--- title: "Column 350x550 with major axis moment" subject: "Design of RCC Structure" chapter: 10 key: "semester_7/design_of_rcc_structure:column-350x550-with-major-axis-moment" source: https://www.bctengineer.com/q/semester_7/design_of_rcc_structure/column-350x550-with-major-axis-moment site: BCT Engineering --- # Column 350x550 with major axis moment Design of RCC Structure · Chapter 10: Design of compression members: Columns - Asked in: 2081 Baisakh, 10 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-350x550-with-major-axis-moment - Whole chapter: https://www.bctengineer.com/md/semester_7/design_of_rcc_structure/chapter-10 ## Question Design longitudinal and transverse reinforcement in a rectangular RC column of size 350 mm x 550 mm subjected to a factored axial load of 900 kN and moment equal to 200 kN-m with respect to the major axis. Take unsupported length of 3 m and effective length of 3.6 m. Use M25 concrete and Fe415 grade steel. ## Short answer Provide 8-16 mm bars (0.84%) and 8 mm ties @ 250 mm c/c. The column is short; uniaxial moment capacity 231.7 kN·m exceeds the design moment 200 kN·m. ## Answer #### Data and assumptions - Column 350 mm (width $b$) × 550 mm (depth $D$); $P_u = 900$ kN; $f_{ck} = 25$ MPa, $f_y = 415$ MPa. Clear cover 40 mm (IS 456 cl. 26.4.2.1), 8 mm ties. - Moment about major axis: $M_{ux}$ = 200 kN·m. - Sizes are given as $b \times D$ with $D \ge b$; moments $M_{ux}$ act about the major axis (depth $D$) and $M_{uy}$ about the minor axis (depth $b$). #### Slenderness | Axis | $l_e$ (mm) | Dimension (mm) | $l_e/$dim | Type | |---|---|---|---|---| | x-x (about major) | 3600 | 550 | 6.55 | short | | y-y (about minor) | 3600 | 350 | 10.29 | 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: $e_x = 3000/500 + 550/30 = 24.3$ mm (min. 20 mm); adopt 24.3 mm; $M_{ux,min} = P_u e = 21.9$ kN·m - About y-y: $e_y = 3000/500 + 350/30 = 17.7$ mm (min. 20 mm); adopt 20.0 mm; $M_{uy,min} = 18.0$ kN·m #### Design moments - Design moments: $M_{ux} = 200.0$ kN·m (not less than the minimum-eccentricity values). #### Longitudinal reinforcement $\dfrac{P_u}{f_{ck} b D} = \dfrac{900000}{25 \times 350 \times 550} = 0.187$ 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 | $p$ (%) | $d'/D$ | $M_{ux1}$ (kN·m) | $M_{ux}$ required | Ratio | |---|---|---|---|---|---| | 8-16 φ | 0.84 | 0.102 | 231.7 | 200.0 | 0.863 ok | #### Check $M_{ux} = 200.0$ kN·m $\le M_{ux1} = 231.7$ kN·m. Minimum eccentricity about the minor axis: $P_u e_y = 18.0$ kN·m $\le M_{uy1} = 137.4$ kN·m. Both are satisfied; the section is **safe**. Provide **8-16 mm** bars ($A_{sc} = 1608$ mm², $p = 0.84\%$), within 0.8% to 4%. #### Lateral ties - Diameter $\ge \max(\phi_{max}/4,\ 6) = \max(16/4, 6) = 6$ mm → provide 8 mm. - Pitch $\le \min$(least lateral dimension, $16\phi_{min}$, 300 mm) $= \min(350, 256, 300) = 256$ mm → provide 8 mm ties @ 250 mm c/c. #### Detailing ```text CROSS-SECTION 350 x 550 +-------------------------+ | o o o | | | | | | | | | | o o | | | | | | | | | | o o o | +-------------------------+ o = 16 mm bars, ties 8 mm @ 250 c/c ``` **Answer:** 350 × 550 mm column with 8-16 mm longitudinal bars ($p = 0.84\%$) and 8 mm ties @ 250 mm c/c. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. For le = 3.6 m and a 350 x 550 section, why is no additional moment needed? A. Only the major axis is considered B. Both le/D = 6.55 and le/b = 10.29 are below 12, so the column is short C. The moment is acting about the major axis only D. Pu is small Answer: B. A column with le/dimension below 12 on both axes is short, so slenderness moments are ignored. (Key point: Short column classification) 2. About the minor axis, L/500 + b/30 = 17.7 mm. What eccentricity is used and what moment results? A. 17.7 mm, 15.9 kN·m B. 24.3 mm, 21.9 kN·m C. 20 mm, 18.0 kN·m D. 30 mm, 27 kN·m Answer: C. emin must be at least 20 mm, so 20 mm governs: Pu*e = 900 x 0.020 = 18.0 kN·m. (Key point: Minimum eccentricity about minor axis) 3. Which limit gives the tie pitch of 256 mm (provided 250 mm) with 16 mm bars and b = 350 mm? A. 16 times the smallest bar diameter = 256 mm B. Least lateral dimension = 350 mm C. 300 mm D. Largest bar diameter / 4 Answer: A. Pitch <= min(350, 16 x 16 = 256, 300) = 256 mm, so 250 mm c/c is provided. 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