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AVEVA Plant

(12 Series)

Structural Modelling

(Basic)

TM-1101

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Revision Log

Date Revision Description of Revision Author Reviewed Approved

09/05/2008 0.1 Issued for Review KB

15/05/2008 0.2 Reviewed KB NG

27/05/2008 1.0 Approved for Training 12.0.0.3 KB NG RP

15/01/2009 2.0 Approved for Training 12.0.SP3 KB NG RP

Updates

All headings containing updated or new material will be highlighted.

Suggestion / Problems

If you have a suggestion about this manual or the system to which it refers please report it to the AVEVA Group Solutions Centre at gsc@aveva.com

This manual provides documentation relating to products to which you may not have access or which may not be licensed to you. For further information on which products are licensed to you please refer to your licence conditions.

Visit our website at http://www.aveva.com

Disclaimer

Information of a technical nature, and particulars of the product and its use, is given by AVEVA Solutions Ltd and its subsidiaries without warranty. AVEVA Solutions Ltd. and its subsidiaries disclaim any and all

warranties and conditions, expressed or implied, to the fullest extent permitted by law.

Neither the author nor AVEVA Solutions Ltd or any of its subsidiaries shall be liable to any person or entity for any actions, claims, loss or damage arising from the use or possession of any information, particulars or errors in this publication, or any incorrect use of the product, whatsoever.

Trademarks

AVEVA and Tribon are registered trademarks of AVEVA Solutions Ltd or its subsidiaries. Unauthorised use of the AVEVA or Tribon trademarks is strictly forbidden.

AVEVA product names are trademarks or registered trademarks of AVEVA Solutions Ltd or its subsidiaries, registered in the UK, Europe and other countries (worldwide).

The copyright, trademark rights or other intellectual property rights in any other product, its name or logo belongs to its respective owner.

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Copyright

Copyright and all other intellectual property rights in this manual and the associated software, and every part of it (including source code, object code, any data contained in it, the manual and any other documentation supplied with it) belongs to AVEVA Solutions Ltd. or its subsidiaries.

All other rights are reserved to AVEVA Solutions Ltd and its subsidiaries. The information contained in this document is commercially sensitive, and shall not be copied, reproduced, stored in a retrieval system, or transmitted without the prior written permission of AVEVA Solutions Limited. Where such permission is granted, it expressly requires that this Disclaimer and Copyright notice is prominently displayed at the beginning of every copy that is made.

The manual and associated documentation may not be adapted, reproduced, or copied in any material or electronic form without the prior written permission of AVEVA Solutions Ltd. The user may also not reverse engineer, decompile, copy or adapt the associated software. Neither the whole nor part of the product described in this publication may be incorporated into any third-party software, product, machine or system without the prior written permission of AVEVA Solutions Limited or save as permitted by law. Any such unauthorised action is strictly prohibited and may give rise to civil liabilities and criminal prosecution.

The AVEVA products described in this guide are to be installed and operated strictly in accordance with the terms and conditions of the respective licence agreements, and in accordance with the relevant User Documentation. Unauthorised or unlicensed use of the product is strictly prohibited.

Printed by AVEVA Solutions on 16 January 2009

© AVEVA Solutions and its subsidiaries 2001 – 2007

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1 Introduction ... 9 1.1 Aim ... 9 1.2 Objectives ... 9 1.3 Prerequisites ... 9 1.4 Course Structure... 9

1.5 Using this guide ... 9

2 Setting Up the Design Database Hierarchy for Structural Modelling... 11

2.1 How PDMS Stores Structural Modelling Data ... 11

2.2 Considerations When Creating the Hierarchy for Structural Models... 11

2.3 Creating Structural Administrative Elements ... 12

2.4 Starting the Structural Modelling Applications ... 13

Exercise 1 – Creating the Design Hierarchy ... 14

3 Beams & Columns ... 15

3.1 How PDMS Represents Structural Profiles ... 15

3.2 Initial Settings... 17

3.2.1 Section Specification... 17

3.2.2 Storage Areas ... 18

3.2.3 Automating Profile and Primary Node Allocations ... 19

3.2.4 Pline Rules ... 19

3.3 Creating Sections... 21

3.3.1 The Section form... 21

3.4 Section Connectivity ... 23

3.4.1 Checking Connectivity... 25

3.5 Creating a Pipe Rack - A Worked Example ... 26

3.5.1 Initial Settings ... 27

3.5.2 Creating Sections... 28

Exercise 2 – Creating an Equipment Support Frame... 30

4 Modifying Structural Sections... 32

4.1 Positioning... 32 4.1.1 Explicitly (AT) ... 32 4.1.2 Relatively (BY)... 33 4.1.3 Extend Through... 33 4.1.4 Extend By ... 35 4.1.5 Drag Explicitly... 36

4.1.6 Align Secondary Nodes... 37

4.1.7 Joint Freedom ... 37

4.2 Orientation ... 38

4.2.1 Axes ... 38

4.2.2 Rotate... 39

4.2.3 β Angle (Beta Angle) ... 39

4.2.4 Flip... 40

4.3 Copying... 40

4.3.1 Copying with Multiple Attached ... 40

4.4 Modifying the Pipe Rack - A Worked Example ... 42

4.4.1 Copy Offset ... 42

4.4.2 Position Relative... 42

4.4.3 Using a List... 42

4.4.4 Extend Through... 42

4.4.5 Create Additional Sections... 42

Exercise 3 – Modifying the Equipment Support Structure... 44

5 Beam & Column Utilities ... 45

5.1 Bracing Configurations ... 45

5.1.1 Available Bracing Configurations ... 47

5.2 User Defined Pline Rules ... 48

5.3 Bracing Gaps... 49

5.3.1 Available Gapping Configurations... 51

5.4 Splitting Structural Elements... 52

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5.5 Splicing Sections ... 54

5.6 Merging Sections ... 55

5.7 Fillet Sections... 56

5.8 Mitring Sections ... 57

5.9 Pline Rules and Bracing Configurations - A Worked Example ... 59

5.9.1 Create a Pline Rule ... 59

5.9.2 Create Bracing ... 59

5.9.3 Bracing Gaps... 60

Exercise 4 – Adding Bracing to the Equipment Support Structure ... 61

6 Section Fittings and Joints... 62

6.1 Section Fittings ... 62

6.1.1 The Create Fitting form ... 62

6.1.2 Creating Section Fittings ... 63

6.2 Joints... 65

6.2.1 Joint Specification form ... 65

6.2.2 Modify Joint Specification... 67

6.3 Creating Section Fittings and Joints - A Worked Example ... 68

6.3.1 Section Fittings... 68

6.3.2 Joints ... 69

Exercise 5 – Adding Section Fittings and Joints to the Equipment Support Structure... 70

7 Panels & Plates ... 72

7.1 How PDMS Represents Panels & Plates ... 72

7.2 Panel Hierarchy and Attributes ... 72

7.2.1 PANE element... 72 7.2.2 PLOO element... 73 7.2.3 PAVE element... 73 7.3 Initial Settings... 73 7.3.1 Panel Specification... 73 7.3.2 Storage Areas ... 73 7.4 Creating Panels ... 74

7.4.1 The Create Panel form... 74

7.4.2 Hints on Creating Panels ... 76

7.5 Modifying Panels... 77

7.5.1 The Loop Vertex Editor form ... 77

7.5.2 Moving the Panel Origin... 80

7.5.3 Modifying Panel Thickness ... 81

7.5.4 Modifying Panel Justification... 81

7.6 Connecting Panels... 82

7.6.1 Connection Modes ... 82

7.6.2 The Panel Connection Form ... 83

7.6.3 Panel to Section Connections ... 83

7.6.4 Panel to Panel Connections... 84

7.7 Creating and Modifying Panels - A Worked Example ... 85

7.7.1 Creating the Panel ... 85

7.7.2 Modifying the Panel... 87

7.7.3 Using a Vertex Group... 88

7.8 Connecting Panels – A Worked Example... 90

Exercise 6 - Creating and Modifying Panels... 91

8 Negative Extrusions ... 92

8.1 Negative Extrusion Hierarchy and Attributes ... 92

8.1.1 NXTR element... 92

8.1.2 LOOP element... 92

8.1.3 VERT element... 92

8.2 Creating Negative Extrusions... 93

8.2.1 The Create Negative Extrusion form... 93

8.2.2 Representation... 93

8.2.3 Settings ... 93

8.2.4 Create Methods... 93

8.3 Modifying a Negative Extrusion ... 94

8.4 Creating and Modifying Negative Extrusions - A Worked Example ... 94

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9 Panel Fittings ... 96

9.1 Creating a Panel Fitting... 96

9.1.1 The Create Panel Fitting form ... 96

9.2 Modifying Panel Fittings ... 98

9.3 Creating and Modifying Panel Fittings - A Worked Example ... 98

10 Standard AVEVA Generic Types ... 100

10.1 Generic Type BOX... 100

10.2 Generic Type ANG ... 101

10.3 Generic Type TUBE ... 102

10.4 Generic Type BEAM... 103

10.5 Generic Type DINI ... 104

10.6 Generic Type BSC... 105

10.7 Generic Type DINU... 106

10.8 Generic Type TEE ... 107

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1 Introduction

AVEVA PDMS allows designers to utilise an array of applications contained within the program modules. This training guide provides basic discipline specific training for the Structural Modelling application contained within the Design module.

1.1 Aim

The aim of this training guide is to provide designers with the basic knowledge and skills necessary to create and modify structural models.

1.2 Objectives

• Introduce PDMS concepts specific to the Structural Modelling application.

• Make designers aware of the administration elements required by the application. • Explain how to create a variety of structural elements.

• Explain how to manipulate and modify structural elements.

• Understand how to apply section fittings, section joints and panel fittings.

1.3 Prerequisites

Trainees must have completed the PDMS Foundations training course.

1.4 Course Structure

Training will consist of oral and visual presentations, demonstrations, worked examples and set exercises. Each workstation will have a training project, populated with model objects. This will be used by the trainees to practice their methods, and complete the set exercises.

1.5 Using this guide

Certain text styles are used to indicate special situations throughout this document, here is a summary; Menu pull downs and button press actions are indicated by bold dark turquoise text.

Information the user has to Key-in will be bold red text. Annotation for trainees benefit:

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Additional information

Refer to other documentation

System prompts should be bold and italic in inverted commas i.e. 'Choose function' Example files or inputs will be in the courier new font, colours and styles used as before.

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2 Setting Up the Design Database Hierarchy for Structural Modelling

PDMS data is stored in a hierarchical structure, similar to the directories and sub-directories used to access computer files. The Structural Modelling application requires specific administrative elements to be in place in order to maintain the system hierarchy. These administrative elements are considered in the sections that follow.

2.1 How PDMS Stores Structural Modelling Data

As with all PDMS Design databases that store discipline design data, the topmost element is the WORLD which owns the administrative sub-levels elements SITE and ZONE.

For structural modelling, the element types used below a ZONE are:

• Structure (STRU) • Framework (FRMW) • Subframework (SBFR)

The SBFR level is optional as structural components may be owned by a FRMW or a SBFR or a combination of both. The elements that represent physical structural components are: • Section (SCTN)

Panel (PANE)

Generic Section (GENSEC) – curved section.

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GENSECs are covered in the TM-1201 Structural Modelling (Advanced) training guide.

2.2 Considerations When Creating the Hierarchy for Structural Models

The splitting up of the database hierarchy for other disciplines may be more obvious than for the structural model. For example pipes may be grouped in zones by system, piping class or fluid code, and equipment may be grouped in zones by equipment type, systems, or physical location.

The structural hierarchy has more administrative elements than other disciplines. This allows the model to be broken down further. The hierarchy breakdown should be well thought out and have a meaningful structure.

Some company/project procedures require the structural model to be broken down by project build methodology, weight control purposes, material purposes, etc. If such procedures are not in use,

consideration should be given to the drawing deliverables that will be produced from the structural model. Draft, the PDMS Drawing Production module, uses a similar concept of a Draw List to that used in Design to define the contents of a ‘View’ on the drawing sheet. The construction of these Draft Draw Lists is greatly aided by a good hierarchy breakdown and well named significant elements.

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2.3 Creating Structural Administrative Elements

Before modelling can commence, the required hierarchy elements must be created. From the Design General application only SITE and ZONE elements can be created as these are common to all disciplines. The standard structural hierarchy elements may be created from the Create pull down menu in the Beams & Columns or the Panels & Plates application.

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The Walls & Floors and Access, Stairs & Ladders applications create their own hierarchy elements.

To create the structural administrative elements, select Create>Structure…, Create>Framework… or

Create>Sub-Frame… from the main menu to display the relevant form:

Significant elements, e.g. SITE, ZONE, STRU, FRMW and SBFR should normally be named to facilitate navigation around the model and to ease creation of Draw Lists and other model tools.

The Create forms enable the element’s Purpose attribute to be set to a pre-defined list of values by using the Purpose pull-down.

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Note: These standard Purpose attribute settings are used by the Walls & Floors and other applications.

The Purpose attribute may be set manually via the command line to any value which may be used by the other applications.

Clicking the Attributes… button on any of the Create forms displays the Modify Attributes form.

The Modify Attributes form shows the editable attributes for the element type being created. Some attributes are common whilst others are specific to the element.

Clicking an attribute, e.g. Function, displays a relevant form that enables the attribute value to be set.

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2.4 Starting the Structural Modelling Applications

The PDMS Design module contains four Structural applications to assist designers in creating structural models. These applications are:

• Beams & Columns – creation of structural profile elements • Panels & Plates – creation of plate type elements

• Walls & Floors – creation of wall, floor and screed elements

• Access, Stairs & Ladders – creation of access ways, stair towers, stair flights, ladders, platforms and hand railing elements.

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Note: The Walls & Floors and Access, Stairs & Ladders applications are not covered in this Training

Guide.

These applications may be accessed from the main menu by selecting: Design>Structures>Beams & Columns… (or other structural application) from the main menu.

Once the desired application has loaded, the Structures toolbar is displayed Beams & Columns

Panels & Plates Walls & Floors

The other applications may be started by selecting from the main menu again or by selecting one of the

application buttons on the Structures toolbar. The current application button is disabled.

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Exercise 1 – Creating the Design Hierarchy

The aim of this exercise is to create a simple hierarchy for the storage of structural elements created in worked examples and other exercises of this training guide.

• Login to the PDMS Design Module using the following details: Project: Sample

Username: USERA Password: A MDB: TRAINA

• Enter the Beams & Columns application by selecting Design>Structures>Beams & Columns… from the main menu.

• Check that you are at World (WORL) level in Design Explorer and select Create>Site… from the main menu to display the Create Site form:

Enter STABILISER in the Name textbox: and press the Return (Enter) key to confirm the name.

Click the OK button on the form to create the SITE element and dismiss the form. Note that the new element appears in the Design Explorer as the current element.

• Repeat this process using the appropriate options from the Create menu to create a Zone named

STRU.ZONE, a Structure named PIPERACK and a Framework named ROW_6.

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The row IDs referred to in the worked examples and exercises, e.g. ROW 1, reflect a pre-defined user

grid that is maintained for training purposes.

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3 Beams & Columns

The Beams & Columns application facilitates the creation of structural profiles, e.g. Pre-cast concrete profiles, steel I-beams, T-sections, Channels, Angles, Circular Hollow Sections, etc., in the design model. The application enables the profiles, once created, to be manipulated and modified to create the desired structural configuration. The application also enables the insertion of Catalogue fitting components, e.g. stiffeners, lifting lugs, etc, onto profiles and the application of Catalogue based joints to connected profiles.

3.1 How PDMS Represents Structural Profiles

To ensure design consistency and conformity to national or company standards, the definition of all profile shapes used in structural modelling are held in a Catalogue database.

Each individual structural profile (column, beam, brace, etc.) is represented in Design by a Section (SCTN) element. The SCTN has lots of attributes, many of which are set by placing or manipulating the element whilst others may be set via the Appware or manually. The definition of cross-sectional shape geometry of the profile is defined in a catalogue database. The shape is usually defined parametrically, such that the same definition may be used for many different profiles with the same generic shape but differing values e.g. depth, width, web thickness, flange thickness, etc.

The SCTN has a Specification Reference (Spref) attribute which points to a Specification Component (SPCO) element in the catalogue database. The specification acts as a selection mechanism and filters the available profiles to the user depending on choices made. The SPCO points at a Structural Profile (SPRF) element (also held in the catalogue database) via its Catalogue Reference (Catref) attribute. The Catref in turn references the geometry definition and other elements.

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Note: The SCTN may directly

reference the SPRF via its Spref attribute. However, this must be done manually via the command line or programmatically via a user macro or application.

When a profile is added to the design model, the position, orientation, and other attributes are set for the item in the Design database. However, the physical properties of the profile are specified by setting a cross-reference, called a Specification Reference (the Spref attribute of a SCTN), that points to an appropriate specification component in the Catalogue database. This specification component (SPCO) points, via its Catref attribute, to the catalogue profile component (SPRF).

The 2D cross-sectional geometry of a particular SCTN (I-beam, T-section, Channels, Angles, etc.) is defined in the Catalogue and the SCTNs SpecRef attribute is set to that profile. All other aspects of the SCTN geometry are defined by setting specific design attributes. Most of these attributes are set automatically by PDMS as the element is specified or manipulated graphically.

Two of the most important attributes are the Position Start (POSS) and Position End (POSE) which effectively determine the length and orientation of the element. These positions are determined from graphical picks, explicit co-ordinates, direction and distance or a combination of these methods. The 2D cross-section is ‘extruded’ from the POSS to the POSE.

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To provide a method of referring to individual edges and faces of the SCTN, each is identified by a named line running along the length of the profile. These lines, which are specified within the 2D geometry in the Catalogue, are called Plines. A section has a number of Plines that have a two, three or four letter abbreviation set to its PKEY attribute.

As an example, some of the most commonly used Plines for an I-shaped profile might be positioned and named as shown:

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3.2 Initial Settings

Before starting to create sections in the model some initial default settings must be made to suit the planned method of working.

3.2.1 Section Specification

The Default Section Specification, together with its Justification, Member line and Joint line settings (these terms are explained later), is displayed on the Beams & Columns toolbar.

The Default Section Specification is shown initially displayed as Unset, i.e. no section is specified.

Clicking the Set Default Profile Specification button displays the Section Specification (Default) form. This form is divided into two main areas, Specification Data and Pline Settings.

3.2.1.1 Specification Data

The default profile is selected by clicking the Specification button and selecting the required standard from the Catalogue entries displayed.

Following selection of the standard, the required profile is selected from the Generic Type list (which shows the range of profile types available in the Catalogue).

Having selected the profile type, a list of available serial sizes is displayed in the window below. Use the cursor to select the desired size from the scrollable list.

PDMS provides several standard specifications, for example British, American, Japanese, DIN, etc., which may be augmented or replaced by specific company standards.

3.2.1.2 Pline Settings

The Pline Settings lists allow the following attributes for the chosen section to be set: • Justification

• Member line • Joint line.

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Justification - sets the justification of the section, i.e.

Member line - sets the position of the line to be displayed in Draft, e.g. the section centreline.

Joint line - sets the Pline for joint geometry (normally NA).

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Note: The Joint line is not within the scope of this module.

Clicking the Apply button on the Section Specification (Default) form sets the section profile that will be used. The section specification and Pline settings are displayed on the Beams & Columns toolbar.

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Note: The Pline settings are displayed in the order Justification/Member line/Joint line.

3.2.2 Storage Areas

The Design database Storage Areas specify which Framework (or Subframe), SCTNs and PNODs (see Structural Connections) will be stored in when created. The storage areas should be specified prior to commencement of creating components for that particular area of the model. The current storage areas are displayed on the Beams & Columns toolbar.

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Making the Framework (or Subframe) where the components will be stored the CE and clicking the button to the left of the appropriate storage area sets the CE as the storage area and displays it on the toolbar.

The settings may also be made by selecting Settings>Storage Areas… from the main menu to display the Storage Areas form.

Making the FRMW or SBFR that will store the components the CE and clicking on the storage area required in the form sets it to the CE.

3.2.3 Automating Profile and Primary Node Allocations

By default, each time a new section is created it will automatically be associated with a profile from the catalogue that is the Default Profile Specification. Also by default, Primary nodes will not be created automatically at unconnected section ends. These defaults are controlled by the following buttons on the Beams & Columns toolbar.

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For an explanation of Primary Nodes (PNOD) see the Structural Connections section.

3.2.4 Pline Rules

The final setting to be made before commencing creation of profiles is the Pline Rule. When a section is created and connected to an existing section, the end points of the new section are usually positioned automatically by reference to the current Pline Rule. If this rule has not been set-up properly, the geometry at the point of connection may not be appropriate. Pline Rules determine which Pline of the existing section will be used to trim the new section to.

With no Pline rule set, which is the default setting, the new section is trimmed to the extremities of the existing section.

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In this example, the new section has terminated at the extremity of the existing section instead of the web, i.e. the NARO Pline.

With an appropriate Pline rule set, the new section will trim to the required Pline (i.e. the NAR Pline) and give the desired result.

PDMS provides one predefined Pline rule named Normal that cannot be modified. The Normal Pline rule is: PKEY EQ ‘NA’ OR CCON EQ ‘ANY’

This means that a new section will connect to the NA Pline unless it first encounters a Pline whose CCONNECTION (abbreviated to CCON) is set to ANY.

Pline rules are also used to determine the availability of Plines for graphical picks when creating or positioning panels, fittings, etc. The Pline is available if it meets the criteria set out in the Pline Rule. Pline rules are set by selecting Settings>Pick Filters>Plines… from the main menu to display the Pline Filter form.

Available Pline Filters are displayed. Selecting the required rule with the cursor sets the rule and the form is dismissed.

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3.3 Creating Sections

Sections are created by selecting Create>Sections>Straight… from the main menu to display the Section form and activate Positioning Control toolbar.

3.3.1 The Section form

The Section form is divided into three areas which are explained in the following sections:

3.3.1.1 String Method

On the Section form, the method by which sections will be created can be specified by clicking one of the three option buttons.

Single – Start and End Points are individually defined for each section.

Continuous – Start point of subsequent sections is the end point of previous.

Radial – Start position for subsequent sections is the same as first.

3.3.1.2 Create Option

Initially, when the Section form is displayed, there is only one active button under Create Option to define the start of the section explicitly, which is the only practical option at this stage.

This button is used to define the start of the section explicitly, i.e. by entering explicit X, Y and Z co-ordinates.

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It should be noted that the start position of the section may also be defined by other options under the

Create Option or by using the Positioning Control toolbar if the context is right, for example there is a

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Clicking the Explicit button displays the Define section start

form.

The required East (X), North (Y) and Up (Z) co-ordinates may be entered and the Start position will be shown by an aid in the 3D View. The default wrt World, defines the co-ordinate system by which the position is specified.

Clicking the OK button on the Define section start form confirms the entered co-ordinates and changes the Creation Option display by activating a second button.

The end position may now be defined by using either of the two buttons. Clicking the Explicit button again will display the Define section end form which is used in exactly the same way as the Define section start form.

Clicking the Direction & Distance button will display a different Define section end form. A direction, with respect to the World or other co-ordinate system, is entered together with the required distance from the section start position. As the distance is entered and return pressed, the end position will be shown in the graphical view and an aid line drawn from the start to the end position.

It should again be noted that the end position of the section may also be defined by other options under Create Option or by the Positioning Control toolbar if the context is right.

The other Creation Option buttons are:

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Perpendicular From - creates a section perpendicular to the section specified for the new section start

Perpendicular To – creates a section perpendicular to a selected section.

By default, Secondary Nodes are automatically created. This facility may be switched off by un-checking the Secondary Nodes check box under Creation Option. For an explanation of Secondary Nodes see Structural Connections.

3.3.1.3 Verification

The Verification section of the Section form contains a Confirm check box that allows the user to check the position of each new section before it is added to the database. If the Confirm box is checked the Accept and Reject buttons are enabled, to accept or reject the section creation in the displayed location.

The Redefine Start button may be clicked at any time during section creation to start the definition of the section again.

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3.4 Section Connectivity

A connection between two SCTN elements is facilitated by a Secondary Joint (SJOI) element.

The SJOI is owned by a Secondary Node (SNOD), which is positioned on the

justification line of the Owning section at the intersection between the Attached and Owning sections.

Sections are connected automatically when they are created, providing the Secondary Nodes check box on the Section form is checked.

When SCTN elements are connected the SJOI element is created, owned by the SNOD element of the Owning section.

The SJOI has a Cref (connection reference) attribute that points to the name of the Attached section.

The Attached section has two attributes, Joistart (Joint start) and Joiend (Joint end) that point to the name of the SJOI element by which they are attached to their respective Owning members, thus creating a ‘circular’ reference.

SCTN elements may also be connected explicitly by using the Connect menu. Selecting Connect>Connect from the main menu prompts the user to choose the section to attach to and the section end(s) to be attached. The selection process is terminated by pressing the Esc key.

SNODs and SJOIs will be created at each Owning/Attached intersection. Where two or more sections connect to the Owning section at the same point, a single SNOD is Attached created which owns two or more SJOI elements. The Cref attribute of each SJOI points to the name of the relevant Attached section. Connections may be updated following position changes to the owning or attached sections by using one of the following selections from the Connect menu:

Connect>Trim to Pline - Trims the section to a Pline selected by the system in accordance with current Pline rule, i.e. the POSL attribute of the SJOI element is modified.

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Connect>Trim to Section - Trims the section according to the current POSL setting of the PJOI

element. This may result in the attached member not being correctly connected, e.g. if the Beta Angle of the Owning SCTN has changed.

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The Joint Dominant and Joint Subordinate options are detailed later in this training guide.

Secondary Node (SNOD) elements are positioned along the justification line of the owning section at the POSS or POSE position of the attached member(s). An SNOD elements primary function is to own an SJOI element and allow one section to connect part way along another.

SNOD elements are owned by the Owning section.

Secondary Joint (SJOI) elements are used to connect two sections where they intersect at an SNOD and their primary functions are:

• providing connectivity to the structural model • trimming attached members

• holding the Specification Reference for a joint.

SJOI elements are owned by an SNOD.

Primary Node (PNOD) elements have two main functions:

• as analytical points when using PDMS data for structural analysis

• to own a Primary Joint for referencing a catalogue joint element on an un-connected section end. A PNOD element may be created automatically, see Initial Settings, or explicitly at section ends by selecting Create>PNode at SCTN end from the main menu.

PNOD elements are owned by FRMW or SBFR elements, and sit at the same level in the hierarchy as

SCTN elements. PNOD elements may own more than one Primary Joint element (PJOI). PJOI elements are used for referencing a catalogue joint element on an unconnected section end, for example a baseplate for a stanchion.

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3.4.1 Checking Connectivity

The connectivity of sections in the model can be checked by navigating to a suitable element in the hierarchy, e.g. a FRMW or SBFR, selecting

Query>End Connections… from the main menu to display the Highlight Connections form.

The form will show all SCTN elements in the CE that have Both ends connected, Neither end connected and One end connected.

Checking the appropriate check box will

graphically highlight the SCTN elements of the CE in each category in the colour shown on the form. The default colours can be changed by clicking on the colour button to display a colour form for that selection.

Clicking a colour button will set that colour for the selected category.

For the One end unconnected category the SCTN will display a tag at the unconnected end as well as being displayed in the highlight colour.

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3.5 Creating a Pipe Rack - A Worked Example

This worked example demonstrates how to construct some initial frames for a simple pipe rack using different section sizes. The text and accompanying drawings provide step-by-step guidance to create the Pipe Rack.

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3.5.1 Initial Settings

• Ensure the Beams & Columns application is current or select Design>Structures>Beams & Columns

from the main menu to enter the application

• Make initial settings for the storage areas. Ensure that SBFR ROW_6 is the CE and click the Set Section Storage Area and Set Node Storage Area buttons on the Beams & Columns toolbar. • For the Default Profile Specification, click the Set Default Profile Specification button on the Beams &

Columns toolbar, set the specification to British Standard and the Generic Type to Universal Columns. Select 203x203x46kg/m from the displayed list, set the Justification to NA, leaving the Member line and Joint line at NA. Click on the Apply button and then the Dismiss button on the form. • The Beams & Columns toolbar should now look like this:

• Set the Pline rule to Normal by selecting Settings>Pick Filters>Plines… from the main menu and selecting Normal from the displayed Pline Filter form.

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• Select Utilities>User Grid Systems… from the main menu to display the User Grid Systems form.

Select Stabiliser_Grid from the Grid Systems list and click the Gridline IDs radio button. Click the

Display button and the Set View Limits to Grid button.

3.5.2 Creating Sections

• Create the first section by selecting Create>Sections>Straight…

from the main menu to display the Section form. Make sure that the String Method is set to Single and that the Create Secondary Nodes check box is checked.

• Click the Explicit button to display the Define section start form. Enter the co-ordinates West 305360, North 309680, and Up

100400.

• Click the OK button.

• Click the Direction and Distance button on the Section form to display the Define section end form.

• Enter the Direction as U and a Distance of 6000. Click the OK

button.

• With the Section form still displayed click the Explicit button again, noting on the Define section start form that the displayed co-ordinates are those defining the end position of the previously created SCTN.

• Enter the section start co-ordinates as: West 305360

North 304800

Up 100400

• After clicking the OK button on the Define section start form, click the Direction and Distance button to display the Define section end form and enter the Direction as U and a Distance of 6000. Click the OK button.

• Click the Walk to Draw List button on the 3D View and set the view direction to Iso 3. There should now be two parallel 203x203x46kg/m sections in the 3D View.

• The next task is to create two horizontal beams for the pipe rack frame using the cursor to select the start and end positions of the sections rather than enter explicit co-ordinates. Change the Default Section Specification to Universal Beams 203x133x25kg/m, the Justification line to TOS and create the horizontal sections using the Positioning Control toolbar. Set the Pick Type to Element and Pick Method to Snap.

• Click the first column created near to its upper end to define the Start position of the new section, noting that the Start label is displayed adjacent to the section. Click the upper end of the second column created to define the End position of the new section. A new UB 203x133x25kg/m section is created spanning between the two columns.

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• Set the Positioning Control toolbar Pick Method to Distance and enter a distance of 1520. Click near

the upper end of the first column, then near the upper end of the second column, to create a new horizontal beam. Note that the beams have been trimmed to the TOS or BOS Pline of the columns. • Toggle wire frame display mode on by pressing F8 on the keyboard and zoom in to one of the

connections and note the SNOD that has been created.

• Next the 1000mm long stub on the southern column will be created. Set the Pick Method on the Positioning Control toolbar back to Snap and click near the top of the southern column. Use the Direction & Distance button with a direction of S WRT /* and a distance of 1000 to create the beam. • Save Work.

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Exercise 2 – Creating an Equipment Support Frame

The exercises contained in this training guide allow the user to create an equipment support frame using a range of standard sections, bracing members, panels, and fittings. The drawings below, coupled with instructions in each exercise, provide the information necessary to model the structure correctly. Equipment Support Structure Frame

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In the Zone STRUC.ZONE create a new STRU named EQUIP_SUPPORT and a FRMW named ROW_C. Model Row C (only) of the structure using the drawings above to ascertain co-ordinates, dimensions and profile sizes. The other parts of the structure will be modelled in later exercises.

Remember to reset storage areas and check the Pline rule. Check all the sections are correctly connected.

L

Note: the columns of Frame C will not be orientated correctly when modelled; however, they will be

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CHAPTER 4

4 Modifying Structural Sections 4.1 Positioning

Elements that have position attributes (for example SCTNs) can be re-positioned in a variety of ways. The two main methods are position Explicitly and position Relatively.

4.1.1 Explicitly (AT)

Positioning explicitly allows the user to position elements at specific co-ordinates with respect to the WORLD or other design elements. Selecting Position>Explicitly (AT)… from the main menu will display the Positioning Control toolbar and the Explicit Position form. By default the Start position of the current element is displayed showing East/West, North/South and Up/Down co-ordinates with respect to the world.

The Datum options list allows the user to specify the point on the element to which the position co-ordinates will apply. The user may specify Start, End, Centre or Designate Position.

Depending on the option specified applying modified co-ordinates will have the following effect on the element:

Start - Relocates the start position of the element to the specified co-ordinates, leaving its end position unchanged.

End – Relocates the end position of the element to the specified co-ordinates, leaving its start position unchanged.

Centre – Relocates the entire element, locating its centre at specified co-ordinates and modifying the start and end positions.

Designate Position – used in conjunction with the Positioning Control toolbar, the user can specify a point on the element for re-positioning. The entire element is relocated, or re-orientated, with the Designated Position at the specified co-ordinates and the start and end positions modified.

On opening the Explicit Position form a ‘bounding box’ is displayed around the element together with an axes aid, showing the cardinal directions, and a label showing the Start position.

Changing the Datum re-displays the axes aid and label to the specified position.

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To define a position explicitly, enter the required co-ordinates in the appropriate direction textbox. If

necessary, use the wrt textbox to identify the element whose co-ordinate system is to be used for the position data. The bounding box will adjust to show the new position and clicking the Apply button on the form will re-position the element.

To define a position by reference to existing design items, use the Positioning Control toolbar and the cursor to identify the required positions by picking them in the graphical view. If required, use the Lock check boxes to fix the current co-ordinate along any axis.

To position another section, use the Select menu options on the form to change the focus of the form. Use the CE or Owner option if the required item is selected in the design explorer, or use the Pick or Pick Owner option and then select the required item with the cursor when prompted. The form will display the current position and the user can then change any part of this by entering new values.

4.1.2 Relatively (BY)

Positioning relatively allows the user to position elements by a specified distance, along one or more axes, from its current position. The directions can be with respect to the world or other design elements. Selecting Position>Relatively (BY)

from the main menu displays the Positioning Control toolbar and the Position By form.

The form allows the user to specify a distance along a single axis or varying distances along any combination of the three axes. By default the axes directions are with respect to the world although any valid design element may be used. An axes aid is displayed at the start position of the current element.

Entering distances against any of the axes will display a New Position label at the entered distance(s) from the current position, thus enabling the user to see if the new location for the element is correct.

Clicking the Apply button on the form moves the entire element to its new location.

The Positioning Control toolbar and the cursor can also be used to define distances graphically. Having picked two points the distances will be entered against the relevant axes on the form. If required, use the Lock check boxes to fix the current co-ordinate along any axis.

An alternative method of re-positioning the start or end of a SCTN element is to use Extend Through or Extend By functions.

4.1.3 Extend Through

Extend Through allows the user to specify a plane, position and orientation to extend either end of the section to. The section will only extend along its Z axis, i.e. its extrusion direction, as the plane is infinite in its planar dimensions. In PDMS a plane’s direction is defined by the direction of a vector normal (i.e.

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perpendicular in all directions) to the plane. The position of the plane is defined by the start position of that vector. Selecting Position>Extend>Through… displays the Extend Section – Relative form.

The End of Section list allows the user to specify which end of the section will be extended (or trimmed) to the plane. Four choices are available to the user.

Nearest end – This is the default setting. The end of the section nearest to the plane will be repositioned.

Start – The start position of the section will be moved. End – The end position of the section will be moved. Pick – On clicking Apply the user will be prompted to pick which end of the beam is to be re-positioned.

When the Extend Section - Relative form is displayed, a label is placed at each end of the section to identify which end is the Start and which is the End.

The user can define the plane position explicitly by entering co-ordinates in the Plane Direction East/West, North/South and Up/Down

textboxes, or by using the Cursor and

Intersection options from the forms menu and graphically selecting the position.

The Plane Direction is set by default to Up, however any direction can be entered to orientate the plane.

In the picture above the plane has been initially positioned using the Cursor>Element option and then moved be entering a new North co-ordinate. The Plane Direction has been set to S, note the plane aid and direction vector displayed to help the user visualise the position and direction of the plane.

Clicking Apply button extends the end of the current element to the plane.

The position of any Secondary Nodes owned by the section is measured from its start position. If the user requires the Secondary Nodes to stay in their original position when the start position of the section is moved, then the Maintain Sections’ Node Positions check box needs to be selected. Otherwise, the Secondary Nodes will move with the start position, i.e. their Z distance attribute will be maintained. Checking the Cut end(s) to plane check box on the form will orientate the end of the section to the plane direction after it has been extended or trimmed.

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4.1.4 Extend By

Extend By allows the user to lengthen or shorten the section by moving its Start or End position through a specified amount. Selecting Position>Extend>By… from the main menu displays the Extend Section - Explicit form.

When the form is displayed a label is placed at either end of the section to identify the Start and End locations. The Extend pull-down allows the user to select which end of the section will be extended, the choices being Start, End or Pick.

If the Pick option is selected the user will be prompted to select the end of the section that will be re-positioned when the Apply button is pressed.

The user can move the end of a section either by Distance or by a Proportion of the sections current length; by selecting the appropriate option button and entering the desired amount. Entering a positive value will lengthen the section and entering a negative value will shorten it.

To maintain the position of any Secondary Node owned by the section, click the Maintain Sections’ Node Positions checkbox.

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4.1.5 Drag Explicitly

The Drag Explicitly function allows the user to re-position a section and have any attached sections lengths adjust and the Secondary Nodes realign automatically. It is, therefore, equivalent to using three operations, that is Position>Explicitly (AT)…, Connect>Trim to Pline>all attached and Position>Align Secondary Nodes, in one.

Selecting Position>Drag Explicitly… from the main menu displays the Drag Explicitly form and Positioning Control toolbar.

The Datum options list enables the user to select the element Origin or an ID Design point as the point for the dragging operation; however, the Origin co-ordinates with respect to the World are displayed by default.

Any valid design element may be used to define the axis system for the direction boxes by entering the appropriate element in the wrt box.

The Positioning Control toolbar may be used to determine the new position by graphical pick, as described earlier.

A bounding box and axes aid at the start position are also displayed. Entering new co-ordinates in the axes boxes will move the bounding box to the new location.

After clicking Apply the section is re-positioned and all attached sections trimmed to the new joint positions.

All connected sections will trim to the new position of the owning section, adjusting their length as

necessary. The behaviour of the attached sections depends on whether the joint is dominant or subordinate, as described in Joint Freedom later in this session.

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4.1.6 Align Secondary Nodes

When a section that owns Secondary Nodes is repositioned or extended, it is possible that the secondary nodes may become misaligned. This can be corrected by selecting Position>Align Secondary Nodes from the main menu.

This function realigns the node(s) with their attached member(s) andmay be executed from SCTN, STRU, ZONE or SITE level.

4.1.7 Joint Freedom

Where two sections are connected via a joint, the joint may be defined as either dominant or subordinate. This setting, which is determined by the Jfree attribute of the SJOI, controls how the attached section behaves when the section owning the joint is moved.

If the joint is subordinate, i.e. the attached section is dominant and Jfree is set to false, the attached sections will extend or trim, maintaining their original orientation, to the Pline that they were trimmed to on creation.

If the joint is dominant, i.e. the attached section is subordinate and Jfree is set to true, the attached sections will realign to the new joint position.

The column is the owning section with two beam sections attached.

Joint is Subordinate. Column moved, beams extended to original Plines but maintain original orientation.

Joint is Dominant. Column moved, beams extended and realigned to new joint position and cut planes are automatically re-aligned.

The standard default is for joints to be subordinate. This default can be changed by selecting

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Joint freedom can be changed after the joint is created by selecting Connect>Joint Subordinate or

Connect>Joint Dominant from the main menu. The user will be prompted to select the section ends to apply the chosen setting to.

4.2 Orientation

Like positioning, orientating elements in PDMS can be performed in a number of ways. SCTN elements do not have a direct Orientation attribute, however, a pseudo-attribute for orientation can be queried, e.g. Q ORI, which returns the normal orientation format information but is derived from the SCTNs frame of reference, the Start and End positions and the β Angle (Beta Angle) of the SCTN.

Profiles in PDMS catalogues are defined with the NA Pline always pointing in a positive Y direction, i.e. Up, and the extrusion direction as positive Z, in

accordance with the Right Hand Rule:

The Beta Angle default is 0° which places the profile in the model in the orientation they are defined in the catalogue.

4.2.1 Axes

Selecting Orientate>Axes… from the main menu will display the Orientate form.

This form enables the user to change which axis is East, North and Up with respect to the World, or other design element, by using the option lists or entering the appropriate direction in the textboxes. This form only works with elements that have a direct Orientation attribute.

If the user attempts to use this function on an element that does not have a direct orientation attribute, e.g. a SCTN, SBFR or FRMW, a warning message is displayed.

For this reason, this command is not frequently used in the structural discipline.

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4.2.2 Rotate

Selecting Orientate>Rotate… from the main menu display the Rotate form.

By default, the Rotation Axis direction is U and positioned at the Start position of the element. The Rotation Axis Direction may be changed by entering another direction or its reference altered by modifying the ‘wrt’ data.

The centre of rotation, that is, the origin of the Rotation Axis vector, may be positioned by entering a distance against one or more directions. The Angle in degrees by which the element is to be rotated, must be entered in the Angle (º) textbox prior to clicking the

Apply button.

An axis direction aid is displayed, positioned at the centre of rotation, together with an axes aid showing the rotation angles at 90 degree intervals.

In this picture the default Rotation Axis of U is shown, that is the extrusion direction of the section, and the centre of rotation is positioned at the default position of Start Position, that is at the justification Pline TOS.

The centre of rotation can also be set graphically by using the Cursor and Intersection options from the form menu. The results of the rotate command may be simply reversed by giving a negative value to the Angle used and clicking the

Apply button again.

4.2.3 β Angle (Beta Angle)

The β Angle of a SCTN defines the rotation around its Z axis. The effect of changing the β Angle is shown in the diagram below.

In this diagram the Justification Line is set to TOAX. Modifying the β Angle rotates the section around its Z axis defined by the Justification Line.

Selecting Orientate>β Angle from the main menu allows the user to modify the β Angle in positive or negative increments of 90 degrees from the sub-menu.

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The Command Line must be used to set any other values. Entering BANG <value> on the data entry line and pressing the Return key will set the β Angle to the entered value.

4.2.4 Flip

Flip enables the user to change the orientation of sections by exchanging the Start and End positions, that is, the Z direction of the section is orientated through 180º. This only really affects asymmetrical sections such as angles and channels although it may be applied to all section profiles.

After selecting Orientate>Flip from the main menu the user will be prompted to select, using the cursor, the elements to Flip. Having made the selection, pressing the Esc key will flip the chosen sections.

4.3 Copying

PDMS provides three general methods to create copies of elements; Copy Offset, Copy Rotate and Copy Mirror. This functionality is covered in the AVEVA PDMS Foundations training guide.

4.3.1 Copying with Multiple Attached

If a connected section is copied using any of the copy methods, the newly created section will not be connected. There are often times when a multiple copy of a section needs to be made at regular centres, e.g. stringers in a deck or floor panel. This could be achieved by using a multiple Copy Offset; however, each end would need to be connected after copying. PDMS provides a utility that copies a selected member and produces multiple copies with connection details the same as the original.

Selecting Create>Sections>Multiple Attached… prompts the user to select the section to be copied if a SCTN element is not already the CE. Upon making an appropriate selection the Section Copy form is displayed.

The user can change the section to be copied by making another section the CE and clicking the CE button on the form

The Number of copies textbox shows the maximum amount of members that can be fitted to the shortest owning section at the current spacing, as shown in the Spacing textbox.

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If the spacing is changed from the default

(1000) to the required distance and then the

Max button clicked,

the maximum number of copies that can be fitted will be recalculated.

A graphical aid shows the user the direction for +ve or –ve spacing with aid lines representing the positions of the new sections to help visualise the results.

In the picture above, the maximum number of sections has been calculated based on the length of the shortest owning section. When the arrangement shown is correct, clicking the Apply button copies the sections and connects them to the owning member(s). Any end preparations (see Structural Detailing) will also be applied.

However, if a value greater than the maximum is specified in the Number of copies textbox such that the copied elements will go beyond the length of the shortest owning section, the copies will be made but the ‘free’ ends will not be connected or end preparations applied.

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4.4 Modifying the Pipe Rack - A Worked Example

In this worked example additional frames and horizontal beams required for the Pipe Rack structure will be created using some of the techniques described in this chapter.

4.4.1 Copy Offset

• Make the Pipe Rack ROW_6 the CE and select Create>Copy>Offset… from the main menu to display the Copy with Offset form. Select Rel. from the to options list, enter 3 in the Number of copies textbox and enter a –5180 in the X Offset textbox. Click the Apply button and click the Yes button on the subsequent confirmation message. Note that the STRU PIPERACK now owns three additional FRMWs. • Make the FRMW adjacent to ROW_6 the CE (it should be FRMW2), select Modify>Name… from the

main menu to display the Name form, enter ROW_4 in the Name textbox and click the Apply button. Leave the form open, make the FRMW adjacent to ROW_4 the CE (it should be FRMW3), click the CE

button on the Name form, enter ROW_2 in the Name box and click the Apply button. Repeat the procedure to name ROW_1. Dismiss the Name form.

4.4.2 Position Relative

• Make ROW_1 the CE and select Position>Relatively (BY)… from the main menu to display the Position By form. Select West from the East/West options list and enter 10 in the textbox.

• Make the column at the intersection of gridlines A and 1 the CE. Right click the SCTN in Design Explorer and select the Rename option from the pop-up menu to display the Name form. Enter A1 in the Name textbox and click the Apply button. Rename the other seven column SCTNs with the appropriate grid references.

4.4.3 Using a List

• Click the Create/Modify Lists button on the Default toolbar to display the Lists/Collections form. Select Add>List… from the form menu to display the Create List form. Enter B2+B4 in the Description textbox and click the OK button. Select Add>Identified from the form menu and graphically select columns B2 and B4, pressing the Esc key to end the selection. The two SCTNs are now in the list. Select Control>Close from the form menu to dismiss the form.

4.4.4 Extend Through

• Select Position>Extend>Through… from the main menu to display the Extend Section – Relative form. Select List from the options list at the top left of the form and select Nearest End from the End of Section options list. Ensure that the Maintain Sections’ Node Positions checkbox is checked and the

Cut end(s) to plane checkbox is unchecked. Select Cursor>Element from the form menu and graphically select a point near the top of column B2 to place a plane aid at the top of the column and populate the co-ordinates on the form. Modify the Up co-ordinate to 107160 and click the Apply button to extend the columns. Dismiss the form.

• Create two new FRMW elements, owned by the PIPERACK ZONE, named ROW_A and ROW_B. Make ROW_A the CE and set the storage areas to this FRMW. Set the Default Profile Specification to

Universal Beam 203x133x25kg/m justified TOS and with the Member line and Joint line set to NA.

4.4.5 Create Additional Sections

• Select Create>Section>Straight… from the main menu to display the Section form. Set the Positioning Control toolbar options to Element and Distance and enter a distance of 3710. Select near the bottom of column A1 to specify the start of the section and then at the bottom of column A2 to specify the end of the section. The section has been created at EL.(+) 104110 T.O.S.

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• Make ROW_B the CE and change the storage areas. Create the beams between the columns as shown

on the drawings. For the beam between columns B2 and B4 the Positioning Control toolbar should be set to Element/Snap and the columns picked very near the top.

• Save Work.

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Exercise 3 – Modifying the Equipment Support Structure

Re-orientate the two columns in ROW_C by 90 degrees. Update the beam connections to these columns and trim the attached sections.

Create FRMW elements for Rows D, E, and F and the additional column at E5 for the stair landing.

Name all of the columns in accordance with the gridline intersections on which they are positioned, e.g. C3, C4, D3, D4, etc.

Create FRMW elements EL(+)104880_TOS and EL(+)107820_TOS.

Create the beams between the Rows at EL(+)104880_TOS. Create the stair half landing east of Row 4. Remember to check the Default Profile Specification before creating the landing.

Create a list of all beams, except the stair landing, at EL(+)104880_TOS. Use the List option on the Copy Offset form to create the beams at EL(+)107820_TOS. Ensure all copied sections are correctly connected. Create the top stair landing at EL.(+) 107820 T.O.S. adjacent to column C4.

Check the end connections for the whole STRU.

The Equipment Support Structure should now look like this:

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5 Beam & Column Utilities 5.1 Bracing Configurations

PDMS provides functionality that enables the user to create bracing from pre-defined configurations which may be adapted to suit most situations. The advantages of using the pre-defined configurations to create bracing, rather than create sections piecemeal are:

• All sections in the configuration are created simultaneously • Initial gaps can be set so that geometry is realistic

• Created sections are automatically connected.

Selecting Create>Sections>Bracing configurations… from the main menu displays the Bracing form.

The Storage area and Section Data parts of the form allows the user to specify a storage area and profile for bracing in a similar manner to setting the default section specification and storage areas, however, the settings made via this form override the default settings. If the bracing configuration selected has more than one element, all sections will be modelled using the section specified. However, any of the elements that make up the configuration may subsequently have their specification or other attributes modified in the usual way.

The Available Bracing Configurations list displays the available configurations. Clicking on a configuration text in the list displays a picture of the configuration. There is more than one choice for some of the

configuration styles, for example A/K Bracing, which cover the majority of possible scenarios. The

configurations may be used where the members are in different orientations to those shown providing the configuration is the same.

The Bracing Plane options list enables the user to specify the plane in which the bracing will be created. The choices are:

• Derived by Section – This is the default and the most commonly used option. The bracing plane direction is orthogonal to both the first section picked and the incoming section nearest to the first pick point.

• Derived by Points – This option is useful for adding bracing between two sections that do not have a third section connected directly between them. The bracing plane is constructed by projecting the second picked point onto the first picked section.

• Defined… - This option allows the user to define the bracing plane explicitly and projects the picked points onto the defined plane. Selecting this option displays the Bracing Plane form and Positioning Control toolbar.

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We nd that if individuals dier in initial wealth and if commodity taxes can be evaded at a uniform cost, preferences have to be weakly separable between consumption and labor

As I will demonstrate, the problem raised by Pound in his 1910 paper is virtually identical to the one Kelsen tried to solve a few decades later: how to build a legal science

de Klerk, South Africa’s last leader under the apartheid regime, Mandela found a negotiation partner who shared his vision of a peaceful transition and showed the courage to

Note: if you want to burn your current movie production to a disc right away, go directly to the Create Disc module. In the Create Disc module you can create a disc menu, produce

The aim of this paper was to explore the effects on the French forest sector of three policies to mitigate climate change: a fuelwood consumption subsidy (substitution), a payment