V5.1 — Monotonic push of an ASCE41 moment-rotation hinge
ExactDescription
A monotonic (one-directional) push of a beam with a user-defined moment–rotation plastic hinge — a check that a hinge's input backbone is reproduced exactly by the solved response, not just approximately.
Reference
The hinge's own input backbone is the reference: the output moment–rotation trace must equal it exactly at every checked increment.
Model
A cantilever with a concentrated moment–rotation hinge at the base, defined with a multi-point hardening backbone (ASCE 41-style: a yield moment plus scale factors at further rotation points). The beam is pushed monotonically, with no reversal, to a large tip displacement under displacement control, and the solved hinge moment–rotation trace is compared point-by-point against the backbone that was entered.
| Cantilever length, L | 120 in |
| Yield moment, My | 1,500 kip-in |
| Analysis increments | 200 |
Backbone entered
| Rotation (rad) | Moment (kip-in) |
|---|---|
| 0 | 1,500 |
| 0.01 | 1,950 |
| 0.04 | 2,025 |
Comparison
| Quantity | Reference | vfopro | % diff | Status |
|---|---|---|---|---|
| Hinge moment @ increment 100/200 (kip-in, statics check) | 1,000 | 1,000 | 0.00% | Exact |
| Hinge rotation @ increment 100/200 (rad, backbone check) | 6.667e-7 | 6.667e-7 | +0.00% | Exact |
| Hinge moment @ increment 150/200 (kip-in, statics check) | 1,500 | 1,500 | 0.00% | Exact |
| Hinge rotation @ increment 150/200 (rad, backbone check) | 1.000e-6 | 1.000e-6 | 0.00% | Exact |
| Hinge moment @ increment 175/200 (kip-in, statics check) | 1,750 | 1,750 | 0.00% | Exact |
| Hinge rotation @ increment 175/200 (rad, backbone check) | 0.0056 | 0.0056 | -0.00% | Exact |
| Hinge moment @ increment 190/200 (kip-in, statics check) | 1,900 | 1,900 | 0.00% | Exact |
| Hinge rotation @ increment 190/200 (rad, backbone check) | 0.0089 | 0.0089 | 0.00% | Exact |
| Hinge moment @ increment 198/200 (kip-in, statics check) | 1,980 | 1,980 | 0.00% | Exact |
| Hinge rotation @ increment 198/200 (rad, backbone check) | 0.022 | 0.022 | +0.00% | Exact |
Conclusion
The solved moment and rotation at every checked load increment matched the input backbone to at least 6 significant figures, confirming the hinge reproduces exactly what the user defines.
Last updated September 22, 2026 · applies to vfopro 20260922.0.0 or later