Free-Body Diagram

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

{
    "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:

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:

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:

ML: [
    {
        x: 1.8,        // Location along beam
        M: 50,         // Moment magnitude
        label: "M1"    // Optional label
    }
]

Reactions (R)

Reactions include support information and magnitudes:

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

{
    "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:

{
    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:

{
    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:

{
    "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

Units: Ensure consistent units throughout all load and dimension parameters
Load Combinations: Create separate diagrams for different load combinations
Labels: Use clear, descriptive labels for loads and reactions
Visibility: Use visibleIf conditions to show diagrams only when relevant
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.

Guides

Analysis Calculators

Design Calculators

Calcs Builder

Implementation

Plot Parameters

Load Data Formats

Point Loads (PL)

Distributed Loads (DL)

Moment Loads (ML)

Reactions (R)

Example Implementation

Special Features

Column Mode

Load Factoring

Integration with Beam Solvers

Best Practices

​Implementation

​Plot Parameters

​Load Data Formats

​Point Loads (PL)

​Distributed Loads (DL)

​Moment Loads (ML)

​Reactions (R)

​Example Implementation

​Special Features

​Column Mode

​Load Factoring

​Integration with Beam Solvers

​Best Practices

Implementation

Plot Parameters

Load Data Formats

Point Loads (PL)

Distributed Loads (DL)

Moment Loads (ML)

Reactions (R)

Example Implementation

Special Features

Column Mode

Load Factoring

Integration with Beam Solvers

Best Practices