Confinement Design and Detailing of RC Column
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1. Input Parameters
| Location of Site: | |
| Importance Class of Structure: | |
| PGA on rock (g): | |
| Ground Type: |
Note:
a. Characteristic Compressive Strength (fck) is the characteristic (5%) cylinder strength determined as per EN 206-1.
b. Rebar Class:
Rebar Class B are commonly used in low-to-moderate seismicity regions. Class A rebars (lowest ductility category) and Class C rebars (highest ductility category used in high seismicity regions) are not considered in this design.
c. Normalised Design Axial Force (vd):
$$ {v_{d} = \frac{N_{Ed}}{A_{C} \times f_{cd}}}$$ Where,
'NEd' is the design axial force including seismic action,
'Ac' is the cross-sectional area of RC column, and
'fcd' is the design concrete cylinder strength determined as per Clause 3.1.6 of Eurocode 2 Part 1 (2004).
| Column Size, bc x hc (mm x mm): | |
| Concrete Clear Cover (c): | Characteristic Compressive Strength (fck): |
| Rebar Class: | |
| Diameter of Vertical Reinforcements (φv): | |
| Diameter of Stirrups (φs): | |
| Normalised Design Axial Force (vd): | Structural Type: |
| Fundamental Natural Period, T1 (sec): | |
| Clear Length of the Column, lcl (mm): | |
| Transfer Structure: |
2. Results
The confinement demand of the column, and the confinement capacity of the optimal solution (solution with a minimum number of stirrups provided at maximum allowable spacing, and meeting the confinement demand) are presented in Table 1. Similarly, the reinforcement detailing, and the strength interaction diagram (P-N curve) are presented in Figure 2, and Figure 3, respectively.The value of confinement demand is determined using Eq (1). $$ {C_{d} = \frac{30 \,v_{d}\, μ_{ϕ} \times 0.0022 \,b_{c}}{b_{o}}-0.035}\tag{1}$$ 'bo' is the distance confined by the stirrups as shown in Figure 1 and is calculated from Eq (2). $$ {b_{o} = b_{c} - 2c - φ_{s}}\tag{2}$$ The values of normalised design axial force 'vd ', width of column 'bc', concrete cover 'c', and diameter of stirrups 'φs' are defined in Section 1 (Input Parameters).
Similarly, Curvature Ductility Factor (μϕ) is determined from the value of behaviour factor (qo) using Eqs (3a and 3b):
For T1 ≥ TC , $$ {μ_{φ} =2qₒ - 1}\tag{3a}$$ For T1 < TC , $$ {μ_{φ} = 1 + 2(qₒ - 1) \times \frac{T_{C}}{T_{1}}}\tag{3b}$$ Where,
The result of confinement demand (Cd) is presented in Table 1.
To determine the confinement capacity, first, the allowable minimum number of vertical reinforcements: nb (along bc) and nh (along hc) in the member are determined using Eqs (4-6). Then, the confinement parameters for the case of stirrups spacing not exceeding the minimum of (bo/2 , 175 mm, and 8φv) are determined using Eq (8-14). Finally, the confinement capacity is calculated by substituting the values of the confinement parameters in Eq (7). The detail of the optimal solutions along with the confinement capacity is shown in Table 1. $$ {n_{b} \ge \frac{b_{o} - φ_{s} - φ_{v}}{200}}\tag{4}$$ $$ {n_{h} \ge \frac{h_{o} - φ_{s} - φ_{v}}{200}}\tag{5}$$ $$ {h_{o} = h_{c} - 2c - φ_{s}}\tag{6}$$ $$ {C_{c} = α_{n} \times α_{s} \times ω_{wd}}\tag{7}$$ $$ {α_{n} = 1- \frac{(n_{b}-1)b_{i}^2 +(n_{h}-1)h_{i}^2}{3b_{o}^2}}\tag{8}$$ $$ {α_{s} = (1- \frac{s}{2b_{o}})(1- \frac{s}{2h_{o}})}\tag{9}$$ $$ {ω_{wd} = \frac{(n_{b}\,b_{o} + n_{h}\,h_{o})a_{s}\,f_{yd}}{b_{o}\,h_{o}\,s\,f_{cd}}}\tag{10}$$ $$ {b_{i} = \frac{b_{o} - n_{b}φ_{v}}{n_{b}-1}}\tag{11}$$ $$ {h_{i} = \frac{h_{o} - n_{h}φ_{v}}{n_{h}-1}}\tag{12}$$ $$ {a_{s} = \frac{\pi \,φ_{s}^2}{4}}\tag{13}$$ $$ {f_{cd} = \frac{α_{cc} \times{f_{ck}}} {γ_{c}}}\tag{14}$$ Where,
'αn' is the cross-sectional area reduction factor,
'αs' is the elevational reduction factor,
'ωwd' is the mechanical volumetric ratio,
'bi' and 'hi' are clear distance between consecutive longitudinal rebars constrained by the stirrups, 'as' is the area of individual stirrup,
'fcd' is design concrete cylinder strength,
'γc' is the partial safety factor for concrete and a value of 1.5 is adopted in this program, and
'αcc' is the coefficient taking account of long term effects on the compressive strength and of unfavourable effects resulting from the way the load is applied. αcc of 0.85 is adopted in this program.
Table 1: Confinement parameters, and comparison of the confinement capacity of the optimal solutions with the confinement demand.
Figure 3. Elevational view of the column.
Figure 3. Strength interaction diagram (design axial load vs moment diagram) for the most optimal solution (first solution presented in Table 1).
3. References:
- Department of Standards Malaysia (2017). MS EN 1998-1:2015 Malaysia National Annex to Eurocode 8: Design of structures for earthquake resitance – Part 1: General rules, seismic actions and rules for buildings.
- European Commitee for Standardization (2004). EN 1998-1:2004 Eurocode 8: Design of structures for earthquake resistance - Part 1 : General rules, seismic actions and rules for buildings.
- Department of Standards Malaysia (2017). MS EN 1998-1:2010 Malaysia National Annex to Eurocode 2: Design Of Concrete Structures. Part 1-1 : General Rules And Rules For Buildings.
- European Commitee for Standardization (2004). EN 1992-1-1:2004 Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings.
- Looi, D.T.W.; Tsang, H.H. and Lam, N.T.K. (2020). SIMPLIFYING EUROCODE 8 DUCTILE DETAILING RULES FOR REINFORCED CONCRETE STRUCTURES.