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Engineering operators

10 operators in the engineering category of the live registry. Each is a named formula you can compose inside a state contract or call directly through POST /api/zeq/compute. KO42 is always on; add up to three more per call (total ≤ 4), per the 7-step protocol.

OperatorDescriptionEquation
BEAM_DEFLECTIONMaximum deflection of a cantilever beam under a point load, derived from Euler-Bernoulli beam theory relating load, length, and flexural rigidity.\delta = \frac{PL^3}{3EI}
BEAM_MOMENTMaximum bending moment at midspan of a simply supported beam under a central point load, equal to one quarter of force times span.M = \frac{PL}{4}
BEAM_SHEARMaximum shear force at the supports of a simply supported beam under a central point load, equal to half the applied force.V = \frac{P}{2}
BUCKLING_CHECKEuler critical buckling load for slender columns, giving the axial force at which a column becomes elastically unstable under compression.P_{cr} = \frac{\pi^2 EI}{(KL)^2}
FEA_DISPLACEMENTGlobal finite element equilibrium equation relating the assembled stiffness matrix and nodal displacement vector to the applied force vector.[K]\{u\} = \{F\}
FEA_STIFFNESSElement stiffness matrix assembled by integrating the product of strain-displacement and constitutive matrices over the element volume.[K] = \int_V [B]^T[D][B] dV
MOMENT_INERTIASecond moment of area computed by integrating the square of the distance from the neutral axis over the cross-section, governing bending resistance.I = \int y^2 dA
STRESS_ANALYSISNormal stress defined as applied force divided by cross-sectional area, the foundational relation of strength of materials.\sigma = \frac{F}{A}
STRESS_PRINCIPALPrincipal stress formula finding the maximum and minimum normal stresses on planes where shear stress vanishes in a 2D stress state.\sigma_{1,2} = \frac{\sigma_x + \sigma_y}{2} \pm \sqrt{(\frac{\sigma_x - \sigma_y}{2})^2 + \tau_{xy}^2}
STRESS_VON_MISESVon Mises equivalent stress combining principal stresses into a single scalar for predicting yielding under multiaxial loading conditions.\sigma_{vm} = \sqrt{\sigma_1^2 - \sigma_1\sigma_2 + \sigma_2^2}

Compute with one of these​

curl -sS -X POST https://zeqsdk.com/api/zeq/compute \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{"operators":["BEAM_DEFLECTION"],"inputs":{}}'

The response carries the bare physics value, its unit and uncertainty, the generated master equation, and a signed envelope you can verify on any node.

See also​