> ## Documentation Index
> Fetch the complete documentation index at: https://calcs.com/docs/llms.txt
> Use this file to discover all available pages before exploring further.
# Free-Body Diagram
> Plot free-body diagrams with all factored loads and reactions for specific load combinations
The Free-Body Diagram is used throughout the modern platform to plot a free-body diagram with all factored loads and reactions for a specific load combination. It uses diagram widget type `"beamFreeBody"`.
## Implementation
```json theme={null}
{
"type": "sheetTemplateWidgets",
"attributes": {
"type": "diagram",
"diagram": [
{
"type": "beamFreeBody"
}
],
"equation": [
{
"result": "{PARAMETERS}",
"condition": "CONDITIONS"
}
],
"referenceId": "free_body_diagram"
}
}
```
## Plot Parameters
| Parameter | Format | Example | Description |
| ---------- | ---------------- | ------------------- | ------------------------------------------------------------------------------------------------------------------------------ |
| xData | array of numbers | `remote.plot.x` | X coordinates along the beam |
| PL | array of dicts | `remote.plot.fbPL` | Point load locations and magnitudes |
| DL | array of numbers | `remote.plot.fbDL` | Distributed load values at each X-coordinate |
| ML | array of dicts | `remote.plot.fbML` | Moment load locations and magnitudes |
| AL | array of dicts | `remote.plot.fbAL` | Axial load locations and magnitudes |
| ADL | array of numbers | `remote.plot.fbADL` | Axial distributed load values at each X-coordinate |
| R | array of dicts | `remote.plot.fbR` | Reaction magnitudes and locations |
| lenConvert | number | `0.001` | (defaults to `0.001`) Conversion factor for lengths |
| lenUnit | string | `"m"` | (defaults to `"m"`) Unit for lengths |
| plUnit | string | `"kN"` | (defaults to `"kN"`) Unit for point loads |
| mlUnit | string | `"kNm"` | (defaults to `"kNm"`) Unit for moment loads |
| dlUnit | string | `"kN/m"` | (defaults to `"kN/m"`) Unit for distributed loads |
| column | boolean | `false` | (defaults to `false`) Whether to plot free body diagram vertically, adjusting text locations appropriately |
| allFactor | number | `1` | (defaults to `1`) Factor by which to adjust all load and reaction values. Useful to display FBD including k1 factors in timber |
| wall | number | `0` | (defaults to `0`) Height of the wall to display |
## Load Data Formats
### Point Loads (PL)
The point loads array contains dictionaries with load information:
```javascript theme={null}
PL: [
{
x: 2.5, // Location along beam
P: 150, // Load magnitude
label: "P1" // Optional label
},
// ... more point loads
]
```
### Distributed Loads (DL)
Distributed loads are provided as an array of values corresponding to the x-coordinates:
```javascript theme={null}
xData: [0, 1, 2, 3, 4, 5], // X coordinates
DL: [0, 10, 10, 15, 15, 0] // Load values at each x coordinate
```
### Moment Loads (ML)
Moment loads follow a similar format to point loads:
```javascript theme={null}
ML: [
{
x: 1.8, // Location along beam
M: 50, // Moment magnitude
label: "M1" // Optional label
}
]
```
### Reactions (R)
Reactions include support information and magnitudes:
```javascript theme={null}
R: [
{
x: 0, // Support location
Ry: 125, // Vertical reaction
Rx: 0, // Horizontal reaction (if any)
Mz: 0, // Moment reaction (if any)
type: "pin" // Support type
}
]
```
## Example Implementation
```json theme={null}
{
"type": "sheetTemplateWidgets",
"attributes": {
"type": "diagram",
"diagram": [
{
"type": "beamFreeBody"
}
],
"equation": [
{
"result": "{
xData: remote.plot.x,
PL: remote.plot.fbPL,
DL: remote.plot.fbDL,
ML: remote.plot.fbML,
R: remote.plot.fbR,
lenUnit: \"m\",
plUnit: \"kN\",
dlUnit: \"kN/m\",
mlUnit: \"kNm\"
}",
"condition": "@default"
}
],
"referenceId": "load_combination_fbd",
"label": "Free Body Diagram - Ultimate Limit State",
"showInSuperSummary": true
}
}
```
## Special Features
### Column Mode
Set `column: true` to display the free-body diagram vertically, which is useful for column analysis:
```javascript theme={null}
{
column: true,
wall: 3000, // Height of wall/column in mm
// ... other parameters
}
```
### Load Factoring
Use `allFactor` to apply additional factors to all loads and reactions:
```javascript theme={null}
{
allFactor: 1.2, // Apply 20% additional factor
// ... other parameters
}
```
This is particularly useful in timber design where k1 factors need to be displayed in the free-body diagram.
## Integration with Beam Solvers
Free-body diagrams are typically used with beam solver results:
```json theme={null}
{
"type": "sheetTemplateWidgets",
"attributes": {
"type": "remote",
"solver": "beam",
"equation": [
{
"condition": "@default",
"result": "{
L: beam_length,
r: support_data,
PL: point_loads,
DL: distributed_loads,
// ... other beam parameters
}"
}
],
"referenceId": "beam_analysis"
}
}
```
## Best Practices
1. **Units**: Ensure consistent units throughout all load and dimension parameters
2. **Load Combinations**: Create separate diagrams for different load combinations
3. **Labels**: Use clear, descriptive labels for loads and reactions
4. **Visibility**: Use `visibleIf` conditions to show diagrams only when relevant
5. **Solver Integration**: Always source data from beam solvers for accuracy
Free-body diagrams are excellent for verification and presentation. They help engineers quickly verify that loads and reactions are properly balanced and correctly applied.
The free-body diagram shows factored loads for the specified load combination. Ensure that the load factors applied in the beam solver match what you want to display in the diagram.