IMPLEMENTATION OF DISPLACEMENT-BASED DESIGN PHILOSOPHY FOR BRIDGES IN A CHALLENGING SEISMIC AND GEOTECHNICAL ENVIRONMENT

Transcription

1 IMPLEMENTATION OF DISPLACEMENT-BASED DESIGN PHILOSOPHY FOR BRIDGES IN A CHALLENGING SEISMIC AND GEOTECHNICAL ENVIRONMENT Anton Kivell 1, Caudillo Aguas 2, Ronald Wessel 3, Jamil Khan 4, Geoff Brown 5 ABSTRACT: The draft form of the NZTA (New Zealand Transport Agency) Bridge Manual Appendix on Displacement-based Design for bridges has been used in the design of the bridges along the MacKays to Peka Peka Expressway (M2PP). This has been done in close interaction with the NZTA to clarify and refine the document prior to its formal release. The Displacement-based Design (DBD) approach required interaction with the technical staff at the NZTA national office and implementation of the draft Displacement-based Design guidelines for the 3 rd Edition of the NZTA Bridge Manual. The displacement-based approach allowed for more in-depth analysis of the proposed structures and an improved understanding of their inelastic seismic behaviour, particularly when interacting with poor soil conditions. This allowed for greater confidence in the seismic performance in a ULS event than would be provided by a traditional force-based design approach (FBD). This paper will discuss the approach to seismic bridge design for M2PP using Displacement-based Design methods and how the challenges described above were overcome. KEYWORDS: Seismic, Displacement based design, Bridges 1 Anton Kivell, Structural Engineer, Beca Ltd. Anton.Kivell@beca.com 2 Cauldillo Aguas, Structural Engineer, Beca Ltd. Caudillo.Aguas@beca.com 3 Ronald Wessel, Senior Bridge Engineer, Beca Ltd. Ronald.Wessel@beca.com 4 Jamil Khan, Associate - Structural Engineering, Beca Ltd. Jamil.Khan@beca.com 5 Geoff Brown, Technical Director Bridging, Beca Ltd. Geoff.Brown@beca.com

2 1 INTRODUCTION While Displacement-Based Design (DBD) is not a new design methodology, it is only now starting to be implemented in industry. DBD has been said to allow for improved efficiency in design and allows for better prescription of performance levels. However, the economic competitiveness of displacement-base against Force-based design came into question on the MacKays to Peka Peka Expressway Alliance (M2PP). Inherent differences between the two methodologies (FBD and DBD), and inconsistencies in their treatment of near-fault effects and acceptable strain limits caused difficulties in justifying the use of DBD on this project. Through extensive interaction with the NZTA s technical staff, and clarification of the draft displacement based design appendix for the NZTA Bridge Manual [1], a design methodology was produced using displacement based design philosophies that could be used in the design of the bridge for M2PP. This paper outlines this methodology and its development throughout the project. 2 PROJECT BACKGROUND The MacKays to Peka Peka section of the SH1 - Wellington Northern Corridor Road of National Significance (RoNS) passes through the Kāpiti Region, 60km north of Wellington, New Zealand and will be built to expressway standards i.e. four-lane, median divided. The project will be delivered by a consortium (the MacKays to Peka Peka Expressway Alliance) formed of NZ Transport Agency (NZTA), Fletcher Construction, Higgins Contractors and Beca. The seven RoNS projects are based around New Zealand's five largest population centres. The focus is on moving people and freight between and within these centres more safely and efficiently. The RoNS are lead infrastructure projects that is, they enable economic growth rather than simply responding to it. The purpose of the SH1 Wellington Northern Corridor improvements is to improve the efficiency of State Highway traffic to and from Wellington CBD, port and airport and improve the resilience of the primary link to Wellington. The key post-disaster role of the Expressway is to provide a modern and reliable crossing over the Waikanae River. In addition to the 182m long Waikanae River crossing, 16 other bridges are to be constructed, crossing local roads and waterways. The challenges associated with this project are considerable and unique compared to many other bridge projects in New Zealand. The high seismicity of the Kāpiti coast, combined with a ULS design return period of 2,500 years, produces design peak ground accelerations of up to 0.98g. To compound this, most of the route is on poor soils which are expected to liquefy under approximately a 1/250 year event to depths of 6-12m. Combined, these factors have forced innovation, and adoption of advanced design procedures and technology, to overcome the extreme demands placed on these structures. 3 DISPLACEMENT BASED DESIGN The formulation for the Displacement-base Design methodology is collated from wider research in Displacement Based Design of Structures, by Priestley, Calvi and Kowalsky [2]. In this book, the limitations, variation and inadequacies of the traditional Force-based design methodology are outlined and explained in depth, and a design philosophy based on calculation of the required lateral resistance to achieve a predetermined displacement is proposed. The predetermined displacement is based on the damage limits deemed to be acceptable for each level of design limit state and are often defined by material strain limits, or limits required by non-structural components of the structure. This methodology does not require an assumption around the structural ductility to allow implementation of the equal displacement or equal energy assumptions used in force based methods. Rather, the ductility of individual inelastic components in the structure are determined at the required design limits states. The damping for these elements is determined depending of the structural material/arrangement of the elements and then, based on the individual contribution to resisting base shear and displacement participation, the damping of the whole system is calculated. A quick calculation method for this process, based on structural ductility, is presented by Priestley et al.[2] for common structural system. A key assumption of displacement-based design is that the component yield displacement is independent of the strength of the component, and dependent solely on the element s geometry. This is inconsistent with the approach of using cracked section properties based on the section s gross section dimensions to calculate element stiffness, as used in force-based design methods. There are a number of inconsistencies between the two methods which raise issues around the efficiency of design, these which will be discussed later in this paper. Priestley et al. [2] present a displacement-based design method called Direct Displacement-Based Design in which the structure is converted to a single degree of freedom system with equivalent mass and height. Based on the yield displacement and allowable ultimate displacement, the structural ductility is calculated and the using the appropriate structural system formula, the system damping determined. Using the ultimate displacement and effective mass, the effective (inelastic) structural period is calculated, then from this and the

3 structural damping, the design acceleration can be derived. This process is shown visually in Figure 1 in a diagram taken from Priestley et al. [2]. From the effective mass and the design acceleration, a base shear is then calculated and distributed appropriately over the structure. equivalent spectral displacement was calculated and then both values plotted against each other. The acceleration, and subsequent displacement, were scaled by the damping scaling factor, which will be explained later in this paper. The demand curve defines the base shear resistance required for a given ultimate structural displacement for a given level of damping. It forms a design envelope with which the required design acceleration can be read off of any given displacement. 4.1 Rigid Foundations For a ridged foundation the displacement capacity at ULS can be determined by identifying the desired plastic mechanism and calculating the plastic hinge rotation capacity based on the strain limits in the Draft DBD7 [1]. The yield deflection is then added to this to give the ultimate deflection. These two parameters also allow calculation of the element s ductility and thus corresponding damping. This process can be undertaken simply by hand or spreadsheet allowing for rapid iteration of designs. Figure 1: Direct Displacement-Based Design Design example, Source: Priestley et al. [2]. Figure 2 shows an example of such a plotted pushover curve (in blue). This example has been overlaid with the 5% damping acceleration-displacement curve which indicates the spectral acceleration-displacement envelope (demand). 4 M2PP SEISMIC DESIGN PHILOSOPHY The seismic design of the M2PP bridges followed the recommendations in the Draft Amendment to the Bridge Manual "Proposed Provision for Deflection-Based Design", (Draft DBD7) dated 23 rd February 2013 [1] with agreed modifications. This methodology largely follows the proposed approach by Priestley et al. "Displacement- Based Seismic Design of Structures"[2]. Slight modifications were made to the application of the displacement-based, or deflection-based, approaches to improve the design process. While the final method is based around displacement-based design principals, the design itself is not initially based on a specific displacement limit. This is due to the significant influence of foundation flexibility on the structural displacement. To account for this highly non-linear foundation behaviour, pushover analysis of prospective designs were combined with the spectral acceleration-displacement demand curve. This methodology follows the assessment approach used in NZSEE Guidelines [3]. The demand curve is derived from the demand spectra provided from a site specific seismic hazard study undertaken for the project area. From this spectra the Figure 2: Example pushover design showing the unmodified 5% damping demand curve (dashed), the damping reduced curve for 15.5% damping demand curve, and a pushover curve in dark blue. Through the process outlined in DBD7 [1], based on the damping contribution from each yielding element, the structural damping was calculated at 15.5%. This reduced the demand curve in both acceleration and displacement. If in the example pushover curve, the critical structural element was to reach its material strain limit in its critical element at Point 1, then its design would be said to be inadequate and would require revision to either improve

4 its strength or displacement capacity. At Point 2, the structure meets the demand curve and so its design is adequate, and at Point 3 the design exceeds the demand spectra and so the design is also adequate, but may be reduced to meet the demand spectra if required. 4.2 Flexible Foundations The foundation system at the pier locations for the M2PP bridges were deep concrete bored piles. This foundation system was adopted due to the liquefaction risk and the poorer soil in the upper levels. These piles ranged in diameter from 2.1m to 3.0m with lengths ranging from 20m to 42m. The bored piles were heavily reinforced with reinforcement contents nearing the allowable limits in NZS3101:2006[4]. Early analysis showed that the pile displacements contributed significantly to the overall lateral displacements, with approximately half the displacement being attributed to foundation deformation. The displacement of the bridge is made up of three primary components which are shown in Figure 3. The first of these is the elastic displacement of the piers, which is added to by their plastic displacement once yielding of the pier occurs. The pier is supported by the foundation, the top of which displaces under lateral loading and also rotates, resulting in additional displacement of the centre of mass of the structure. At yielding of the pier, the yield displacement of the pier is added to the foundation contribution and further displacement is only gained through inelastic pier deformation. Figure 3: Combination of Pier and Pile behaviour. Unlike other structural elements, where forcedisplacement characteristics can be easily calculated from the DBD7 formula, pile behaviour is highly non-linear and dependent on the soil properties. Furthermore, damping of piles is dependent on soil characteristics and differs from other components. For these reasons it was advantageous to separate the pile deformation contribution from that of the piers, abutments and bearings. The pile analysis program LPILE [5] was used to determine the force-displacement and moment-rotation characteristics of the pile head. LPILE is primarily a geotechnical software package that develops a multispring model of the pile and its surrounding soil. It has a comprehensive suite of soil models and is able to determine moment-curvature behaviour of reinforced concrete sections. Furthermore, LPILE allows moment-curvature relationships to be input or imported from other sources. The section designer from SAP2000 allowed for calculation of the moment-curvature behaviour of the bored piles with the inclusion of the strain limits provided in DBD7 and allowance for confined and unconfined concrete characteristics. These relationships were used in the pile head pushover analyses undertaken in LPILE that were used to determine the characteristics for the pile head springs. Combination of the rigid foundation methodology and the pile head spring was done in a spreadsheet where the pile head deformation varied with applied shear and moment in accordance with a regression curve through the pile head data point. The spreadsheet calculated the global structural damping, damped demand curve, pier displacement, pile displacement and any other deformations (bearing or abutments etc.), depending on the pier s design moment capacity, producing a pushover curve for the structure. Once created and relevant parameters provided, determination of the design moment demand simply required increasing of the pier s capacity until the pushover curve (capacity curve) exceeded the spectral acceleration-displacement demand curve as shown in Figure Abutment Form The site conditions provided a further challenge at the abutments. The high ULS ground accelerations combined with poor soil conditions results in loss of embankment stability under even moderate levels of shaking. The extent of ground improvement required to stop permanent embankment deformation was considered not economically viable. As a result, embankments were designed to deform under ground shaking. This deformation was limited to control plastic rotations developed in the abutment steel H-piles at depth. Early analysis revealed that the abutments would be unable to sustain the combined effects of deck inertial motions and embankment displacement in the longitudinal direction. As a result of this it was decided

5 DSF that the bridge deck would not be restrained at the abutments in the longitudinal direction, hence it is designed to slide on the abutments. This placed a higher demand on the bridge piers as they were the sole system resisting lateral loads. 4.4 Modification of the Damping Scale Factor For damping greater than 5%, the displacement spectrum may be reduced by the damping scale factor (DSF) the formulation of which is shown below. DSF = M = (0.07 / ( sys)) α This factor is to be applied to the elastic displacement spectrum. Where α is the damping scale exponent. α = was used for stiff non-liquefied conditions, assumed to coincide with near fault behaviour, and α = 0.50 for nominal/ liquefied conditions. The need to differentiate between various alpha values is derived from the draft amendment DBD7 [1]. Within 10km of a known active fault, where forward directivity is considered likely, an alpha value of 0.25 instead of 0.5 is suggested, lowering the effectiveness of structural damping. It is assumed that the forward directivity pulse associated with near fault shaking is limited to the initial stages of shaking. At this time it was assumed that vulnerable soil layers would not have developed sufficient build-up of pore water pressure to induce liquefaction. It was further assumed that by the time pore water pressure has built up to a significant level to liquefy vulnerable soil layers, pulse loading had ceased. The NZTA has been made aware of a report published by the Pacific Earthquake Engineering Research Centre (PEER) [6] which was used to determine the Damping Scaling Factor (DSF) based on earthquake magnitude, structural period, distance to fault and level of damping, instead of assuming a value which is stated to be conservative in the commentary of the Draft DBD7 [1] DSF α = 0.5 α = Period 2 3 Figure 4: Comparison of Damping Scale Factors (DSF) from the PEER Report 2012/01 Figure 4 compares the DSF based on the method described in the PEER report, using the relevant values for the M2PP project, with the DSF values suggested in DBD7. In the light of this report, the Site Specific Seismic Hazard Analysis (SSSHA) report and further consultation with the NZTA an intermediate alpha value of was agreed to be acceptable for capturing the impact of near fault effects on the effectiveness of structural damping for this project. It is interesting to note that inclusion of near-fault effects would not have been required if the design had been carried out using NZS1170.5:2004 [7] due to the elastic periods of the bridges never exceeding 1.5 seconds. 4.5 Plastic Hinging Below Ground Level The Draft DBD7 [1] states that for seismic design based on ductile response, plastic hinges shall be at locations accessible for inspection or repair. It was agreed with NZTA, plastic hinge locations below ground will be allowed as per the Bridge Manual [8]. Design of the steel H-piles at bridge abutments was based on allowable rotations in plastic hinges to NZS3404:1997 [9], as opposed to limiting rotations to ductility = 3, which is stated for structures with hinges below ground as required by the Bridge Manual. This ductility limit is implied for structures where the plastic hinges below ground will sustain repeated inelastic cyclic loading. The primary source of deformation for the abutment piles is embankment failure which is a monotonic deformation. Following a ULS event it is expected that the piles will be deformed but will retain their vertical load carrying capacity. Vertical capacity was ensured by limiting plastic hinge rotations to those in NZS3404:1997. Under ULS shaking, hinging of the concrete pier piles is likely under liquefied conditions. An agreement was reached with NZTA related to the performance criteria of

6 sub-soil plastic hinges that are inaccessible for repair or inspection. The design conditions were that steel strains must be kept to less that ε s = and that concrete strain be kept to below ε c = These limits are more stringent than those for above ground plastic hinges and more stringent than those in NZS3101:2006. However, Priestley et al. [2] allows for a longer plastic hinge length in pile/column scenarios. Equation 1 is outlined in Figure 5 with the equation for the plastic hinge length of inground pile/column plastic hinges and description of parameters. to combine the orthogonal actions. Through implementation of this, M2PP bridges were essentially designed for 105% of seismic loading in all directions. ((100% 2 +30% 2 ) 1/2 = 104.4%. The spectral accelerationdisplacement envelope was scaled by 104.4% and rotated about the acceleration axis to the required direction of assessment. A visual representation of the SRSS design spectra envelope used is shown in Figure 6. LP = D +0.1(H-HCP) 1.6D (1) Figure 6: Combination of orthogonal actions using the SRSS rule. Figure 5: Plastic hinge length for column/piles used for inground plastic hinges, Source: Priestley et al. [2] 4.6 P-Delta Effects DBD7 [1] recommended for reinforced concrete elements, that the flexural demand was increased by 50% of the calculated P-Delta moment when the P-Delta moment exceeded 5% of the pier-base moment capacity. If the P-Delta moment was less than 5% of the moment capacity, then P-Delta effects were ignored. P-Delta moments were kept below 30% of the pier-base moment capacity. 4.7 Combined Transverse and Longitudinal Seismic Action It was agreed with the NZTA that a combination of the orthogonal seismic actions would be undertaken in accordance with the Bridge Manual [8] i.e.: 100% transverse + 30% longitudinal, and 30% transverse + 100% longitudinal However, this methodology did not translate into the displacement based methodology where elements are expected to exceed their flexural moment capacity and deform plastically. Hence, to allow for this the SRSS (Square Root of the Sum of the Squares) method was used 5 COMPARISON WITH TRADITIONAL FORCE BASED METHODS A full technical critique of the comparison between forcebased and displacement based methods is given in Priestley et al. [2]. In this, a number of the short-comings associated with the force-based theory are outlined, and some of these have been covered earlier in this paper. In the following section the effects of the differing methods on the design outcome are outlined. 5.1 Ductility and Damping The fundamental concepts behind force based design revolve around the equal energy/displacement theories. The M2PP multi-span bridges generally fall into the longer period region of this, where equal displacement theory governs the displacement, and displacement of the structure is constant regardless of its strength. The Bridge Manual [8] would allow a maximum ductility of μ=3.0 for hinging below ground and μ=6.0 where hinging occurs above ground. Up until the 2006 amendments to NZS3101 [4] there was no limit on the level of plastic rotation which was allowed in plastic hinge region at ULS. In 2006, rotation limits were introduced which allow up to ~40mrads for sections detailed for full ductility. For the highly reinforced sections used on the M2PP project achieving 40mrads of plastic rotation proved to be very difficult to achieve when using the material strain limits from DBD7 [1], even when using the ductile detailing requirement of NZS3101:2006 [4].

7 Spectral Acceleration (g) With no specific material strain limits prescribed in NZS3101:2006, designers would be justified in using the maximum hinge rotation limit in their design which may not always be achievable. This places a more stringent limit on designers using the displacement based approach with reduced displacement capacity, along with reduced ductility and associated damping. In regions of high seismic hazard, with structures designed for long return periods (1/2500year etc.) and with flexible foundations, the ability of the structure to achieve ductilities of 3.0 and 6.0 comes into question. Foundation flexibility restricts the available structural ductility to μ= in the case of many of the M2PP bridges. With a plastic mechanism forming in the piers the maximum plastic displacement is equal to ~200mm. Similar plastic displacement also occurred for pile hinging using the reduced strain limits with a longer plastic hinge length and deeper plastic hinge. As a result, it was found that flexible foundations were unable to achieve higher levels of ductility, as can be seen in Figure 7 where flexible foundation design achieves a ductility of approximately 1.5, whereas the rigid foundation design achieves closer to ductility Rigid Foundation Demand (16% Damping) Rigid Foundation Pushover Flexible Foundation Demand (10% Damping) Flexible Foundation Pushover Displacement (mm) Figure 7: Example comparison between rigid and flexible foundation designs and achievable ductility Pushing the plastic mechanism below ground into the piles would allow this to increase, however the piles must be able to support the structure under lower bound (liquefied) and upper bound soil conditions, which were vastly different when considering a liquefiable zone ranging between 6m and 12m below the pile head. Determination of a single structural yield point on a pushover curve can prove troublesome with hinges forming at different times combining with general soil non-linearity. The yield point is critical in determining the ductility values used in forced based design which in turn have a large influence on the design acceleration, leaving it up to the designers to determine an appropriate yield displacement. The Displacement based methods allow for the damping of components to be aggregated together based on their individual damping characteristics to give a more realistic representation of the level of damping/ductility in the system. The effect of this could work in both ways, reducing costs with increased risk, for an optimistic engineer, or increasing costs and reduced risk to a pessimistic engineer. The elastic or initial period of the structure becomes redundant in the displacement method with the effective period at the design limit state becoming the more influential factor. With the high level of soil-structure interaction involved in the design of the M2PP bridges, the initial period carries limited usefulness after the structure has deformed from its initial state. However, with the initial state providing the stiffest response, as used in force-based design, this would produce a higher spectral demand. 5.2 Near Fault Factor With the majority of the M2PP expressway located ~2km from the Ohariu fault, near fault loading was required to be considered. There is limited understanding around near fault behaviour of structures and associated forward directivity which is reflected in the variation in the ways in which it is dealt with in the two design methods. In force based design, long period structures within 20km of a known major fault line are required to increase their design acceleration, the level of increase increases with structural period and decreases with distance to the fault. As mentioned earlier, while the M2PP bridges were within 20km of a major fault line, none of them displayed an elastic period greater than 1.5 seconds and so they are not required to have their design loads increased for near fault effects under NZS1170.5:2004 [7]. However, under the draft DBD7 [1], near fault effects and forward directivity is dealt with through a reduced effectiveness of damping. As discussed earlier the damping exponent decreases from 0.5 to 0.25 in DBD7 when the site is within 10km of a known fault line. This reduces the effectiveness of damping under the near fault case, resulting in a larger seismic demand spectra for structures of all periods. 5.3 Structural Performance Factor and Material Strengths and Strength Reduction Factors NZS1170.5:2004 [7] allows for a further reduction in seismic loading for ductile structures through the application of the structural performance factor, Sp. This accounts for a number of aspects, such as the use of nominal strengths for materials and rewards the structure

8 for a robust, ductile detailing by allowing a ductile structure to reduce the seismic demands to 70% of the design value. In the 3 rd edition of the Bridge Manual [10], the structural performance factor has been altered to account for different soil classes with its effectiveness reduced for sites where the ground surface is near to bedrock. In the draft DBD7 [1], the Structural Performance Factor is replaced by an increased material strength. A factor of 1.1 is applied to the nominal reinforcing steel strengths and 1.3 applied to the nominal concrete strength. Furthermore, the strength reduction factor for flexure of plastic regions is 1.0, whereas 0.85 is used in NZS3101:2006 [4] for force-based design. When comparing these factors in the two approaches there is approximately a 15% increase in the final demand to capacity relationship for the displacement based method when the structural performance factor, material strengths and strength reduction factors are considered. 6 CONCLUSIONS The Draft NZTA Bridge Manual Deflection-Based Design Appendix [1] was implemented in the seismic design of the bridges on the M2PP Expressway. The methodology was adapted from the displacement-based methods to allow for contribution foundation flexibility, and minor modifications made to integrate the philosophical framework of the project under the guidance of the NZTA. There are a number of differences between the traditional force-based design methodology and displacement-based methodology, particularly in the way in which they deal with the determination of limit states, ductile response and near-fault seismic loading. Inconsistencies were also found in implementing displacement based methods within material codes which had been intended to be used for force-based design. Displacement based methods allow for structures to be designed to more realistic levels of performance. The method allows for limit states to be defined through material strains levels as opposed to the approximate method of limiting structural ductility, giving the designer greater control, and the client greater confidence in how their structure will perform under a given level of shaking. The application of displacement based methods resulted in a similar design being produced when compared to an equivalent force based design. However, implementation is situations where seismic loading in less severe and improved ground conditions may produce differing results to those determined by force-based methods. ACKNOWLEDGEMENTS The authors would like to acknowledge the numerous and continuing contributions of the NZTA in the development and implementation of the Draft DBD7 document which formed the basis for the design of the M2PP Bridges. Particular acknowledgement needs to go to Don Kirkcaldie, John Wood, Nigel Lloyd and Nigel Priestley who worked together to produce the Draft DBD7 document. Thanks must also be given to the M2PP Alliance members who were open to, and encouraging of, the displacementbased design philosophy. Final thanks go to members of the Beca staff who provided assistance and shared their knowledge with the authors, particular thanks should go to Nik Stewart, Andrew Dickson, Ted Polley and Rob Jury. REFERENCES [1] New Zealand Transport Agency. NZTA Bridge Manual Draft Appendix A: proposed provision for deflection Based Design, Draft DBD7, 23/2/2013 [2] Preistley, M. J. N., Calvi, G. M. and Kowalsky, M.J., (2007). Displacement Based Design of Structures. IUSS Press. [3] New Zealand Society of Earthquake Engineering, Assessment and Improvement of the Structural Performance of Buildings in Earthquake, [4] Standards New Zealand, NZS3101:2006, Concrete Structures Standard, Part 1 The Design of Concrete Structures, 2006, ISBN [5] Ensoft, Inc. LPILE v6, (2013) [6] Rezaeian, S., Bozorgnia, Y., Idriss, I.M., Campbell, K., Abrahamson, N., and W. Silva (2012). Spectral damping scaling factors for shallow crustal earthquakes in active tectonic regions, PEER Report 2012/01, Pacific Earthquake Engineering Research Center, University of California, Berkeley, CA. [7] Standards New Zealand, NZS1170:2004 Structural design actions, Part 5: Earthquake actions - New Zealand, 2004, ISBN [8] Transit New Zealand, Bridge Manual Second Edition, [9] Standards New Zealand, NZS3404:1997, Steel Structures Standard, [10] New Zealand Transportation Authority, Bridge Manual Third Edition, 2013.