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.
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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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