# Documentation

## Model Box Beam

### Model Overview

You can model an extrusion with a hole. One example is the box beam. Specifying hollow cross-sections must satisfy the cross-section guidelines. See Revolution and General Extrusion Shapes. In this example, you specify the cross-section coordinates of a box beam. For an example that shows you how to model an I-beam extrusion, see Model I-Beam.

### Modeling Approach

To represent the box beam geometry, first identify its cross-section. This is the 2-D area that you sweep along an axis to obtain the 3-D box beam. You can the specify the cross-section coordinates using the Solid block. The figure shows the box beam cross-section that you specify in this example.

The [0 0] coordinate identifies the solid reference frame origin. To place the reference frame at the center of the box beam, specify the coordinates so that the [0 0] coordinate is at the cross-section center. By parameterizing the cross-section coordinates in terms of relevant box beam dimensions, you can later change the box beam dimensions without having to reenter the cross-section coordinates. The figure shows the cross-section dimensions and coordinates that you must specify to represent the box beam.

Using the cross-section points that the figure shows, you define the coordinate matrix as:

```OuterCS = [A, B, C, D, E]; InnerCS = [F, G, H, I, J]; CS = [OuterCS; InnerCS];```

### Build Solid Model

1. At the MATLAB® command prompt, enter `smnew`. A new SimMechanics™ model opens with some commonly used blocks. Delete all but the Solid block.

2. In the Solid block dialog box, specify the following parameters. You later initialize the different MATLAB variables in a subsystem mask.

ParameterSelect or Enter
Geometry > Shape`General Extrusion`
Geometry > Cross-Section`CS`, units of `cm`
Geometry > Length`L`, units of `cm`
Inertia > Density`Rho`
Graphic > Visual Properties > Color`RGB`

3. Select the Solid block and generate a new subsystem, e.g., by pressing Ctrl+G.

### Define Solid Properties

In the subsystem mask, initialize the solid parameters. Then, in the subsystem dialog box, specify their values.

1. Select the Subsystem block and create a subsystem mask, e.g., by pressing Ctrl+M.

2. In the Parameters & Dialog tab of the Mask Editor, drag six Edit boxes into the Parameters group and specify these parameters.

PromptName
`Length``L`
`Height``H`
`Width``W`
`Thickness``T`
`Density``Rho`
`Color``RGB`

3. In the Initialization tab of the Mask Editor, define the cross-section coordinates and assign them to MATLAB variable `CS`:

```D1 = W/2-T; D2 = H/2-T; OuterCS = [-W/2,-H/2; W/2,-H/2; W/2,H/2; ... -W/2,H/2; -W/2,-H/2]; InnerCS = [-D1,-D2; -D1,D2; D1,D2; D1 -D2; -D1,-D2]; CS = [OuterCS; InnerCS];```

4. In the Subsystem block dialog box, specify the numerical values of the solid properties. The table shows some values that you can enter.

ParameterEnter
Length`10`
Height`4`
Width`2`
Thickness`0.2`
Density`2700`
Color`[0.85 0.45 0]`

### Visualize Solid Model

You can now visualize the box-beam solid. To do this, look under the Subsystem mask—e.g., by selecting the Subsystem block and pressing Ctrl+U—and open the Solid block dialog box. The solid visualization pane shows the solid that you modeled.

Parameterizing the solid dimensions in terms of MATLAB variables enables you to modify the solid shape without having to redefine its cross-section coordinates. You can change the solid size and proportions simply by changing their values in the Subsystem block dialog box. The figure shows some examples.