Reinforced Concrete Strengthening Verification Studies
This article summarizes the verification studies of the reinforced concrete strengthening module and their results. The formulas were compared with an independent implementation and hand calculations, and their effects were followed through analysis results on sample reinforced concrete buildings (frame, shear wall and infill wall variants).
1. Results unchanged while strengthening is off
Even when strengthening data is defined, while the main option is off, the performance assessment results of all elements of the sample building were compared line by line with the results before the strengthening module was added, and zero difference was found. This comparison is repeated in every edition.
2. Annex 15B formulas and the FRP chain
| Verification | Method | Result |
|---|---|---|
| κa, εf, ρf, fl, fcc, εcc (continuous and strip wrapping, circular, ellipse, including aspect ratio exceedance; 7 cases) | Comparison with an independent implementation | Largest relative difference 3.3·10⁻¹³ % |
| Vf (continuous, strip, including the case where the strip spacing condition is not satisfied; 5 cases) | Comparison with an independent implementation | 1.7·10⁻¹³ % |
| Vf in the analysis chain | FRP applied to 12 columns and 17 beams | Beam shear contribution identical to the unit test value (281.0 kN) |
| Section effect | FRP on the 12 columns of the 1st storey | Only the results of these columns changed; curvature capacity +3.6% (expected effect of the Annex 15B idealization) |
| Lap-splice length (15B.9–15B.11) | Hand calculation | Required FRP thickness and intermediate quantities identical; required thickness zero where the existing stirrup is sufficient |
3. Column jacketing, steel and RC jacketing, external stirrups
| Verification | Result |
|---|---|
| Stiffness: 10 cm, 4-face jacket on the 12 columns of the 1st storey | First period 0.3252 → 0.2811 s; it returns exactly when the option is turned off |
| Capacity: same columns | Yield moment ratio in the jacketed columns at most 1.34 (50×50 → 70×70 cm, with the 0.9 factor) |
| Jacket longitudinal reinforcement: 8Ø16 | Bar layout and areas identical to the hand calculation; column yield moment ratio (reinforced/unreinforced) averages 1.36; U, L and single-side layouts in 3-, 2- and 1-face jackets verified by hand |
| Jacket models (Composite, Code letter, Jacket only; 8 cases) | Transformed section properties identical to the independent calculation with a relative difference ≤ 4·10⁻¹⁵; hand calculation checks consistent. Period and capacity ordering as expected |
| Jacket stirrups | Shear contribution identical to the hand calculation (Ø10/100, 2 legs: 435.4 kN, with the 0.9 factor) |
| One-sided jacket | In the asymmetric section the ± capacities are calculated separately and the smaller is taken; in the 4-face jacket the results are identical to the symmetric case |
| Steel jacketing (Vj) and external stirrups (Vw) | Calculated values identical to the formula; Vj identical to the value in the window summary |
| RC jacketing | Shear strength ×0.9; flexure and stiffness do not change |
4. New strengthening shear wall
In the sample building with shear walls, one shear wall was marked as a “new strengthening shear wall”:
| Run | Periods | Shear wall |
|---|---|---|
| Unmarked (ordinary shear wall) | T1 = 0.3175 s | Ordinary shear wall |
| Marked, option off | T1 = 0.4087 s | Not in the before-strengthening model |
| Marked, option on | Identical to the unmarked run | Anchorage demand q = 332.4 N/mm, capacity qr = 367.2 N/mm, ratio 0.905 |
It was verified through mass breakdowns that, while the option is off, the self-weight of the shear wall is removed from the storey weight, the building weight and the finite element masses, and that the slab load resting on the wall is distributed to the neighbouring supports with the total preserved. The anchorage values are identical to the hand calculation.
5. Infill wall strengthening (Annex 15C)
In the shear wall building variant, one wall was converted into an infill wall (654 × 260 cm net, 24 cm thick, columns 50×50) and two methods were calculated:
| Run | Program | Hand calculation |
|---|---|---|
| Steel-mesh reinforced plaster (30 mm, 2 faces) | ad = 911.2 mm; kd = 77,678.6 kN/m; Vd = 1294.9 kN | ad = 911 mm; kd = 77.66 MN/m; Vd = min(1825; 1295) = 1295 kN |
| FRP diagonal strip | ad = 931.7 mm; kt = 1627.5 kN/m; Tf = 34.4 kN; Vd = 313.9 kN | kt = 1627.5 kN/m; Tf = 34.4 kN; Vd = 313.9 kN |
| Steel-mesh reinforced plaster, option off | Results identical to the building without strengthening | — |
In pushover analysis, the one-way strut setup was compared with a symmetric paired setup: same number of events and a base shear difference smaller than 0.01% (the total horizontal stiffness is the same; the difference is only in the distribution of strut forces). The events where the diagonal struts reached capacity were verified by hand calculation: the compression strut was removed from the model at N = Vd / cos θ, and the FRP tension tie at T = Tf.
In a test model prepared with inputs that do not satisfy the code conditions (small corner radius, thin wrapping, short lap splice, insufficient anchorage, thin plaster and high opening ratio), the expected error and warning lines dropped into the project check list without repetition.
6. Before / after comparison
On the sample building, the analysis was first run with the option off (before), and then with jacketing applied to 12 columns and the option on (after). The comparison block correctly reported the building level, the criteria percentages, the 12 strengthened elements and the damage distribution. No difference in damage, failure mode or building level was found between running the two runs one after the other in the same session and running them separately.
7. Interface and saving
- The Strengthening tab in the three properties windows was checked for multiple selection, the activation of options according to element type, and the carry-over of values from a previous element.
- The strengthening data was saved in both text and binary project formats and re-opened, and read back exactly the same. Old project files open without strengthening.
It is essential that all results produced by the software are checked by the responsible engineer.