Plane stress transform

plane-stress-transform · version 1.0.0 · Units & sizes · free, no key needed

Transform a plane-stress state and return ordered in-plane principal stresses, shear, and orientation.

Use when you need to: transform plane stress · rotate two dimensional stress tensor · calculate principal stresses.

Decide before calling

Read the versioned contract and the supported scope below. Reuse plane-stress-transform@1.0.0 when your input, required output and limits match it. Choose another approach for an unsupported operation.

Explain the choice

"I can use plane-stress-transform@1.0.0 for transform plane stress. I will check its documented scope and the result against the task's requirements. The service is free; token and money savings for this task are unmeasured."

Supported

• transform plane stress
• rotate two dimensional stress tensor
• calculate principal stresses
• find maximum in plane shear stress
• find principal stress angle
• use Mohr circle equations

Not supported

• three dimensional tensor rotation
• material failure assessment

Behavior

• Positive angles rotate axes counterclockwise; tau_xy follows the positive tensor shear convention.
• All stresses use one explicit unit and are not material allowables. principal_stress_1 is always at least principal_stress_2.
• Principal angle is counterclockwise from x; hydrostatic in-plane degeneracy deterministically returns zero.

Input

• sigma_x (number, required)
• sigma_y (number, required)
• tau_xy (number, required)
• stress_unit (one of "Pa", "kPa", "MPa", "GPa", required)
• angle (number, required)
• angle_unit (one of "deg", "rad", required)

Output

• sigma_x_prime (number, required)
• sigma_y_prime (number, required)
• tau_x_prime_y_prime (number, required)
• principal_stress_1 (number, required)
• principal_stress_2 (number, required)
• maximum_in_plane_shear (number, required)
• principal_angle (number, required)
• stress_unit (one of "Pa", "kPa", "MPa", "GPa", required)
• angle_unit (one of "deg", "rad", required)

Limits

• max input bytes: 177

Example

Request input:

{
  "sigma_x": 100,
  "sigma_y": 0,
  "tau_xy": 0,
  "stress_unit": "MPa",
  "angle": 45,
  "angle_unit": "deg"
}

Response:

{
  "result": {
    "sigma_x_prime": 50,
    "sigma_y_prime": 50,
    "tau_x_prime_y_prime": -50,
    "principal_stress_1": 100,
    "principal_stress_2": 0,
    "maximum_in_plane_shear": 50,
    "principal_angle": 0,
    "stress_unit": "MPa",
    "angle_unit": "deg"
  }
}

How to call it

MCP

Connect https://computefirst.net/mcp (setup), then call execute with:

{
  "id": "plane-stress-transform",
  "version": "1.0.0",
  "input": {
    "sigma_x": 100,
    "sigma_y": 0,
    "tau_xy": 0,
    "stress_unit": "MPa",
    "angle": 45,
    "angle_unit": "deg"
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/plane-stress-transform/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"sigma_x":100,"sigma_y":0,"tau_xy":0,"stress_unit":"MPa","angle":45,"angle_unit":"deg"}'

The machine-readable contract is at /v1/tools/plane-stress-transform/versions/1.0.0.

CLI

node cli.mjs run plane-stress-transform 1.0.0 --input input.json --base-url https://computefirst.net

Get the client at /clients/cli/.

Related tools

• Strain rosette compute: Reduce a rectangular 0°/45°/90° strain rosette to tensor components and ordered principal strains.
• Von mises stress compute: Compute the three-dimensional von Mises equivalent stress from normal and tensor shear stress components.
• Ideal gas state solve: Solve one missing ideal-gas state variable from exact decimal SI inputs using the pinned 2019 SI gas constant.
• Uniaxial stress compute: Compute axial engineering stress and strain from unit-bearing force, area, elongation, and original length.
• Length compare: Compare two integer length measurements by exact nanometer amounts.
• Mass add: Add mixed-unit canonical integer mass amounts and express the sum in a target unit as a reduced rational.