Pushover Analysis Verification Studies
This article summarizes how the StatiCAD pushover engine and the reinforced concrete performance assessment chain were verified, and the results. Reinforced concrete example buildings exhibiting both frame and shear wall behaviour were used as test structures.
1. Verification approach
- Same model, independent solver: StatiCAD automatically transfers the pushover model (nodes, members, rigid diaphragm, masses, load pattern and the hinge capacities it has computed itself) to SAP2000; SAP2000 pushes it with its own nonlinear solver. The comparison is thus a repeatable model-to-model comparison free of manual data entry errors.
- The reference is SAP2000 V27: It was chosen as the verification reference because it is an internationally recognised, independent solver.
- The focus of the comparison is the performance point: The engineering decision is made at the demand point. Therefore the main criteria are the agreement of the displacement, base shear, hinge state distribution and building decision at the demand point. Curve peak values are a secondary indicator because of modelling differences (see Section 6).
The same comparisons can be reproduced in every project with the “Verify with SAP2000” and “Continue calculations with the SAP2000 result” options in the pushover window.
2. Modal verification
In the frame example, the first natural vibration period of the transferred model in SAP2000 was found to be the same as in StatiCAD: T1 = 0.6061 s (StatiCAD) / 0.6063 s (SAP2000). The design spectrum inputs (SDS, SD1) matched exactly with the independent calculation.
3. Damage comparison at the demand point — the main verification
From the hinge state table of SAP2000, the hinge state of the step corresponding to the demand displacement is read and compared with the StatiCAD damage table:
| Run (shear wall building, EPP) | StatiCAD | SAP2000 |
|---|---|---|
| +X, demand u = 3.45 mm | 4 yielded ends (Significant Damage), building: Controlled Damage | 4 hinges in the same region — exact match |
| −Y, demand u = 13.4 mm | 1–2 yielded ends, building: Limited Damage | 0–1 hinges at the yield limit — consistent |
Result: At the demand point where the engineering decision is made, the two independent solvers produce the same damage table and the same building decisions.
4. Summary comparison of the eight direction combinations
In the “Continue calculations with the SAP2000 result” mode, all eight TBDY direction combinations were solved in SAP2000 and automatically tabulated with the StatiCAD results (shear wall example, EPP; u: demand roof displacement):
| Direction | StatiCAD u [mm] | StatiCAD level | SAP2000 u [mm] | SAP2000 level |
|---|---|---|---|---|
| +X+0.30Y | 3.45 | KH | 3.45 | KH |
| +X−0.30Y | 3.45 | KH | 3.45 | KH |
| −X+0.30Y | 3.45 | KH | 3.45 | KH |
| −X−0.30Y | 3.45 | KH | 3.45 | KH |
| +Y+0.30X | 13.40 | SH | 13.36 | KH |
| +Y−0.30X | 13.41 | SH | 13.36 | SH |
| −Y+0.30X | 13.40 | SH | 13.22 | SH |
| −Y−0.30X | 13.39 | SH | 13.22 | SH |
- The demand displacements match exactly (X: 3.45 ↔ 3.45 mm; Y: 13.4 ↔ 13.2–13.4 mm).
- The difference in the base shears at the demand point is about 5–10% in the X direction and 3–13% in the Y direction.
- The building decision is the same in 7 of the 8 directions. The only difference (+Y+0.30X) is a borderline case where the demand falls exactly on the yield limit and is sensitive to the SAP2000 output step resolution.
5. Strain-hardening hinge option
| Run (single direction) | StatiCAD Vroof [kN] | SAP2000 Vroof [kN] | Ratio |
|---|---|---|---|
| +X, EPP | 19,334 | 21,503 | 0.899 |
| +X, strain-hardening | 21,167 | 22,810 | 0.928 |
| −Y, EPP | 10,055 | ~10,990 | 0.915 |
| −Y, strain-hardening | 10,405 | 11,704 | 0.889 |
Strain hardening increases the StatiCAD capacity by 5–10%. The ±0.03 variation in the ratios comes from a small methodological difference in the definition of the hardening slope between the two programs. The curve peak ratios are in the 0.89–0.93 band in unidirectional pushovers, and StatiCAD is consistently on the safe side. The demand point comparisons are not affected by strain hardening.
6. Known differences
| Difference | Source | Effect |
|---|---|---|
| Descending branch in SAP2000 ↔ plateau in StatiCAD | The SAP2000 hinge definition has strength-drop branches; the StatiCAD hinge (EPP or strain-hardening) has no descending branch. | The SAP2000 curve drops after peaking and in some runs stops before reaching the target. It affects the peak value ratios but not the demand point comparison. |
| Elastic stiffness difference in the shear wall model | The strong axis of the shear wall is represented in the pushover model by a single member and rigid arms. | It is one component of the base shear difference at the same displacement. |
| Constant axial force of columns and shear walls | In both solvers the hinges are built with N = G + nQ. | It does not affect the comparison; it is a common assumption. |
| Definition of the hardening slope | The two programs define the hardening branch differently. | ±0.03 variation in the strain-hardening peak ratios. |
| SAP2000 output step resolution | SAP2000 results are recorded in a finite number of steps. | The damage reading is taken from the recorded step nearest to the demand point; it may create decision sensitivity in runs at the yield limit. |
7. Verification of multi-mode pushover
- Elastic consistency (TBDY 5.6.6.1): For each mode, the closed-form spectral displacement was compared with the finite element solution on the same stiffness matrix. In the X and Y directions the deviation was 0.0000% for all modes; the CQC combined roof displacement is the same by both routes.
- Dominant-mode pushover ↔ single-mode pushover: The first-mode pushover of the multi-mode run gave the same demand (36.8 mm), the same number of yielded ends (23) and the same building decision (Controlled Damage) as the single-mode pushover.
- Short-period rule: In the short-period second X mode (T = 0.155 s), CR = 1.030 was applied automatically and the mode remained elastic as expected.
- Modal pattern comparison with SAP2000: The StatiCAD modal load patterns were transferred to SAP2000 and pushed on the same hinged model; agreement within 2–6% was obtained for the dominant mode and about 6% for the second mode.
8. Overall assessment
- In the SAP2000 model-to-model comparison, at the demand point where the engineering decision is made, displacements match exactly, damage tables agree, and building decisions are the same in 7 of 8 directions; the only difference is a documented borderline case.
- The curve peak ratios are in the 0.89–0.93 band in unidirectional pushovers and StatiCAD is consistently on the safe side; each of the remaining differences has been separated out and justified.
- The elastic consistency condition of multi-mode pushover is satisfied numerically.
It is essential that all results produced by the software are checked by the responsible engineer.