curves, it can be seen that the serviceabil-

Figure 6.30Internal section moments and forces at the support locations of the proposed solution

ity combinations are the critical design factor, while ultimate limit state combinations are utilised only about 50%, at the most loaded support locations. This serves to show, that even when notches and reductions of the cross-section due to the support connec- tions (which were omitted from the analysis), are included, the design still has sufficient capacity.

6.5 Cable-stayed solution

Along with the defined algorithms for a girder beam bridge system, a cable-stayed alter- native was considered. Of course, first the validations needed to be done to prove that Karamba can be used to analyse such elements. This proved somewhat harder to do for the following reasons:

• defining a parametric geometry for the pylons and cables and connecting them into a structural system for the use with Karamba is significantly more complicated and time-consuming,

• defining several different materials and cross-sections further complicates the script because the interaction needs to be defined in their joints manually,

• the cables need to be analysed with 2^nd order theory,

• because there is no cable component in Karamba, they need to be modelled as circular beam elements,

• the cable behaviour can be best approximated by setting them to only carry loads in tension (they are ignored in the analysis in case of compression) and so that they do not have bending stiffness - but that also means that they will only elongate and not sag,

• optimising this analytical model goes further than only analysing the bridge deck.

All of this means that when comparing these elements with models created in RFEM, the internal forces, moments, and deflections were completely different. The reason for this is that the stiffness of each individual cable and also the pylons affects the overall stiffness of the model. There is also little room for simplifying the model by, for example, assuming the total rigidity of the pylons, because that does not represent the reality adequately.

Possible solutions to this problem that were considered were to replace the cables with spring supports, which was quickly discarded, since there is no way of defining their individual stiffness accurately. The second approach was to load each cable with a post- tensioning force in order to minimise their deformation in the neutral state (only loaded by self-weight). The problem is that the planned bridge curve is in no way symmetric, so each cable would need to have a unique post-tensioning force. They were modelled by applying an initial strain load (ε0[mm/m]) to each of the cables. The deformation was converted into stress according to Hooke’s law for linear elastic materials.

The balancing of the forces was attempted with the evolutionary solver Galapagos. In this case, the input parameters for the optimisation were the cable initial strain loads and the output was the maximum deformation of the bridge deck, as seen in Figure 6.31. The solver’s goal was to alternate the input parameters (the negative sign denotes tension) to arrive at the minimal possible umax.

Figure 6.31 Coupling Galapagos and Karamba for the evolutionary solving of post- tensioning forces in cables

For the purposes of analysing this approach, the test model with the geometry seen in Figure 6.32 was constructed. The portal frames were positioned at 25, 50, and 75%

of the bridge length. The materials used were S355 grade structural steel for the cables and the portal frames and GL32H glulam for the bridge deck. The connection between the cables and the deck was modelled with infinitely rigid members.

In Figure 6.33, the result of the analysis can be seen. The top part shows the defor- mation under self-weight when no post-tensioning forces are applied to the cables, and the bottom when the forces calculated with the Galapagos’ evolutionary optimisation are applied. The deformations are scaled a hundred times and are shown in purple, while the

Figure 6.32 Geometry of the cable-stayed test model used to analyse the effects of post-tensioning in cables

undeformed model is shown in green for comparison. Along with the deformations, the models show the axial load diagram on members (red - tension, blue - compression).

Figure 6.33 Comparison between cable-stayed test models before and after applying Galapagos to find post-tension forces in cables

Using this procedure, progress was beginning to show in the more complicated ap- plication of the cables into the Karamba algorithms. Although this is not an accurate approach regarding the cables, it at least enables the superstructure to be analysed for internal forces, moments, and deformations realistically, through the application of loads and load combinations. However, it should be pointed out that when more than one pair of cables is applied on each side of the portal frame, Galapagos analysis shows that some of them carry compressive forces. Although they get ignored in the subsequent analysis, it seems strange that a solution where all the cables are loaded with a tensile force is not found. On the other hand, the time it takes to run a Galapagos optimisation exponen- tially increases when more and more cables are added. Each cable is an additional input parameter in the gene pool.

Unfortunately, due to a lack of time, the cable-stayed solution was not investigated further, but at this level, the following can be concluded: the idea behind the imple- mentation of the parametric environments was to have an instant output of results that could be used for numerous configurations of the model. It hardly seems profitable then to have to run an evolutionary solver, which depending on the complexity of the model could run for several minutes or even hours.

Chapter 7

Additional Considerations

With the end of the previous chapter, the use of parametric environments for analysis came to a conclusion. A proposal for the bridge curve has been made and the relevant design values have been gathered. The next logical step in the project was therefore, to analyse the proposals made in the conceptual stage regarding the viability of the connection concepts. Following is the design of non-structural components, such as the balustrade and possible cladding.

7.1 Connections

When talking about connections, there are two distinct types to consider. First are the longitudinal connections, joining the individual prefabricated elements into the bridge superstructure, and the second, the connections of the superstructure with the supporting pillars. Both types however, have the same principles when designing their joints. The connecting member will in both cases be a multi-component joint made out of metal. It is not however the metal segment that is problematic when connecting timber elements, it is how this component is fixed onto the timber profile. Transferring the actions from the timber element to the steel connection means high local stresses, and depending on their orientation according to the timber grain, these can result in several failure mechanisms.

In connection viability considerations, it was therefore this part that was the subject of analysis. It has furthermore, been assumed that moisture induced variations in the massive block glulam section do not cause problematic internal stresses. The only stresses on the connecting members therefore, were the ones originating from the loading.

In Chapter 4, it has been established that perpendicular to grain resistance of timber is much lesser than that parallel to grain. While both types of connections transfer stresses perpendicular to grain, they act in different directions. Supporting the superstructure from bellow will mostly result in compressive, while the longitudinal connections will almost always have at least some degree of tensile perpendicular to grain stresses. The resistance of timber in the latter case is significantly smaller, which is why the longitudinal connections were taken as the basis for the validation calculations.

Principles of timber connection design are explained in standard EN 1995-1-1:2004 and EN 1995-2:2004 in the case of bridge elements. The design considerations in this project however, are related to massive glulam block sections, for which connections are

to find design solutions and analysis procedures regarding the approaches discussed in Chapter 5.

Glued-in rods

The first analysed connection type was the one where threaded metal rods are glued into the end of the timber member. This means that the rods are glued parallel to the grain, but loaded perpendicularly. The dominant failure mechanism in such connections will, in the majority of cases, be the embedment of the metal fastener into timber. This ductile-type failure, is normally followed by the splitting of the timber perpendicular to grain.

In order to determine the required distances between the rods (seen in Figure 7.1), and the design resistance of the connection, the German code DIN 1052:2004 was used.

Figure 7.1 Minimal distance between parallel to grain glued-in threaded rods loaded perpendicular to grain (taken from DIN 1052:2004)

The code states, that in rods glued-in parallel to grain, the characteristic value of the embedment strength (fh,1,k), shall be assumed as 10% of the corresponding value for rods glued perpendicular to grain (f_h,90,k). The following set of expression is therefore used to determine the characteristic embedment strength:

fh,1,k = 0,1·fh,90,k (7.1)

fh,α,k = f_h,0,k

k₉₀·sin²α+ cos²α (7.2)

fh,0,k = 0,082·(1−0,01d)·ρk (7.3)

k₉₀ = 1,35 + 0,15d (7.4)

where, α is the angle of action to the grain,ρ_k is the characteristic density of timber, andd is the diameter of the fastener. For the rod diameter, the code specifies a range be- tween 6 and 30mm. The final resistance of a single shear connection (R_la,k) is calculated with Eq. 7.5, according to the failure mechanism seen in Figure 7.2, using Johansen’s model (Blass and Sandhaas, 2017). The failure mechanism of a thick metal-plated con- nection predicts, that the embedment strength of timber will be reached and two plastic hinges will occur in the fastener.

R_la,k =p

M_y,k·f_h,1,k·d (7.5)

Figure 7.2 Failure mechanism of the steel-to-timber joint according to Johansen’s model (taken from Blass and Sandhaas (2017))

M_y,k is the characteristic yield moment of the fastener, which is for metal rods with a circular cross-section, according to DIN 1052:2004, obtained with the following expression:

M_y,k = 0,3·f_u,k ·d^2,6 (7.6)

Because the glued-in rods also experience an axial load, the pull-out resistance (R_ax,k) needs to be examined as well. This is obtained with the following set of equations:

Rax,k =min

(f_y,k·A_ef

π·d·l_ad·f_k1,k (7.7)

l_ad,min =max

(0,5d²

10d (7.8)

f_k1,k = 5,25−0,005l_ad (7.9)

where, f_y,k is the characteristic yield strength of the fastener, A_ef is the effective area of the threaded rod, and l_ad is the glued length of the rod.

The design values of the connection are calculated with Eq. 6.11, where the partial factor for material properties, in the case of connections, equals γ_M = 1,3 (EN 1995-1- 1:2004). The combined effect of lateral and axial action on the glued in rods is validated with the following expression:

F_la,d R_la,d

2

+

F_ax,d R_ax,d

2

≤1 (7.10)

It was found through these calculations, that the resistance of the shear connection is extremely small and not sufficient to withstand the stresses in the connections of the proposed models. This claim is backed by calculations, which can be seen in Appendix C.

Slotted metal plates with dowel connectors

The second examined approach consisted of slotted metal plates, connected with metal fasteners and inserted into the end grain of the timber element. The capacity of this connection was calculated based on the failure mechanisms of dowel-type steel-to-timber connections with two shear planes. In EN 1995-1-1:2004, the failure mechanisms seen in Figure 7.3. A thick metal plate was assumed (t_p > d).

Figure 7.3 Failure mechanisms of the dowel-type steel-to-timber joints in double shear (taken from EN 1995-1-1:2004)

The characteristic load-carrying capacity per shear plane per fastener according to these failure mechanisms is calculated with expressions 7.11 and 7.12 (in order of appear- ance in the figure). The contribution of the rope effect in dowels (F_ax,Rk), according to Johansen’s theory, was omitted from the expressions, because it equals zero.

• Steel plate of any thickness as the central member of a double shear connection (f, g, h):

F_v,Rk =min











fh,1,k·t1·d fh,1,k·t1·d·hq

2 + _f^4My,Rk

h,1,k·d·t²₁ −1 i 2,3p

My,Rk·fh,1,k·d

(7.11)

• Thick steel plates as the outer members of a double shear connection (l, m)

F_v,Rk =min

(0,5f_h,2,k·t₂·d 2,3p

M_y,Rk·f_h,2,k·d (7.12)

where, t_i is the thickness of the timber element, andf_h,i,k is its characteristic embed- ment strength. The design values of the connection are calculated with Eq. 6.11. In multiple shear plane connections, each shear plane is a part of a series of three-member connections. The total capacity is therefore obtained by multiplying the smallest per shear capacity with the number of shear planes (Blass and Sandhaas, 2017). This princi- ple is presented in Figure 7.4, whereF_v,1,Rd is the capacity per shear of a "t_o−steel−t_o"

connection,F_v,2,Rda "steel−t_i−steel" connection, andF_v,3,Rda "t_i−steel−t_i" connection (t_o is the thickness of the outer andt_i the inner timber member).

Figure 7.4 Calculating the capacity of a multiple shear plane steel plate connection (taken from MetsäWood)

Using this connection method with the dowel spacing rules presented in Figure 7.5, a functional connection was obtained. It was found that with a pair of slotted plates on each side of the beam, with 16 M30 dowels in each of them, the design loads are well within the resistance limits, as can be seen in the calculations in Appendix C.

Figure 7.5Minimal parallel and perpendicular to grain spacing for dowel-type connectors (taken from EN 1995-1-1:2004)

It should be pointed out that the connections in this chapter were only analysed in regards to the transfer of forces from timber to steel. This part was considered to be the most critical, while the actual steel segments (beyond the dowels), of this multi- component connection, were assumed to be functional by default. In order to actually construct the connections, these would have to be examined and dimensioned accordingly, but in this stage, the driving factor was the timber capacity. The final designed connection is presented in Figure 7.6.

Figure 7.6Final design proposal of the pinned connection with slotted metal plates and dowel-type fasteners (all measures are in cm)

7.2 Protection of the cross-section and balustrade

The design of the Breiðholtsbraut timber footbridge concluded with a segment on the protection of the cross-section and a concept for the design of the safety railing. It has been emphasised throughout this report, that durability protective measures in the form

of structural protection are one of the most important factors that determine the longevity of the structure. This is why it was ensured, during the design of the cross-section, that, as a bare minimum, the deck would provide a rain shield of at least 30^◦ to the main block glulam beam.

Furthermore, as an added bonus, the mono-axially curved bridge design creates a constant tilt in the bridge that ensures efficient run-off of water. If it proved necessary, due to the effects of the road traffic underneath the bridge, the entire cross-section could be enclosed with cladding. This would shield the bridge from any effects of water spraying and filth sticking to its underside, but would also somewhat spoil the overall appearance.

Being made of timber itself, the deck would need protective layers as well. It was already established, that the covering surface of the deck would be made of a bituminous layer acting as the hydrophobic barrier to the timber. Such layers can have issues bonding to the surface of the preservative treated glulam timber, but these are mainly present with higher lateral loads, such as for example breaking and accelerating of vehicles on heavy duty road bridges. As a result of the climate of the location, the topmost layer on the bridge surface would also be fitted with an anti-slip coating.

One of the most important parts of the bridge appearance is the balustrade. This is not only an aesthetic feature however. It primarily acts as the safety barrier, but can be incorporated in the form of parapet beams into certain structural systems as well. For that reason, a section in EN 1991-2:2003 discusses its loading scenarios and methods of analysis. In this project the balustrade had no structural function so it was not a subject of detailed research. For the purposes of model visualisation however, a concept was included.

The final cross-section proposal can be seen in Figure 7.7, along with the geometry, protective layers, and the balustrade design concept.

Figure 7.7 Final design proposal of the bridge cross-section (all measures are in cm)

Chapter 8 Conclusion

In this chapter, the concluding remarks are gathered, as well as the possibilities and pro- posals for future research in this specific topic and generative design algorithmic modelling in general.

8.1 Timber footbridge

During the project, a study has been made into the methods and principles applied in the earliest design stages of conventional design. The importance of individual parameters and distinct stages in the decision-making process have been outlined in a study of a tim- ber footbridge. It has been concluded that the nature of the curved bridge severely limits the possible applications of timber structural systems, demanding that unconventional structural components, methods, and considerations be used in its design. Nevertheless, a viable timber solution has been found for the alternative superstructure design of the concrete Breiðholtsbraut highway footbridge.

It has been proven through the use of Eurocode standards that with implementing the correct structural and preventative measures, the durability of the superstructure is competitive with that of exposed concrete and steel bridges. Furthermore, the initial misconception that the static height of the bridge profile would need to be significantly higher to account for the decrease in the rigidity of the system has been proven incorrect.

In fact, the proposed solution shows that the structure functions well within the limits of serviceability and ultimate limit states according to provisions of the Eurocode standards.

Although the lowest natural vibration frequencies were identified as a potential issue in the subsequent stages of the design, these are believed to be manageable through the use of well established engineering approaches. In retrospect, it has been shown that a timber design of the footbridge is a viable and arguably a preferable solution for not only the structural, but also logistical and environmental reasons.

8.2 Parametric modelling

In parallel with the conventional design methods was the application of generative para- metric algorithms in the computer aided design environment of Rhino’s plug-in Grasshop- per. Two distinct uses of these have been made in the project. The first was the creation

of parametrically driven visual models created purely for the graphic visualisation and communication of component concepts. The other more pronounced use was the creation of integrated dynamic models, which would by means of structural calculation, provide added value to the design procedure.

While the initial project goal was to establish an evolutionary algorithm, which would, on the same principles as described by Von Buelow (2012); Mueller and Ochsendorf (2013), provide a generative tool that would aid the designer in the choice of the structural system, this was proven to be completely unrealistic. The reasons for this are that the choice of a structural system can go into so many different ways, it would be impossible to define the input parameters of such an optimisation procedure. Furthermore, the question whether that would be practical in the first place is raised. Considering the process of the initial design explained in the conventional design part of the project, it is clear that the parameters influencing the decision-making process are so numerous and diverse that it would take an enormous effort to compare them and define their individual importance. At the same time, the "state-of-the-art" approaches in this field show that significant simplifications need to be made in order to even obtain some form of constructive results. Implementing this on the bridge, the size of the one in this project therefore proved to be impossible. It could, however, be done on a severely simplified two-dimensional representation of the model with only certain optimisation variables, but that would hardly be representative of the reality.

Nevertheless, integrated dynamic optimisation algorithms were implemented into the visual programming script in the form of simplified structural calculations. These were introduced at a later developed design stage, where the model was already defined enough to have the basic structural system, geometry, and components outlined. However, the program was created, in a way where all of these remained input variables which could be altered at any given time. Importance was put on the simplicity of the results of the automatic dynamic algorithms in order to be able to obtain instantaneous feedback of the proposal efficiency as the design space was explored. The results were therefore represented as utilisation values of the design according to calculation procedures defined by the Eurocode standards. The utilisation values were presented for the ultimate as well as serviceability limit states based on the load combinations defined by the user.

It has been proven through validation examples that the parametric structural en- gineering tool Karamba can be used with sufficient accuracy with timber, even though it has primarily been made for concrete and steel materials. Nonetheless, it showed significant setbacks and limitations in this regard as well. Because there are no native cross-sections for timber elements in the program, these need to be modified from steel or concrete ones. This limits the analysis to a small range of profile possibilities, and even those need to be double-checked in order to prove that they behave correctly. Fur- thermore, the extent of the use of Karamba with timber structures was the output of the internal forces, moments, deflections, and natural frequencies, which is why in order to obtain the mentioned utilisation results, these needed to be processed through additional user-defined algorithms.

The downsides of this entire procedure is the shear amount of time it takes to create an integrated dynamic algorithm. During the modelling, a large number of components had to be specifically made for the use with this particular project. And while the parametric scripts were written with the possibility of reuse in mind (and were reused for

the purposes of a cable-stayed alternative to the girder beam bridge), it is questionable how useful they would be on structural forms with more significant differences such as the truss- or an arch-type system. However, if enough time was invested into the creation of a larger component library which would cover all structural systems of bridges, the reuse of components on further projects would be a considerable advantage.

In conclusion, the use of parametric environments does add value to the design process in a way where the project has a better definition of the feasibility during the transition into the detailed stage, but the use of these tools is not economically justified in the earliest pre-conceptual design stages, where the design freedom is too great and the design is subject to very rapid and significant changes.

8.3 Future work

As explained in Chapter 3, the most important aspect of computational design tools created for the early design, apart from a comprehensive output of results, is a user- friendly graphical interface. The script created for the purposes of this thesis is in no way a simple and user-friendly way of operating the algorithms. Therefore, for this script to be useful for anyone else but the author, it would need to be thoroughly restructured, and transformed so that the only instance of the script the user would be exposed to would be the input parameter panel, a visual viewport of the resulting model, and the numerical result panel. In this way, even individuals with limited or no knowledge of visual programming in parametric environments would be able to benefit from the use of the program.

Along with this, the obvious topic for further research is the implementation of other structural systems in order to construct a framework for the design freedom beyond just a single type of structural form. But such research will not be economically profitable until the tools for analysis within the parametric environments reach a level of complexity and accuracy where the designer can use them with the same degree of certainty as a commercial software, the likes of RFEM.

Bibliography

Aicher, S. and G. Stapf

2014. Block glued glulam–bridges, beams and arches. World Conference on Timber Engineering, Quebec City, Canada.

Almegaard, H.

2016. Lecture notes 11995 Design - theory and methods E16: What is engineering design? DTU - Technical University of Denmark.

Architizer, Inc

n.d. Anaklia-Ganmuhkuri Pedestrian Bridge. https://architizer.com/projects/

anaklia-ganmuhkuri-pedestrian-bridge/(accessed 20.11.2017).

ASTM International

2012. ASTM D9-12, Standard Terminology Relating to Wood and Wood-Based Prod- ucts. ASTM International, West Conshohocken, PA.

Bengtsson, C. and C. Johansson

2002. GIROD: Glued in Rods for Timber Structures, SP rapport. Sveriges provnings- och forskningsinstitut (SP).

Billington, P. N., H. Shirley-Smith, and D. P. Billington

2017. Bridge-engineering. Encyclopædia Britannica. https://www.britannica.com/

technology/bridge-engineering (accessed 20.10.2017).

Blass, H. and C. Sandhaas

2017. Timber Engineering - Principles for Design:. KIT Scientific Publishing.

Broer.no

n.d. Flisa Bru. http://broer.no/bro/index.php?ID=63 (accessed 20.11.2017).

Brown, N., J. De Oliveira, J. Ochsendorf, and C. Mueller

2016. Early-stage integration of architectural and structural performance in a para- metric multi-objective design tool. In International Conference on Structures and Ar- chitecture.

Christer, S.

2017. Personal correspondence with Steve Christer of Studio Granda.

Crocetti, R.

2016. Large-span timber structures. In key-note paper, Proceedings of the World

Congress on Civil, Structural, and Environmental Engineering (CSEE’16) Prague, Czech Republic.

Davidson, S.

2014. Grasshopper3D: Algorithmic Modeling for Rhino (Version August-27, 2014).

[Computer software: plug-in] Obtained from: http://www.grasshopper3d.com/page/

download-1.

DIN 1052-10:2012

2012. Herstellung und Ausführung von Holzbauwerken - Teil 10: Ergänzende Bestim- mungen (Design of timber structures - Part 10: Additional provisions). Standard, DIN - Deutsches Institut für Normung.

DIN 1052:2004

2004. Entwurf, Berechnung und Bemessung von Holzbauwerken - Allgemeine Bemes- sungsregeln und Bemessungsregeln für den Hochbau (Design of timber structures - General rules and rules for buildings). Standard, DIN - Deutsches Institut für Nor- mung.

Dlubal Software GmbH

2016a. Add-on Module RF-DYNAM Pro. https://www.dlubal.

com/en/products/rfem-and-rstab-add-on-modules/dynamic-analysis/

rf-dynam-pro-equivalent-loads.

Dlubal Software GmbH

2016b. RFEM 5 (Version 5.12.01). [Computer software] Obtained from: https://www.

dlubal.com/en.

Dlubal Software GmbH

2017. Personal correspondence with the support team of Dlubal.

EN 14080:2013

2013. Timber structures - Glued laminated timber and glued solid timber - Require- ments. Standard, CEN - European Committee for Standardisation.

EN 1990:2002

2007. Eurocode - Basis of structural design. Standard, CEN - European Committee for Standardisation.

EN 1990:2002/A1:2005

2005. Eurocode - Basis of structural design (annex to EN 1990:2002). Standard, CEN - European Committee for Standardisation.

EN 1991-1-1:2002

2002. Eurocode 1: Actions on structures - Part 1-1: General actions - Densities, self-weight, imposed loads for buildings. Standard, CEN - European Committee for Standardisation.

EN 1991-1-3:2003

2003. Eurocode 1: Actions on structures - Part 1-3: General actions - Snow loads.

Standard, CEN - European Committee for Standardisation.

EN 1991-1-4:2005

2005. Eurocode 1: Actions on structures - Part 1-4: General actions - Wind actions.

Standard, CEN - European Committee for Standardisation.

EN 1991-2:2003

2003. Eurocode 1: Actions on structures - Part 2: Traffic loads on bridges. Standard, CEN - European Committee for Standardisation.

EN 1992

2004. Eurocode 2: Design of concrete structures. Standard, CEN - European Commit- tee for Standardisation.

EN 1993

2004. Eurocode 3: Design of steel structures. Standard, CEN - European Committee for Standardisation.

EN 1995-1-1:2004

2004. Eurocode 5: Design of timber structures - Part 1-1: General - Common rules and rules for buildings. Standard, CEN - European Committee for Standardisation.

EN 1995-2:2004

2004. Eurocode 5: Design of timber structures - Part 2: Bridges. Standard, CEN - European Committee for Standardisation.

EN 301:2013

2013. Adhesives, phenolic and aminoplastic, for load-bearing timber structures. Clas- sification and performance requirements. Standard, CEN - European Committee for Standardisation.

EN 335:2013

2013. Durability of wood and wood-based products - Use classes: definitions, applica- tion to solid wood and wood-based products. Standard, CEN - European Committee for Standardisation.

EN 350:2016

2016. Durability of wood and wood-based products. Testing and classification of the durability to biological agents of wood and wood-based materials. Standard, CEN - European Committee for Standardisation.

Epp, G., A. Gerber, and L. Epp

2013. Footbridge over the bow river in banff. Proc. 2nd International Conference on Timber Bridges (ICTB2013 - Las Vegas, September 30 - October 3, 2013). WoodWorks - Wood Products Council.

Ferguson, I.

1997. Environmental Properties of Timber. Forest & Wood Products Research &

Development Corporation, Bond University.

Forest Products Society and Forest Products Laboratory (U.S.)

2010. Wood Handbook: Wood as an Engineering Material, General technical report FPL. Forest Products Society.

Franke, B., R. Widmann, A. Müller, and T. Tannert

2013. Assessment and monitoring of the moisture content of timber bridges. In Pro- ceedings international conference on timber bridges, Las Vegas.

Frazer, J.

2016. Parametric computation: History and future. Architectural Design, 86(2):18–23.

GLTA

2014. Glulam Production. Glued Laminated Timber Association. http://www.

glulam.co.uk/about_production.htm (accessed 25.10.2017).

GLTA

2014. Introducing Glulam. Glued Laminated Timber Association. http://www.

glulam.co.uk/introducingGlulam_specificationhints.htm(accessed 5.10.2017).

Google

2013. Google Street View images of the Breiðholtsbraut highway. https://www.

google.dk/maps/@64.1007679,-21.8309464,16.25z (accessed 20.12.2017).

Jiang, X., K. Tanaka, and M. Inoue

2012. Strength properties of gir (glued-in-rod) joint system subjected to shearing and tensile force. InBiobase Material Science and Engineering (BMSE), 2012 International Conference on, Pp. 297–301. IEEE.

Kuklik, P. and A. Hansen

2008. Handbook 2 - Design of Timber Structures According to EC 5. Leonardo da Vinci Pilot Project.

Linville, J. D.

2012. Timber Construction Manual, sixth edition. John Willey & Sons.

MetsäWood

2013. Kerto manual - bolted connections. https://www.metsawood.com/global/

Tools/kerto-manual/Pages/Kerto-manual.aspx(accessed: 4.12.2017).

Mettem, C.

2013. Timber Bridges. Taylor & Francis.

Miebach, F.

2011. Sneek bridges show potential of timber. Structural Engineering & Design, 12(5):15–19.

Mueller, C. and J. Ochsendorf

2013. From analysis to design: A new computational strategy for structural creativity.

InProceedings of the 2nd International Workshop on Design in Civil and Environmental Engineering, Worcester, Massachusetts, USA, 28-29 June 2013. Worcester Polytechnic Institute (WPI).

Negendahl, K.

2015. THE STED NETWORK - Sustainable Transformation and Environ- mental Design Network. http://stednetwork.org/index.php?p=/article/2015/

what-is-sted (accessed 15.12.2017).

Negendahl, K., T. R. Nielsen, and O. Schrøder

2016. Consequence Based Design. An approach for integrating computational collabo- rative models (Integrated Dynamic Models) in the building design phase. PhD thesis, Technical University of Denmark, Department of Civil Engineering.

Nordic Innovation

2012. Nordic Built - Joining forces for a sustainable built environment. http://www.

nordicinnovation.org/nordicbuilt/ (accessed 15.12.2017).

Opačić, M.

2017. Individual course report - Structural analysis during erection of a structure.DTU - Technical University of Denmark. Unpublished.

Preisinger, C.

2016. Karamba User Manual for Version 1.2.2. http://www.karamba3d.com/news/

new-manual/.

Preisinger, C.

2017a. Karamba3D: Parametric Engineering (Version 1.3.0 - Unreleased). [Computer software: add-on] Obtained from: https://www.rhino3d.com/.

Preisinger, C.

2017b. Personal correspondence with Clemens Preisinger of Karamba3d.

Ritter, M.

1990. Timber Bridges: Design, Construction, Inspection, and Maintenance. Datamo- tion Publishing LLC.

Robert McNeel & Associates

2014. Rhinoceros: Modeling Tools for Designers (Version 5.0). [Computer software]

Obtained from: https://www.rhino3d.com/.

Rolvink, A., J. Coenders, and C. Mueller

2014. State on the art of computational tools for conceptual structural design. In Proceedings of the IASS-SLTE 2014 Symposium" Shells, Membranes and Spatial Struc- tures: Footprints", Brasilia, Brazil, 15-19 September 2014. International Association for Shell and Spatial Structures (IASS).

Rutten, D.

n.d. Galapagos Evolutionary Solver. [Computer software: add-on] Obtained from:

http://www.grasshopper3d.com/group/galapagos.

Schumacher, P.

2009. Parametricism: A new global style for architecture and urban design. Architec- tural Design, 79(4):14–23.

Sétra

2006 (2007). Timber bridges: How to ensure their durability. Technical guide SETRA, Paris, France.

Simon, A. and J. Koch

2016. The new generation of timber bridges–durable by protection. World Conference on Timber Engineering, Vienna, Austria.

Steiger, R., E. Serrano, M. Stepinac, V. Rajcic, C. O’Neill, D. Mcpolin, and R. Widmann 2015. Reinforcement with glued-in rods, Pp. 133–159. Shaker.

Structurae

2005. Crest - Pont de bois - Vue de la sous-face du tablier et des bracons sur ap- pui. Photo: Jacques Mossot. https://structurae.info/ouvrages/pont-de-bois (accessed 21.11.2017).

Structurecraft

2016. Bow River Pedestrian Bridge, Banff. Photo: Paul Zizka. https:

//structurecraft.com/projects/bow-river-pedestrian-bridge (accessed 20.11.2017).

Thelandersson, S. and H. Larsen

2003. Timber Engineering. John Wiley & Sons.

Thompson, M.

2009.Guide to Bridge Technology Part 5: Structural Drafting. Austroads Incorporated.

Tlustochowicz, G., E. Serrano, and R. Steiger

2011. State-of-the-art review on timber connections with glued-in steel rods. Materials and structures, 44(5):997–1020. Springer.

Von Buelow, P.

2007. Advantages of evolutionary computation used for exploration in the creative design process. Journal of Integrated Design and Process Science, 11(3):5–18.

Von Buelow, P.

2012. Paragen: Performative exploration of generative systems. Journal of the Inter- national Association for Shell and Spatial Structures, 53(4):271–284.

Wikimedia Commons

2005a. Da Vinci Bridge. Photo: Åsmund Ødegård. https://commons.wikimedia.

org/wiki/File:Da_Vinci_Bridge.jpg (accessed 20.11.2017).

Wikimedia Commons

2005b. Holzbrücke bei Essing 1.jpg. Photo: Brego. https://commons.wikimedia.

org/wiki/File:Da_Vinci_Bridge.jpg (accessed 20.11.2017).

Zwierzycki, M.

2015. Anemone (Version 0.4 Fourth release). [Computer software: add-on] Obtained from: http://www.food4rhino.com/app/anemone.

ÍST EN 1991-1-4:2005/NA2010

2010. National Annex to Eurocode 1: Actions on structures - Part 1-4: General actions - Wind actions. Standard, Iceland’s Standards Council.

Appendices

Appendix A

Design sketches, concepts and notes

Appendix B

Grasshopper scripts

Appendix C

Connection calculations

DIN 1052:2004-08

12 Connections with pin shaped metallic fasteners

Calculating the capacity of parallel to fibre glued in rods which are loaded perpendicularly Using glued-in rod fasteners of size M30 and grade 8.8

ρk 440 kg m³

 fuk 800 N

mm²

 d30mm

14.3.2 Stress perpendicular to rod axis

fh0k 0.082 1 0.01 d

mm

 

 

 ρk

kg m³

 N

mm²

 25.256 N

mm²





 (203)

k90 1.35 0.015 d

mm

 1.8

 α90deg (204)

fh90k fh0k

k90 sin ( )α²cos( )α²

14.031 N mm²





 (202)

fh1k 0.1 1.25 fh90k 1.754 N mm²





 fh2kfh1k (14.3.2 (5))

β fh1k fh2k 1



Myk 0.3 fuk d

mm

 

2.6

 mm³1.66210⁶N mm

 (208)

The calculated embedment capacity of one glued-in rod loaded perpendicular to grain is:

kmod 0.9 γM1.3

Rlak 2β

1β 2 Myk fh1kd13.226 kN

 (191)

ΔRlak 0.25 Rlak  3.307 kN (209)

Rlad





11.446 kN



 (195)

Limiting distances for rods glued parallel to fibre and loaded perpendicular

Embedment strength according to Johansen equations for steel-to-timber joints with thick steel plates

Reference: Blass, H.J. (2017), Timber Engineering - Principles for Design E2.4 failure mechanism E

b1 4 Myk fh1k d

 0.355 m



FvRk fh1k d  b118.705 kN

FvRd FvRk kmod γM

12.95 kN





14.3.3 Stress in the direction of the rod axis

fyk 640 N mm²



Aef π d

2

 

2

 706.858 mm ²



lad max 0.5 d²

mm10d







^{0.45 m}

 (277)

fk1k 5.25 0.005 lad

mm

 







N mm²

 3 N

mm²





 (Tabelle F.23)

The calculated capacity of one glued-in rod loaded parallel to grain is:

Raxk min fyk Aef^





Raxd Raxk kmod γM

88.085 kN





14.3.4 Combined axial and perpendicular to rod stress

(279)

DS/EN 1995-1-1 + AC:2007

8.2 Lateral load-carrying capacity of metal dowel-type fasteners 8.2.3 Steel-to-timber connections (double shear plane)

Using dowel type fasteners of size M30 and grade 8.8

t1150mm t2150mm d30mm

ρk 440 kg m³

 fuk 800 N

mm²



fh1k 0.11 1 0.01 d

mm

 

 

 ρk

kg m³

 N

mm²

 33.88 N

mm²





 fh2kfh1k

MyRk 0.3 fuk d

mm

 

2.6

 mm³1.66210⁶N mm

 ...(expression for bolts?)

FaxRk0kN ... contribution to the Johansen part in dowels is 0%

Steel plate of any thickness as the central member of the double shear connection:

(f) FvRk.ffh1k t1 d152.46 kN

(g) FvRk.g fh1k t1 d 2 4 MyRk fh1k t1 ²d

 1









 FaxRk

 4 173.212 kN



(h) FvRk.h 2.3 MyRk fh1k d FaxRk

 4 94.542 kN



Thin steel plate as the outer members of a double shear connection:

(j) FvRk.j0.5 fh2k t2d76.23 kN

(k) FvRk.k 1.15 2 MyRk  fh2kd FaxRk

 4 66.851 kN



Thick steel plate as the outer members of a double shear connection:

(l) FvRk.l0.5 fh2k t2d76.23 kN

(m) FvRk.m 2.3 2 MyRk  fh2kd FaxRk

 4 133.702 kN



Considering, that the thin steel plate failing (k) on both sides of the member is the critical failure mechanism, the thickness of the steel plate will be t.s>d (>30mm). This makes the critical mechanism (j/l) which is the embedment of the steel dowel into timber.

FvRk FvRk.j 76.23 kN  

According to linear interpolation between the thin (k) and thick (m) plate failure mechanism, the thickness of the plate should be 0.57d to make the failure mechanism (j/l).

0.5 FvRk.j FvRk.k

 0.57

The calculated capacity is that of one shear plane in one stiffner. Since, there are 2 shear planes per each stiffner, this should be factored!

kmod 0.9 γM1.3

FvRd FvRk kmod γM

52.775 kN





Rvd 4 FvRd  211.098 kN

Reference: Blass, H.J. (2017), Timber Engineering - Principles for Design E15 Joints with multiple shear planes

Limiting distances for dowel type fasteners perpendicular to grain

E11 Joints loaded perpendicular to grain

Reference: Blass, H.J. (2017), Timber Engineering - Principles for Design

Appendix D

Plans and views of the bridge design

proposal