DESIGN AND INSPECTION OF LONG SPAN...

10
1 Global director RM Bridge, Bentley Systems Austria GmbH, Graz, Austria 2 Senior Product manager, Bentley Systems Austria GmbH, Graz, Austria 3 Senior consultant, Bentley Systems Austria GmbH, Graz, Austria 4 Product manager, Bentley Systems, Pittsburgh, USA V.Samec, J.Stampler, H.Sorsky, T.Gilmore. Design And Inspection Of Long Span Suspension Bridges Bridge Information Modelling, Proceedings of the Istanbul Bridge Conference, 2014. Istanbul Bridge Conference August 11-13, 2014 Istanbul, Turkey DESIGN AND INSPECTION OF LONG SPAN SUSPENSION BRIDGES BRIDGE INFORMATION MODELLING V. Samec 1 , J.Stampler 2 , H.Sorsky 3 , T. Gilmore 4 ABSTRACT In the design process of long-span suspension bridges the consideration of many challenges needs to be fulfilled: a highly non-linear behaviour of the structure, the need of optimization the geometry of suspension cables, when designing the sag-profile as well as optimization of erection procedure. Additionally wind effect is a major point because the extraordinary slenderness of these structures yields a considerable susceptibility for wind-induced vibrations. When design challenges are successfully closed, the bridge needs to be maintained and inspected over its entire life cycle. During the lifetime of a bridge a huge amount of data related to all aspects of the bridge is collected and must be managed. Not every piece of data is necessary for every participator in bridge management, but there will be overlapping occurrences. Therefore it seems natural to collect all the data in one well organised data pool, which can be accessed by all persons or institutes involved in the bridge construction and maintenance. A corresponding data model which is called BrIM Bridge Information Modelling is being developed by the bridge engineering division of Bentley Systems. Mobile inspection represents a novel solution, which helps asset owners streamline the process of planning inspections, collecting and managing inspection data, and complying with government reporting requirements. The central part of the project is to create a common data interchange interface for a wide range of design CAD, project management and inspection tools usually applied in bridge design and construction. The application of such a distributed model eases the communication of the human network behind such a bridge. This contribution explains the necessary concepts of data flow and organization from the viewpoint of the construction design and structural analysis. The data flow will show how the preliminary design can be used for structural design and ultimately how obtained calculation results can be incorporated into the following construction process. The same model can be used for inspection of the bridge over its lifetime allowing for a seamless linkage of information and allowing for proven asset management techniques to be used.

Transcript of DESIGN AND INSPECTION OF LONG SPAN...

Page 1: DESIGN AND INSPECTION OF LONG SPAN …istanbulbridgeconference.org/2014/ISBN978-605-64131-6-2/papers/203.pdfBehaviour of suspension bridge – analysis and design During the analysis

1Global director RM Bridge, Bentley Systems Austria GmbH, Graz, Austria 2Senior Product manager, Bentley Systems Austria GmbH, Graz, Austria 3Senior consultant, Bentley Systems Austria GmbH, Graz, Austria 4Product manager, Bentley Systems, Pittsburgh, USA

V.Samec, J.Stampler, H.Sorsky, T.Gilmore. Design And Inspection Of Long Span Suspension Bridges –

Bridge Information Modelling, Proceedings of the Istanbul Bridge Conference, 2014.

Istanbul Bridge Conference August 11-13, 2014

Istanbul, Turkey

DESIGN AND INSPECTION OF LONG

SPAN SUSPENSION BRIDGES – BRIDGE

INFORMATION MODELLING

V. Samec1, J.Stampler2, H.Sorsky3, T. Gilmore4

ABSTRACT

In the design process of long-span suspension bridges the consideration of many challenges

needs to be fulfilled: a highly non-linear behaviour of the structure, the need of optimization

the geometry of suspension cables, when designing the sag-profile as well as optimization of

erection procedure. Additionally wind effect is a major point because the extraordinary

slenderness of these structures yields a considerable susceptibility for wind-induced vibrations.

When design challenges are successfully closed, the bridge needs to be maintained and

inspected over its entire life cycle.

During the lifetime of a bridge a huge amount of data related to all aspects of the bridge is

collected and must be managed. Not every piece of data is necessary for every participator in

bridge management, but there will be overlapping occurrences. Therefore it seems natural to

collect all the data in one well organised data pool, which can be accessed by all persons or

institutes involved in the bridge construction and maintenance.

A corresponding data model which is called BrIM – Bridge Information Modelling – is being

developed by the bridge engineering division of Bentley Systems. Mobile inspection represents

a novel solution, which helps asset owners streamline the process of planning inspections,

collecting and managing inspection data, and complying with government reporting

requirements. The central part of the project is to create a common data interchange interface

for a wide range of design CAD, project management and inspection tools usually applied in

bridge design and construction. The application of such a distributed model eases the

communication of the human network behind such a bridge.

This contribution explains the necessary concepts of data flow and organization from the

viewpoint of the construction design and structural analysis. The data flow will show how the

preliminary design can be used for structural design and ultimately how obtained calculation

results can be incorporated into the following construction process. The same model can be

used for inspection of the bridge over its lifetime allowing for a seamless linkage of information

and allowing for proven asset management techniques to be used.

Page 2: DESIGN AND INSPECTION OF LONG SPAN …istanbulbridgeconference.org/2014/ISBN978-605-64131-6-2/papers/203.pdfBehaviour of suspension bridge – analysis and design During the analysis

Design And Inspection Of Long Span Suspension Bridges – Bridge

Information Modelling

V. Samec1, J.Stampler2, H.Sorsky3, T. Gilmore4

ABSTRACT

Long span suspension bridges represent some of the most remarkable, yet most vulnerable,

assets in road networks. Due to their important role in the transportation network, the design,

construction, and the following surveillance and maintenance must be performed very

thoughtfully. During the design process, bridge designers must consider and meet many

challenges: the highly non-linear behaviour of the structure, the optimization of the geometry

of suspension cables, and wind effect. The extraordinary, ultrathin design of these structures

yields significant susceptibility for wind-induced vibrations. When design challenges are

successfully satisfied, the bridge needs to be maintained and inspected over its entire life

cycle. A corresponding data model - called BrIM – Bridge Information Modelling – is being

developed by the bridge engineering division of Bentley Systems. Mobile inspection

represents a novel solution, which helps asset owners streamline the process of planning

inspections, collecting and managing inspection data, and complying with government

reporting requirements.

Introduction

Construction of modern-type suspension bridges dates back more than 125 years and

continue to instil special fascination with engineering elegance combined with a touch of

lightness, destined to become lasting landmarks. For bridge engineers, this fascination is also

derived from the size of these structures,

with allowable spans being longer than for

any other bridge type. Long spans

combined with extraordinarily thin lines

present outstanding challenges for any

bridge designer. Modern construction

techniques and materials, as well as

increasing experience and expertise in

bridge design, allow for the possibility of

increasing span lengths on large bridges.

An example of such an evolution is shown

e.g. in Figure 1.

The thinness and kinematical conditions of these structures result in large displacements due

to the permanent loads. Continuous change of structural systems and form finding processes

prove to be an issue for every bridge design engineer. The form finding process is a complicated

iterative process, where the shape of the suspension cables and the hangers need to be

identified.

Figure 1. Evolution of span length

of suspension bridges

Page 3: DESIGN AND INSPECTION OF LONG SPAN …istanbulbridgeconference.org/2014/ISBN978-605-64131-6-2/papers/203.pdfBehaviour of suspension bridge – analysis and design During the analysis

An even greater challenge is the simulation of the erection process. Asymmetric loading due

to traffic causes large displacements and requires non-linear traffic analyses.

Last but not least, a major engineering challenge posed by long suspension bridges is their

susceptibility to wind-induced vibrations. An important topic in wind analysis is the data

management and information interchange.

After the successful construction of the bridge, maintenance and inspection play an important

role in the bridge life cycle, performed in a timely manner throughout at least 80% of the entire

bridge’s lifetime. Huge amounts of data related to all aspects of the bridge are collected and

then appropriately managed. Not every piece of data is necessary for every participator in

bridge management, but there will be overlapping occurrences. Therefore, it seems natural to

collect all the data in one well-organized data pool, made accessible to all persons or institutes

involved in the bridge construction and maintenance.

The central part of the project is to create a common data interchange interface for a wide range

of design CAD, project management, and inspection tools usually applied in bridge design and

construction. The application of such a distributed model eases the communication of the

human network behind such a bridge.

Because of the complexity of the task, many engineers working in different fields must work

more closely together. In this sense, not only do the analysis methods fill an important role, but

the data storage and interchange model also perform to accomplish an efficient design process.

Behaviour of suspension bridge – analysis and design

During the analysis of long-span bridges, especially for cable-suspended bridges, non-

linear effects often reach magnitudes that make it imperative to include them in their structural

analysis. The basic conundrum presented by such a non-linear structural analysis is how to

consistently combine different non-linear behaviours. Time-effects (if concrete is used as

material) have to be coupled with the continuous change of the structural system, the cable-

sagging, the P-delta effects and the large displacement theory. [1]

The shape of the bridge is a non-linear function of the loading, deviating a great deal from the

hypothetical “stress-less” shape. Due to the high non-linearity of the problem, the usual

straight-forward design approach for conventional structures – i.e. using the desired design

shape in the analysis and compensating the deformations in the erection process by applying

appropriate pre-camber values – is no longer suitable. Therefore, a complicated form-finding

process with taking into account geometrical non-linearities is required.

In addition to the geometric non-linearity, various other non-linear mechanisms generally

occur. They require, on the one hand, the use of special element type and, on the other hand, a

global solution concept, dealing with the different non-linearity types in a comprehensive

approach [2].

Typical problems requiring special element types are for instance [3]:

Cable sagging, requiring special cable elements. These elements describe the non-linear

stiffness due to sagging. A special element type has been developed. It guarantees stable

behaviour even with very large displacements and any imperfection of the stress-less

geometry as shown in Figure 2.

Page 4: DESIGN AND INSPECTION OF LONG SPAN …istanbulbridgeconference.org/2014/ISBN978-605-64131-6-2/papers/203.pdfBehaviour of suspension bridge – analysis and design During the analysis

Figure 2. Special cable element for calculating large displacements

Fixing the suspension cable at the top of the pylon generally induces high and excessive

bending moments in the pylon. Therefore, a saddle is usually arranged on the top of the

pylon allowing for slipping of the suspension cable in the erection process. This connection

is modelled by friction elements, where the transmitted horizontal forces are a function of

the vertical redirection force (Figure 3). Special care is taken to simulate additional p-delta

and large displacement effects, which are coupled with moving the saddle at the top of the

pylon.

The lateral gaps between the main girder and the pylon legs are modelled with special gap

elements, which confine the free lateral displacements of the main girder to a certain

amount.

Eccentric hinge elements allow for simulating any distance pieces required in the

construction stage for keeping the individual segments in position without inducing

excessive constraints.

Figure 3. Schematic view of a suspension bridge

The form finding process – i.e. determining the theoretical “stress-less” state of the structural

components – is a backward iteration process, being rather complicated and time consuming.

An alternative to the conventional approximate calculation, the Additional Constraint Method

has been provided in the program RM Bridge in order to find and optimize the shape of the

suspension cables and the hangers. The preliminary design usually starts from the final

structural system where the deformation state due to permanent loads is calculated. The stress-

less design geometry is then appropriately modified, if pre-cambering is required. The final

hangers

suspension cable

sag

saddle

anchor block

y

x

Deformed Geometry

(Under the Load)

1

A(xA/yA)

2

3

4

5

6

19 n = 21

20

B(xB/yB)

L, A, q

y

x

F = q L

Start Geometry – Stress Free

L0=EA*L/(EA+N)=konstant

Extremely robust cable

element is developedy

x

y

x

Deformed Geometry

(Under the Load)

Deformed Geometry

(Under the Load)

1

A(xA/yA)

2

3

4

5

6

19 n = 21

20

B(xB/yB)

L, A, q

y

x

F = q L

Start Geometry – Stress Free

1

A(xA/yA)

2

3

4

5

6

19 n = 21

20

B(xB/yB)

L, A, q

y

x

F = q L

1

A(xA/yA)

2

3

4

5

6

19 n = 21

20

B(xB/yB)

L, A, q

y

x

F = q L

Start Geometry – Stress Free

L0=EA*L/(EA+N)=konstant

Extremely robust cable

element is developed

Page 5: DESIGN AND INSPECTION OF LONG SPAN …istanbulbridgeconference.org/2014/ISBN978-605-64131-6-2/papers/203.pdfBehaviour of suspension bridge – analysis and design During the analysis

defined stress-less design geometry can then be used for performing a detailed construction

stage analysis, with the option of accumulating permanent loads. This allows for the calculation

of the stressing state and geometry of the structure for all construction stages.

Some aspects of using this method in the design process have been successfully used for the

longest suspension bridge in Norway - Hardanger Bridge. This bridge has been opened in

August 2013 and crosses the Hardanger fjord with a main span of 1310 m, ranking it at no. 10

in the current global list of the longest suspension bridges (Figure 4).

Figure 4. Hardanger Bridge, Norway

The Norwegian road authority, Statens Vegvesen, in close collaboration with TDA Norway

and Bentley Systems Austria team in Graz, the supplier of the software package RM Bridge,

performed the design work.

The form-finding process with using the AddCon method was based on the provisional

assumption of a straight girder. Three sets of constraints were applied to get the required cable

lengths, yielding the desired shape under permanent loading. These constraints are:

vertical displacements of the bottom points of the hangers must be zero.

horizontal displacements of the top points of the hangers must be zero.

the main cable sagging must get the intended value, i.e. vertical displacement of the

central hanger top point must be zero.

The continuous change of structural systems is another major reason for experiencing non-

linear optimization problems. The mechanisms of typical construction sequences produce large

displacement effects due to the installation of new segments and corresponding loadings and

to redistribution of loading already applied to the structure. The second effect is mainly

produced by the main suspended cable moving into the new position – to fulfil global loading

equilibrium. The fact that already applied loading is redistributed to the new structural system

in each change of the structural system (or applying the new loading) does not allow classical

approach in finite element analysis with one “reference” structural system. In reality, each

construction stage has its “own” structural system where the same segments, cables, and

hangers have completely different 3D coordinates and orientation [4].

A further great challenge is the simulation of the erection process. The procedure of connecting

the different girder segments individually to their respective hangers causes continuous,

considerable changes to the sagging curve of the suspension cables in accordance with the

weight of the already mounted segments. This leads to high up and down movements of the

deck segments during erection. Preliminary hinged connections with some spacing have to be

Page 6: DESIGN AND INSPECTION OF LONG SPAN …istanbulbridgeconference.org/2014/ISBN978-605-64131-6-2/papers/203.pdfBehaviour of suspension bridge – analysis and design During the analysis

applied between the segments in order to prevent inducing impermissible constraints and

uncontrolled segment movement.

An approximate of the final shape is reached when all segments are mounted. Controlled

removal of the distance pieces closes the gaps between the segments and launches the welding

process. The actual final shape is reached when all segments are snugly welded. Continuous

adaptation of the mathematical model is recommended in the erection phase. Any deviations

from predicted behaviour can be detected in an early stage. In addition, required compensation

measures can easily be fixed by performing appropriate erection control calculations.

Dynamic wind impact: Most of the bridges of such enormous span length are also subject to

strong wind forces due to their exposed placement. Because of their thin design and related

dynamic behaviour, it is no longer sufficient simply to treat wind gusts and other fluctuations

by equivalent static wind forces. Instead, different investigation methods developed for such

extreme situations must be applied to examine the interaction between the bridge and any

oncoming winds.

The first step to the numerical modelling is a careful investigation of the airflow around the

concerned bridge cross sections. This is done by applying a CFD (Computer Fluid Dynamic)

module. The subsequent wind buffeting analysis separates static and dynamic wind force

contributions. The static part can be applied as distributed constant load. The dynamic wind

load can be split into aerodynamic damping and stiffness and contributions due to fluctuating

wind. The structural response is calculated by transforming the equations into modal space and

frequency domain. By providing suitable wind profile data, the excitation power spectrum can

be calculated and the structure peak response can be estimated by statistical methods.

By solving simplified versions of the buffeting and flutter equations, wind checks can be

obtained for galloping, torsional divergence, torsional flutter, and classical flutter phenomena.

According critical wind velocities can be estimated.

Wind calculations were performed for the Hardanger Bridge in Norway (Figure 5).

Figure 5. Structural model of Hardanger Bridge, Norway

CFD (Computer Fluid Dynamic)

investigations were performed for the main

girder with traffic. The two driving lanes are

loaded with traffic, according to the sketch

presented in Figure 6.

Figure 6.Cross-section for traffic calculation

Page 7: DESIGN AND INSPECTION OF LONG SPAN …istanbulbridgeconference.org/2014/ISBN978-605-64131-6-2/papers/203.pdfBehaviour of suspension bridge – analysis and design During the analysis

Three different cases were considered: with both lanes loaded, only with the left lane and only

with the right lane. Since the application of traffic causes a symmetry break of the cross section

layout, the CFD (Computer Fluid Dynamic) calculations must be performed for wind coming

from the left (-10° to 10°) as well as

from the right (170° to 190°). The

computed results for the case with

both traffic lanes are indicated in

Figure 7. It can be observed that the

slope of the lift coefficient for wind

coming from the left is negative for

negative angles. By evaluating the

Glauert-Den Hartog criterion, slightly

negative values are obtained, which

indicates a tendency for galloping [5].

Figure 7. Steady state coefficients CD

(x), CL (o) and

CM (D) for traffic on both lanes for wind from left (solid) and right (dashed).

Based on this set of basics functions, the buffeting analysis was performed for a wind profile

where the mean wind is given by a logarithmic distribution and the power spectral density is

of Kaimal type. By comparing with results for static wind only, static and dynamic lateral

forces are of same magnitude. The twisting moment is larger for the dynamic wind; due to the

fluctuating vertical wind component, the effective wind incident angle varies more than static

effects only. Thus, the overall twisting of the deck is amplified and the internal moment is

consequently higher (Figure 8).

Figure 8. Internal shear force (left) and longitudinal twisting moment (right) due to lateral wind

Inspection of long span bridges

With a goal of consolidating inspection data into one highly accessible database,

Bentley works closely with their clients to efficiently configure and utilize the web-based BrIM

System during inspection and maintenance via the 3-D visualization tool.

Using 3-D Visualization, Engineers can interactively “fly-through” and zoom throughout the

structure. A variety of views are available which provide multiple angles and viewpoints for

given components. By scrolling over an individual member, users can view the member name

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

-10 -8 -6 -4 -2 0 2 4 6 8 10 [°]

CD

,CL, C

M [

1]

170 174 178 182 186 190

Page 8: DESIGN AND INSPECTION OF LONG SPAN …istanbulbridgeconference.org/2014/ISBN978-605-64131-6-2/papers/203.pdfBehaviour of suspension bridge – analysis and design During the analysis

and location quickly. If a particular component requires further review, users can simply click

on that component, and a separate window will appear which displays all of the information

that has been entered relevant to the component. Users can then view ratings, remarks,

properties, historical trends, and recent/historical pictures. The software enables a “drill-down”

feature which involves clicking on a picture to see enlarged views of defects with additional

detail (Figure 9). This tool can be utilized from any computer with a web browser and does not

require expensive CAD software.

Figure 9. Components that return under a specific query light up in a designated color.

With the new Mobile App, users can not only operate the 3-D visualization tool while in the

field, but they can attach photos, video files, and audio clips to individual elements within the

visualization. This unique feature streamlines the entire process and saves a significant amount

of Engineers’ precious time. Inspectors and maintenance crews now have access to the design

information via the actual design and construction files during an inspection. All 3-D design

files are available in the field on a mobile device.

Most clients require a single System that could be easily accessed by its Engineers. Thus, the

System establishes a high-level of consistency in formatting and quality for all inspection and

management users. This consistency is seen across all platforms, including mobile devices used

for data collection and file uploading while in the field. Bentley continues to improve its

System by eliminating errors from redundant data entry and dramatically increasing the

reliability of the information obtained via inspections since the data is utilized to make critical

capital planning and maintenance decisions. Bentley is stepping up their System by offering

the 3-D visualization tool, a clear, interactive visual reference of a bridge and its elements,

linking back to report data, historic data, uploaded and attached files, and other crucial

information. Bentley strives to develop a one-stop location for all bridge data (inspections, as-

built drawings, load ratings, work orders, etc.) and make that information available securely

via the internet from any office or other approved location. The 3-D tool and the new mobile

application help Bentley reach this goal. This integrated BrIM System serves a variety of users

(Executives, Managers, Maintenance Personnel) while providing different permission levels

Page 9: DESIGN AND INSPECTION OF LONG SPAN …istanbulbridgeconference.org/2014/ISBN978-605-64131-6-2/papers/203.pdfBehaviour of suspension bridge – analysis and design During the analysis

and functions to meet their unique levels of authority. The permission levels prevent a user

from seeing or accidentally corrupting data they should not have access to in the first place.

Overall, the common goal in Bentley’s System implementation is to dramatically streamline

the inspection and management process for all inventory bridges and save time, costs, and

increase the operating efficiency and safety of the bridges.

For an inspection, users can choose to pre-load information from the most recent inspection

into the forms. When data is pre-loaded, color coding systems are utilized to clearly show what

data fields are changed and what data has remained the same from the previous inspection.

The other option is for users to utilize blank inspection forms without the pre-loaded data. The

3-D visualization tool can also serve as the primary point of data entry. Users are able to collect

data and enter it directly into the system and access it later for review via the 3-D tool.Data

fields that appear on different forms but reference identical information (i.e. Deck rating) are

automatically linked together within the software. This information only needs to be entered

once and is automatically transferred and entered on all other relevant forms within the System

and eventually transferred to the BrIM. The System includes tools for multiple engineers to

simultaneously enter data, photos, and other resources. Even with the flexibility of the System,

users maintain the highest standards of security and controlled all viewing permissions through

usernames and passwords. Each individual component of the bridge is a unique asset in the

System which allows data to be viewed, stored, and retrieved at a very granular level.

The System supports uploading of pictures, diagrams, and other file types. Adding, labelling,

and organizing pictures, sketches, and other files into reports is traditionally a time-consuming

process for all parties. Using the System, inspectors select the files (pictures, etc.) from their

computer or external device and quickly upload those resources into the inspection forms at

desired locations. After being

uploaded, the pictures appear as

thumbnails and are automatically

created and displayed on the

screen. Descriptions can be added

to the pictures, and those

descriptions can be carried over

into the inspection report and/or

used as an ongoing resource. All

uploading tools are also available

on mobile devices with Bentley’s

Mobile App, allowing users to link

photos, videos, and other files

directly to the report and the 3-D

visual of the bridge (Figure 10).

Figure 10: With the Mobile

application, users can enter data into an inspection report in the field.

Users are able to integrate coding manual pages as PDF files within the System. The coding

manuals can appear as PDF files and eliminate the need to bring hard copies to the bridge site

for reference. This feature integrates hundreds of pages of detailed information in an easily

accessible PDF format. Pictures can also be correlated to condition ratings as a visual tool to

standardize the way that all Inspectors rate different components of the bridge. The 3-D

Page 10: DESIGN AND INSPECTION OF LONG SPAN …istanbulbridgeconference.org/2014/ISBN978-605-64131-6-2/papers/203.pdfBehaviour of suspension bridge – analysis and design During the analysis

visualization tool provides another option for viewing PDF files, linking each element in the

bridge directly to historic reports and summary report along with other important data.

Managers are then able to search across any field or combination of fields from the inspection

reports. Results are displayed in grid form and also exported to a number of GIS and 3-D BrIM

tools without the need to install additional, costly software.

Conclusions

Overall, Bentley’s BrIM System will provide the solution for modelling, analysis, design and

maintaining long span bridges and preventing the inevitable deterioration due to dynamic wind,

seismic and traffic. Due to the slenderness of the suspension bridge structures, special attention

has to be turned on wind-induced vibrations, with static and dynamic wind excitations to be

investigated. An integral solution of the different topics related to wind impact is shown in the

paper. As an example, the integrated investigations performed in the Hardanger Bridge project

have been presented. This integrated approach considerably eases and enhances the overall

design process.

The 3-D models, created and completed during the design of the bridge, continue to serve its

users throughout the lifecycle of the bridge. Not only does it help bridge designers visualize

their new architecture, but it also continues to help contractors during construction, inspectors

during bridge inspections, maintenance crews sent to seek out a faulty bridge element, and

other ongoing operations of the bridge. The consistent use of the 3-D visualization tool

provides valuable information to bridge owners, inspectors, and maintenance crews while

increasing the return on investment in the design phase. With the ability for this tool to operate

on mobile devices, the 3-D visualization tool simply increases in value, making all construction

and design files, inspection and maintenance reports, and related photos and files readily

available to users in the field.

References

1. Janjic D., Sorsky H., Consistent Non-Linear Structural Analysis Of Long-Span Bridges, Proceedings: EASEC-Symposium 2006, Bangkok

2. Janjic D., Bokan H., Stampler J., Computer Aided Design & Erection of Long Suspension Bridges, Proceedings: IABSE-Symposium 2007, Vancouver

3. RM Bridge V8i, User Guide, Bentley Systems, December 2012

4. Janjic D., Bong-Gyo J., Hyun-Sok C., Gwangyang Bridge – Numerical Simulation of Construction Sequence, Proceedings: IABSE-Symposium 2010, London

5. Janjic D., Stampler J., Domaingo A., Wind and extremely long bridges – a challenge for computer aided design, Proceedings: IABSE-Symposium 2008, Chicago