Static and Dynamic Analysis. of Spaceframes

Transcription

1 Static and Dynamic Analysis of Spaceframes Procedure Guide TDV Ges.m.b.H. Dezember 2001

2 Disclaimer and Copyright Disclaimer Much time and effort have gone into the development and documentation of RM2000 and GP2000. The programs have been thoroughly tested and used. The user accepts and understands that no warranty is expressed or implied by the developers or the distributors on the accuracy or the reliability of the program. The user must understand the assumptions of the program and must apply engineering knowledge and skill to independently verify the results. Copyright The computer programs RM2000, GP2000 and all the associated documentation are proprietary and copyrighted products. Ownership of the program and the documentation remain with TDV Austria. Use of the program and the documentation is restricted to the licensed users. Unlicensed use of the program or reproduction of the documentation in any form, without prior written authorization from TDV is explicitly prohibited. RM2000 and GP2000 Copyright and support in Central Europe Tcl Copyright The Regents of the University of California Tcl Copyright Karl Lehenbauer and Mark Diekhans. Tcl Copyright Bell Labs Innovations for Lucent Technologies Tcl Copyright Sun Microsystems, Inc. Microsoft Windows Copyright Microsoft Corporation All rights reserved by TDV Ges.m.b.H. Austria

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4 Procedure Guide Contents I Contents CONTENTS...I PIER SUPPORT DEFINITION USING GP MULTIPLE BEARING/SPRING SUPPORT DEFINITION USING GP MULTIPLE BEARING SUPPORT DEFINITION FOR TWIN GIRDERS USING GP MULTIPLE BRG SUP DEF N - TWIN GIRDERS PLUS TWIN PIERS - GP CROSS SECTION WITH VARIABLE DEPTH USING GP ORTHOGONAL GRILLAGE DEFINITION USING GP COMPOSITE DEFINITION USING GP TENDON DEFINITION & CALCULATION USING RM CREEP & SHRINKAGE CALCULATION USING RM LOAD MANAGE DEFINITION USING RM STAGE DEFINITION & CALCULATION USING RM FIBRE STRESS CHECK CALCULATION NONLINEAR TEMPERATURE GRADIENT CALCULATION DEFINING A LIVE LOAD USING RM USING ADDCON (KASP) WITH A SIMPLE EXAMPLE USING ADDCON WITH A SIMPLE CABLE STAY BRIDGE EXAMPLE RESPONSE SPECTRUM CALCULATION USING RM ULTIMATE MOMENT CHECK...28 PLOTTING THE RESULTS IN RM

5 Pier Support Definition using GP2000 Procedure Guide 1 Pier Support Definition using GP2000 Node 111 Support Spring 1205 CP0 Node 1205 Add Column Add Connection (Spring 1205) Support Spring 1200 (see Multiple Bearing FC) Insert Segment Assign CS and Numbering Cross-Section Reference Point Group Segment-List Insert a new Connection Then continue as follows: - Choose a name - Change typ to Pier - Check/modify Reference Segment - Check/modify Segment Point - Choose the Connection Point (CP0) Repeat assigning a cross-section and numbering procedure for the Column Attention: The height 0 is the top of the support/column! See Multiple Bearing FC Choose the required Column segment, change to the segment list and choose the segment point to be connected (usually last segment point) Spring Between 2 Nodes Define the 1 st Connection Point (LH Window) Define the 2 nd Connection Point (RH Window) Constants Element Number (1205 here) Node 1: (1205 here), not eccentric Node 2: (111 here), eccentric

6 Multiple Bearing/Spring Support Definition using GP2000 Procedure Guide 2 Multiple Bearing/Spring Support Definition using GP2000 AXIS 1 Node 101 Y Z (Node 1100) CP0 The element start and end for the eccentric springs are defined by the directions CP0 CP1 or vice versa and CP0 CP2 or vice versa N.B. CP1 is the position of the bearing element 1101 CP2 Is the position of the bearing element 1102 CP1 (Spring Element 1101) Spring Element 1100 Node 0 CP2 (Spring Element 1102) Supposition: Axis, Cross Section for girder plus Segment numbering and assignment and Part numbering and assignment already made Add Connection Points Cross-Section Define the Connection between Top of Spring Support (Spring 1100) and Ground Reference Point Group Define the Connection Points Segment-List Connection Insert a new Connection Spring-0 Define the 1 st Connection Point (LH Window) Select Reference Point Group and insert a new one called Supports for example. Choose a reference point icon, select the required intersection point, choose Connection Point from the list and assign a name say CP0 (define the support points CP0, CP1 and CP2). Choose the axis segment, change to the segment list and select the segment point for the spring connection. Station 0 for example Select Connection Choose Insert in the new input window LH Window Segment Point 1 Part 1 Check/modify the segment point and part to be connected Select Spring-0 ( for connection to ground Select CP0 (located at the spring element end node) for the connection point in Connection window N.B. The connection to node 0 is automatically assigned

7 Multiple Bearing/Spring Support Definition using GP2000 Procedure Guide 3 Select Constants Number the Element Select Constants to modify spring stiffness, element numbers and eccentric connections Enter the Element number (1100 for the spring from ground (Node 0 ) to CP0 (Node 1100 ) De-select Conn. To node for part for Node 2 and enter 1100 for the node. Define eccentric connection for Spring 1101 Change Values Insert a new Connection Spring Between 2 Nodes Define the 1 st Connection Point Change default spring and support constants if necessary. Confirm with OK twice. N.B. The default orientation for the spring is: The local X-direction vertical: Vertical support Cx=1e8kN/m Choose Insert to define the connection for spring element (Element 1101 is located at position CP1 ) - Connect node 1100 to node 101 with eccentric connections. LH Window Segment Point 1 Part 1 Check/modify the segment point and part to be connected Select Spring between 2 Nodes. Select CP0 (located at the spring element toground end node) for the connection point in the Connection Point window Define the 2 nd Connection Point Select CP1 (located at the LH bearing pos n ) for the connection point in the Connection Point window Constants Number the Element Select Constants to modify spring stiffness, element numbers and eccentric connections. Put in the Element number (1101) for the LH Bearing (from CP0 (Node 1100 ) to girder element node 101 ). Select: Conn. to node for part for node 2. ( The end node (node 2) of the spring will then be automatically connected to the girder node 101) De-select: Conn. to node for part for node 1 and enter 1100 for the start node number for node 1 Repeat procedure Define eccentric connection for Spring 1102 Repeat the above procedure for RH Bearing Element (number 1102) Spring between 2 nodes Conn n pnt CP0 LH window Conn n pnt CP2 RH window Element 1102 De-select for node 1 enter 1100

8 Multiple Bearing Support Definition for twin girders using GP2000 Procedure Guide 4 Multiple Bearing Support Definition for twin girders using GP2000 Part 1 Part 2 AXIS Y Z Node 1100 CP0 The element start and end for the eccentric springs are defined by the directions CP0 CP1 or vice versa and CP0 CP2 or vice versa N.B. CP1 is the position of the bearing element 1101 CP1 (Spring Element 1101) CP2 (Spring Element 1102) Spring Element 1100 Node 0 Supposition: Axis, Cross Section for girder plus Segment numbering and assignment and Part numbering and assignment already made Add Connection Points Cross-Section Define the Connection between Top of Spring Support (Spring 1100) and Ground Reference Point Group Define the Connection Points Segment-List Connection Insert a new Connection Select Reference Point Group and insert a new one called Supports for example. Choose a reference point icon, select the required intersection point, choose Connection Point from list and assign a name say CP0 (define the connection points CP0, CP1 and CP2). Choose the axis segment, change to the segment list and select the segment point for the spring connection. Station 0 for example Select connection Choose Insert in the new input window Spring-0 Define the 1 st Connection Pint (LH Window) LH Window Segment Point 1 Part 1 Check/modify the segment point and part to be connected Select Spring-0 ( for connection to ground) Select CP0 (located at the spring element end node) for the connection point in the Connection Point window N.B. The connection to node 0 is automatically assigned

9 Multiple Bearing Support Definition for twin girders using GP2000 Procedure Guide 5 Select Constants Number the Element Select Constants to modify the spring stiffness, element numbers and eccentric connections. Enter the Element number (1100 for the spring from ground (Node 0) to CP0 (Node 1100) Deselect Conn. to node part for Node 2 & enter 1100 for the node. Define eccentric connection for Spring 1102 Change Values Insert a new Connection Spring Between 2 Nodes Change default spring and support constants if necessary. Confirm with OK twice. N.B. The default orientation for the spring is: The local X-direction vertical: Vertical support Cx=1e8kN/m Choose Insert to define the connection for the spring element (Element 1102 is located at pos n CP2 ) Connect node 1 to node 101 with eccentric conections. LH Window Segment Point 1 Part 1 Check/modify the segment point and part to be connected Select Spring between 2 Nodes. Define the 1 st Connection Point (LH Window) Select CP0 ( located at the spring element end node) for the connection point in the Connection point window and set Part to 1. Define the 2 nd Connection Point (RH Window) Select CP2 ( located at the RH bearing pos n ) for the connection point in the Connection point window and Change Part Number set Part to 2. Define eccentric connection for Spring 1101 Constants Number the Element Repeat procedure Select constants to modify spring stiffness, element numbers and eccentric connections. Put in the Element number (1102) for the RH Bearing (from CP0 (Node 1100 ) to the girder part 2 element node 102 ). Select: Conn. to node for part for node 2. ( The end node (node 2) of the spring will then be automatically connected to the girder part node 102) De-select: Conn.. to node for part for node 1 and enter 1100 for the start node number for node 1 Repeat the above procedure for the LH Bearing Element (number 1101) Spring between 2 nodes Conn n pnt CP0 and Part 1 LH window Conn n pnt CP2 and Part 1 RH window Element 1101 De-select Conn. To for node 1 enter 1100

10 Multiple Brg Sup defn - twin girders plus twin piers - GP2000 Procedure Guide 6 Multiple Brg Sup def n - twin girders plus twin piers - GP2000 Part 1 Part 2 AXIS The element start and end for the eccentric springs are defined by the directions CP1 101 or vice versa and CP2 102 or vice versa Y N.B. CP1 is the position of the bearing element 1101 CP2 Is the position of the bearing element 1102 Z CP1 (Spring Element 1103) Element 1102 Node 1102 Element 1101 Node 1101 Node 0 Node 1103 Spring Element 1100 Node 1113 Node 1111 Node 0 CP2 ((Spring Element 1113) Element 1112 Node 1112 Element 1111 Spring Element 1110 Supposition: Main Girder Axis and segment, Cross Section for the girder plus the cross section for the piers plus the Segment numbering and assignment and Part numbering and assignment for the main girder axis already made. (N.B. The Pier cross section must be defined with the intersection of the two main axes (purple lines) in the centre of the section) Define CP1 & CP2 the Main Girder Connection Points Cross-Section Reference Point Group Select the girder cross section Select the main segment then select Reference Point Group and insert a new one called Supports for example. Define the Connection Points Choose a ref. point icon, select the required intersection point on the girder cross sect, choose Connection Point from list and assign a name say CP1 (define the conn n points CP1 and CP2 at the centre of each beam soffit). Define the Pier Segments 2 & 3 Segment Select Segment and define the segments for all the piers say Segments 2 & 3 for the twin Piers at Main Girder segment 1 segment point 1 and segments 3 & 4 for the twin piers at Main Girder segment 1 segment point 6. N.B. The Main Girder segment 1 must have been completely defined before the new segments can be properly specified. Select the Type pull-down-menue arrow and choose Pier Assign the connection point for this segment to the Main Girder segment 1. Select the Connection Point pull-down-menue arrow and choose CP2 for seg 3 ( CP1 for seg 2)

11 Multiple Brg Sup defn - twin girders plus twin piers - GP2000 Procedure Guide 7 Segment Points Choose the segment from the segment list ( segment 2) Select the segment icon Insert the segments points for the Pier at segment 2 N.B. height 0 is at the top of the pier the other segment points have negative values say Pier 1 connection to ground is at height 10 and top is at height 0 in steps of 5 metres. Assign Pier cross section & Select the Edit icon and assign the pier cross section to the segment points. Choose Parts and then the Edit icon Enter the material type, and the start element number and node numbers Add Connection Points Repeat Segment Connection Element No Start Node End Node Repeat the above procedure for all the piers located on the respective segments. Define the connection between the pier segment and the Main Girder segment 1. Segment Select the Pier Segment for the connection definition. say segment 3 Segment-List Choose Segment list and then the place on the segment list that the connection is to be made: Segment point 3 node 1103 for example for the bearing connection Connection Select connection Insert a new Connection Spring between 2 nodes Define the 1 st Connection Point Define the 2 nd Connection Point Choose Insert in the new input window LH Window Segment Point 3 Part 1 Check/modify the segment point and part to be connected. (Part 1 point 3) Select Spring between 2 nodes The connection to the node at the top of the pier is automatically assigned if the correct segment point is chosen Part 1 Point 3 in this example (see above). RH Window Segment Point 1 Part 2 Check/modify the segment point and part to be connected. Select the Connection Point pull-down-menu arrow and choose CP2 for segment 3 ( CP1 for segment 2) Select the correct part part 2

12 Multiple Brg Sup defn - twin girders plus twin piers - GP2000 Procedure Guide 8 Select Constants Number the Element Select Constants to modify the spring stiffness, element numbers and eccentric connections. Enter the Element number (1113 for the spring from Node 1113 of the Pier (Node 1) to Node 201 on the main girder - (Node 2 ) Select Conn. to node part for Node 1 & for Node 2. Define eccentric connection for Spring 1110 to ground Change Values Insert a new Connection Connection Change default spring and support constants if necessary. Confirm with OK twice. N.B. The default orientation for the spring is: The local X- direction vertical: Vertical support Cx=1e8kN/m Close the connection window & select point 1 in the segment list. Choose connection and then choose Insert to define the connection for the spring element (Spring element to ground) Spring -0 LH Window Segment Point 1 Part 1 Check/modify the segment point and part to be connected Select Spring 0 for the ground connection. Constants Select Constants to modify spring stiffness, element numbers and eccentric connections. Number the Element Repeat procedure Put in the Element number (1110) for the spring connection to ground for the pier at segment 3. De-select: Conn.. to node for part for node 2 and enter 1111 for the end node number for node 2 Repeat the above procedure for the LH Bearing Element (number 1103) and the ground connection (number1100) on segment 2 Spring between 2 nodes Conn n pnt CP1 and Part 1 segment point 1 RH window Element 1103 Spring -0 Element 1100 De-select Conn. To for node 2 enter 1101

13 Cross Section with variable depth using GP2000 Procedure Guide 9 Cross Section with variable depth using GP2000 Basic Cross Section HQS (variable) Value = 4,0 m HQS f(x) Variable Cross Section depth 3,0 m 5,0 m 3,0 m 0,0 m 30,0 m 50,0 m 70,0 m 100,0 m Segment length Input the Basic Cross Section Insert cross 1 Cross Section Select the Cross sec arrow and the insert symbol Accept the default name (cross1) Define the Cross-Section Define of a Function (Formel, Table) Connecting Variable and Function Insert Var 1 Construktion Line Element(s) Create Table Insert Table Select Segment Variables Select Variable and create with Insert a new Variable (HQS) with the Value 4,0 m and Type Length. Create a construction line in dependence on this Variable (HQS). Define all the other construction lines which are necessary to defining a complete cross section. Define all the elements in the complete cross section. Select Formula and creat with Insert a new Table (Radio Buttons) with the Type Length and name HQS_Tab. Define a new Table item in the lower Table. Interpolation linear (see userguide), Variable A: Segment length and Variable B: Cross Section depth. Do Insert after until the required function is defined. With INFO Button the create function can be shown. Select the necessary Segment. N.B. CS had to assign to the segment! Select Variables (radio buttons). Click the modify function in the lower liste and assign the existing Variabel an Expression (function) for example HQS_Tab(sg). (Attention: from point, to point, step) N.B. (sg) assign the function global and (sl) assign the function local (see user guide).

14 Orthogonal Grillage Definition using GP2000 Procedure Guide 10 Orthogonal Grillage Definition using GP2000 Input the axis geometry Insert Axis 1 Insert seg1 Select the Axis arrow and the insert symbol Select the Segment arrow and the insert symbol Accept the default name Insert cross1 Select the Cross sec arrow and the insert symbol Accept the default name Horizontal axis starting point Straight Line Insert axis starting point for Horizontal alignment. Select P o. Accept the default values Select the straight line symbol & input 140 (metres) Select Vertical Axis icon Input the Cross Section geometry Vertical axis starting point Insert a straight line Cross Section Parallel Line Element(s) Insert axis starting point for Vertical alignment: Select P o. Accept the default values Select the straight line symbol & Input 140 (metres) and close the axis definition when finished Define the Cross-Section Define all the construction lines necessary for defining the complete cross section (all the beams) Define all the elements in the complete cross section (all the beams) Part(s) Modify Part(s) Define as many parts as there are beams in the cross section (3 in this example) by clicking on the intersecting CL s over the centre of the beams to define the reference point Select the element part number in the cross section to modify the number will change to the number shown in the Part window Modify the element numbers to match the relevant Part number

15 Orthogonal Grillage Definition using GP2000 Procedure Guide 11 Reference Point Group Define the Connection Points Assign a name to each different point Select the Ref point arrow at the top of the screen and the insert symbol - Accept the default name Click on the intersection point of the CL s at the bottom of each beam in the position where the bearings are to be placed and select Conection Point Name the points Sup1 ; Sup2 ; & Sup3 Segment Insert From 0 To 140 Step 4 Modify Assign cross sections to all the points Numbering Starting at the top of the list: Assign beam numbers and material numbers to the parts Segment Support Station Select the station for the first line of supports (Station 0) Insert a new Connection Select Spring-0 Export to RM Constants Select next support Recalc (ESSENTIAL) RM Insert element 1101, change Connection point to sup1, change Part to Part1, insert the appropriate spring stiffnesses Repeat for Part2 Sup2 El 1102 Repeat for Part3 Sup3 El 1103 Select the next support position in the table (Position 11 in this example) Repeat the above procedure for all the support positions N.B. Do not change Alpha 1 to 90 degrees the program does this automatically! Select RM to export the structural geometry to RM N.B. Only the main beams and the bearings below them have been prepared the transverse beams defining the grillage must be inserted from RM2000 in the normal way STRUCTURE-ELEMENT

16 Composite Definition using GP2000 Procedure Guide 12 Composite Definition using GP2000 (Supposition: Bridge axis, Segment already defined) Node Part 3 Node Part 2 Node Part PART 1 2 PART 2 PART 3 Input the Cross Section geometry Cross Section Parallel Line Element(s) Create Parts Composite Modify Part(s) Insert a new Cross-Section in the Cross-Section list and open it. Input all the construction lines necessary for defining the complete cross section (all the beams) Define all the elements in the complete cross section (all the beams) Select the Parts pull-down-menu arrow and insert 2 additional parts (2+3). The node for the new part must be selected immediately after clicking the insert button. Click on Part3 and then COMPOSITE to define the Composite section: Choose Part 1 and Part 2 and confirm with OK Select the element part number in the cross section for modification the number will change to the number shown in the Part window. Element numbers must be the same as their Part numbers Assign the Element Numbers Segment Modify Insert segment points e.g. from 0 to 140 Step 4 Assign cross sections to all the points Numbering Define Supports Starting at the top of the list: Assign beam element numbers and material numbers to the parts automatically N.B. Elements numbers can be directly defined by selecting the parts radio button and then the edit icon. Recalculate Select re-calculate before exporting RM Select RM to export the data to RM2000

17 Tendon Definition & Calculation using RM2000 Procedure Guide 13 Tendon Definition & Calculation using RM2000 Define the tendon profiles & assign to elements Structure Tendon Insert all the tendon constants (top) Assignment Assign the tendon(s) to the elements in the structure (bottom) Define the tendon geometry Structure Tendon Geometry Assign the tendon geometry control point relative to a node or an element number. N.B. For the profile to be viewed, it must either be a Standard Profile or have been made defined in GP2000 Define the prestressing load set & load case Schedule Loads LSet Insert a new loadset called prestressing Pre/Post tensioning Tendons Define the tendons to be stressed in this load set

18 Tendon Definition & Calculation using RM2000 Procedure Guide 14 Schedule Loads LCase Define a prestressing loading case & assign the load set to it Define the stressing actions Schedule Stage Tendon PREL Specify the factor to multiply the max allowable tendon stress (typically 1.05), specify the stress-label (i.e. CS1). Specify the wedge slip in metres - (typically 0.006m) Calculating the prestressing Schedule Stage Action Calculation Action Stress Define the stress label (i.e. CS1) Calc Calculate the prestressing loading case Grout Select Constants to modify the spring stiffness, element numbers and eccentric connections.

19 Creep & Shrinkage Calculation using RM2000 Procedure Guide 15 Creep & Shrinkage Calculation using RM2000 (Supposition: Bridge axis, girder cross section & permanent loading cases already defined) Import the variables FILE Import Import the creep & shrinkage variables into the RM-Project-Database (e.g. CEB78.rm or CEB90.rm..) Select the additional material definitions ASCII -Partial Variable PROPERTIES Material / Info Select the Variable checkbox and choose the file containing the creep & shrinkage variables (e.g. CEB78.rm, CEB90.rm..) from the //TDV2000/Rm8 program directory and confirm with OK. N.B. The variables can also be imported via File\Defaults\variable\mark all\copy Select the Info button & then the time dependent functions for creep & shrinkage (see below), PH(t) EPS(t) EMOD(t) Click on the pull-down menu arrow s for the creep coefficient, the shrinkage coefficient & the E-Modulus and select C78sh, C90sh etc..as appropriate for each. N.B.: Sig-Zy, Conc and Z-Typ must be defined for all model codes except CEB78. Confirm with OK STRUCTURE Define Time, Age, Temperature Element Time Input the Age of the Concrete, the shrinkage time, the Relative Humidity and the Temperature for the elements using the MODIFY BUTTON, confirm with OK and close the window

20 Creep & Shrinkage Calculation using RM2000 Procedure Guide 16 Loading Case CONSTRUCTION SCHEDULE Loads Lcase Define a new blank loading case (e.g.: 601 for Creep & Shrinkage in construction stage 1), containing no load set. (it is not necessary to define a load set for creep & shrinkage) Calculation Action Stage Select Stage Action Select Action Calculation Action Select Calculation Action Creep Select CREEP Inp2: Number of Time Steps (e.g:.1) Out1: Loading case Number (e.g.: 601) Out2: List-File Delta-T (Day): length of Creeping Time since last creep calculation

21 Load Manage Definition using RM2000 Procedure Guide 17 Load Manage Definition using RM2000 (Supposition: Structural System, Loadsets & Loadcases already defined) LoadInfo I II Description G Selfweight G Additional permanent load G Additional permanent 300 load PT Prestressing C&S Creep & Shrinkage Load Management is used for the automatic accumulation and superposition processes of certain files during the construction schedule analysis. Define the Load Management Schedule Loads Lmanage Load Info Lcase Select insert Enter a new Load Info name (e.g.:g1; G2; G3). Enter the loading case numbers for the accumulated loading results e.g. G1 type loading results should be stored in LC 100 & in LC1000 Repeat for PT, C&S... N.B. Superposition files can also be chosen for the loading result accumulation. Change to Loading case Modify Select the loading cases to be assigned to the Load Info groups and insert the appropriate LoadInfo name (e.g. G1). Repeat for other loading cases Stage / Action Initialise The loading case numbers assigned for accumulated results in load management must be initialised (in the Schedule) before use: Initialise all the relevant Loading Case numbers & Envelope using LcInit, Supinit. (e.g.: 100, 500, 600, 1000 ) and the Superposition files

22 Stage Definition & Calculation using RM2000 Procedure Guide 18 Stage Definition & Calculation using RM2000 (Supposition: Whole Structural System already defined) Stage 1 Stage 2 Stage 3 Define the Loading Cases Schedule Loads Define the Stages LSet LCase Stage Insert Activation Action Define the relevant Loadsets for the construction stages (e.g.: 101 for Selfweight in the first CS, 102 Selfweight second CS etc..) and the relevant Loading cases (e.g.: 101 for Selfweight in the first CS, 102 Selfweight second CS etc..) Insert all the Stages (3 construction stages needed in this example stage 1 to 3) N.B. stages can be used for things other than actual construction stages i.e. for a clearer calculation procedure (e.g. traffic calculation in a separate stage etc..) Activate the relevant elements and springs in each stage (e.g.: in Stage 1 all the elements that are constructed in stage 1 etc.) Add all the actions required in the different stages (e.g.: Calculation action of loading case 101 in Stage 1 etc..)

23 Fibre Stress Check Calculation Procedure Guide 19 Fibre Stress Check Calculation 1. GP2000: (Supposition: Bridge axis & girder cross section already defined) Specify the Stress Points Cross-Section Reference Point Point Insert Specify Stress Points Recalculate Select the Girder cross section and open it. Unlock the cross section if necessary. Insert a new reference point group to identify the Stress Points (say STRESS) Choose a point Insert symbol to specify the Stress Points (SPtop & SPbot say) Select the Refrence Point Group pull-down menue arrow to change the type to Stress Point. Specify the position of the Stress points in the cross section at top and bottom respectively Select re-calculate before exporting 2. RM2000: Call for Fibre Stress calculation in the Schedule RM Schedule / Stage Calculation Action FibChk Results\PlSys Recalc Select RM to export the data to RM2000 Select Schedule/Stage Fibre stress results for both combination files and loading cases can be plotted and/or printed to a file. Fibre Stress output listing FibChk prepares an output listing of the fibre stress results and annotates overstressed results. Inp1: Loading case or Combination File Inp2: Factor F1;F2 User Defined Stress limits (defined as a proportion of the limits defined in Properties\material\I\Fibre Stress check) Out1: -blank Out2: File name for printout Fibre Stress Plot Select Results\PlSys to specify the fibre stress plots: Basic definition Select Results\PlSys\Macro\Load case plot, stresses or Superposition plot, stresses to get a basic Fibre Stress Plot The Plot file prepared by the Macro can be easily edited to display additional results refer Results in User Guide. Select Recalc to get output listing Results can be plotted immediately after the relevant loading case/sup file calculation.

24 Nonlinear Temperature Gradient Calculation Procedure Guide 20 Nonlinear Temperature Gradient Calculation 1. GP2000 INPUT: (Supposition: Bridge axis & girder cross section already defined) Temperature difference Temperature difference Deckdepth d 0.45d T1 T2 MINUS T3 T4 T5 T3 PLUS T2 1.0 or d-0.20 T1 C 0.45d T8 T7 T6 T4 T5 T Node 101 Specify the additional Temperature Points in GP2000 Cross-Section Additional Lines Reference Point Select the relevant cross section and open it lines must be inserted in the cross section at each of the temperature change points T1 to T8 here (some variables depth construction lines are required here ) Insert two new reference point groups with the name TEMP-MINUS and TEMP-PLUS Point Insert Select the appropriate construction line intersection point to define the temperature points (T1-T6) in the cross-section, name the points appropriately and enter the specified temperature difference. N.B. The temperature points must be defined in consecutive order and must not be defined in a random order or the program will misinterpret the data.

25 Nonlinear Temperature Gradient Calculation Procedure Guide 21 Create Table Recalculate/RM If the deck has a variable depth, it is necessary to create an additional table defining the location of the temperature points that vary with the deck depth. - ref User Guide The revised GP2000 data must be Recalculated and the exported to RM2000 before completing the temperature input in RM RM2000 INPUT: Specify the additional Input in RM2000 Schedule Create Loads- Load set Change to the RM2000 Schedule Prepare a blank Load set, note the set number and describe it as T-MAX Create Load case Define a Loading case containing the T-MAX load set Stage - Action Temp-Var Calc Repeat Insert a calculation action TempVar : Inp1: Group-name (TEMP-MAX, named in GEOP2000) Out1: Load-set number defined above for T-MAX Insert a calculation action CALC : Inp1: Loading case number defined for T-MAX Repeat the above procedure for T-MIN. The program prepares and stores the full load-set input data for T-MAX and T- MIN from the above data Recalc Part 2

26 Defining a Live Load using RM2000 Procedure Guide 22 Defining a Live Load using RM2000 Input the Lanes Schedule Enter a lane number Loads LANE Input the elements and the lane eccentricity i.e. input Lane 1 and Lane 2 with eccentricity (e=+/-1.5m) using MACRO2 Lane 1 Macro e Input the Load Train Schedule Loads LTRAIN Define the loading simulating the load train. (Refer User guide) i.e. input the load train 1 Calculate Loading Schedule Stage Envelope action Supinit Initialise all the superposition files that will be used. i.e. live.sup, livele.sup, liveri.sup

27 Defining a Live Load using RM2000 Procedure Guide 23 Calculation Action i.e. Define the influence lines for lanes 1 and 2 infl Inp1 Inp2 Out1 Out2 LIQV 1 LIF 1 Calculation Action LiveL Define loading input files & output files for the lane results: i.e.: Inp1 Inp2 Out1 Out2 LiveL 1 1 livele.sup LiveL 2 1 Livere.sup Envelope Action Combine the lanes with the appropriate combination code (supadd, supand, supor) SupAnd

28 Using ADDCON (KASP) with a simple example Procedure Guide 24 Using ADDCON (KASP) with a simple example (Supposition: Whole Structural System already defined) Node 1 20 m Define the Loading Cases for the Constraint Criteria Element 1200 Node 11 L.C. 1 UDL=15kN/m 20 m Node 21 Unit settlement = 0.001m Schedule Loads LSet LCase The Structure: A 2 X 20 metre span continuous beam with a uniform loading of 15kN/m. The Problem: Find the amount of settlement required at Element 1200 such that the moments at node 11 due to the sum of L.C. 1 (15kN/m) plus this settlement loading case is exactly 500kNm. The Solution: Apply a Unit Settlement Loading of 0.001m (L.C. 2) and use KASP to factor this unit settlement such that in combination with L.C.1 the required result is achieved. Define the two load sets and the two loading cases (e.g.: L.C. 1 is a UDL of 10kN/m from Elem 1 to Elem 20 and L.C. 2 is a Settlement of 0.001m at the beginning of element 1200.) Define the Constraint Criteria AddCon Loads Elements Choose AddCon and insert the Additional Constraint (Top table) Insert the loading cases applicable to the Constraint criteria. (Bottom Table) Loading case 1 as FIXED LCFIX with the factor as 1.0 Loading Case 2 as VARIABLE LCVAR with the factor as VAR Insert the Constraint Criteria under Elements (Mz = 500kNm at node 11): Start the Iterative Calculation Stage Action Element 10 End DOF Mz Val-max = val-min = -500 Select stage to define the iterative calculation Select Action Re-start Insert Re-start in the Action column of the Schedule

29 Using ADDCON with a simple Cable Stay bridge example Procedure Guide 25 Using ADDCON with a simple Cable Stay bridge example (Supposition: Whole Structural System already defined) Node 1 Spring El 100 L.C. 1 UDL=105kN/m Cable El 2001 Cable El m Define the Loading Cases for the Constraint Criteria 31 Spring El Node m Element 1200 Schedule Loads Cable El 2004 Cable El 2003 Spring El 300 The Structure: A 2 X 20 metre span continuous beam. Top of pylon 10 m above girder. The Loading Uniform loading on the girder including self weight of 105kN/m. Unit Cable Stressing to 1000kN Unit Settlement at top of elements 100 and 300 of 0.1m The Problem: Find the appropriate cable stressing forces and support movements to ensure that the girder moments at the cable supports and the pylon from the combination of these loading cases with the uniform loading on the girder (L.C. 1) is exactly -500kNm. A Solution: Stress cables 2002 and 2003 in one loading case Apply other Unit Loading Cases ( stressing cables 2001 & 2004 and settlement at 100 and 300) as separate loading cases. Use KASP to factor the unit loading cases such that in combination with the uniform loading, the required result is achieved (-500 knm in the 5 places) 5 Unit Loading Cases 5 constraints ( moments at 5 places) LSet LCase Define the six load sets and the six loading cases: L.C. 1 UDL of 105kN/m Element 1 to 20 L.C. 2 Stress Cable 2002 and 2003 to 1000kN L.C. 3 Stress Cable 2001 to 1000kN L.C. 4 Stress Cable 2004 to 1000kN L.C. 5 Apply 0.1m settlement at Element 100 end. L.C. 6 Apply 0.1m settlement at Element 300 end. Define the Constraint Criteria To Stage AddCon Loads To Elements Choose AddCon and insert the Additional Constraint (Top table) Insert the loading cases applicable to the Constraint criteria. (Bottom Table) Loading case 1 as FIXED LCFIX with the factor as 1.0 Loading Cases 2-6 as VARIABLE LCVAR with the factor as VAR

30 Using ADDCON with a simple Cable Stay bridge example Procedure Guide 26 Elements Insert the Constraint Criteria under Elements (Mz = 500kNm): Elements 5 to 17 in steps of 3 at element begin DOF Mz Val-max = val-min = -500 Start the Iterative Calculation Stage Select stage to define the iterative calculation Action Select Action Re-start Insert Re-start in the Action column of the Schedule using: Constraint No: 1 Tolerance 1e-5

31 Response Spectrum Calculation using RM2000 Procedure Guide 27 Response Spectrum Calculation using RM2000 (Supposition: Structural System already defined) Specify the Response Spectrum Specify the Loading and- Masses Properties Variable Schedule Loads LSet LCase Insert the Response Spectrum using both Formula and Table to define the values. N.B. The program expects OMEGA for the abscissa (horizontal ordinate) and must be told via Formula what is given in terms of OMEGA. The type of vertical ordinate is defined in the Schedule/Loads/Seismic Specify the Earthquake masses and the mass of the structural System (e.g.: Selfweight ) and sum it up to one loading case (e.g.:lc100) Specify the Additional Actions SEISMIC (upper window ) SEISMIC (lower window) Stage / Action Caclculation Action Eigen Enter the seismic loading input: Number of seismic LC (e.g.: 1) Modal-File: (e.g.: eig1001.mod) Rule: (ABS, SRSS, DSC, or CQC) Duration: Seconds (e.g.: 10) Specify the Response Spectrurm: Type of Resp.Spec. graph: d,v or a Load vector components definining the direction of the displacement, velocity or acceleration (e.g.: Vec-Vx = 1) Damping Factor: loagarithmic decrement (e.g.: 0.05 = 5%) Insert the Calculation Action EIGEN: Inp1: Number of natural modes Inp2: Reference LC (e.g.: LC100) Out1: (e.g.: eig1001.mod) Out2: (e.g.: eigen.lst) Envelope Action Supin Initialize all new *.sup files: Out1: (e.g.: seismic-x.sup) Calculation Action RespS Recalc Insert the Calculation Action RESPS: Inp1: Number of Seismic Load (e.g.:1) Out1: (e.g.: seismic-x.sup)

32 Ultimate Moment Check Procedure Guide 28 Ultimate Moment Check 1. GP2000 INPUT: (Supposition: Bridge axis & girder cross section already defined) Specify the additional reinforcement Cross-Section Reference Point Point Insert Select the relevant cross section and open it. Unlock the cross section if necessary. Insert new reference point group(s) to identify the additional reinforcement i.e REINFtop & REINFbot etc Choose a point Insert symbol to specify the reinforcement positions Specify Reinforcement Recalculate Specify position of additional reinforcement in cross section (top, bottom, left, right) reinforcement area is allocated in RM2000 Select re-calculate before exporting 2. RM2000: Specify the material Stress/Strain curves RM Properties Material Prestr.steel Select RM to export the data to RM2000 Select Prestressing Steel Info Select Info Ultimate load check Select the ultimate load check pulldown menu arrow EPS1-8 Select the EPS1-8 pull-down menu arrow EPS1-8 SIG1-8 Input the Stress/Strain values for the material N.B. ε n-1 <ε n and σ n-1 <σ n Repeat Repeat the above input procedure for defining the material properties for the concrete and the reinforcement

33 Ultimate Moment Check Procedure Guide 29 Insert the Group Reinforcement Area(s) Structure\ Element\ Reinf Select Structure\Element\Reinf To define the area of reinforcement to be allocated to the reinforcement Group(s) N.B. If one group name was used (in GP2000) for several separate points or polygons, the defined area will be equally divided between these points or polygonal lines Edit Select Edit to modify the reinforcement area for the elements for the relevant reinforcement groups Insert UltChk Command into the Schedule Schedule \Stage\Action Insert Envelope Action Select Schedule \Stage\Action To call for the Ultimate Moment check to be made. Select Insert and go to the place in the Schedule where the Ultimate Moment Check is to be made Select Envelope Action Supinit Select SupInit to intialise a new superposition file for the results from the Ultimate Moment of Resistance calculations (say UltMz1.sup) Calculation action Select Calculation Action UltChk Select UltChk to call for the Ultimate Moment calculation. Inp1: i.e.comb1.sup (The combination file containing the applied ultimate loading) Inp2: UltMz (type of Ultimate check) Out1: UltMz1.sup (Output file data, available for further operations).

34 Plotting the Results in RM2000 Procedure Guide 30 Plotting the Results in RM2000 (Supposition: Structural Calculation finished) Specify a Plot file using a Macro*** Display plotfiles during the Calculation Results PlSys \Macro Show\Plot to File PlSys Modify Schedule\ Stage \ Action Select Results to access the plotting facility Select PlSys and then Macro Select one of the plot-macros offered (e.g.: Load case plot, forces or load case plot, stresses etc). Complete the input for the macro in the displayed screen. Select item to be plotted (e.g.: Bending Moment Mz, Normal Force N, which LC etc.). Define a plot input file name (e.g.:pl_100mz.rm) Confirm with OK. Click Show to view the plot and Plot to File to store the plot file for future viewing Modify a plot file Select the file to be modified from the list opened by clicking on the file pull-down menu arrow at the top of the screen Modify the properties (e.g.: colours, scale factor etc.) by going to the line (e.g.: PLPEN or PLSCAL) and clicking modify. Additional plot commands can also be entered. It is possible to display the prepared plots during the calculation run..select Schedule\ Stage \ Action to insert the plot command. ***Plot Files can also be prepared without using the Plot Macros but the simplest way for the plot file preparation is to start with a file prepared with the Macro and then to edit it. Plot Action PlSys Recalc View Plotfiles Insert the Plot Action PLSys at the appropriate place in the stage the plot will be displayed at that stage of the calculation: Inp1: plotfile name (e.g.:pl_100mz.rm) The plots that are displayed on the screen are not stored unless specifically requested with Plot to File refer above! Plot Files that have been stored can be viewed in detail and printed via the CRT symbol. Choose CRT Choose the desired Plot File from the displayed list.