This section provides a summary of key formulas and clauses used in structural design, based on selected international standards. For full details, always refer to the latest editions of the respective codes.

ACI 318 (American Concrete Institute) - Building Code Requirements for Structural Concrete

• Flexural Strength ($M_n$): Clause 21.2.2.4 for $a = (A_s f_y) / (0.85 f'_c b)$. $M_n = \phi A_s f_y (d - a/2)$. $\phi$ factors from Chapter 21.
• Shear Strength ($V_c$): Clause 22.5.5.1. $V_c = \phi \times 2\lambda\sqrt{f'_c} b_w d$. $\phi$ factor for shear is 0.75.
• Minimum Flexural Reinforcement: Clause 9.6.1.2. $A_{s,min} = \max(\frac{0.25\sqrt{f'_c}}{f_y} b_w d, \frac{1.4}{f_y} b_w d)$.
• Deflection Control: Table 24.2.2. General limits for beams and one-way slabs.
• Column Axial Load Capacity: Clause 22.4.2. For tied columns, $P_n = 0.80 \phi [0.85 f'_c (A_g - A_{st}) + f_y A_{st}]$. $\phi$ factor for columns is 0.65.
• Walls - Minimum Vertical Reinforcement: Clause 11.6.1.1. $0.0012 A_g$ to $0.0020 A_g$ (depending on bar type).
• Walls - Minimum Horizontal Reinforcement: Clause 11.6.1.2. $0.0020 A_g$ to $0.0025 A_g$ (depending on bar type).
• Walls - Design Strength: Chapter 11 provides general provisions for walls. Design for combined axial load and flexure (similar to columns or beams depending on slenderness and eccentricity).
• Footings - Bearing Strength (Concrete): Clause 22.8. $ \phi 0.85 f'_c A_1 $. When $A_2 > A_1$, bearing strength can be multiplied by $ \sqrt{A_2/A_1} \le 2 $. $\phi = 0.65$.
• Footings - One-Way Shear: Clause 22.5.5.1. $V_c = \phi \times 2\lambda\sqrt{f'_c} b_w d$. $\phi = 0.75$. Critical section at distance 'd' from face of column.
• Footings - Two-Way Shear (Punching): Clause 22.5.5.1. $V_c = \phi \times (2 + 4/\beta_c)\lambda\sqrt{f'_c} b_o d$ or $V_c = \phi \times (\alpha_s d/b_o + 2)\lambda\sqrt{f'_c} b_o d$ or $V_c = \phi \times 4\lambda\sqrt{f'_c} b_o d$. $\phi = 0.75$. Critical section at distance 'd/2' from face of column.

IS 456:2000 (Indian Standard) - Plain and Reinforced Concrete - Code of Practice

• Limit State of Collapse (Flexure): Clause 38. For singly reinforced, $M_u = 0.87 f_y A_{st} d (1 - \frac{A_{st} f_y}{b d f_{ck}})$. Maximum depth of neutral axis $x_{u,max}$ (Clause 38.1).
• Limit State of Collapse (Shear): Clause 40. Nominal shear stress $\tau_v = V_u / (b d)$. Design shear strength of concrete $\tau_c$ (Table 19, based on $p_t$ and $f_{ck}$).
• Minimum Reinforcement (Beams): Clause 26.5.1.1. $A_s / (b d) = 0.85 / f_y$.
• Minimum Reinforcement (Slabs): Clause 26.5.2.1. For HYSD bars, $0.12\%$ of gross area; for mild steel, $0.15\%$.
• Columns Axial Load Capacity: Clause 39.3. $P_u = 0.4 f_{ck} A_c + 0.67 f_y A_{sc}$.
• Walls - Vertical Reinforcement: Clause 32.5. Minimum $0.0012 A_g$ for HYSD bars ($0.0015 A_g$ for mild steel). Maximum $4\%$ of gross cross-sectional area. Spacing not more than $3 \times$ wall thickness or $450$ mm.
• Walls - Horizontal Reinforcement: Clause 32.5. Minimum $0.0020 A_g$ for HYSD bars ($0.0025 A_g$ for mild steel). Spacing not more than $3 \times$ wall thickness or $450$ mm.
• Walls - Design Considerations: Slenderness limits (Clause 32.2), effective length factor (Clause 32.3). Concentric/eccentric loading design methods (Clause 32.6).
• Footings - Bending Moment: Clause 34. For isolated footings, critical section at the face of the column.
• Footings - One-Way Shear: Clause 34.2.4. Critical section at distance 'd' from face of column. Design shear strength $\tau_c$ (Table 19).
• Footings - Two-Way Shear (Punching): Clause 34.2.4. Critical section at distance 'd/2' from face of column. Permissible shear stress $k_s \tau_c'$, where $\tau_c' = 0.25\sqrt{f_{ck}}$. $k_s = (0.5 + \beta_c)$ or $1.0$, whichever is less, $\beta_c$ is ratio of shorter side to longer side of column.
• Footings - Bearing Pressure: Clause 34.4. Bearing stress on concrete not to exceed $0.45 f_{ck}$ for plain concrete or $0.45 f_{ck} \sqrt{A_2/A_1}$ for reinforced concrete (not exceeding $2 \times 0.45 f_{ck}$).

BS 8110-1:1997 (British Standard) - Structural Use of Concrete - Part 1: Code of Practice for Design and Construction

• Moment of Resistance: Clause 3.4.4.4. $M = A_s f_y z$ where $z = d(0.5 + \sqrt{0.25 - K/0.9})$ and $K = M_{design} / (f_{cu} b d^2)$.
• Shear Resistance ($V_c$): Clause 3.4.5. The design concrete shear stress $v_c$ depends on $100 A_s/(b_v d)$, $d$, and $f_{cu}$ (Table 3.9). $V_c = v_c b_v d$.
• Minimum Area of Tension Reinforcement: Clause 3.12.5.3. Typically $0.13\%$ for beams.
• Column Axial Load Capacity: Clause 3.8.4. Column design often uses design charts or simplified formulas considering short/slender columns and uniaxial/biaxial bending.
• Walls - Vertical Reinforcement: Clause 3.9.3. Generally $0.4\%$ to $4\%$ of concrete area. Spacing not greater than $3 \times$ wall thickness or $450$ mm.
• Walls - Horizontal Reinforcement: Clause 3.9.3. Generally $0.25\%$ to $4\%$ of concrete area. Spacing not greater than $3 \times$ wall thickness or $450$ mm.
• Walls - Design Method: Slenderness ratio (Clause 3.9.1). Design as stocky (Clause 3.9.3.6) or slender walls (Clause 3.9.3.7). Often uses design charts for walls with moments.
• Footings - Bending Moment: Clause 3.12.3. Critical section at face of column.
• Footings - Punching Shear: Clause 3.7.7. Critical perimeter at $1.5d$ from face of column. Design punching shear stress $v_c$ (Table 3.9). Enhance $v_c$ based on $2d$.
• Footings - One-Way Shear: Clause 3.4.5. Critical section at $d$ from face of column. Design shear stress $v_c$ (Table 3.9).
• Footings - Bearing Capacity: Clause 3.1.2. Allowable bearing pressure on concrete.

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