Check for punching (two-way) shear around columns in flat slabs and isolated footings. Failure occurs along a critical perimeter at d/2 from the column face. Compare nominal shear stress τv with permissible τc; if exceeded, increase depth, provide shear reinforcement, or add a column capital/drop panel.
Step 1 — Critical Perimeter (Cl 31.6.1)
Located at d/2 from the periphery of the loaded area. d = effective depth of slab/footing.
| Case | Value | Factor / Formula | Note |
|---|
| Square column (a × a) | bo = 4 × (a + d) | — | Total perimeter at d/2 from face |
| Rectangular column (a × b) | bo = 2 × (a + b + 2d) | — | — |
| Circular column (dia D) | bo = π × (D + d) | — | — |
| Edge column | bo = 2(a + b/2 + d) | — | Reduced perimeter — only 3 sides effective |
| Corner column | bo = 2(a/2 + b/2 + d) | — | Only 2 sides effective |
Step 2 — Punching Shear Force
| Case | Value | Factor / Formula | Note |
|---|
| Net upward pressure (footing) | qu = (Pu / A) − γ_soil × df | — | Use NET soil pressure |
| Shear force (footing) | Vu = qu × (A − A_critical) | — | A_critical = (a+d)² for square column |
| Shear force (flat slab) | Vu = wu × (panel area − critical area) | — | Less self-weight inside the perimeter |
| Nominal shear stress | τv = Vu / (bo × d) | — | Compare with τc |
Step 3 — Permissible Shear Stress τc (Cl 31.6.3)
τc' = ks × 0.25 × √fck, where ks accounts for column shape
| Case | Value | Factor / Formula | Note |
|---|
| fck = 20 MPa, ks = 1.0 | 1.118 N/mm² | ks × 0.25 × √20 | M20 concrete |
| fck = 25 MPa, ks = 1.0 | 1.250 N/mm² | ks × 0.25 × √25 | M25 — most common |
| fck = 30 MPa, ks = 1.0 | 1.369 N/mm² | ks × 0.25 × √30 | — |
| fck = 35 MPa, ks = 1.0 | 1.479 N/mm² | ks × 0.25 × √35 | — |
| fck = 40 MPa, ks = 1.0 | 1.581 N/mm² | ks × 0.25 × √40 | High-strength |
Shape Factor ks (Cl 31.6.3.1)
Reduces τc for elongated/non-square columns
| Case | Value | Factor / Formula | Note |
|---|
| βc = 1.0 (square) | ks = 1.0 | — | βc = short side / long side of column |
| βc = 0.8 | ks = 1.0 | — | ks = 0.5 + βc, but ≤ 1.0 |
| βc = 0.6 | ks = 1.0 | — | Capped at 1.0 |
| βc = 0.5 | ks = 1.0 | — | Capped at 1.0 |
| βc = 0.4 | ks = 0.9 | — | 0.5 + 0.4 = 0.9 |
| βc = 0.2 | ks = 0.7 | — | 0.5 + 0.2 |
Step 4 — Decision
| Case | Value | Factor / Formula | Note |
|---|
| If τv ≤ τc' | OK — no shear reinforcement | — | Safe; provide minimum slab steel |
| If τc' < τv ≤ 1.5 τc' | Provide shear reinforcement | — | Per Cl 31.6.3.2 — bent bars, stirrups, shear studs |
| If τv > 1.5 τc' | Increase depth | — | Or provide drop panel / capital — shear steel alone insufficient |
Quick Footing Depth Check (preliminary)
| Case | Value | Factor / Formula | Note |
|---|
| qu × (B² − a²) ≤ 4 (a+d) d τc' | Solve for d | — | Square column on square footing |
| Try d = 1.5 × column dim (initial) | — | — | Then refine with full check |
| Check both punching AND one-way shear | — | — | One-way shear at distance d from column face |
Notes
• Effective depth d is the slab/footing depth less cover and half the bar diameter
• Use the smaller d (along x or y) for two-way shear checks
• Punching shear governs depth in flat slabs and isolated footings, NOT bending
• Drop panels increase the punching perimeter — most cost-effective fix
• Column capital increases the column 'effective dimension' and thus the perimeter
• Shear studs and bent bars work but are detailing-intensive — depth increase is preferred
• For raft foundations, punching shear is checked at every column individually
• Eccentric loading on column adds an additional moment-induced shear (Cl 31.6.2.2) — increase τv by ~20% as a quick allowance
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