THE PARAMETRIC DESIGN OF A STEEL PIPE BRIDGE

Creation of a parametric model

Bachelor’s thesis

Hämeenlinna University Centre, Degree Programme in Construction and Civil Engineering

Spring 2021

Darya Samoilova

Construction and Civil Engineering, Bachelor of Engineering Abstract

Author Darya Samoilova Year 2021

Subject The Parametric Design of a Steel Pipe Bridge

Supervisor Cristina Tirteu

Pipeline bridges are a vital part of a process plant. Their design process is time-consuming,

facing constant updates from involved technology groups. These structures have repetitive

geometry, which makes them suitable for automation. At the moment new approaches of

the parametric design could be applied for this purpose, as it allows the development of

easily adjustable models.

The thesis aims to create a parametric model for the steel pipe bridge to be applied in the

early stages of the project, thereby facilitating the design process. The thesis consists of

descriptions of pipeline bridges, their configuration, types, and sizes, which are later

embodied in a parametric model.

The visual programming tool Grasshopper in Rhinoceros 7 was used for scripting the

parametric algorithm, which was also fully integrated into Tekla Structures. The workability

of the developed algorithm was proved by carrying out a series of tests, which showed the

speed and accuracy of the implementation of the desired shapes. The algorithm has the

potential to be used by structural engineers for setting the basic structure of the pipe bridge

ready for further detailing.

Keywords Pipeline bridge, parametric design, Grasshopper, Tekla Structures, Rhinoceros,

visual programming

Pages 34 pages and appendices 4 pages

Contents

1 INTRODUCTION .......................................................................................................... 1

1.1 Background ...................................................................................................... 1

1.2 Aim and limitations .......................................................................................... 2

2 KNOWLEDGE BASE ..................................................................................................... 2

2.1 Pipeline bridge ................................................................................................. 2

2.2 Process piping .................................................................................................. 3

2.2.1 Pipes ..................................................................................................... 3

2.3 Considerations ................................................................................................. 4

2.4 Sizing ................................................................................................................ 6

2.5 Types ................................................................................................................ 7

2.6 Structural elements of a pipeline bridge ......................................................... 8

2.7 Material ............................................................................................................ 9

2.8 Cross-sections ................................................................................................ 10

2.9 Parametric Associative Design ....................................................................... 10

2.9.1 Potential of parametric modeling in construction engineering......... 11

3 METHODS ................................................................................................................. 12

4 SOFTWARE ................................................................................................................ 12

4.1 Rhinoceros 3D ................................................................................................ 13

4.2 Grasshopper ................................................................................................... 13

4.2.1 Interface ............................................................................................. 13

4.3 Tekla live-link.................................................................................................. 14

4.4 Tekla BIM........................................................................................................ 15

5 PARAMETRIC MODEL OF THE PIPELINE BRIDGE ...................................................... 15

5.1 Development Concept ................................................................................... 15

5.2 Parameters ..................................................................................................... 16

5.3 Creation of geometry of pipeline bridge ....................................................... 18

5.4 Integration with Tekla .................................................................................... 25

5.5 Tests ............................................................................................................... 26

5.5.1 Test 1 .................................................................................................. 26

5.5.2 Test 2 .................................................................................................. 28

6 CONCLUSION ............................................................................................................ 31

6.1 Further use ..................................................................................................... 32

REFERENCES ..................................................................................................................... 33

Appendices

Appendix 1 Documentation for Test 1

Appendix 2 Documentation for Test 2

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1 INTRODUCTION

1.1 Background

Pipeline bridges are sometimes referred to as the "arteries" of an entire process plant as they

support the pipeline laid throughout the plant's layout. They belong to non-building structures,

and each pipeline bridge system is usually designed from scratch following the facility's needs, as

there is no ready-made solution. In most cases, it is a structure with repetitive elements where the

structure's functionality is valued over appearance. Since an inadequate design of pipe bridge may

lead to defects and improper sizing in structures, this vital area requires considerable planning and

coordination with other technology groups regarding construction. In real life, the final piping,

equipment, and load information are not available at an early stage in most projects. The initial

design can be updated multiple times over the project's life cycle, which is time and cost-

consuming for all parties involved.

Construction companies are always looking for ways to make the design process more efficient,

either by developing standardized solutions or suggesting different work approaches. The

conventional way of designing pipeline bridges is a long step-by-step process, where a single

change requires remaking everything.

The use of parametric modeling greatly simplifies this process, as the geometry of the parametric

model can be quickly adjusted by modifying specific parameters according to the project's

changes. It also allows analyzing and testing a variety of design results from basic concept design

to construction documentation stages. This approach gives more control over the design to the

contractors and provides a better understanding of the process to the clients. Studying

relationships and incorporating fundamental aspects of the actual construction, such as material,

structural properties, and manufacturing technologies, into the design process became possible

using parametric software (Kalsi, 2015). Therefore, this thesis will consider the ways of integrating

parametric design at the early stages of designing a pipe bridge.

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1.2 Aim and limitations

The thesis aims to create a parametric model of the steel pipe bridge for use in the early stages of

the project, thereby facilitating design. The developed parametric model should include all the

main elements of the pipeline bridge structure and should be able to control its properties. Using

this model, even with a small amount of information available, the start of the modeling process

of the pipeline bridge should be possible. By manipulating the values of the parameters, the main

view of the pipe rack can be set and immediately integrated into the BIM (Building Information

Modeling) software for further modeling or used as a model for calculations. Depending on the

project, each pipeline bridge has distinctive characteristics that may go beyond the capabilities of

the developed model. In this case, the algorithm can be used as a base or modified, taking into

account new features.

2 KNOWLEDGE BASE

2.1 Pipeline bridge

A pipeline bridge, also known as a pipe rack, is an essential frame structure in a process plant. It

carries pipes and cable trays from one piece of equipment to another within one process unit or

from one unit to another.

The choice of design and solution for pipe racks is based on building codes, standards, regulations,

and legislation. When it comes to European standards, pipeline bridges should be built according

to Eurocodes and National Annexes. However, the methods of determining loads in there are not

fully compatible with pipe bridge structures as they are not part of conventional buildings and

structures. Specific design criteria for such systems are challenging to identify.

Previous works on this topic were mainly focused on the conventional design methods for specific

cases, while this thesis considers the parametric approach to make a universal model that can be

applied in various projects.

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2.2 Process piping

The importance of a pipe rack is that it supports and routes all process piping, which in turn

regulates the flow of a wide range of fluids and gases in industrial environments. According to

Moran (2017, p. 483), the piping layout can constitute about 30% of the capital cost of the plant

therefore it has a major influence on the economics of plant design. The ultimate goal is to provide

a cost-effective and simple yet flexible layout. The choice of design, materials, and manufacturing

method for piping systems should be based on standards and codes determined for a specific

plant, location, and other factors.

2.2.1 Pipes

The pipe rack serves as a carrier for a variety of pipelines. It is essential to identify these pipelines

before beginning the pipeline bridge design. It is customary to place different types of lines on

certain parts of the pipe rack. Process lines, relief-line headers, and utility headers are the three

types of pipelines guided in the pipe bridges that are defined by Bausbacher & Hunt (1993).

1. Process lines are a group of pipes that serves different needs. Process lines connect nozzles

on process equipment that are separated by more than 6 meters, product lines that run

from vessels, exchangers, or pumps to the unit limits to storage or header arrangement

outside the plant, charge lines that connect to exchangers, furnaces, or other process

equipment.

2. The relief header is a piping system that connects all the relief valve outputs into a single

pipe or header, leading to the relief scrubber and then to the vent.

3. There are two types of utility lines in the pipeline bridge: utility headers that provide

service to all the plant's facilities and utility lines that serve one or two pieces of equipment

in the plant.

Pipe placing

Process lines are usually carried on the lower tier of pipe racks, while utility lines are held on the

top. Heavy lines with large diameters are mounted over or near the pipe bridge columns,

regardless of function. Shorter pipe runs, savings on piping costs, and better process flow

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conditions are ensured by placing process lines in the lower tiers (Drake & Walter, 2010). In case

of leakage of aggressive or flammable process materials, such a layout eliminates the risk of

corrosion or fire. For a better understanding, Figure 1 illustrates an example of how piping can be

placed on the pipe rack.

Figure 1. Typical cross-section of layout at piperacks (Moran, 2017, s. 497).

2.3 Considerations

Pipeline bridges require considerable planning and coordination with all disciplines not only to

facilitate a logical design that involves a lot of engineering calculations but also to reduce

construction costs (Barker, 2018). Table 1 shows the work responsibility distribution between the

engineers involved in the pipe rack design.

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Table 1. Work Responsibility. Updated from Khan (2020).

Responsible Engineer Work Scope

Piping Engineer Determination of the basic dimensions of the pipeline bridge

Piping and equipment load calculations on a pipeline bridge

Structural Engineer

Selection of profile size of the structural member according to the different loads on a pipeline bridge

Selection of bracing

Civil Engineer Foundation calculations

Electrical/Instrument Engineer

Electrical/Instrument cable tray calculations

Fire Engineer Fire-proofing load

The generation of a line-routing diagram is the starting point in the development of any piping

rack. A line-routing diagram is completed based on the line's size, line's number, pipe material,

operating temperature, and other information obtained from P&I (Piping and Instrumentation)

Diagram. Later, all piping system data are combined with pipe rack general arrangement drawing.

Following the completion of the line-routing diagram, work on the rack configuration, width,

height, structural column spacing, number of levels and bays, and their elevations should begin.

The pipeline bridge configuration is influenced by the overall location of lines, units, and

equipment. The shape is adapted to the project needs and can be a straight-line, C-shape, T-shape,

L-shape, or U-shape, as shown in Figure 2. This thesis is focused only on the straight-line pipe rack.

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Straight-line configuration C-Shape configuration T-Shape Configuration

L-Shape Configuration U-Shape Configuration

Figure 2. Pipeline Bridge common configurations.

2.4 Sizing

Any pipe bridge design is aiming to achieve a simple, economical and standardized solution. Thus,

a maximum width of 10 m with a bent spacing of 6 m and a tier distance of 3 m is considered as

the thumb's rule for the initial configuration of the pipeline bridge. (Moran, 2017) The

measurements of the structure can be rounded off to the next whole number after reviewing all

the conditions and arrangements. However, the final dimensions of the structure are decided

based on considerations described below.

• Width

It is essential to establish the width of the pipeline bridge early in the project, based on the little

information available as the exact number and size of pipes are not yet known. In practice,

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designing with an additional 20–50% width allowance for plant expansion is recommended. Rack

widths can be changed to suit the needs of the plant they support, rather than being constant in

the facility. A two-level rack can be used where a width greater than 10 m is needed to

accommodate all the piping, with the second level 1.5 m above the first.

• Height

The height of the rack is determined based on the largest pipeline size supported by the structure

and the size of the branch so that all the small branches can be accommodated in the gap

between tier to tier. Branching from both sides top and the bottom should be considered. (Khan,

2020)

Moran (2017) asserts that when vehicular access underneath the pipeline rack is not needed, a

minimum elevation of 3.6 m is sufficient. Vehicles must ride under racks that are at least 4.5

meters above plant paving or road surfaces. The clearance of 4.5 meters under the rack is enough

for most road vehicles. If cranes/equipment movement under the pipeline bridge or rail crossing is

required, a minimum height is 6 m and 7 m, respectively.

• Length

The length of the piping bridge is calculated using a unit plot plan. It depends on several factors,

such as the number of units and the plant's size.

• Spacing

The distance between the columns of pipe racks should be determined by taking into account the

economics of the pipe span and the structure of the truss to provide a double span for crossing the

road or avoiding underground obstacles.

2.5 Types

The existence of various types of pipeline bridges is due to differences in the project's needs;

therefore, before starting the design, it is necessary to decide which type to use. Three types of

pipe bridges can be defined: continuous pipeline bridge (conventional) system, non-continuous

pipeline bridge system, modular pipeline bridge.

• Conventional pipeline bridges

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Conventional pipe rack systems consist of frame assemblies with the transverse beams and the

columns connected by the longitudinal struts and the vertical bracing. Beam struts provide

longitudinal stability and support for transverse pipes.

• Non-continuous pipeline bridges

Non-Continuous pipe rack comprises independent cantilevered, freestanding 2D frames not

dependent on longitudinal beam struts for system stability. In the longitudinal direction, the

transverse frame columns will act as cantilevered columns (Drake & Walter, 2010). Where

applicable, this system can result in lower expenses of installation.

• Modular pipeline bridges

Modular pipe racks consist of several parts that are prefabricated offsite and then brought on-site

either in easy-to-assemble parts or in a completed state. Once they are transported to the desired

location, they are placed on a permanent foundation and assembled. In terms of design,

companies offer economical and practical solutions while still allowing modifications of the

structure to satisfy the client's requirements. Overall modular pipeline bridges are safe, durable,

and efficient structures that are easy to maintain and reconfigure. (STI Group, 2015)

After gеtting аcquainted with all types of bridgеs, it was decided to focus further work only on

сonventional systеms.

2.6 Structural elements of a pipeline bridge

The structure of the pipe bridge adapts to the requirements of the project but consistently

maintains repetitive shape and, in the case of conventional systems, consists of the following

elements: columns, transverse beams (supports for piping), longitudinal struts (main chords), and

a bracing system. The principal elements of the pipeline bridge structure are illustrated in Figure 3.

A general rule for designing a pipeline support system is to consider it as a rigid frame in a

transverse direction and as braced in longitudinal (El-Reedy, 2017). The pipe rack's structural

elements must be able to withstand axial loads, shears, and moments.

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Figure 3. Typical structure of pipeline bridge. Updated from Bridge Brothers (2018).

Lele (n.d.) explains that vertical bracing can transfer longitudinal forces from the beam struts to

the foundations where moment-resisting frame structure is not used in the longitudinal direction.

In case of high bending stresses, the use of horizontal bracing is required. It also provides lateral

restraint to the structure and helps to transfer horizontal forces to the column. According to

Bendapudi (2010), if the contents of the pipes contain dangerous material, plan bracing can be

provided in seismically active areas. Plan bracing is used for long spans, such as at pipe bridge

roadway crossings, to avoid torsional instability. The bracing between columns provides lateral

stability to the structure and helps to transfer horizontal forces.

Dhanpurwala (2016) states that "the bracing members can be arranged in different forms to carry

solely tension or alternatively tension and compression". Choosing and optimizing the right

structure is quite a difficult task, as the conventional design method allows to develop and

consider a limited amount of solutions in a short time. For that reason, the developed parametric

model will include the option to choose a suitable bracing system.

2.7 Material

The most common materials for constructing pipe racks are steel and concrete. Concrete pipeline

bridges are more robust and resilient to damage and corrosion but also more expensive, so the

need for fireproofing can justify their appliance. The concrete pipe racks have a high initial cost but

no subsequent maintenance costs, whereas the steel pipe racks, though initially cheaper and have

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lesser construction time, require regular coat painting due to corrosion, especially in coastal areas.

In this thesis, only steel pipe bridges were considered. Rathdore (2016) claims that steel pipe racks

better for fast construction and it is a better option when construction time is limited by tight

deadlines.

2.8 Cross-sections

The type and size of the cross-section for the members of the pipeline bridge depend on the loads

and are decided after a calculation that follows the requirements of Eurocode 1993-1-1. Based on

the reviewed literature and real cases, the I-sections and hollow square/rectangular sections are

used the most for the pipe bridges. The typical cross-sections that are used in pipe bridges are

shown in Figure 4. The I/H shape is extremely efficient at resisting flexure and compression.

Normally, the wide flange profile is a cross-section choice for columns and horizontal beams.

Typical Hollow Square/Rectangular section (SFS-EN 10210-2, 2019)

Typical I/H shape section (SFS-EN 10365:2017, 2017)

Figure 4. Cross-sections used in pipeline bridges.

2.9 Parametric Associative Design

Parametric design is a type of design that is driven by logic and involves algorithms with

parameters that can be modified to produce a variety of results. Parametric modeling is not a

novel concept; what is new is that it is being performed on a device and in a unique manner.

Assasi (2019) describes that in Parametric Associative Design the way of solving design problems is

"based on translating the relationships between internal and external variables affecting the

design elements into parameters and parametric equations which could be used to inform the

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design of complex systems". It allows controlling the design process more precisely; it is excellent

for remodeling structures and accuracy for digital fabrication.

In this design method, a huge amount of data and calculations are processed through the flow of

algorithms. The design of complex objects consists of a layering of levels and forms with different

hierarchies, each associated with its own logic and details. These levels are all intertwined, and

their components affect one another, which is why this approach is referred to as "associative."

(Khabazi, 2010) The endpoint of one curve created by the associative method might be the middle

point of another circle, and any change in the curve would cause the circle to change as well. The

main point of it is that all of the created geometries are easily adjustable. Designers have constant

access to all aspects of the design product, from the beginning to the end. The algorithm's inputs

may be altered, and the result may also be revised since the design product is the outcome of an

algorithm. By modifying simple geometrical parameters, it is now possible to digitally draw a

model and create hundreds of project variations. Material characteristics, fabrication constraints,

and assembly logic may all be embedded in parameters.

2.9.1 Potential of parametric modeling in construction engineering

The use of parametric modeling for the creation of complex structures with unusual geometry is

widely known. However, the possibilities of parametric modeling in the construction sector are not

limited to this. Many structures have repeating geometry that can be automated with the right

approach.

Unlike traditional CAD software which is merely based on geometric objects that every single

change needs to modify all appropriate components in order to fix the design, parametric design

tools can make associations between geometrics and operations as well as link them together and

with others via explicit or implicit stated relationships (Kalsi, 2015).

The parametric modeling process has tremendous potential to save time and resources, as it is

allowed to automate modifications in the model. The first step towards optimization is the

efficient calculation of different configurations, which is possible using parametric associative

geometry models (Ledermann et al., 2005). Most software that supports parametric modeling

tools also supports smooth compatibility with other conventional software.

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Some software programs already adapted the basics of parametric modeling enabling control of

modifying properties of a bunch of elements by adding a single variable. Specialized software like

Grasshopper may establish relationships between project parameters, allowing one to alter in

response to alterations in others.

3 METHODS

In this thesis, the method comprises a design concept and a developed algorithm. The design

concept is based on the information described in the knowledge base part, while the developed

algorithm was embodied based on the concept idea by utilizing parametric software capabilities.

Figure 5 illustrates a modeling process used in the thesis.

Figure 5. Work approach for creating a parametric model.

First, literature sources about the design process of pipeline bridges were obtained and studied.

Further, in order to understand the principles of parametric thinking, various materials related to

the topic and guides to parametric software were studied. The concept that employs obtained

data was formulated and a parametric model of the pipe rack was developed. The model was

tested and then presented in the thesis.

4 SOFTWARE

In this thesis, mainly three software were used in a linked workflow, as seen in Figure 6. The

geometry was created by visual programming in the Grasshopper environment and was visualized

in Rhino 7. Although the script used none of the Rhino 7 functions, this software still needs to be

mentioned since Grasshopper is integrated into it. The export of the model's geometry to the

Tekla was done through Grasshopper's plugin called Tekla live-link. The exported model in Tekla

serves for further detailing, documentation and still can be changed by the manipulations in

Grasshoppers script.

Literature review

Software learning

Creation of algorithm

Testing Presentation

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Figure 6. Software workflow.

4.1 Rhinoceros 3D

Rhinoceros is a 3D computer graphics and computer-aid design application software that focuses

on generating mathematically accurate representations of curves and freeform surfaces in

computer graphics (McNeel, 2014). Software industries offer a range of plugins that support and

extend Rhinoceros' capabilities in various fields such as engineering, architecture, rendering and

animation, and others.

4.2 Grasshopper

Grasshopper is a Rhinoceros 3D-integrated graphical form generator. It is a tool based on a

particular way of thinking for design issues, called the Parametric associative method. (Khabazi,

2010) It does not need any previous programming or scripting experience yet encourages

architects and designers to create complex parametric objects. The form's dimensions are

constrained, but they can easily be changed by adjusting the various parametric sliders in the

Grasshopper model space.

4.2.1 Interface

Grasshopper's interfaces utilize visual programming, which allows managing logic elements

graphically rather than textually. Grasshopper offers a wide range of numerical components and

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functions that allow the creation of different algorithms with similar results depending on the

designer's approach.

Component Panels and Canvas are the two most significant aspects of the Grasshopper interface.

The component panel consists of all design elements, while Canvas is a workspace where

components and algorithms are set up.

There are two types of objects that are used for modeling: parameters and components.

Parameters can be defined as objects that store data. Components are objects that perform

actions based on the input. Components can carry out a wide range of functions. (Payne & Issa,

2009) In general, a variable receives data from one or more sources and returns the output.

Component with input data should relate to the processing component and then link the output to

the other component; it can continue until the desired algorithm's outcome is achieved. As

parameters or geometry are changed, the modifications occur across all functions, and the

geometry is redrawn. All geometry created with the different Grasshopper components will

appear in the Rhino window.

4.3 Tekla live-link

The Grasshopper's plugin called Tekla live-link enables algorithmic modeling into Tekla Structures

using Rhino / Grasshopper. Link is an addon to Grasshopper, which contains components that can

create and interact with parts in real-time in Tekla Structures (Tekla Structures, 2021). These

components are shown in Figure 7. In the initial design process, it can effectively assist the

architectural vision. Tekla's live- link made it possible to create complex detailed steel elements

parametrically. The link contains the main tools that Tekla has for structure modeling, like adding

steel and concrete components, connecting or cutting parts, and assigning attributes. With this

plugin, all modifications of the parameters made in Grasshopper are immediately displayed in

Tekla.

Figure 7. Tekla components in Grasshopper.

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4.4 Tekla BIM

Tekla Structures is already a powerful BIM tool for structure modeling that enables managing

projects from an idea to the fabrication stage. It suggests versatile design solutions but still has

room for improvements. The article about parametric modeling in Tekla Structure Blog (n.d)

accurately points out that structural models created as a result of integration between

Grasshopper and Tekla "can be used throughout the project lifecycle from managing changes and

avoiding errors to finding clashes and producing better quality structures with less waste, all the

way to asset management". Figure 8 clearly shows how information is exchanged between the

parametric and BIM models.

Figure 8. InternalBIMworkflowmodel (Hudson, 2010).

5 PARAMETRIC MODEL OF THE PIPELINE BRIDGE

5.1 Development Concept

The desired outcome of the thesis is to get a ready-to-use parametric model of the pipeline bridge

that can be easily adjusted in accordance with input data set by the designer and defined by

project specification. After the shape was determined and all the details gathered during the

design process, the pipe bridge system could be built entirely using parametric algorithms. The

parametric model should be able to visualize the possible geometry of a pipe rack structure;

however, considering the variety of all existing pipeline bridge configurations, the creation of a

single algorithm for all of them does not seem possible. Therefore, the algorithm developed for

the thesis can be applied only for the conventional single-line steel pipe bridges. The algorithm is

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created based on the data obtained during research in the Grasshopper environment, with

components from the Tekla live-link plugin. The created geometry automatically shows on the

Tekla model, with the selected cross-sections and material, and all changes made in Grasshopper

are simultaneously displayed in the Tekla as well. Previously, the typical structure of the pipeline

bridge was described in the thesis.

5.2 Parameters

The first step for developing a parametric algorithm for the pipeline bridge is defining all input

parameters. It was decided to divide the structure into the following nine groups of members:

Columns, Main Chords, Support Bracing, Cable Trays, Pipe Support Beams, Horizontal Diagonals,

Verticals, Diagonals and Horizontals. For better visualization, all groups are represented in Figure

9. Each group can be assigned with the properties set by the user, for example, material and cross-

section of the structural member.

Columns Main Chords

Support Bracing Cable Trays

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Pipe Support Beams Horizontal Diagonals

Verticals Diagonals

Horizontals

Figure 9. Highlighted members visualized by Rhino 7.

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5.3 Creation of geometry of pipeline bridge

The utilization of the script begins with defining the starting point of the parametric model, which

is the base point of one of the bridge's end columns. All values in the algorithm are in millimeters.

At the same time a user decides the angle of the direction of the bridge relative to this point in the

XY-plane. The final structure of the pipe rack can be located from -180 to 180 degrees from the

starting point. The Grasshopper's definition for these actions can be seen in Figure 10.

Figure 10. The starting point of the parametric model.

The script creates the pipeline bridge's geometry based on the parametric input values presented

in Figure 11. The user defines numeric values for height, width, length, elevation, and the number

of column sets. After that, the user decides the number of vertical beams in one span of the

pipeline bridge and the number of diagonals between columns, if there are any, and the number

of tiers for pipe support. Finally, the user chooses the pattern of diagonals individually for the

Diagonals, Horizontal Diagonals, and Support Diagonals from eight available variants. Figure 12

represents a side view of the pipeline bridge with different Diagonals patterns. Pattern Diagonals 6

and 7 can not be selected for Support Diagonals, as there are no additional beams between the

spans. Additionally, the user can add cable tray beams and define the amount of it, the length,

side of placing, the distance between a cable tray and horizontal beam.

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Figure 11. Inserted parametric values and their graphical representation in Rhino 7.

Pattern Diagonals-0: no diagonals Pattern Diagonals-1: single-diagonal, alternate

direction bracing

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Pattern Diagonals-2: single-diagonal, alternate direction bracing (inverted)

Pattern Diagonals-3: single diagonal bracing in one direction

Pattern Diagonals-4: single diagonal bracing in one direction (inverted)

Pattern Diagonals-5: X-bracing

Pattern Diagonals-6: single diagonal bracing, alternating each span

Pattern Diagonals-7: single diagonal bracing, alternating each span (inverted)

Figure 12. All available pattern types for diagonals.

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The setting of the model's geometry starts with creating the first bay points in the YZ-plane by

point starting point displacement in several directions driven by parametric values. The points are

connected by a line component, which creates initial two-dimensional frame consist of columns

and horizontal beams. Figure 13 is showing the Grasshopper definition for the first bay in the

structure.

Figure 13. A basic-2D frame of parametric bridge.

The script uses the values obtained by mathematical operations on the parametric values. For

ease of use, especially for those values that were used more than once, separate boxes were

created—for example, Distance between chords and Column Spacing as depicted in Figure 14.

From the panel, the user can check the numeric value of the obtained data, and if it exceeds the

maximum allowable value, parametric inputs can be corrected.

Figure 14. Calculated parametric values in Grasshopper.

In some cases, the task requires the use of additional parameters. A custom script could be

developed, for example, in Python to expand the functionality of the Grasshopper. In the

algorithm developed for this thesis, there is one custom component, which basically sets the range

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of values for the elevation height, limiting them with the minimum value defined by the user and

maximum total height value. The component and python script can be seen in Figure 15.

Figure 15. Custom Python component for Elevation.

When the geometry of the two-dimensional frame was defined, to distribute it on the length of

the bridge the series component was utilized to count the number of copies of the selected lines

and points and copy it in the X-direction. After that, points lying in the same plane in the upper

part were selected and connected by a vector with an assigned value for the length of the bridge.

These actions generate the columns, end span horizontals, and main chords, as displayed in Figure

16.

Figure 16. The basic structure of a pipeline bridge.

After that, the creation of horizontal beams, vertical beams, and diagonals has been started. The

same logic and component set was used to create the vertical, plane, and support bracing.

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However, there were some differences. Firstly, the one span has been taken as an initial segment.

The main chord lines were divided by the number of segments in one span. Then the collection of

points obtained was combined in XY-plane for plane bracing and in XZ -plane for vertical bracing,

while for support bracing, the points were obtained from the division of column line below the

chords in the YZ-plane as shown in Figure 17.

The instructions below are for vertical bracing. Relative Item component was used to extract two

lists from a single list and, depending on the relative offset input, create a line between output A

and B. Different offsets allowed to construct the verticals/horizontals and diagonals with a

different direction. For the verticals, before putting the list in the tree, the start and endpoints

were eliminated from it as verticals from the start and end of the span would be intersected with

the columns. Then the diagonals list was divided again, but this time by Dispatch Component that

allowed getting diagonals with alternating direction. The various diagonal outcomes were merged

and collected in a Stream Filter Component to create different patterns. Finally, verticals and

diagonals were distributed on the whole length of the structure and both sides in Y-direction. The

developed script in Grasshopper and its visual representation in Rhino can be seen in Figures 18

and 19.

(1) vertical

(2)plane

(3) support

Figure 17. The collection of points used for vertical/plane/support bracing.

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Figure 18. The Grasshopper script for vertical bracing.

Figure 19. The created vertical bracing with pattern type 2.

The part of the script for creating additional pipe support beams was added because in many

projects there is a need for additional levels in the pipeline bridge. Distance between pipe support

beams was determined by the division of distance between chords by the number of tiers. Then all

lower horizontal beams created previously were copied on that distance with a series component

(for the case when there is more than one beam should be created). The part of the script for the

pipe support beam is shown in Figure 20.

Figure 20. The Grasshopper script for pipe support beams.

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The cable trays were created by adding series of lines with a certain length on the given distance

from upper horizontal beams, distributed on the whole length of the bridge with the step equal

length of one segment in the span.

5.4 Integration with Tekla

As soon as the geometry creation of a pipeline bridge was completed, the Tekla components were

added to the algorithm. The final output of the member's curve was connected with Tekla's

components for beam/column composing. The attributes are also added into the algorithm, such

as material, profile, position, and numbering. All the components involved in the creation of

column members in Tekla are presented in Figure 21. The material and profile for members are

chosen either from the Tekla catalog or inserted by hand in the text panel. The attributes for the

component can be selected as default properties or decided by the user. There are attributes for

the columns endplate in the algorithm that controls the size of the plate, bolts size, distance, and

tolerance.

Figure 21. Set of Grasshopper components used for displaying columns in Tekla.

After all member parameters were linked with Tekla components in the same manner, the whole

structure was finally integrated into the Tekla Structures. The two parametric model views are

presented in Figure 22. One is algorithm visualization in Rhino 7 and the other in Tekla structures.

The model is accurate and easy to use, with the ability to display all changes made in Grasshopper

simultaneously.

26

(1)

(2)

Figure 22. The visual representation of Grasshopper’s algorithm in (1) Rhinoceros 7, (2) Tekla

Structures.

5.5 Tests

The functionality of the developed algorithm is proven by testing. Although the features of the

software used made it possible to see the result of the algorithm in action step by step as it was

developed, two sets of tests with various input data were carried out to verify the workability of

the pipeline bridge parametric model. The testing procedure was as follows: first, a new empty

model was opened in Tekla, then the file with the algorithm in Grasshopper was launched. Input

data was selected at random. Material and cross-sections for the members were selected either

from Tekla's catalog or inserted by the user. The general arrangement drawings were generated

from the resulting structure and used as evidence for the algorithm's functioning.

5.5.1 Test 1

The starting point for the first test model was chosen as follows: { 2500, 3000, 5000 }. All bridge

geometry is built at an angle of 30 degrees relative to the x-axis. The bridge is assigned with a

height of 10 meters, a width of 5 meters, and a length of 50 meters. The height of the elevation is

6 meters. There are five sets of columns along the entire length at the same distance from each

other, which construct four equal spans with column spacing of 12,5 meters. There are two

vertical sets in one span, making the distance between verticals equal to 4,166 m. The

configuration consists of 3 tiers to support pipes and one cable tray support beam on the left side

with a length of 1,3 meters located on 0,8 meters from the upper horizontal beam side. There are

three diagonals between one set of columns divided into three equal spans of 2 meters. The

27

diagonals are created as single-diagonal, alternate direction bracing (inverted); the horizontal

diagonals as single diagonal bracing, alternating each span; and support diagonals as single

diagonal bracing. Figures 23 and 24 illustrate inputs made for test 1. The 3D model generated with

the specified inputs is shown in Figure 25.

Figure 23. Grasshopper inputs for test 1.

Figure 24. Calculated dimensions for test 1 in Grasshopper.

For demonstration, steel grade S355J2 for pipe rack’s structural members and the profiles with the

following values were used:

• Main Chords-HEA360

• Columns-HEA450

• Verticals-CFRHS200X200X8

• Vertical Diagonals-CFRHS150X150X12.5

• Horizontal Beams-HEA200

• Horizontal Diagonals-CFRHS180X180X10

• Cable tray Support Beams-HEA140

28

• Support Bracing Beams-CFRHS200X200X10

• Pipe Support Beams-HEA200

Figure 25. Output Tekla model from test 1.

The more detailed information for the results of the first test can be obtained in Appendix 1. As

shown in the drawing of Appendix 1 dimensions, сross-sections and material correspond to those

indicated in the script, which proves the successful integration of the working parametric model

from the Grasshopper into the Tekla.

5.5.2 Test 2

The starting point for the second test model was chosen with the following coordinates: { 0, 0,

7600 }. The pipeline bridge was constructed at an angle of -55 degrees relative to the x-axis. The

designated height is 8,750 meters, the width is 6,200 meters, and the length is 32,350 meters. The

height of the elevation is 4,500 meters. There are four sets of columns along the entire length at

the same distance from each other, which construct three equal spans with column spacing of

10,783 meters. There is one set of verticals in one span, which makes the distance between

verticals equal to 5,391 meters. The configuration consists of four tiers to support pipes and no

cable trays. There are two diagonals between one set of columns with two equal spans of 2,250

meters. The diagonals are created as single diagonal bracing, alternating each span (inverted); the

horizontal diagonals as X-bracing; and support diagonals as single-diagonal, alternate direction

29

bracing (inverted). Figures 26 and 27 illustrate input values that define the geometry of the

pipeline bridge made for test 2.

Figure 26. Grasshopper inputs for test 2.

Figure 27. Calculated dimensions for test 2 in Grasshopper.

In test 2, the material and profiles input was taken from the text panel; it was decided to assign

different steel grades for groups of members that are shown in Table 2. The column endplate type

was chosen from the Tekla catalog and its attributes were taken from text panel information as

well. The plate component and its attributes can be seen in Figure 28 and the 3D model generated

in Tekla with the inputs specified in test 2 is shown in Figure 29.

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Table 2. Cross-sections and material for structural members selected for test 2.

Columns- RHS350*12 S355JR

Main Chords- RHS300*10

S235JR Verticals- RHS250*12

Horizontal Beams- RHS250*200*12

Pipe Support Beams- RHS250*200*12

Vertical Diagonals- RHS200*12

S235J0 Horizontal Diagonals- RHS160*120*12

Support Bracing Beams- RHS200*10

Attributes are written in the text panel in

Grasshopper. By order: the distance between bolts along the length of the plate, the

distance between bolts along the width of the plate, plate’s length, plate’s width, plate’s

thickness, bolt’s diameter, tolerance.

The same attributes automatically displayed in the Tekla component properties

Figure 28. Column endplate attributes.

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Figure 29. Output Tekla model from test 2.

Appendix 2 consists of a drawing and part list for a structure build by test 2 settings and should be

referred to for more details. The dimensions coincide with the input parametric values; the cross-

section and material in the Tekla model are the same as those specified in the algorithm. Based on

the results of the two tests, it can conclude that the parametric algorithm does its job of

generating the pipeline bridge structure and successfully export it to Tekla Structures.

6 CONCLUSION

The thesis achieved its goal of creating a parametric model for a pipeline bridge. The model is

ready to use as a tool to quickly create the shape and direction of the bridge for further detailing.

The entire geometric structure can be defined by the user along with the profile's cross-sections

and material selection and instantly displayed in Tekla with the possibility of adjustment. As

predicted, the repetitive structure of the pipeline bridge was easy to automate, and even when

creating only a basic model, the algorithm plays as a time-saving tool for the user. The tests

carried out confirmed the absence of errors, which allows ensuring the generation of an accurate

structure according to the intended design.

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Modeling with a parametric approach is fundamentally different from the conventional methods

for working with pipeline bridges. At the very beginning, the parametric approach may take more

time since it is necessary to process a large amount of information in order to link it in the

algorithm. However, this may make sense in the long term since the more complex and diverse

the model, the more quick and accurate design solutions it can provide. In the case of the

developed algorithm, the user has the opportunity to choose the appropriate type of bracing

following the specified requirements, which means that the model is not limited to one design

solution.

To summarise the above, parametric modeling is an excellent tool for creating design solutions in

a new way; the currently developed model has the potential to be used in the pipeline project,

simultaneously allowing improvement and future development.

6.1 Further use

As it was mentioned before, The Grasshopper algorithm can further be developed into a more

complex and full definition that will also include structural analysis and more versatile options. The

following may constitute the object of future development:

• Including Finite Element Analysis in the script via Karamba (Grasshopper plugin)

• Adding an option to create a pipeline bridge with a non-consistent span length, as in real

life this is usually the case

• Adding more Tekla components to create steel connections

• Enabling more pipeline bridge configurations in the script

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Appendix 1 / 1

Appendix 1: Documentation for Test 1

Drawing

Appendix 1 / 2

Part List Table

PartPos Profile No. Material Length (mm) Net Area(m2) for one Net Area(m2) for all Net Weight(kg) for one Net Weight(kg) for all

B-/1   CFRHS180X***   24   S355J2   6509   4.41   105.77   329.88   8338.22  

B-/2   CFRHS150X***   24   S355J2   5776   3.10   74.30   281.29   7481.24  

B-/3   HEA360   16   S355J2   12500   22.93   366.80   1401.23   21430.50  

B-/4   CFRHS200X***   16   S355J2   4000   3.06   49.00   186.02   3086.75  

B-/5   HEA140   12   S355J2   1300   1.03   12.39   32.06   369.58  

B-/6   CFRHS200X***   15   S355J2   5385   4.08   61.16   306.76   4819.18  

B-/7   HEA200   16   S355J2   5000   5.68   90.88   211.28   3205.94  

B-/8   CFRHS200X***   10   S355J2   5000   3.79   37.85   284.82   2983.00  

B-/9 HEA200   32   S355J2   5000   5.68   181.76   211.28   6411.88  

C-/1   HEA450   10   S355J2   9970   20.05   200.50   1393.11   13443.49  

Total for         175 members 1180.41 72417.59

Appendix 2 / 1

Appendix 2: Documentation for Test 2

Drawing

Appendix 2 / 2

Part List Table

PartPos Profile No. Material Length (mm) Net Area(m2) for one Net Area(m2) for all Net Weight(kg) for one Net Weight(kg) for all

1001   PL25*500   8   S235JR   500   0.55   4.40   49.06   392.50  

B-/1   RHS300*10   12   S235J0   10783   12.95   155.42   981.90   11782.80  

B-/2   RHS200*20***   12   S235J0   6865   5.50   66.02   486.32   5835.83  

B-/3   RHS160*12***   24   S235J0   8216   4.55   109.31   396.28   9510.66  

B-/4   RHS250*20***   28   S235JR   6200   5.56   155.67   497.60   13932.86  

B-/5   RHS250*12   6   S235JR   4250   4.26   25.57   381.13   2286.80  

B-/6   RHS200*10   8   S235J0   6596   5.28   42.28   393.50   3147.97  

B-/7   RHS200*10   4   S235J0   6200   4.97   19.87   369.89   1479.57  

C-/1   RHS350*12   8   S355JR   8725   12.23   97.85   1111.20   8889.62  

Total for         110 members 676.39 57258.59