Column Design and Behavior
📌 Columns are structural elements primarily designed to resist compressive loads (axial load), typically having square, rectangular, or circular cross-sections where the longitudinal length is greater than the cross-sectional dimensions.
📌 Columns are classified as short columns, governed by compressive strength based on material capacity, or tall columns, where slenderness ratio introduces flexural moments and lateral deformation (buckling).
📌 Typical reinforced concrete columns use either rectangular ties (hoops) or spiral reinforcement to confine the concrete core, impacting load capacity and ductility.

Ultimate Load Capacity Calculation
📌 The ultimate load ($P_n$) calculation for square/rectangular columns involves $0.80 P_0$, derived from $0.80(0.85 f'_c(A_g - A_{st})) + f_y A_{st}$.
📌 Spiral reinforcement columns are considered significantly stronger and more ductile than tied columns because the spiral wrapping provides a high confining effect on the concrete core, resisting premature failure under eccentric loading (like earthquake forces).
📌 For eccentric loading ($P_u$ with moment $M_u = P_u \times e$), analysis must account for both axial load and bending, requiring determination of the plastic centroid and resulting tensile/compressive stresses in the steel reinforcement.

Stress and Strain Analysis in Eccentric Loading
📌 When an eccentric load is applied, the column cross-section experiences a combination of compression on one side and tension on the other, analogous to beam analysis but with an axial component.
📌 The strain distribution is assumed to be linear, with the concrete reaching a maximum compressive strain of $\epsilon_c = 0.003$ at the outermost compression fiber.
📌 The failure mode (ductile/tension-controlled vs. brittle/compression-controlled) is determined by the position of the neutral axis ($c$) relative to the balance point ($c_{bal}$), which dictates the yield condition of the tension steel ($\epsilon_s = \epsilon_y$).

Key Points & Insights
➡️ Spiral columns offer superior ductility and ultimate load-bearing capacity compared to tied columns due to the significant confining effect provided by the continuous spiral reinforcement.
➡️ Column design rarely involves pure axial load; the presence of eccentricity ($e$) generating a moment ($M_u$) must be integrated into the ultimate capacity analysis ($P_u-M_u$ interaction).
➡️ The failure mode in eccentrically loaded columns is critically dependent on the neutral axis depth ($c$); a deeper $c$ generally indicates a more ductile, tension-controlled failure.
➡️ For tied columns, the ultimate capacity ($P_0$) is reduced to $80\%$ of the theoretical maximum capacity due to the reduced effectiveness of the rectangular ties in confining the concrete.

📸 Video summarized with SummaryTube.com on Dec 01, 2025, 03:50 UTC