Rigid steel portal frame under UDL — bending + axial deformation (CSI 1-018)

• elasticBeamColumn — Euler-Bernoulli (no shear area, TclBuilder.ts:465)
• endReleases (My) — pinned column-beam joints, production penalty release
• Section.stiffScale — CSI-style property modification factor (area/izz)
• Distributed load (eleLoad -type -beamUniform)
• Deflection vs unit-load / virtual-work method (Cook & Young 1985)

A one-story, one-bay rigid steel bent (W8X31) carries a uniform vertical load across its beam. The base supports and the two beam-to-column joints are all pins, so the frame reduces to a determinate system for this symmetric vertical load: each column behaves as a pure two-force (axial-only) member, and the beam behaves as an ordinary simply-supported beam under UDL. STRIX reproduces the pinned joints with production endReleases (My = free at each column top) and isolates the bending and axial contributions separately using Section.stiffScale — the same "property modification factor" technique CSI SAP2000 uses in this exact verification example. Because elasticBeamColumn carries no shear-area term (Euler-Bernoulli only, same scope as SB1), the shear-deformation sub-model from CSI 1-018 is out of scope; the bending-only and axial-only STRIX runs sum to the combined-model result, matching the additive structure of the unit-load integral itself.

1. Midspan deflection Uz — combined (axial+bending)dTotal = V*H/(E*A) + 5*w*S^4/(384*E*Iz) (unit-load method, no shear term)= −69.372833 mm
2. Midspan deflection Uz — bending only (area x1e5)dBending = 5*w*S^4/(384*E*Iz) (simply-supported UDL beam, midspan)= −69.179684 mm
3. Midspan deflection Uz — axial only (Iz x1e7)dAxial = V*H/(E*A) (pin-pin column, 2-force member)= −0.193149 mm

CSI SAP2000 Software Verification Example 1-018 'Bending, Shear and Axial Deformations in a Rigid Frame'; independent reference = unit-load (virtual-work) method, Cook & Young, Advanced Mechanics of Materials, 1985, p.244. STRIX omits the shear term (elasticBeamColumn has no shear-area argument, TclBuilder.ts:465 — Euler-Bernoulli only, same scope as SB1) and re-derives the axial + bending terms from scratch via sb9Theory(); the result matches CSI's published in-lb values (converted to N·mm) to 6 significant figures: axial 0.0076043 vs CSI 0.00760 in, bending 2.7236096 vs CSI 2.723610 in.

Rather than a mesh sweep (this is a single-discretization determinate/closed-form problem, not a convergence study), the three rows isolate each deformation mode using CSI's own "property modification factor" technique: bendingOnly inflates the section area ×10⁵ to suppress axial deformation, and axialOnly inflates the strong-axis inertia ×10⁷ to suppress bending. All three reproduce the unit-load reference to under 0.02% — the small residual comes from the production endReleases penalty pin (a finite, not exactly-zero, release stiffness), which is itself the real production code path being verified.

1. Cook, R. D. & Young, W. C. — Advanced Mechanics of Materials. Macmillan, 1985. Unit-load (virtual-work) method, p.244.
2. CSI — SAP2000 Software Verification, Example 1-018: Bending, Shear and Axial Deformations in a Rigid Frame (independent reference method + property modification factors).
3. AISC — W8X31 section properties (A, Iz, Iy, J).
4. OpenSees — element elasticBeamColumn (Euler-Bernoulli); STRIX endReleases (penalty pin) + Section.stiffScale.

Engine

v1.0.6 (opensees.pyd)

Run date

2026-07-11

Record

records/SB9.json

Evidence archive

verif-evidence-eng1.0.2-win-x64.zip · SB9/

sha256

(pending publish)