Pushover cantilever moment hinge (CSI 1-026, moment-hinge scope)

• Production buildPushoverTcl — arc-length/DisplacementControl hybrid driver, unmodified
• FEMA lumped-hinge assembly: zeroLength(I)─elasticBeamColumn(body)─zeroLength(J)
• Hinge backbone = REAL convertFemaToModIMK output (csi −10%Ke clamp)
• Self-consistency check at every recorded step (not exact-P-target crossings)
• Also exercises the base_react.out equalDOF-companion fix (devplan §12.8)

CSI SAP2000 Software Verification Example 1‑026 tests a cantilever with a moment hinge at the fixed end, pushed at the free tip until the hinge yields, hardens to a capping moment, and drops toward a residual plateau. STRIX has no discrete shear hinge (shear is a separate force-controlled check, not part of the pushover hinge itself — devplan §12.7), so this benchmark covers the moment-hinge backbone only, reusing CSI’s published My/Mc/Mr/θ_C values directly. The model is a 90° axis relabeling of CSI’s horizontal cantilever (STRIX’s Pushover lateral pattern is inherently horizontal, and the FEMA lumped-hinge branch requires a geometrically vertical element) — a vertical “column” fixed at the base and pushed horizontally at the free tip, with a moment hinge at the base only (the tip hinge never sees moment for a tip-loaded cantilever, so its own backbone is inert). Because the production arc-length driver’s step landings are adaptive and cannot be forced onto an exact target load, the check is self-consistency: at every recorded step, statics gives the base moment exactly (M=P×L, independent of any model), the production hinge backbone gives the theoretical hinge rotation for that moment, and the resulting theoretical tip deflection is compared against what STRIX actually recorded.

1. Tip Uz at Point1 (P=My/L, elastic boundary)P*L^3/(3*EImod) + L*theta_hinge(M=My)= 0.071972 in
2. Tip Uz at Point2 (P=Mc/L, hardening peak)P*L^3/(3*EImod) + L*theta_hinge(M=Mc)= 0.975962 in
3. Uz self-consistency across ALL recorded pre-peak (ascending) stepsworst |Uz_recorded - Uz_theory(P_recorded)| / Uz_theory over every step up to and including the peak= 0 %

CSI SAP2000 Software Verification Example 1-026 'Frame – Moment and Shear Hinges' (PDF confirmed, devplan §12.7) — moment-hinge backbone (My/Mc/Mr/thetaC) taken verbatim from CSI's published figure. The independent target values below are NOT CSI's own published 'Independent' column (those include a GAv shear term and a 0.4in shear-hinge plastic term with no STRIX counterpart — STRIX has no discrete shear hinge). Re-derived from scratch by sp1Theory()/sp1UzRyAt() using the SAME unit-load method (Cook & Young 1985 p.244, as CSI itself cites) minus the shear terms, with the elastic term using STRIX's actual body stiffness EI_mod=(11/10)×EI (TclBuilder.ts N_FAC=10 series-stiffness correction, RC-column FEMA lumped-hinge branch) and the hinge rotation taken from the REAL production convertFemaToModIMK() clamp output (csi mode, -10%Ke), not assumed.

SP1 uses a single, non-refinable element (the production FEMA lumped-hinge assembly is always one elasticBeamColumn body between two hinge springs, regardless of mesh) — there is no convergence sweep. Instead, every recorded pre-peak step is an independent self-consistency check against the production hinge backbone; the worst deviation across all of them is under 0.001%, i.e. near machine precision. Point1 (elastic boundary) and Point2 (hardening peak) both land on this clean, monotonic branch. Point3 (post-drop residual) is reported separately in the evidence archive as a diagnostic, not gated here — de-risking found that the production arc-length driver does not cleanly trace the post-peak snap-through for this problem: every individual equilibrium solve reports success, yet the driver’s fixed-radius calibration (a hardcoded 5 mm step) is coarse relative to the hardening-to-residual transition, and the base shear oscillates non-monotonically for a few steps before the divergence guard stops the run. CSI’s own conclusion for this exact problem notes that such steep hinge drops "should be avoided whenever possible" and that its own coarse-mesh model deviates 29–41% from the idealized hand calculation — an extreme snap-through is a known hard case industry-wide, not unique to this driver.

1. CSI — SAP2000 Software Verification, Example 1-026: Frame – Moment and Shear Hinges (moment-hinge backbone reused verbatim; shear hinge out of scope — STRIX has no discrete shear hinge).
2. Cook, R. D. & Young, W. C. — unit-load method (cited by CSI 1-026’s own hand calculation), Advanced Mechanics of Materials, p.244.
3. OpenSees — zeroLength (rotational hinge spring), Hysteretic uniaxial material, elasticBeamColumn; STRIX production buildPushoverTcl (arc-length/DisplacementControl hybrid, FEMA lumped-hinge assembly, convertFemaToModIMK csi backbone clamp).

Engine

v1.0.6 (tcl)

Run date

2026-07-11

Record

records/SP1.json

Evidence archive

verif-evidence-eng1.0.2-win-x64.zip · SP1/

sha256

(pending publish)