--- title: "Column 350x350, 1440 kN, ductile detailing" subject: "Design of RCC Structure" chapter: 10 key: "semester_7/design_of_rcc_structure:column-350x350-1440-kn-ductile-detailing" source: https://www.bctengineer.com/q/semester_7/design_of_rcc_structure/column-350x350-1440-kn-ductile-detailing site: BCT Engineering --- # Column 350x350, 1440 kN, ductile detailing Design of RCC Structure · Chapter 10: Design of compression members: Columns - Asked in: 2076 Chaitra, 12 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/design_of_rcc_structure/column-350x350-1440-kn-ductile-detailing - Whole chapter: https://www.bctengineer.com/md/semester_7/design_of_rcc_structure/chapter-10 ## Question Determine the longitudinal and transverse reinforcement of RC column subjected to a factored axial load of 1440 kN and factored moment $M_{ux}$ about major axis of 195 kNm and $M_{uy}$ about minor axis 180 kNm. The size of column is 350 mm x 350 mm and unsupported length of 3.60 m. Adopt M20 concrete and Fe500 grade (TMT) steel. Also do the ductile detailing of transversal reinforcement. ## Short answer The 350x350 mm section is inadequate; enlarge to 450x450 mm. Provide 12-25 mm bars (Asc=5890 mm2, p=2.91%), 8 mm ties at 220 mm c/c outside the confining zone, with special confining reinforcement as per IS 13920. ## Answer #### Check of the given section 350 × 350 mm Even with the largest practical steel (for example 14-25 mm bars, $p = 5.6\%$), the interaction ratio is 1.77 > 1 for $P_u = 1440$ kN with the given moments. The given section is therefore too small, and the column must be enlarged. #### Data and assumptions - The section given in the question (350 × 350 mm) is checked first and found inadequate (see above), so a revised section 450 × 450 mm is designed. - Column 450 mm (width $b$) × 450 mm (depth $D$); $P_u = 1440$ kN; $f_{ck} = 20$ MPa, $f_y = 500$ MPa. Clear cover 40 mm (IS 456 cl. 26.4.2.1), 8 mm ties. - Moments: about major axis (x-x) $M_{ux}$ = 195 kN·m; about minor axis (y-y) $M_{uy}$ = 180 kN·m. - Effective length is taken equal to the unsupported length, 3.6 m. #### Slenderness | Axis | $l_e$ (mm) | Dimension (mm) | $l_e/$dim | Type | |---|---|---|---|---| | x-x (about major) | 3600 | 450 | 8.00 | short | | y-y (about minor) | 3600 | 450 | 8.00 | short | Both ratios are below 12, so the column is **short**; no additional moment is required. #### Minimum eccentricity (cl. 25.4) $$ e_{min} = \max\left(\frac{L}{500} + \frac{D}{30},\ 20\right) $$ - About x-x: $e_x = 3600/500 + 450/30 = 22.2$ mm (min. 20 mm); adopt 22.2 mm; $M_{ux,min} = P_u e = 32.0$ kN·m - About y-y: $e_y = 3600/500 + 450/30 = 22.2$ mm (min. 20 mm); adopt 22.2 mm; $M_{uy,min} = 32.0$ kN·m #### Design moments - Design moments: $M_{ux} = 195.0$ kN·m, $M_{uy} = 180.0$ kN·m (not less than the minimum-eccentricity values). #### Longitudinal reinforcement $\dfrac{P_u}{f_{ck} b D} = \dfrac{1440000}{20 \times 450 \times 450} = 0.356$ Bars are chosen so that $p$ lies between 0.8% (minimum) and 4% (practical maximum; IS 456 cl. 26.5.3.1 allows 6%). The uniaxial capacities $M_{ux1}$, $M_{uy1}$ at $P_u$ are read from the SP-16 interaction charts for rectangular sections; here they are computed by strain compatibility with the IS 456 stress block and the design stress-strain curve of steel (same basis as the charts), with effective cover $d' = 40 + 8 + \phi/2$. | Trial | $p$ (%) | $d'/D$ | $M_{ux1}$ | $M_{uy1}$ | $P_u/P_{uz}$ | $\alpha_n$ | $(M_{ux}/M_{ux1})^{\alpha_n}+(M_{uy}/M_{uy1})^{\alpha_n}$ | |---|---|---|---|---|---|---|---| | 10-25 φ | 2.42 | 0.134 | 271.5 | 304.0 | 0.398 | 1.33 | 1.142 ✗ | | 16-20 φ | 2.48 | 0.129 | 292.7 | 292.7 | 0.393 | 1.32 | 1.110 ✗ | | 12-25 φ | 2.91 | 0.134 | 330.6 | 330.6 | 0.362 | 1.27 | 0.974 ✓ | #### Check $P_{uz} = 0.45 f_{ck} A_c + 0.75 f_y A_{sc} = 0.45 \times 20 \times 196610 + 0.75 \times 500 \times 5890 = 3978$ kN $\dfrac{P_u}{P_{uz}} = \dfrac{1440}{3978} = 0.362$, so $\alpha_n = 1.27$ (IS 456 cl. 39.6; linear between 1.0 at 0.2 and 2.0 at 0.8). $$ \left(\frac{M_{ux}}{M_{ux1}}\right)^{\alpha_n} + \left(\frac{M_{uy}}{M_{uy1}}\right)^{\alpha_n} = \left(\frac{195.0}{330.6}\right)^{1.27} + \left(\frac{180.0}{330.6}\right)^{1.27} = 0.974 \le 1.0 $$ The interaction condition is satisfied; the section is **safe**. Provide **12-25 mm** bars ($A_{sc} = 5890$ mm², $p = 2.91\%$), within 0.8% to 4%. #### Lateral ties - Diameter $\ge \max(\phi_{max}/4,\ 6) = \max(25/4, 6) = 6$ mm → provide 8 mm. - Pitch by IS 456 $\le \min$(least lateral dimension, $16\phi_{min}$, 300 mm) $= \min(450, 400, 300) = 300$ mm. For ductile detailing, IS 13920 limits the spacing outside the confining zone to half the least lateral dimension = 225 mm → provide 8 mm ties @ 220 mm c/c outside $l_o$. #### Ductile detailing of transverse steel (IS 13920) - Special confining length at each end: $l_o \ge \max(D,\ L/6,\ 450) = \max(450, 600, 450) = 600$ mm → provide 600 mm from each joint face. - Spacing of hoops within $l_o$: $\le \min(b/4,\ 6\phi_L,\ 100) = \min(112, 150, 100) = 100$ mm, and not less than 75 mm → 100 mm c/c. - The bars are about 110 mm apart (more than 75 mm), so the two intermediate bars on each face are held by cross-ties: a rectangular hoop plus 2 cross-ties in each direction. - Area of one hoop leg: $A_{sh} \ge 0.18\, s\, h\, \dfrac{f_{ck}}{f_y}\left(\dfrac{A_g}{A_k} - 1\right)$, where $h$ is the longer c/c distance between adjacent hoop legs or cross-ties (not more than 300 mm), here $h \approx 135$ mm; $A_k = 370 \times 370 = 136900$ mm² (core measured to the outside of the hoop); $A_g = 202500$ mm². $A_{sh} = 0.18 \times 100 \times 135 \times \dfrac{20}{500} \times \left(\dfrac{202500}{136900} - 1\right) = 46.6$ mm² - An 8 mm leg gives 50.3 mm² $>$ 46.6 mm², so 8 mm hoops and cross-ties @ 100 mm c/c are adequate. Hoops have 135° hooks with a 6φ (≥ 65 mm) extension. - Outside $l_o$: 8 mm ties @ 220 mm c/c ($\le b/2 = 225$ mm). #### Detailing ```text CROSS-SECTION 450 x 450 +-------------------------+ | | | o o o o | | | | | | o o | | | | o o | | | | | | o o o o | | | +-------------------------+ o = 25 mm bars; hoop + 2 cross-ties each way 8 mm @ 100 c/c over 600 mm at each end, 8 mm @ 220 c/c in the middle region ``` **Answer:** 450 × 450 mm column with 12-25 mm longitudinal bars ($p = 2.91\%$); 8 mm hoops with cross-ties @ 100 mm c/c over 600 mm at each end, and 8 mm ties @ 220 mm c/c in the middle region. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why was the given 350 x 350 mm section replaced by 450 x 450 mm? A. The column was slender B. Even with very heavy steel the interaction ratio stayed above 1 C. Fe500 steel cannot be used in 350 mm columns D. The minimum eccentricity was exceeded Answer: B. With 14-25 mm bars (5.6%) the interaction ratio is still 1.77 > 1, so the section must be enlarged. (Key point: Adequacy of given section) 2. At each column end the special confining length lo is the greatest of which values? A. Smallest of D, L/6 and 450 mm B. D, L/6 and 450 mm C. b/4 and 100 mm D. 16φ and 300 mm Answer: B. IS 13920 requires lo not less than the larger lateral dimension, clear height/6, and 450 mm; here L/6 = 600 mm governs. (Key point: Confining length lo) 3. What spacing is used for hoops within lo? A. Not more than 300 mm B. Not more than 225 mm C. Not more than b/4 and 100 mm, not less than 75 mm D. Equal to the bar diameter Answer: C. Closely spaced hoops (here 100 mm) confine the concrete; spacing is limited to min(b/4, 100) and not less than 75 mm. (Key point: Hoop spacing in lo) 4. The required Ash = 127.7 mm² is checked against 3 legs of 8 mm = 151 mm². What does this show? A. The hoop spacing must be increased B. The provided hoop steel is adequate C. The column is slender D. The hooks are too short Answer: B. 151 mm² exceeds 127.7 mm², so the 8 mm hoop with cross-ties provides enough confining steel. 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