Tutorial X Tract

XTRACT Cross Section Analysis Of Structural Components

Beginning Level - Example 1

XTRACT - Cross Sectional Analysis of Structural Components - 1

Introduction This beginning example outlines the basis features of XTRACT. In this example, a new project will be started, a section will be created from the template, the section will be copied and modified, and both a moment curvature analysis and axial force-moment analysis will be performed. The results will be viewed and interpreted and output reports printed. Contents of this detailed example include: • An outline of the basic flow of the program • Step-by-step instructions on creating a cross section using the section template. • Detailed instructions on how to analyze the section within the interface • Methods by which to access the various output capabilities • How to structure and print the various output reports

Program Flow The following outlines the basic flow of the program from creating a new project to creating cross sections to viewing analysis data. This example will present each of the following steps in detail: • Create a new project by clicking the 'New' icon on the main toolbar. • Within the new project creation wizard, select begin from Template. • Enter section data, material models, specify mesh size, and create cross section. • Add analyses to the created section. • Analyze. • View output results in the ’Interactive Output’ dialog. • Add a graph to compare analysis results from the different cross sections. • View and print ’Analysis Reports’. XTRACT - Cross Sectional Analysis of Structural Components - 2

Creating a New Project To create a new project, click the 'New' button (

) or from the title bar drop-down menu select

New. When the ’New Project’ icon is clicked the new project wizard form is opened (Figure 1).

Figure 1. New Project Wizard.

In this dialog box enter the information particular to the project. Information entered here is reproduced in the headers of the various output reports generated after analyses. Once the information has been entered, click the ’Forward’ button to continue. The next page of the wizard defines how to begin the project (Figure 2). Projects can begin from a section created from the section template, imported from a section file, or from a blank slate (a user defined section). In this example, the section will be created from the template. In the ’Start From’ drop-down menu, select ’Template’, choose the kip-in unit system, and enter the section name as ’Section1’. Click the ’Begin XTRACT’ button to continue.

XTRACT - Cross Sectional Analysis of Structural Components - 3

Figure 2. New Project Wizard - Page 2.

In the first page of the template (Figure 3) select the rectangular column with the triple hoop transverse reinforcing configuration. Select #4 at 4in on center for the spacing of the transverse reinforcing and click the ’Next’ button. On Page 2 of the template (Figure 4), enter 48in as the section width and height and enter 24 - #8 for the longitudinal reinforcement. For the triple hoop transverse reinforcement layout, there are only three options for the number of longitudinal reinforcing bars - 12, 18, and 24. The number of bars offered in this drop-down box are contingent on the type of transverse reinforcement layout selected. The number of bars offered will satisfy ACI column requirements for spacing and transverse reinforcement and will be consistent with the selected confinement configuration. If more reinforcing bars are required, they can be added later in the project. Note that when creating a section with the section template, the design log updates with the user input information as the template progresses. This information will be automatically printed in the section report after the section has been discretized. Click the ’Next’ button to continue to Page 3 of the template.

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Figure 3. Section Template - Page 1.

In Page 3 of the template (Figure 5), the user is prompted to select the material models that are to be associated with the various shapes in the cross section. XTRACT has 6 predefined material models as well as a general user defined material stress strain model. The 6 preset models can be used to describe behavior of the steel, unconfined concrete, and confined concrete. The user defined model can be used to crete any type of material behavior. Typical concrete cross sections will consist of 3 different material models: unconfined concrete (cover), confined concrete (core), and the longitudinal reinforcing steel model. To add the materials, click either the ’Add New’ button or to use an existing material, select it from the drop-down list of available material models. To edit an existing material, click the ’Edit’ button after selecting the material to edit. Because no materials have been created in this project, new materials need to be added. After clicking the ’Add New’ button, the ’Unconfined Concrete’ model dialog box in opened (Figure 6). In this dialog box enter the properties of the unconfined material stress strain model. The input parameters give options for varying the crushing and spalling strain. The crushing strain is the XTRACT - Cross Sectional Analysis of Structural Components - 5

Figure 4. Section Template - Page 2.

strain at which excessive cracking begins to occur followed by a rapid degradation in strength to the spalling strain. The spalling strain is the point at which the concrete stress goes to the post crushing strength. Typical values for the crushing and spalling strain for unconfined concrete are 0.004 and 0.006 respectively. Other input parameters include the post crushing strength, the 28-Day compressive strength, and an option for tension in the concrete. If a tension strength (rupture stress) is specified in the stress strain relation, the model assumes stress strain linearity with a slope of the concrete modulus of elasticity up to the rupture stress. In addition, the user can input the yield strain of concrete. This parameter is used to define the first yield limit state criteria for some of the analysis options described later in this example. In addition, for heavily loaded columns, this value is used to define the bilinearization of the moment curvature diagram (see the Bilinearization of the Moment Curvature Diagram in the XTRACT help file for more discussion).

XTRACT - Cross Sectional Analysis of Structural Components - 6

Figure 5. Section Template - Page 3.

Finally, the user is prompted to enter the ’Failure Strain’. Each material has a failure strain that will end computation of the moment curvature analysis. When analyzing a confined concrete component for the ultimate strain limit state, crushing and spalling of the confined cover is expected. Thus, when spalling of the cover occurs, the computation should not stop. If analyzing a section where cover spalling is not to control termination of the analysis, enter a large number in this text field (i.e. 1.0 - strain of 100%). If analyzing a cross section where computation should terminate when the cover spalls, enter the crushing or spalling strain in this text field. After entering the data, click the ’View’ button to view the data. Click the ’Apply’ button to view the material AND add it to the project. For this example, click the ’Apply’ button then close this form. Once the unconfined material has been added to the project and the form is closed, the user is directed back to Page 3 on the template. Next, for this example, the confined concrete model needs to be added. To open the ’Confined Concrete’ material model dialog box, click the ’New’ button next to the ’Column Core Concrete’ frame (Figure 7). XTRACT - Cross Sectional Analysis of Structural Components - 7

Figure 6. Unconfined Concrete Stress Strain Model Dialog.

The ’Confined Concrete’ material model dialog box is similar to the unconfined material dialog box (Figure 8). For the confined mode, the confined strength and strain capacity of confined concrete is dependant on the transverse reinforcing details provided by the user. When the template is used, this increased strength and increased strain capacity is automatically calculated for the transverse reinforcing details and column size provided. To view the input parameters that are used in calculation of the confined concrete strength (Figure 9), click the ’Equals’ button next to the ’Confined Concrete Strength’ text box (

). For detailed information on the input parameters and ref-

erences for the model used to find the confined concrete strength, see the ’Confined Concrete Strength Calculator’ help page in the XTRACT help file. If any of the parameters in the dialog box XTRACT - Cross Sectional Analysis of Structural Components - 8

Figure 7. Section Template - Page 3.

change, click the ’Equal’ sign at the bottom of the dialog box to recalculate the confined concrete strength. In addition, because the template was used, the confined concrete strain was automatically calculated. To view the input parameters for calculation of the confined concrete strain (Figure 10), click the ’Equal’ sign next to the ’Crushing Strain’ text box on the ’Confined Concrete’ dialog box. For more information on this form, consult the XTRACT help file. In this example, because the template is used, the input parameters for this calculation are automatically entered and thus no changes are required in either the ’Confinement Calculator’ or the ’Crushing Strain Calculator’. After entering the material parameters for the confined concrete model, click the ’Apply’ button. When the model is applied to the project, a warning message will occur for this example (Figure 11). Because the confinement properties for this cross section are such that it results in large allowable crushing strain, the warning message is given to remind the user to carefully exam-

XTRACT - Cross Sectional Analysis of Structural Components - 9

Figure 8. Confined Concrete Stress Strain Model Dialog.

ine the details. Typically, to go beyond a 0.02 strain for confined concrete, the details and construction quality need to be carefully controlled. To limit the maximum to 0.02 click the ’Yes’ button on this error message. When the error message closes, 0.02 is replaced in the ’Confined Concrete’ model dialog. To apply the material model, click the ’Apply’ button then close this form. After adding the confined concrete model. the user is directed back to Page 3 of the template. In this dialog box, click the ’Add New’ button in the ’Longitudinal Steel’ frame to open the steel material model (Figure 12). In this form, select the ’A615 Grade 60’ type steel from the ’Steel Standard’ drop-down box. By selecting the steel grade, the input parameters for the steel model are entered automatically. The default material parameters for the various material models proXTRACT - Cross Sectional Analysis of Structural Components - 10

Figure 9. Confined Concrete Strength Calculator.

Figure 10. Confined Concrete Strain Calculator.

XTRACT - Cross Sectional Analysis of Structural Components - 11

Figure 11. Warning Message Shown when the Compressive Strain Capacity of the Confined Concrete Exceeds 0.02.

Figure 12. Parabolic Steel Stress Strain Model Dialog.

vided by XTRACT can be found in the ASTM standards. To use different material parameters, enter them in the appropriate text box. Click the ’Apply’ button to add this material model to the project.

XTRACT - Cross Sectional Analysis of Structural Components - 12

After applying the ’Parabolic Strain Hardening Steel Model’ click the ’Next’ button to move the last page of the template (Figure 13). On this last page of the template the user can change the sec-

Figure 13. Section Template - Page 4.

tion name or the default mesh. The default mesh is set as the minimum outside dimension divided by 16. For most applications, this approximation will give reasonable results without too much computational demand imposed on the computer system. Click the ’Create Section’ button to generate the new cross section. When the template form closes, the screen should appear as shown in Figure 14. This section was created with a 3in mesh. The mesh size is the average distance between the corner points of the triangulation. The fuchsia colored edges of the section visible on the screen is the unconfined concrete. The grey interior is the core concrete material and the small black solid circles are the longitudinal reinforcing steel. The yellow line seen off to the left of the screen is part of the bounding box. The entire section must be contained inside the bounding box. The green outlines of the each shape is called the shape boundary and is used to define each shape. More information on the bounding box and XTRACT - Cross Sectional Analysis of Structural Components - 13

Figure 14. Section Builder.

the shape boundaries can be found in the XTRACT help file. Each section is created from a series of shapes that can be resized and edited as necessary. The dark grey background is the builder. The builder is the window where the sections are created.

Copying and Modifying the Section After the section has been created, it can be edited. But, because the section has been created using the template, if the section is modified, the input information for the template section will be lost. To view the section report (that can be printed) open the project manager by the clicking the icon on the main builder toolbar. In the project manager, double click the ’Section Report’ icon (

) as shown in Figure 15. The section report shows the properties of the section including the

centoid coordinates, moment of inertia, and names of the material models with the cross section. In addition, if the section was created using the template, the section report will show the parameXTRACT - Cross Sectional Analysis of Structural Components - 14

Figure 15. Project Manager.

ters the user input during the course of the section creation. After viewing the report, close the window. In this example, the section will be copied then modified. On the main toolbar, click the Add/ Remove Section Icon (

) to open the ’Add/Remove Section’ dialog box (Figure 16). In this

Figure 16. Add/Remove Section Dialog.

form, select the ’As a copy of’ in the ’Add Section’ drop-down box and select ’Section1’ as the section to be copied. Enter ’Section2’ as the new section name, and click the ’Add’ button. In the project manager, click the folder for ’Section2’ to set that section as the active section thereby bringing it to the front of the screen. When a builder is in view, the ’Section Builder’ is always in one of 5 build modes. By default, each section begins in the lock mode. When selecting another mode, other than lock, all analysis data is erased to protect consistency of output results. Also, if the section was creating using the XTRACT - Cross Sectional Analysis of Structural Components - 15

template, clicking out of lock mode erases the template data. For this example, click the ’Draw/ Import Shape’ icon on the builder tools toolbar (

) to open the ’Draw/Import Shape’ dialog box

(Figure 17). When the mode is changed from lock, a warning message will show explaining that

Figure 17. Draw/Import Shapes Dialog.

the template data will be removed if the build mode is changed from lock (Figure 18). Click ’OK’.

Figure 18. Warning Message Regarding Removal of Template Section Data.

For this example, a hole is to be added to the center of the cross section. In the ’Draw/Import Shape’ dialog, select the ’Import Shape’ tab, and select the shape type as ’Circle’. Enter 12in for the diameter and click the ’Import’ button. The circle, drawn to scale, appears on the existing section. Using the mouse, drag the circle to the (0,0) coordinate (Figure 19). The current mouse coorXTRACT - Cross Sectional Analysis of Structural Components - 16

Figure 19. Importing a Hole in the Concrete Cross Section.

dinates are always shown on the bottom of the builder. When dragging the shape, the current x and y coordinates of the centroid of the shape are also automatically updated in the ’Draw/Import Shape’ dialog box. When the shape has been moved to the proper coordinate, click the ’Discretize’ button on the ’Draw/Import Shape’ dialog to open the ’Discretizer’ dialog box (Figure 20). Select

Figure 20. The Discretizer.

XTRACT - Cross Sectional Analysis of Structural Components - 17

the material as ’Delete’, select the option for ’No Cover’, leave the mesh size as 0.9in, and click the ’Discretize’ button. After closing the ’Discretizer’ dialog and the ’Draw/Import Shape’ dialog the section should appear as shown in Figure 21.

Figure 21. Section Discretized with a Central Hole.

Loadings and Analysis XTRACT has three loading (or analysis types) available to the user: Moment Curvature, Axial Force-Moment Interaction, and Capacity Orbit (moment-moment interaction). In this example, a moment curvature and an axial force-moment interaction analysis will be added to both sections. The add a moment curvature analysis, select ’Moment Curvature’ from the ’Loadings’ title bar menu. In the ’Moment Curvature’ dialog box enter the information shown in Figure 22. Moments will be incremented about the x axis, the constant axial load is specified at 200kips, the animation and show graph options should be checked, and the option to calculate moment rotation should be XTRACT - Cross Sectional Analysis of Structural Components - 18

Figure 22. Moment Curvature Loading Dialog.

selected. For the plastic hinge length, enter 24in. Enter the name of the loading as ’MC1’ applied on ’Section1’. When all the data has entered, click the ’Apply’ button. Then, change the name of the loading to ’MC2’ and the ’Applied on Section’ drop-down menu to ’Section2’. Click ’Apply’ again to add this loading. Close the ’Moment Curvature’ dialog box. To see the loadings applied to the project, open the Project Manager and expand the ’Section1’ and ’Section2’ directories as shown in Figure 23. The Project Manager is the corner stone of XTRACT. All sections, reports, analysis, and analysis data can be accessed from the Project Manager by double clicking the item of interest. To add the axial force-moment interaction loading select ’PM Interaction’ from the ’Loadings’ title bar menu. In the ’Axial Force Moment Interaction’ dialog box, enter the information shown in Figure 24. In this dialog, the user has the option for entering the limiting strains. The limiting stains dictate the maximum strains at which the interaction surface is calculated. For more information on limiting strains consult the XTRACT help file. Each material has a default PM InteracXTRACT - Cross Sectional Analysis of Structural Components - 19

Figure 23. Accessing the Moment Curvature Loading from the Project Manager.

Figure 24. Axial Force-Moment Interaction Loading Dialog.

tion strain. For unconfined concrete, it is .003. For confined concrete, it is the strain at peak stress. For steel, it is the strain as the onset of strain hardening. For this example, enter ’PM1’ for the loading name applied to ’Section1’ and click the ’Apply’ button. Then, enter ’PM2’ as the loading XTRACT - Cross Sectional Analysis of Structural Components - 20

name, and change the ’Applied to Section’ drop-down selection to ’Section2’. Click the ’Apply’ button. Check the Project Manager to insure that the loadings have been properly added to each of the two sections in the project.

Analyze the Cross Section To analyze the cross sections with the defined loadings, click the ’Analysis’ button on the main toolbar (

). The analysis windows will appear when each analysis begins. The analysis window

shows the current state of the analysis. When the analysis has completed, the screen should contain four windows showing the animation of the last load step in the analysis side by side with a plot of the analysis results. The options for ’Show Animation’ and ’Show Graph’ set in the loading dialog boxes control whether or not the animation and graphics are shown. The analysis result windows from the moment curvature and axial force-moment interaction analyses for ’Section2’ are given in Figure 25 and Figure 26, respectively. The color coded images in the animation show the state of the material for each analysis step during analysis. The dark blue represents compression in the concrete, the white is crushing of the concrete, the yellow steel bars represents the yield plateau, the green bars show the longitudinal reinforcement in the strain hardening range of the material model, and the fuchsia and grey in the concrete represent zero or tensile strain. Close the four windows.

Viewing Results After analyses has been performed, analysis results can be accessed from the Project Manager. After analysis of a particular loading, the loading becomes a folder inside the Project Manager. Click the ’+’ next to the folder to expand the folders and the ’-’ to collapse them. In the Project Manager, expand the ’Section1’ section folder and then the ’MC1’ loading. Double click on the ’Interactive Output’ icon in the Project Manager as shown in Figure 27 to open the ’Interactive Output’ dialog box. The ’Interactive Output’ dialog is way to step through the analysis slowly XTRACT - Cross Sectional Analysis of Structural Components - 21

Figure 25. Analysis Result Windows for the Moment Curvature Analysis on the Section Containing a Central Hole.

XTRACT - Cross Sectional Analysis of Structural Components - 22

Figure 26. Analysis Result Windows for the Axial Force-Moment Interaction Analysis on the Section Containing a Central Hole.

XTRACT - Cross Sectional Analysis of Structural Components - 23

Figure 27. Project Manager Showing Access to the Interactive Output.

viewing all information produced from analyses of the cross section. For this example, set the load step to 17 using the slide bar at the top of the ’Interactive Output’ dialog box, select the ’Data to View’ option as ’Fiber/Bar Property’, select the plots to ’Moment about the X-axis’ verses ’Maximum Steel1 Material Stress’ and ’Moment about the X-axis’ verses ’Minimum Confined1 Material Stress’. Click the bottom outside fiber of the cross section (Figure 28). Note that the minimum stress (and strain) for each material is the maximum compression stress (and strain). The maximum values (positive) are for tensile stresses or strains. When the ’Fiber/Bar Property’ option is set, the data shown in the table is for the selected fiber or reinforcing bar. To change the selected fiber or bar, click desired fiber or bar. Use the zoom in and zoom out buttons on top of the ’Interactive Output’ dialog box to zoom in or zoom out of the graphic of the cross section. The plot directly below the cross section shown shows the stress strain relation of the selected fiber/bar. The small yellow ’+’ on each of the plots indicates the location on the curves that correspond with the analysis step selected from the slide bar at the top of the form. Using the slide bar, change the analysis step and watch the figure and plots change. The ’Interactive Output’ dialog can be most helpful for troubleshooting analyses to find input errors when results do not match expectation. Close the ’Interactive Output’ dialog. XTRACT - Cross Sectional Analysis of Structural Components - 24

Figure 28. Interactive Output Dialog.

Plotting Results and Exporting Data From the main toolbar, click the ’Add Graph’ icon (Figure 29). In these plots, any data can be plot-

Figure 29. XTRACT Main Toolbar.

ted against any other data. In this form, plot the two axial force-moment interaction diagrams together. Enter ’Interaction Surfaces’ for the ’Graph Name’. Select ’Section1’ with loading ’PM1’. Select ’Moments about the X-Axis’ for the ’X-Axis Data’ to plot and ’Axial Force’ for the ’Y-Axis Data’ to plot. Click the ’Add Plot’ button. Then, using the same method, add the axial force-moment diagram results ’Section2’ with the ’PM2’ loading (Figure 30). Note that when XTRACT - Cross Sectional Analysis of Structural Components - 25

Figure 30. Graph Dialog Showing Comparison between the two Analyzed Cross Sections.

passing the mouse across the graph, critical data is updated in the table reflecting results particular to the loading and the analysis step closest to the mouse. To print this plot, click the ’Print’ icon on the Graph toolbar. To add more plots, click the ’Add Graph’ button the Graph toolbar. There is no limit to the number of plots that can be added in XTRACT. To access the plots after creating them, and closing them, use the Project Manager (Figure 31). After closing the ’Interaction Surfaces’ plot, expand the ’Section Output’ folder under the ’MC2’ loading in the Project Manager. Double click ’Moments about the X-Axis’ then double click the ’Curvatures about the X-Axis’ data labels. Double clicking data labels opens the ’Project Output’ dialog box. In the ’Project Output’ dialog box, single click the headers (Mxx and Kxx) for the columns of data (Figure 32) to highlight them. To export the data, either click the ’Save’ button to save the data in a comma delimited text file or right click the data, select copy, and paste directly in to Excel or a similar type spread sheet program. XTRACT - Cross Sectional Analysis of Structural Components - 26

Figure 31. Project Manager Showing Access to the Data Graphs.

Finally, to view or print the analysis reports, double click the ’Analysis Report’ icon in the Project Manager under the ’MC2’ loading (Figure 33). Analysis reports are available for all loadings. In addition, similar material model reports are available for all material models used in an XTRACT project. ’Material Reports’ are available in the ’Materials’ folder in the Project Manager. For the analysis report of a moment curvature analysis, a plot of the moment curvature analysis results along with a bilinearization of the diagram is given. A color coded graphic showing the last state in the analysis is also provided. In this report, any of the text that is greyed can be user edited. This includes most of the headers as well as a user comments section. For more information on particular data provided in the analysis reports, consult the XTRACT help file.

Conclusion In this example, a section was created using the template. The section was then copied and edited. In the edited section, a hole was added to the center of the cross section by changing modes in the

XTRACT - Cross Sectional Analysis of Structural Components - 27

Figure 32. Data Viewer.

builder and importing a circular shape. Two moment curvatures and two axial force-moment interaction loadings were added to the project and the sections were analyzed with these project loadings. Using analysis results, plots were added to the project to compare the axial force-moment interaction results for the nearly identical cross sections. Data from moment curvature analysis on the section with the hole was exported and the analysis was viewed in the ’Interactive Output’

XTRACT - Cross Sectional Analysis of Structural Components - 28

Figure 33. Moment Curvature Analysis Report.

dialog showing the relationship between ultimate material stresses and applied x-axis moments. Finally, the one page analysis report summary for the ’MC2’ loading was opened and viewed.

XTRACT - Cross Sectional Analysis of Structural Components - 29

XTRACT Cross Section Analysis Of Structural Components

Beginning Level - Example 2

XTRACT - Cross Sectional Analysis of Structural Components - 1

Introduction This beginning example (Example 2) outlines some of the basic features of XTRACT. Before continuing with this example, it is advised that the reader go through the Step-by-Step Example 1 file located from either the XTRACT folder in the Start Menu, or the Help title bar in XTRACT. In this example, two oblong reinforced concrete sections will be created and their response compared. The columns will be transversely reinforced with interlocking spirals and longitudinally reinforced with #11 reinforcing bars. Contents of this detailed example include: • Adding material models to the project • Step-by-step instructions on creating a cross section from a User Defined Section • How to change the dimensions of the cross section after the section has been meshed • Running multiple moment curvature analyses and moment-moment interaction analyses and comparing results

Creating a New Project To create a new project, click the 'New' button (

), or from the title bar drop-down menu select

‘New’. When the ‘New Project’ icon is clicked the new project wizard is opened. In this wizard, enter the information particular to the project. Information entered here will be printed in the headers of the various output reports that are generated by XTRACT after analysis. Click the ‘Forward’ button to continue. The next page of the wizard defines how to begin the project (Figure 1). Projects can begin from a section created with the section template, imported from a file, or created from a blank slate (a XTRACT - Cross Sectional Analysis of Structural Components - 2

Figure 1. New Project Wizard - Page 2.

user defined section). In this example, the section will be created as a user defined cross section. In the ‘Start From’ drop-down menu, select ‘User Defined’, choose the kip-in unit system, and enter the section name as ‘Section1’. Click the ‘Begin XTRACT’ button.

Add Material Models The New Project Wizard will immediately open the first material model. For this example, because ‘Confined Concrete’ is selected, the user is taken to the ‘Mander Confined Concrete’ model dialog box. In this material parameter input dialog form, enter the values shown in Figure 2 and click the ‘Apply’ button. For this material model, a 28-Day compression strength of 4ksi was assumed with a confined strength of 6ksi. The confined concrete strength is a function of many parameters (See XTRACT Help files for details). To find theoretical strength of the confined concrete by entering these many parameters, click the ‘Equals’ sign next to the ‘Confined Concrete Strength’ text box. Alternatively, if the cross section meets ACI requirements for seismic detailing, the overstrength due to confinement can be assumed at a minimum of 1.3 times the 28-Day Strength. For bridge columns conforming to current Caltrans requirements an overstrength of 1.5 may be assumed - as XTRACT - Cross Sectional Analysis of Structural Components - 3

Figure 2. Mander Confined Concrete Dialog.

is done for this example. For this example, zero concrete tension strength was assumed and the ‘Crushing Strain’ was taken as 0.015. If the section is detailed properly, a minimum confined strain capacity of 0.015 can be assumed as is done for this example. Alternatively, clicking the ‘Equal’ sign will allow a more detailed calculation of this value. Lastly, the ‘Elastic Modulus’ and the ‘Yield Strain’ were taken as default values based on the 28-Day Strength. For more information on the reasons for a user inputted yield strain the reader is advised to consult Step-by-Step Example 1 or the XTRACT Help file. Once the model has been applied, it becomes part of the project. To view materials in the project open the ‘Project Manager’ and expand the materials folder (Figure 3). XTRACT - Cross Sectional Analysis of Structural Components - 4

Figure 3. Project Manager.

After the material dialog box is closed, the blank ‘Section Builder’ is exposed. For this example, two other material models need to be added - ‘Unconfined Concrete’ and ‘Bilinear Steel with Strain Hardening’. From the ‘Materials’ drop-down menu on the title bar, select ‘Mander Unconfined Concrete’. In this form, enter the values shown in Figure 4. For a detailed description of the concrete ‘Yield Strain’ or the ‘Failure Strain’ consult the Step-by-Step Example 1 or the XTRACT Help file. After entering the parameters, click the ‘Apply’ button and close the form. From the ‘Materials’ drop-down menu select ‘Bilinear with Strain Hardening’. On this form, select ‘A706’ from the ‘Steel Standard and Grade’ drop-down menu and click the ‘Apply’ button to add this material model to the project.

Creating the Cross Section After the materials have been added to the project the sections can be created. On the ‘Builder Tools’ toolbar click the ‘Draw Shape’ icon (

) to go into ‘Draw Shape’ mode. On the ‘Draw/

Import Shapes’ dialog click the ‘Import Shape’ tab. In this form select ‘Oblong’ from the ‘Select Shape’ drop-down menu and enter 0.0 for both the ‘X Location’ and ‘Y Location’ text boxes. Enter 0.0 for the rotation, 12.0 for ‘Width’ and 36.0 for the ‘Height’ as shown in Figure 5 (the project units should be in kip-in). Use the vertical scroll bar to access text boxes that are obscured from view. Note that the width of the oblong shape is defined from inside to inside of the semi-circular

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Figure 4. Mander Unconfined Material Model.

ends of the shape. Once the parameters have been entered, click the ‘Import’ button, then the ‘Discretize’ button. Upon clicking the ‘Discretize’ button, the ‘Discretizer’ dialog box will be opened. In the discretizer, enter the values shown in Figure 6 and click the ‘Discretize/Overlay’ button. Then, on the ‘Builder Tools’ toolbar, click the ‘Zoom Section’ button (

). On the ‘Section Builder’ the dis-

cretized oblong shape, in unconfined concrete, should be seen as shown in Figure 7. In the ‘Draw/ Import Shape’ dialog box, select ‘Interlocking Spiral’ from the ‘Select Shape’ drop-down box and enter the values shown in Figure 8. Click the ‘Import’ button then the ‘Discretize’ button to disXTRACT - Cross Sectional Analysis of Structural Components - 6

Figure 5. Add an Oblong Shape.

Figure 6. The Discretizer Dialog Box.

cretize the shape within the cross section. In the ‘Discretizer’ dialog, select the option for ‘No Cover’, enter 2.0 for the mesh size, and select ‘Confined1’ as the ’Section Material’. Click the ’Discretize/Overlay’ button to discretize the shape. On the ’Section Builder’ the cross section shown in Figure 9 should be seen. User defined sections need to created from the outside in. For this example, the outside was created all in unconfined concrete and the inside was created in confined concrete. A thorough explanation of the ‘Order of Section Creation’ is available in the XTRACT Help file. XTRACT - Cross Sectional Analysis of Structural Components - 7

Figure 7. Discretized Oblong Section.

Figure 8. Add an Interlocking Spiral Shape.

XTRACT - Cross Sectional Analysis of Structural Components - 8

Figure 9. Discretized Interlocking Spiral Shape.

Copy and Resize the Cross Section Before adding any steel to the cross section, the section is to be copied and resized. To copy the section, click the ‘Add/Remove Section’ button on the main toolbar (

). In the ‘Add/Remove

Section’ dialog, select the ‘As a copy of’ option in the ‘Add Section’ frame, enter ‘Section2’ as the

XTRACT - Cross Sectional Analysis of Structural Components - 9

‘Section Name’ and click the ‘Add Section’ button as shown in Figure 10. Set ‘Section2’ as the

Figure 10. Add/Remove Section Dialog Box.

active section by single clicking the section name (‘Section2’) in the ‘Project Manager’. To change the geometry of the cross section, click the ‘Remesh Mode’ icon on the ‘Builder Tools’ toolbar (

). In the ‘Remesh Section’ dialog box click the mouse icon to select specific points

in the shape as shown in Figure 11. On the ‘Section Builder’, select the four points as shown in

Figure 11. Remesh Section Dialog Box.

XTRACT - Cross Sectional Analysis of Structural Components - 10

Figure 12 by clicking them once with the mouse. After selecting the four points to move, click the

Figure 12. Select the Points to Move on the Section Builder.

‘Move Points’ icon on the ‘Remesh Section’ dialog (

). Then, either grab any of the selected

points and move them 6 inches to the right or enter 6.0 in the ‘Delta X’ text box. Use the ‘Scroll Shape’ and ‘Scroll Point’ buttons until one of the selected points is highlighted with the larger yellow circle, then click the ‘Modify Point(s)’ button (Figure 13). Repeat this procedure for the intersecting points of the inside interlocking spiral shape (Figure 14) but move those points just 3 inches to the right. To un-select a single point, click the selected point while the ‘Select’ icon is depressed (

) in the ‘Remesh Section’ dialog box. To un-select all

the points, click the ‘Move Shape’ icon (

) then click back to the ‘Select’ icon. Next, click

the word ‘SNAP’ in the bottom left side of the builder and change the snap distance to 1.0 inch. Then click the ‘Move Point’ icon (

) on the ‘Remesh Section’ dialog box, grab the top inter-

secting point and move it downward 1.0 inch to coordinates (3, 14.37). Grab the bottom intersection point and move it upwards 1.0 inch to coordinates (3, -14.37). After relocating the shape points, click the ‘Discretize All’ button to remesh the entire cross section with the new dimensions.

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Figure 13. Remesh Dialog used to Modify Existing Section Coordinates.

Figure 14. Select the Points to Move on the Section Builder.

Generating Steel Reinforcing Bars With the two section created, the longitudinal reinforcing steel needs to be added. First, single click ‘Section1’ in the ‘Project Manager’ to set ‘Section1’ as the active section bringing it into XTRACT - Cross Sectional Analysis of Structural Components - 12

view. Then, to enter into the ‘Add Reinforcing Bars’ mode click the ‘Add Reinforcing Bars’ mode icon on the ‘Builder Tools’ toolbar (

). In the ‘Rebar Characteristics’ box, select bar size as #11,

select the ‘Enter by Coordinates’ and the ‘Generate’ icons, select the option to ‘Generate by Number’, and enter 8 as the number of bars (Figure 15). In the ‘Enter Generation Points by Coordi-

Figure 15. Rebar Characteristics.

nates’ dialog box, click the ‘Stop’ icon in the bottom right side corner of the form to prevent interaction between the mouse and the screen. On the ‘Builder Tools’ toolbar, click the ‘Arc’ icon (

) to generate the bars around an arc.

In the ‘Enter Generation Points by Coordinates’ dialog input the values as shown in Figure 16, then click the Apply button. The coordinates were found from the total width of the interior circular shape (18in radius) less the cover (1.5in) less the assumed diameter of the transverse reinforcing steel (0.5in) less half the diameter of a #11 reinforcing bar. To enter the reinforcing bars for the other side of the left circular shape, change the X-Coordinate in the second bar text box to -21.31 and click the ‘Apply’ button. The first and last bars that were overlapping were removed then reapplied resulting in a total of 14 longitudinal reinforcing bars as shown in Figure 17. To add the longitudinal bars in the other transverse reinforcing spiral, repeat the above procedure using the appropriate coordinates. After completion, the section should appear as shown in Figure 18. XTRACT - Cross Sectional Analysis of Structural Components - 13

Figure 16. Generating Longitudinal Reinforcement.

Figure 17. Cross Section with Generated Rebar.

Again, following the same procedure for bar generation around an arc performed for ‘Section1’, add the double spiral of longitudinal reinforcing bars to ‘Section2’ (Figure 19). Save the file.

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Figure 18. Cross Section with Generated Rebar - Section1.

Figure 19. Cross Section with Generated Rebar - Section2.

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Add Moment Curvature Analyses in the Input File In this section, one moment curvature analysis will be added within the user interface to each section (Section1 and Section2). Then, the input file will be opened and multiple moment curvatures will be added. From the title bar ‘Loading’ menu, select ‘Moment Curvature’. Enter the loading parameters shown in Figure 20 and click ‘Apply’. Change the ‘On Section’ drop-down menu to ‘Section2’,

Figure 20. Moment Curvature Loading for Section1

re-enter the same loading data shown in Figure 20 with the loading name of ‘MCs1’ and click the ‘Apply’ button. Save the file and close XTRACT.

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From WordPad, open the file and scroll down to the loading block for ‘Section1’, ‘MC1’ (Figure 21). Highlight this block of text, copy and paste. In the pasted loading block, change the Begin_Loading NAME = MC1 TYPE = Moment Curvature # Constant loads applied at first step - negative is read as compression. ConstAxial = -100.0 # Incrementing load parameters - Positive increments in a positive direction. IncMyy = 1.0000 Use_Best_Fit = True # Include Plastic Hinge length. Calc_Moment_Rot = False # Analysis Parameters. Method = BiSection N_Steps_Before_Yield = 10 N_Steps_After_Yield = 20 Multiple_On_First_Yield = 2 BS_Tol = 1.0000 BS_Max_Itter = 40 End_Loading #--------------------------------------Figure 21. Loading Block in the Input File.

loading name to ‘MC2’ and the ‘ConstAxial’ value to -2000. Repeat four times (MC3 with -3000, MC4 with -4000). Next, highlight the loading block of text for ‘Section2’, ‘MCs1’ and repeat the steps outlined above with: • NAME = MCs2 ConstAxial = -2000 • NAME = MCs3 ConstAxial = -3000 • NAME = MCs4 ConstAxial = -4000 Save the file and re-open in XTRACT. Open the ‘Project Manager’ to verify that the various loadings were imported correctly.

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Capacity Orbit Analyses To add a capacity orbit analysis, or moment-moment interaction analysis, select ‘Capacity Orbit’ from the ‘Loading’ title menu. Enter the name as ‘CO1y’, enter 1000k as the applied axial load, and select the ‘Analyze at first material yield option’ (Figure 22). Repeat for the following loads

Figure 22. Capacity Orbit for Section 1.

on the following sections: • Section = ‘Section1’ Name = ‘CO1u’ Axial Load = 1000k Orbit Option = ‘Analyze at ultimate material strains’ • Section = ‘Section2’ Name = ‘CO2y’ Axial Load = 1000k Orbit Option = ‘Analyze at first material yield option’ • Section = ‘Section2’ Name = ‘CO2u’ Axial Load = 1000k Orbit Option = ‘Analyze at ultimate material strains’ XTRACT - Cross Sectional Analysis of Structural Components - 18

The moment-moment interaction surface analyzes the cross section at a number of points specified by the ‘Number of Points’ input parameter. Analysis is performed on the cross section at varying angles of loading with the principal bending axis ranging from 0 to 360 degrees. For each analysis, one of the target strains specified for each of the materials will be reached but not exceeded. By specifying the first yield criterion this will result in a moment-moment yield surface. By specifying the ultimate material strains, the ultimate moment-moment interaction surface can be found for the given target axial load. In this project there should be 2 sections each with 6 applied loadings - 4 moment curvatures and 2 capacity orbits. Click the ‘Analyze’ icon (

) from the main toolbar to run the analyses.

Viewing Results After closing the analysis display windows, click the ‘Add Graph’ icon (

) to add graph to the

project. In the graph dialog box, change the name to ‘Sec1 Moment Curv’ and add the ‘Curvatures about the Y-Axis’ data on the X-Axis and ‘Moments about the Y-Axis’ on the Y-Axis. Repeat for all moment curvature loadings applied on ‘Section1’ (Figure 23). This can be repeated for the moment curvature analyses performed on ‘Section2’ allowing comparison of results from the two sections.

The comparison of moment curvature results for varying axial loads applied on

‘Section1’ shown in Figure 23 reveals that there is a higher moment capacity as the axial load is increased (both at yield and ultimate limit states); however, with increasing axial load there is a decrease in curvature capacity. Add a graph called ‘Capacity Orbit Curv’ (Figure 24) - in this graph plot the ‘Curvatures about the X-Axis’ on the Y-Axis of the chart against the ‘Curvatures about the Y-Axis’ on the X-Axis of the chart. Repeat for both ultimate analysis on both cross sections. This chart suggests that ‘Section1’ has more deformation capacity when loaded to the left (bending about the strong axis) where as ‘Section2’ has more deformation capacity when loaded upwards (bending about the weak axis).

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Figure 23. Moment Curvatures for Section 1.

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Figure 24. Graph of X and Y axes curvatures from the Capacity Orbit analyses.

Conclusion This step-by-step example file has demonstrated to the reader how to create a user defined cross section. The example has also demonstrated the use of the remesher and generation of longitudinal reinforcing bars. In addition, the input file was opened and manipulated within a text editor and multiple analyses were performed. For more information on specific details not contained within this example, consult the XTRACT.hlp.

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