Cross-section Solver

The Cross-section Solver provides comprehensive analysis of structural cross-sections, calculating geometric properties, elastic properties, plastic properties, and warping characteristics using the sectionproperties library.

Input Parameters

Most parameters are optional, but enough information must be provided to create a stable structure with:

Both stiffnesses (EA and EI)
Length specification
At least 1-2 supports
At least one strength load case/combination
At least one serviceability load combination

Core Configuration

array

required

Array of section dictionaries following sectionproperties Documentation format with additional Calcs.com-specific entries.Note: You may see std_* parameters in past examples. These don’t do anything currently and are simply passed through. They were intended for cross-section design linking.

string

required

String describing the section type. Full names from sectionproperties documentation are available, plus abbreviated names.

string

Mirror the section about an axis. Options: "x", "y", or "null"

number

Rotate section counterclockwise by specified degrees. Use null for no rotation.

object

Dictionary of material names and their properties.Default: {"default": {"E": 1, "nu": 0, "fy": 1, "color": "#000", "lineWeight": 3}}Properties include:

E: Elastic modulus
nu: Poisson’s ratio
fy: Yield strength
color: Line color
lineWeight: Line weight for display

Analysis Configuration

string

default:"none"

Type of analysis to perform:

"none": No analysis (geometry only)
"elastic": Elastic analysis only
"warping": Elastic + warping analysis
"plastic": Elastic + plastic analysis
"frame": Optimized analysis for frame properties
"full": Complete analysis (elastic + warping + plastic)

string

default:"none"

Geometry validity checking:

"check": Issue error messages for problems
"clean": Try to fix geometry issues automatically
"none": No geometry checking

Mesh and Output Configuration

number

default:"100"

Maximum mesh size = gross area / this factor

string

default:"#AAA"

Color for mesh lines in output

integer

default:"1"

Line weight for mesh lines

float

default:"1e-16"

Tolerance below which results are rounded to zero. Engineering applications typically use 1e-6.

string

required

Unit for length outputs. Must be valid mathjs unit (e.g., ‘m’ for SI, ‘ft’ for US)

string

required

Unit for force outputs. Must be valid mathjs unit (e.g., ‘N’ for SI, ‘kip’ for US)

Output Properties

All outputs are accessible via solverRefId.propertyName where solverRefId is your solver’s reference ID.

Always Available (All Analysis Types)

array

All lines making up the cross-section (excluding mesh)

array

Default dimensions for cross-section diagrams. Includes all input dimensions.

array

2×2 array of outer domain extents: [[xmin, ymin], [xmax, ymax]]

array

n×2 array of all points/nodes: [[x1, y1], [x2, y2], ...]

array

n×2 array of all elements: [[node0, node1], ...]

array

Points located within empty regions

array

Points located within filled regions

array

Amount by which each geometry was shifted

Elastic Results

Available for elastic, warping, plastic, and full analysis types:

Basic Properties

number

Gross area

number

Centroid location (X, Y coordinates)

number

Radius of gyration about centroidal axes

number

Radius of gyration about principal axes

number

Angle of major principal axis

Stiffness Properties

number

Axial stiffness

number

First moment of area about global axes

number

Second moment of area about centroidal axes

number

Second moment of area about principal axes

number

Second moment of area about global axes

Section Moduli

number

Elastic section modulus for positive/negative bending about centroidal X-axis

number

Elastic section modulus for positive/negative bending about centroidal Y-axis

number

Minimum elastic section modulus (min of positive/negative)

number

Elastic section modulus about principal axes

number

Minimum elastic section modulus about principal axes

Same Stiffness Outputs

When all sections have identical stiffness, additional properties without ‘E’ prefix are available: Qx, Qy, Ixx, Iyy, Ixy, I11, I22, I12, Ixxg, Iyyg, Ixyg, Zxxp, Zxxm, Zyyp, Zyym, Zxx, Zyy, Z11p, Z11m, Z22p, Z22m, Z11, Z22

Plastic Properties

Available for plastic and full analysis types:

number

Plastic centroid location

number

Plastic centroid location on principal axes

number

Plastic section modulus about centroidal axes

number

Plastic section modulus about principal axes

Same Yield Stress Outputs

When all sections have identical yield stress: Sxx, Syy, S11, S22

Warping Properties

Available for warping and full analysis types:

Shear Centers

number

Shear center location

number

Shear center on principal axes

number

Taffetz shear center location

Monosymmetry Constants

number

Monosymmetry constants for positive/negative bending about centroidal axes

number

Monosymmetry constants about principal axes

Advanced Properties

number

St Venant’s torsion constant

number

Warping constant

number

Shear area about centroidal axes

number

Shear area about principal axes

Same Stiffness Outputs

When all sections have identical stiffness: J, Iw, Asx, Asy, As11, As22

Frame Properties

For analysisType: "frame" - optimized subset for frame analysis:

number

Gross area

number

Angle of major principal axis

number

Axial stiffness

number

St Venant torsion constant

number

First moment of area about global axes

number

Second moment of area about centroidal axes

Example Usage

{
  "type": "remote",
  "referenceId": "section_analysis",
  "solver": "crossSection",
  "inputs": {
    "sectionsData": [
      {
        "type": "rectangular",
        "b": 200,
        "h": 300,
        "material": "steel"
      }
    ],
    "materialsData": {
      "steel": {
        "E": 200000,
        "nu": 0.3,
        "fy": 250,
        "color": "#1f77b4",
        "lineWeight": 2
      }
    },
    "analysisType": "full",
    "lenUnit": "mm",
    "forceUnit": "N"
  }
}

Best Practices

Analysis Type Selection: Choose the minimum analysis type needed for your calculations to optimize performance
Unit Consistency: Ensure lenUnit and forceUnit match your template’s unit system
Geometry Validation: Use checkGeom: "clean" for robust geometry handling
Material Properties: Define realistic material properties for accurate results
Mesh Control: Adjust defaultMeshFactor based on section complexity and required accuracy

Performance Considerations

"frame" analysis type is fastest and most reliable for basic frame properties
"full" analysis provides complete results but takes longer
Complex geometries may require geometry cleaning (checkGeom: "clean")
Large defaultMeshFactor values create finer meshes but slower analysis

When using complex geometries, test with checkGeom: "check" first to identify potential issues before using "clean" mode.

Guides

Analysis Calculators

Design Calculators

Calcs Builder

Input Parameters

Core Configuration

Analysis Configuration

Mesh and Output Configuration

Output Properties

Always Available (All Analysis Types)

Elastic Results

Basic Properties

Stiffness Properties

Section Moduli

Same Stiffness Outputs

Plastic Properties

Same Yield Stress Outputs

Warping Properties

Shear Centers

Monosymmetry Constants

Advanced Properties

Same Stiffness Outputs

Frame Properties

Example Usage

Best Practices

Performance Considerations

​Input Parameters

​Core Configuration

​Analysis Configuration

​Mesh and Output Configuration

​Output Properties

​Always Available (All Analysis Types)

​Elastic Results

​Basic Properties

​Stiffness Properties

​Section Moduli

​Same Stiffness Outputs

​Plastic Properties

​Same Yield Stress Outputs

​Warping Properties

​Shear Centers

​Monosymmetry Constants

​Advanced Properties

​Same Stiffness Outputs

​Frame Properties

​Example Usage

​Best Practices

​Performance Considerations

Input Parameters

Core Configuration

Analysis Configuration

Mesh and Output Configuration

Output Properties

Always Available (All Analysis Types)

Elastic Results

Basic Properties

Stiffness Properties

Section Moduli

Same Stiffness Outputs

Plastic Properties

Same Yield Stress Outputs

Warping Properties

Shear Centers

Monosymmetry Constants

Advanced Properties

Same Stiffness Outputs

Frame Properties

Example Usage

Best Practices

Performance Considerations