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This option guarantees that new generated Boundary Corners or STM Nodes will be precisely placed on Vertical and Horizontal Guidelines as well as at the intersection of Vertical and Hori

In this document, the task of designing a double corbel is completed to illustrate how the CAST Design Tool (Version 0.9.10) can be used for the design of D- (Discontinuity) Regions Following a brief introduction and description of the CAST graphical user interface, a step-by-step solution is presented In order to describe many of the important features of this program, complete details are provided with associated images from CAST The completion of this exercise and thus familiarization with CAST is estimated to take 60 minutes

Introduction

Figure 1 describes the geometry and loadings for the double corbel structure being considered The thickness of the corbel is

600 mm The concrete strength is 35 MPa, and the yield strength of reinforcement is taken as 420 MPa The corbel supports

an ultimate vertical force of 1000 kN and an ultimate horizontal force of 100 kN at each end and two ultimate point loads of

3000 kN in the supporting column region Bearing plates of 150 mm length x 600 mm width x 25 mm thick are provided at each end of the corbel Figure 2 shows the selected strut-and-tie model for this structure The design will be completed to meet ACI 318-02 Appendix A requirements

Figure 1 The Geometry and the Loadings of the Corbel under Consideration

Figure 2 Strut-and-Tie Model Employed in this Corbel Design

CAST Window

Creation/modification of the structure’s geometry and strut-and-tie model, execution of the truss analysis, and stress checks using CAST Design Tool are all done through the CAST Graphical User Interface (GUI) The CAST GUI that appears on your screen will look similar to Figure 3 This interface consists of several components as labeled in Figure 3 Please familiarize yourself with the names of these interface components as they will be used throughout this handout

Figure 3 A Typical CAST Window

(Click here to view a larger image)

o A closed, non-intersecting polygon that defines the geometry of the structure.

o There are two types of D-Region Boundaries: Outer Boundary (Perimeter) and Inner Boundary (for openings)

o You are allowed to create only one Outer Boundary, but you can create as many Inner Boundaries as you want

o Because there is only one Outer Boundary that should exist in your model and the region inside the Outer Boundary represents the concrete continuum, you are not allowed to copy, cut, or remove it from your model once you create it However, you are surely allowed to change the positions of the Boundary Corners You are also allowed to add and remove Boundary Corners as you wish

 D-Region Boundary Corner:

o Intersection of two Boundary Edges

 D-Region Boundary Edge:

o Line connecting two Boundary Corners

o Place for STM Nodes that possess Bearing Plates, Point Loads, or Point Supports

 Strut-and-Tie Model:

o Internal truss in the D-Region

o Consists of STM Elements interconnected at STM Nodes

 STM Element:

o Component of Strut-and-Tie Model

o STM Elements can be in the form of Struts (compressive STM Elements) or Ties (tensile STM Elements)

o STM Elements have Effective Widths, representing the extent of idealized compressive stress fields (for Struts) or tensile stress fields (for Ties)

 STM Node:

o Component of Strut-and-Tie Model

o Place where one or more STM Elements meet, also called a nodal zone

o There is only one STM Element allowed to frame into an STM Node having Bearing Plates, Point Loads, or Point Supports

 Stabilizer:

o STM Element whose member force is zero

o Stabilizers are not included in the nodal zone construction

o Stabilizers are required to avoid ill-conditioned structure stiffness matrix in truss analysis

o You must always create a stable Strut-and-Tie Model; Stabilizers are identified by CAST during truss analysis

o See Q & A #4 for more detail about Stabilizers

Getting Started

In this section, we start the program, set the units, create a new model file, define project description, define general

properties, setup Guidelines, and save the model in a file

to Programs, point to CAST, and then click CAST This

starts the CAST program A CAST window followed by the

CAST splash screen then appears After this, if the Tip of the Day dialog box like the one shown in Figure 4 is displayed,

close it by clicking the OK button.

Figure 4 The Tip of the Day Dialog Box

Unit of Measure combo box (seeFigure 5) located in the Standard toolbar Since our design problem is given in SI

unit, select SI Unit

Figure 5 The Active Unit of Measure Combo Box Note:You can change the units at any time; CAST will handle

all the conversion automatically1.3

Click the button (or select New from the File menu) CAST responds by displaying the Define Project Description dialog box shown in Figure 6 In this dialog box:

• Change the Project Name text box to Double Corbel

• Provide a name in the Designer text box In our

case, assume that the designers are Sabrina and Julius, so type in Sabrina & Julius

• Change the Date text box to current date, let

say 4/2/2002

• Enter any important notes in the Notes text box In

our case, type in Example for CAST Tutorial

• Click the OK button to confirm the input and close

the window

Figure 6 The Define Project Description Dialog Box Note: The Define Project Description dialog box can be later displayed for editing by clickingProject

Description from the Define menu (or by pressing Ctrl+D

key combination) Alternatively, it can be displayed by clicking the button from the Defining toolbar.

box shown in Figure 7 This dialog box allows us to define the thickness of the structure under consideration, the concrete cylinder strength, and the steel yield strength

• Type in 600 in the D-Region Thickness text box.

• Type in 35 in the Concrete Cylinder Strength,

Ctrl+T key combination) Alternatively, it can be

displayed by clicking the button from

the Defining toolbar.

geometry of the model To do this, clickGuidelines from the Construct menu CAST will display the Construct Guidelines dialog box shown in Figure 8 In this dialog box:

• Check the Glue Boundary Corners or STM Nodes

to Guidelines checkbox to turn on this option If this

option is on, it lets you edit D-Region Boundary Corners and/or STM Node locations by simply editing the Guidelines.

• Check the Snap Boundary Corners or STM Nodes

to Guidelines checkbox to turn on this option If this

option is on, a D-Region Boundary Corner or an STM Node drawn or moved near a vertical and horizontal Guideline will snap to it This option guarantees that new generated Boundary Corners or STM Nodes will

be precisely placed on Vertical and Horizontal Guidelines as well as at the intersection of Vertical and Horizontal Guidelines This option can also be

activated from the Snapping toolbar: when on

and when off

• Select the type of the Guidelines we want to

add/move/delete Let’s begin with the Vertical

Guidelines by clicking on the text box of

the Distance from Y-Axis frame located in

theVertical Guidelines frame.

• Add Vertical Guidelines In our case, we need twelve Vertical Guidelines, i.e., at location X=-1000, X=-910, X=-900, X=-500, X=-250, X=0, X=125, X=250, X=500, X=900, X=910, X=1000 Enter each number

in the text box of the Distance from Y-Axis frame located in the Vertical Guidelines frame followed by clicking the Add button.

• After completing Vertical Guideline locations, do the same for Horizontal Guidelines In our case, we need six Horizontal Guidelines, i.e., at location Y=-600, Y=0, Y=400, Y=900, Y=1000, Y=1500 Enter each

number in the text box of the Distance from Axis frame located in the Horizontal

X-Guidelines frame followed by clicking

the Add button.

• Press the OK button to confirm the input and close

the window

Figure 8 The Construct Guidelines Dialog Box Notes:

• Guidelines are lines that we create to help us determine the geometry of the model The Boundary Corners and STM Nodes of our structural model are usually located at intersections of Vertical and Horizontal Guidelines

• We can later display the Construct

Guidelines dialog box for editing by

clickingGuidelines from the Construct menu (or by

pressing Shift+F3 key combination or by clicking

the button from the Standard toolbar).

• When a Guideline is visible on a display window,

the Construct Guidelines dialog box can also be

displayed by double clicking on the Guideline

• If you want to change a Guideline location (a Vertical Guideline for example):

 Select the Guideline location you want to

change from the list box in the Defined Locations frame.

 The Guideline location value will appear in

the text box of the Distance from Axisframe Edit the value in this text box.

Y- Click the Modify button in the Vertical Guidelines frame.

 Click the OK button to confirm the change

and close the window

• To delete a defined Guideline (a Vertical Guideline for example):

 Select the Guideline location you want to

delete from the list box in the Defined Locations frame.

 Click the Delete button in the Vertical Guidelines frame.

 Click the OK button to confirm the deletion

and close the window

The screen will then refresh and will look similar to Figure 9

Figure 9 CAST Window after Step 1.5

(Click here to view a larger image)

Notes:

• We can have multiple display windows to view our structural model at the same time To add a new

display window, click the Window menu, point

to New Window, and click on one of the Load

Condition names listed To arrange the positions of the display windows, select one of the four options

available (Tile Horizontally/Tile

Vertically/Cascade/Arrange Icons) from

the Window menu.

• We can hide/display the Guidelines of the active

display window by clicking Show Guidelines from the View menu (or by pressing F3 key) Similarly, we

can hide/display the axes shown in an active display

window by choosing Show Axes from

the View menu (or by pressing F4 key).

• In addition to Guidelines, CAST also provides Grid Points to help us determine the geometry of our

model To setup Grid Points, select Grid Points from the Construct menu (or press Shift+F2 key

combination) The Construct Grid Points dialog box

similar to Figure 10 will then appear on the screen In this dialog box, we can:

 Set the horizontal or vertical interval of Grid Points by entering the horizontal or vertical

text box in the Grid Point Interval frame.

 If you want to store the specified horizontal

or vertical Grid Point interval in file to be used for the next opening of CAST, click

the Save As Defaults button The Grid Point

interval will be stored in CAST.INI

 Check the Snap Boundary Corners or STM Nodes to Grid Points checkbox to turn on

this option If this option is turned on, a Region Boundary Corner and/or STM Node drawn or moved near a Grid Point will snap

D-to it This option guarantees that new generated D-Region Boundary Corners and/or STM Nodes will be precisely placed

at the grid points This option can also be

activated from the Snappingtoolbar:

when on and when off

Figure 10 The Construct Grid Points Dialog Box

should save your work at this early stage To save the model for the first time, do the following:

• Select Save As or Save from the File menu (or use

Ctrl+S key combination, or click the button from

the Standard toolbar) CAST responds by displaying the Save As dialog box shown in Figure 11.

• Change the directory to your working directory In this case, assume that the working directory

is c:\CAST\Files

• Provide a file name in the File name text box In this

case, assume that the file name isDCorbel CAST will then automatically build an extension of CST to the file name.

• Click the Save button.

It is also a good idea to save your work from time to time because you will have to do the unsaved work again if your

PC system collapses before you save your work To save

your work, select Savefrom the File menu (or use Ctrl+S key

combination, or click the button from

the Standardtoolbar).

Figure 11 The Save As Dialog Box

Constructing the Model

In this section, we construct the D-Region Boundaries and the Strut-and-Tie Model After that, we define and assign Bearing Plates (if any), Point Loads, and Point Supports

create our D-Region Boundaries If you do not see the

Guidelines on the screen, click Show Guidelines from the View menu This creates a rectangle surrounding the

icon next to it and works as a toggle to turn on/off the

Guidelines Make sure that the Snap Boundary Corners or STM Nodes to Guidelines button located in

the Snapping toolbar is on by clicking it: when on

and when off Click then the button (or click

the Construct menu and then click Outer Boundary) to

switch to the Draw mode Next, create the D-Region Boundary by placing the Boundary Corners at the Guideline intersections as follows:

• Click on the intersection of Guideline X=-1000 and Guideline Y=1000

• Click on the intersection of Guideline X=-500 and

Up to this point, we have finished drawing the geometry of the structure as shown in Figure 12.

Figure 12 CAST Window after Step 2.1

(Click here to view a larger image)

Notes:

• You can create openings within the D-Region, if any,

in the same manner as you create the Outer

Boundary, except that you must click the

button (or click again the Constructmenu and then click Inner Boundaries).

• You must first create the Outer Boundary before you can create Inner Boundaries and Strut-and-Tie Model

• You are allowed to create only one Outer Boundary, but you can create as many Inner Boundaries (to represent openings) as you want

• If you hold the Shift key while drawing, it turns on the orthogonal mode In this mode, all lines you make will be parallel to either X or Y axis

• If you make a mistake, for example, you draw an element at a wrong place, you can undo your work

by clicking the button from the Standard toolbar

or clicking Undo from theEdit menu (or by pressing

Ctrl+Z key combination)

• You can also move/add/remove an Outer or Inner

Boundary Corner by clicking the button to

switch to Modify mode (or by selecting Edit

Boundaries from the Edit menu), and then:

 To move the whole D-Region Boundary, simply drag it to the desired position If the (Snap Boundary Corners or STM

Nodes to Grid Points) or the (Snap Boundary Corners or STM Nodes to Guidelines) option is turned on, the centroid

of the D-Region Boundary enclosed area will

be snapped to any Grid Points or Guidelines while dragging

 Similarly, to move a corner position, drag the

corner to the desired position If the

(Snap Boundary Corners or STM Nodes

to Grid Points) or the (Snap Boundary Corners or STM Nodes to Guidelines)

option is turned on, the corner will be

snapped to any Grid Points or Guidelines while dragging

 To add or remove a corner:

o Right click on a corner or an edge

The pop-up menu similar to Figure

in the display window The middle control is used to adjust the line thickness of D-Region Boundary, STM Element, and Bearing Plate objects and to adjust the diameter of STM Node objects The most right control is used to adjust the length of Point Load and Point Support objects

Figure 13 The Pop-up Menu for Adding or Removing

D-Region Boundary Corners

Again, we will again use the Guidelines to help us create the

geometry Click the button (or select STM Elements from the Constructmenu) to switch to the Draw mode Make sure that the Snap and Glue STM Nodes to Other STM Nodes option is on by clicking it: when on and when off Also, make sure that theSnap STM Nodes

to Boundary Edges option is on by clicking it: when on

and when off The (Snap STM Elements Perpendicular to Boundary Edges) option allows the STM

Elements drawn to be perpendicular to Boundary Edges

We also need to show STM Element and Node IDs for our

later reference This is done by clicking the button from

the Standard toolbar or by selecting Set Object View Options menu from theView menu and then clicking the OK button This will show the Set Object View Options dialog box as shown in Figure 14 In this dialog box, check Node IDs and Element IDs checkboxes in the Strut- and-Tie Model frame, and then click the OK button.

Figure 14 The Set Object View Options Dialog Box

(Click here to view a larger image)

Now, do the following:

• Click on the intersection of Guideline X=-910 and Guideline Y=900, and then click on the intersection

of Guideline X=-250 and Guideline Y=900 This step basically draws STM Element ID E1 (see Figure 15)

• Click on the intersection of Guideline X=-250 and Guideline Y=900, and then click on the intersection

of Guideline X=250 and Guideline Y=900 This step creates STM Element IDE2

• Click on the intersection of Guideline X=250 and Guideline Y=900, and then click on the intersection

of Guideline X=910 and Guideline Y=900 This step creates STM Element IDE3

• Click on the intersection of Guideline X=-910 and Guideline Y=900, and then click on the intersection

of Guideline X=-250 and Guideline Y=0 This step creates STM Element ID E4

• Click on the intersection of Guideline X=910 and Guideline Y=900, and then click on the intersection

of Guideline X=250 and Guideline Y=0 This step creates STM Element ID E5

• Click on the intersection of Guideline X=-250 and Guideline Y=0, and then click on the intersection of Guideline X=250 and Guideline Y=0 This step creates STM Element ID E6

• Click on the intersection of Guideline X=-250 and Guideline Y=-600, and then click on the intersection

of Guideline X=-250 and Guideline Y=0 This step creates STM Element ID E7

• Click on the intersection of Guideline X=-250 and Guideline Y=0, and then click on the intersection of

Guideline X=-250 and Guideline Y=900 This step creates STM Element IDE8.

• Click on the intersection of Guideline X=-250 and Guideline Y=900, and then click on the intersection

of Guideline X=-250 and Guideline Y=1500 This step creates STM Element IDE9

• Click on the intersection of Guideline X=250 and Guideline Y=-600, and then click on the intersection

of Guideline X=250 and Guideline Y=0 This step creates STM Element ID E10

• Click on the intersection of Guideline X=250 and Guideline Y=0, and then click on the intersection of Guideline X=250 and Guideline Y=900 This step creates STM Element IDE11

• Click on the intersection of Guideline X=250 and Guideline Y=900, and then click on the intersection

of Guideline X=250 and Guideline Y=1500 This step creates STM Element IDE12

• Click on the intersection of Guideline X=-250 and Guideline Y=900, and then click on the intersection

of Guideline X=250 and Guideline Y=0 This step creates STM Element ID E13

• Click on the intersection of Guideline X=-250 and Guideline Y=0, and then click on the intersection of Guideline X=125 and Guideline Y=-600 This step creates STM Element IDE14

• Click on the intersection of Guideline X=-910 and Guideline Y=900 Click on the intersection of

Guideline X=-900 and Guideline Y=1000 This step creates STM Element ID E15

• Click on the intersection of Guideline X=910 and Guideline Y=900 Click on the intersection of

Guideline X=900 and Guideline Y=1000 This step creates STM Element ID E16

Figure 15 CAST Window Showing an STM Element and

Guideline Locations(Click here to view a larger image)

Up to this point, we have finished drawing the geometry of the Strut-and-Tie Model Figure 16 shows how the CAST window should look like now

Figure 16 CAST Window after Step 2.2

(Click here to view a larger image)

Notes: When we draw an STM Element, STM Nodes are

automatically provided at each end of the STM Elements

• Again, if you make a mistake, for example, you draw

an element at the wrong place, you can undo your work by clicking the button from

the Standard toolbar or clicking Undofrom

the Edit menu.

• You can also move the position of STM Nodes by

clicking to switch to Modify mode (or by

selecting Drag STM from the Edit menu) and then

dragging the node If the (Snap Boundary Corners or STM Nodes to Grid Points) or the (Snap Boundary Corners or STM Nodes to Guidelines) option is turned on, the node will be

snapped to any Grid Points or Guidelines while dragging

• The Modify mode also allows you to move the position of an STM Element by dragging the element

to the desired position However, the connectivity to the nodes at the ends of the element will be lost If the (Snap Boundary Corners or STM Nodes to Grid Points) or the (Snap Boundary Corners or STM Nodes to Guidelines) option is turned on, the

centroid of the STM Element will be snapped to any Grid Points or Guidelines while dragging

• Pressing the Esc key will terminate the Draw mode and take you back to Select mode

have just drawn Do the following:

 Click on the button from the Drawing toolbar to

be in the Select mode

 Select STM Node IDs N12 (at X=-900 Y=1000) and N13 (at X=900 Y=1000) by either clicking on them or drawing a window completely around them The selected nodes will become star-type shapes as shown in Figure 17

 Click on the button from the Assigning toolbar (or select Bearing Plates from theAssign menu) The Assign Bearing Plates dialog box (Figure 18)

then appears In this dialog box:

 Enter 600 in the Width text box

 Enter 150 in the Length text box

 Enter 25 in the Thickness text box

 Click the OK button to confirm the input and close

the window

After this stage, the CAST window will look similar to Figure 19