Theoretical Basis of Reinforced Concrete Strengthening
This article summarizes which provisions of TBDY 2018 the StatiCAD strengthening module applies and how, the assumptions it makes, and the limits of its scope. The assessment chain itself (Chapter 15, the section fiber model, the 15.8 decision) is in Theoretical Basis of Pushover Analysis; only the parts that strengthening adds to this chain are described here.
1. Basic principle: the same assessment, strengthened elements
According to TBDY 2018 15.9.1, the earthquake safety of a strengthened building is determined with the calculation and assessment principles given for existing buildings. For this reason StatiCAD does not set up a separate “strengthening calculation”: strengthening is a property of the element, and the same assessment chain is run once more with the strengthened section, stiffness and capacity. While the main option is off, the calculation is exactly identical to the before-strengthening state.
According to the TBDY 15.9.3 distinction, FRP wrapping, jacketing, steel and RC jacketing, external stirrups and infill wall strengthening are member strengthening; a new RC shear wall is system strengthening. The module manages both with the same option.
2. Wrapping of columns (15.10.1)
The first sentence of 15.10.1 sets a firm limit: with these methods the flexural capacity of columns cannot be increased. The module enforces this in all three wrapping methods.
2.1 Fibre-reinforced polymer (FRP) wrapping — 15.10.1.3 and Annex 15B
| Quantity | Equation | Application |
|---|---|---|
| Effectiveness factor κa | 15B.7 | 1 for a circular section; b/h for an ellipse; 1 − [(b−2rc)² + (h−2rc)²]/(3bh) for a rectangle. For a section whose aspect ratio exceeds 2.5 (3 for an ellipse), the axial and ductility increase is not applied. |
| Effective FRP strain εf | 15B.3 / 15B.4 | For shear min(0.004; 0.50 εfu); for ductility and axial min(0.50 εfu; 0.01). |
| Lateral pressure fl | 15B.6 | fl = ½ · κa · ρf · εf · Ef; ρf = 2·nf·tf·(b+h)/(b·h) · (wf/sf). |
| Confined strength and strain | 15B.5, 15B.8 | fcc = fcm·[1 + 2.4·(fl/fcm)] ≥ 1.2·fcm; εcc = 0.002·[1 + 15·(fl/fcm)^0.75]. |
| Concrete model | 15B.3(b) | Bilinear σ–ε: (0, 0) → (0.002, fcm) → (εcc, fcc). The FRP model replaces the stirrup confinement; it is not added on top of it. |
| Damage limits | 15B.3(b) | GÖ = εcc (with an upper limit of 0.018), KH = 0.75·εcc, SH = 0.004. |
| Shear contribution Vf | 15B.1 / 15B.2 | Vf = 2·nf·tf·wf·Ef·εf·d/sf; wf = sf in continuous wrapping; in strips the contribution is zero if sf ≤ wf + d/4 is not satisfied. Vr = Vc + Vw + Vf ≤ Vmax. |
| Lap-splice length check | 15B.4: 15B.9–15B.11 | If the existing lap-splice length is entered, the required total FRP thickness is calculated and compared with the provided one, and the result is written to the label. For a section dimension ratio > 2 or plain-surface reinforcement, the “uygulanamaz” (not applicable) label is printed. This check does not change the capacity. |
Since κa is not defined for polygonal columns, FRP is not applied to them and a warning is given.
2.2 RC jacketing (confinement) — 15.10.1.1
Shear and compressive strength are calculated from the gross dimensions of the wrapped section and reduced by 0.9; flexural capacity and stiffness do not change. The confinement effect continues to be read from the existing core.
2.3 Steel jacketing — 15.10.1.2, Eq. 15.3
Vj = tj·b·d/s·fyw is added to the shear strength (tj, b, s: thickness, width and spacing of the horizontal plates). Flexure and ductility do not change.
3. Enlargement of the column section (concrete jacketing) — 15.10.2
It is the only column method that increases flexural capacity. According to the code, flexural, shear and compressive strength and flexural stiffness are calculated with the gross section dimensions and the design properties of the added concrete, and the stiffness and strengths obtained are multiplied by 0.9. The module applies this factor in three places:
- Finite element stiffness: Transformed section properties according to the model selected in the column tab are used (n = E_jacket / E_existing):
- Composite (default): existing section + n × jacket ring; for one-sided jackets, with parallel-axis terms about the composite centroid,
- Code letter: gross section with jacket concrete,
- Jacket only: the existing column is ignored (case of a heavily damaged existing column).
- Section capacity (fiber model): The outer dimension is the jacketed one; the core is the existing column (with the existing concrete and stirrup confinement), the shell is jacket concrete. The jacket longitudinal reinforcement is placed at equal spacing along the jacketed faces (closed perimeter on 4 faces, U on 3, L on 2, single side on 1) and contributes to the flexural capacity.
- Linear path: Shear strength and its upper limit from the jacketed section; EI at yield rotation and plastic hinge length from the jacketed section. If jacket stirrups are entered, they are added to the shear strength.
In 1-, 2- and 3-face jackets the section is asymmetric, so the smaller of the ± moment capacities is used (on the safe side).
4. Wrapping of beams — 15.10.3
The flexural capacity of beams cannot be increased by wrapping. External stirrups (15.10.3.1) are added only to the shear strength as the TS 500 stirrup contribution; there is no confinement effect. Wrapping with FRP (15.10.3.2) enters both the confined model and the shear contribution under the Annex 15B rules (full wrapping; sf ≤ wf + d/4 in strips).
5. Cast-in-place RC strengthening shear wall — 15.10.5
An element drawn in the model as an ordinary RC shear wall is marked as a “new strengthening shear wall”. While the main option is off, the wall is not in the finite element model: it provides no stiffness or strength, and its self-weight and defined additional loads are zeroed; the wall is not a support for the slab and the load of that edge is distributed to the remaining supports. When on, per 15.9.2 it is a new element and is assessed with the material grades given by the user, taking the knowledge level factor as 1.
Anchorage (15.10.5.1/.2): The shear flow between the wall and the existing frame is taken as q = Vd/lw under a pure shear panel assumption; the capacity is the TS 500 shear friction, qr = μ·Asl·fyd. The conditions Ø ≥ 16 mm, depth ≥ 10Ø and spacing ≤ 400 mm are checked. Boundary region (15.10.5.3): If there is an existing column at the end of the wall, it can be used as the boundary region (jacketed if necessary); otherwise a boundary region must be formed. The module looks at the geometry and writes its note. The wall foundation is outside the scope of the module and is reminded in the report.
6. Strengthening of infill walls — 15.10.4 and Annex 15C
6.1 Equivalent diagonal strut model
| Equation | Expression |
|---|---|
| 15C.2 | λd = [Ed·td·sin2θ / (4·Ec·Ik·hd)]^¼ |
| 15C.1 | ad = 0.175·(λd·hk)^−0.4 · rd |
| 15C.3 | kd = ad·td·Ed / rd (axial stiffness of the compression strut) |
| 15C.4 | Vd = Ad·(τd + fyd·ρsh) ≤ 0.22·Ad·fd (steel-mesh reinforced plaster) |
| 15C.6 / 15C.7 | Tf = 0.003·Ef·wf·tf; kt = wf·tf·Ef / rd; wf ≤ ad (FRP tension strut) |
| 15C.5 | Wall material values (hollow factory brick, solid common brick, aerated concrete) |
In linear (modal combination) analysis, since a one-way compression strut cannot be set up, equal axial stiffness is given to the two diagonals; the total horizontal stiffness equals the stiffness of the single compression strut of the code (of the pair in FRP). In pushover analysis, on the other hand, since each pushover direction is a separate model, the struts are one-way and direction-dependent; when the axial force of a strut reaches its capacity, the strut is removed from the model on a brittle assumption and the force is redistributed to the frame.
6.2 Performance assessment
A strengthened infill wall is counted as a vertical element. The damage region is determined by the shear angle: γ = |relative storey drift| / storey height; the TBDY Table 15.2 limits are SH 0.003 / KH 0.005 / GÖ 0.010. In addition, the horizontal component of the axial forces of the diagonal struts under earthquake is compared with the shear capacity; if exceeded, the wall is considered brittle. The conditions on diagonal/thickness, opening ratio, length/height ratio and storey limit are at warning level; anchorage and bolt details are not included in the calculation and are reminded in the summary.
7. Scope limits
- Lap-splice strengthening with FRP is at check level (it has no effect on capacity); FRP is not applied to a polygonal column.
- In one-sided jackets the finite element member axis stays in the existing column (the eccentricity is taken into account in the section capacity); jacket stirrups are assumed to have two legs; no quantity take-off or drawing is produced for the jacket.
- Boundary region design in a new shear wall is not automatic; the wall foundation is out of scope.
- A composite modulus of elasticity is not taken for the infill wall.
- Additional shear-type checks (steel jacketing, external stirrups, anchorage) are reported in the linear assessment.
- Rule violations do not stop the calculation; they drop into the project check list as an error or warning and the decision is left to the engineer.