Ductile design per IS 13920, beam and column

Ductile design of beam flexural reinforcement

1. Analyse the frame for the gravity and seismic load combinations ($1.5(DL\pm EL)$, $1.2(DL+LL\pm EL)$, $0.9DL \pm 1.5EL$) and get the design hogging and sagging moments at the faces of the supports.
2. Check the geometry: $b \ge 200$ mm, $b/D \ge 0.3$, $D \le L/4$.
3. Design the steel for $M_u$ using IS 456 limit state design, keeping $x_u \le x_{u,max}$.
4. Detail it: $\rho_{min} = 0.24\sqrt{f_{ck}}/f_y \le \rho \le 2.5\%$; two bars continuous at the top and bottom; bottom steel at a joint face $\ge 50\%$ of the top steel; capacity at any section $\ge 25\%$ of the maximum end capacity.
5. Shear: design for the shear from the hinge capacities,

$$V_{u} = V_{u,a}^{D+L} \pm 1.4\,\frac{M_{u,lim}^{As} + M_{u,lim}^{Bh}}{L_{AB}}$$

where $M_{u,lim}$ are the moments of resistance of the sagging and hogging steel provided at the two ends A and B. Provide closed stirrups with $135^\circ$ hooks, at spacing $\le \min(d/4,\ 8\phi,\ 100)$ within $2d$ of the joint.

Ductile design of columns (axial load plus biaxial bending)

1. Size: $b \ge 200$ mm and $b/D \ge 0.4$.
2. Design for $P_u$ and the biaxial moments $M_{ux}$, $M_{uy}$ using IS 456 cl. 39.6:

$$\left(\frac{M_{ux}}{M_{ux1}}\right)^{\alpha_n} + \left(\frac{M_{uy}}{M_{uy1}}\right)^{\alpha_n} \le 1$$

with $\alpha_n$ from $P_u/P_{uz}$ (1.0 to 2.0). Longitudinal steel between 0.8% and 4% (IS 13920), including at laps. 3. Strong column-weak beam: $\sum M_{c} \ge 1.4\sum M_b$ at each joint (IS 13920:2016; ACI 318 uses 1.2). 4. Column shear: $V_u = 1.4\,\dfrac{M_{u,lim}^{bL} + M_{u,lim}^{bR}}{h_{st}}$; provide confining hoops over $l_o = \max(D,\ h/6,\ 450)$ at 75-100 mm, with $A_{sh} = 0.18\,s\,h\,(f_{ck}/f_y)(A_g/A_k-1)$.

 BEAM: |hoops 2d @ <=100|   d/2    |hoops 2d @ <=100|
 COLUMN: hoops lo @ 75-100 | normal | hoops lo @ 75-100