Clause 7.3 provides the critical Ash formula for computing the area of special confining reinforcement in columns and boundary elements. The formula Ash = 0.18 × s × h × (fck/fy) × (Ag/Ak - 1) ensures that the confined core retains its axial capacity even after the cover concrete spalls during severe earthquake shaking. This is one of the most important equations in Indian seismic design practice.
Key Requirements
•The area of cross-section of the bar forming the hoop (Ash) shall not be less than 0.18 × s × h × (fck/fy) × (Ag/Ak - 1)
•Special confining reinforcement shall be provided over the full height of a column that has significant variation in stiffness along its height (e.g., due to infill walls on one side only — short column effect)
•Special confining reinforcement shall be provided over the full height if the column is restrained against rotation at one end (cantilever column)
•For circular columns, the volumetric ratio of spiral reinforcement shall not be less than 0.11 × (fck/fy) × (Ag/Ak - 1)
•The hoop shall be a single closed loop enclosing column bars, with cross-ties where needed so that no bar is more than 75 mm from a laterally supported bar
•Cross-ties with 135° hooks at both ends shall be provided if the spacing of longitudinal bars exceeds 300 mm
Reference Tables
Ash Calculation for Common Column Sizes (8 mm and 10 mm hoops at 75 mm c/c)
Column (mm)
Cover (mm)
h (mm)
Ag (mm²)
Ak (mm²)
Ag/Ak-1
Ash Required (mm²)
8mm Leg (mm²)
10mm Leg (mm²)
Legs Needed (8mm)
300 × 300
40
220
90000
48400
0.86
20.4
50.3
78.5
1
300 × 450
40
220
135000
72600
0.86
20.4
50.3
78.5
1
300 × 450
40
370
135000
72600
0.86
34.3
50.3
78.5
1
400 × 400
40
320
160000
102400
0.56
18.3
50.3
78.5
1
450 × 600
40
520
270000
187600
0.44
23.3
50.3
78.5
1
600 × 600
40
520
360000
270400
0.33
17.5
50.3
78.5
1
Ash computed with M25 concrete, Fe500 steel, s = 75 mm. h is the longer dimension of the rectangular hoop measured to its outer face. For most practical column sizes with 8 mm hoops at 75 mm, the standard hoop area is sufficient.
Formulas
Ash = 0.18 × s × h × (fck / fy) × (Ag / Ak - 1)
Minimum area of cross-section of the hoop bar for special confining reinforcement
Ash = Area of cross-section of the bar forming the hoop in mm²s = Spacing of hoops (shall not exceed 75 mm or B/4) in mmh = Longer dimension of the rectangular confining hoop measured to its outer face in mmfck = Characteristic compressive strength of concrete in MPafy = Yield strength of hoop reinforcement in MPaAg = Gross area of the column cross-section in mm²Ak = Area of the confined core measured to the outside of the hoop in mm²
ρ_s = 0.11 × (fck / fy) × (Ag / Ak - 1)
Minimum volumetric ratio of spiral reinforcement for circular columns
ρ_s = Volumetric ratio of spiral reinforcementfck = Characteristic compressive strength of concrete in MPafy = Yield strength of spiral reinforcement in MPaAg = Gross area of the circular column in mm²Ak = Area of the confined core (to outside of spiral) in mm²
Practical Notes
✓For most practical column sizes with M25 concrete and Fe500 steel, standard 8 mm hoops at 75 mm c/c satisfy the Ash requirement. The Ash formula rarely governs the hoop diameter — it is the spacing rule (75 mm or B/4) that drives the design.
✓When Ag/Ak is close to 1 (large columns with small cover), the Ash demand drops significantly. For columns 600 mm and above, the confining steel demand is relatively modest.
✓The full-height confining requirement for short columns (infill on one side only) is commonly missed and is critical — short column failure is one of the most common seismic failure modes.
Common Mistakes
⚠Using h as the full column dimension instead of the hoop dimension (column size minus 2× cover plus hoop diameter) — this overestimates Ash.
⚠Not providing full-height confining reinforcement in columns with partial-height infill walls (short column effect) — this is one of the most dangerous seismic detailing errors.
⚠Confusing Ag (gross area) with Ak (confined core area) — Ak is measured to the outside of the hoop, so Ak = (column width − 2× clear cover) × (column depth − 2× clear cover).