---
title: "Check column 600x400 with 8-28 mm bars"
subject: "Design of RCC Structure"
chapter: 10
key: "semester_7/design_of_rcc_structure:check-column-600x400-with-8-28"
source: https://www.bctengineer.com/q/semester_7/design_of_rcc_structure/check-column-600x400-with-8-28
site: BCT Engineering
---

# Check column 600x400 with 8-28 mm bars

Design of RCC Structure · Chapter 10: Design of compression members: Columns

- Asked in: 2065 Kartik (old course), 10 marks
- Video: [Intro to Interaction Diagrams for Concrete Columns | Reinforced Concrete Column Design](https://www.youtube.com/watch?v=lyQ4WqXPTv8) — Tyler Ley
- 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/check-column-600x400-with-8-28
- Whole chapter: https://www.bctengineer.com/md/semester_7/design_of_rcc_structure/chapter-10

## Question

A reinforced concrete column of size 600 mm x 400 mm with $A_{st}$ = 8-28 mm diameter is subjected to $M_{ux}$ = 350 kN-m, $M_{uy}$ = 50 kN-m and $P_u$ = 2000 kN. Check whether the column is safe for above combination of load and bending moments. Take M20 and Fe415 grades of concrete and steel respectively and the effective cover to reinforcing bar 60 mm.

## Short answer

The 400×600 mm column with 8-28 mm bars is not safe. Under Pu = 2000 kN, Mux = 350 kN·m, Muy = 50 kN·m, the exponent alpha_n = 1.58 and the biaxial interaction sum (350/356.1)^1.58 + (50/213.9)^1.58 = 1.074 exceeds 1.0.

## Answer

#### Data
- Column 400 × 600 mm, 8-28 mm bars ($A_{sc} = 4926$ mm², $p = 2.05\%$), arranged 3 bars on each 400 mm face and 1 bar at mid-height of each side (3-2-3 arrangement). Effective cover $d' = 60$ mm, so $d'/D = 0.10$ (major axis) and $d'/b = 0.15$ (minor axis).
- $P_u = 2000$ kN, $M_{ux} = 350$ kN·m (about the major axis), $M_{uy} = 50$ kN·m; M20 concrete, Fe415 steel. The column is taken as short (no length is given), and the moments are larger than $P_u e_{min}$ (about 40 kN·m), so they are used as given.

#### Uniaxial capacities at $P_u$ = 2000 kN
$\dfrac{P_u}{f_{ck} bD} = \dfrac{2000000}{20 \times 400 \times 600} = 0.417$ and $\dfrac{p}{f_{ck}} = 0.103$.
From the SP-16 interaction chart for Fe415 (or equivalently by strain compatibility, computed here):
- About the major axis: $M_{ux1} = 356.1$ kN·m
- About the minor axis: $M_{uy1} = 213.9$ kN·m

#### Biaxial check (IS 456 cl. 39.6)
$P_{uz} = 0.45 f_{ck} A_c + 0.75 f_y A_{sc} = 0.45 \times 20 \times 235074 + 0.75 \times 415 \times 4926 = 3649$ kN
$\dfrac{P_u}{P_{uz}} = 0.548$, so $\alpha_n = 1.58$ (linear interpolation between 1.0 at 0.2 and 2.0 at 0.8).
$$
\left(\frac{M_{ux}}{M_{ux1}}\right)^{\alpha_n} + \left(\frac{M_{uy}}{M_{uy1}}\right)^{\alpha_n} = \left(\frac{350}{356.1}\right)^{1.58} + \left(\frac{50}{213.9}\right)^{1.58} = 1.074
$$
Since 1.074 $> 1.0$, the column is **not safe** for the given combination of load and moments; the section or the steel must be increased.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. With d' = 60 mm on a 400 x 600 column, d'/D and d'/b are
   A. 0.10 and 0.15
   B. 0.15 and 0.10
   C. 0.06 and 0.04
   D. 0.10 and 0.10
   Answer: A. d'/D = 60/600 = 0.10 (major axis); d'/b = 60/400 = 0.15 (minor axis). (Key point: Effective cover ratios)

2. With Pu/Puz = 0.548, alpha_n is
   A. 1.58
   B. 1.00
   C. 2.00
   D. 0.55
   Answer: A. alpha_n = 1 + (0.548 - 0.2)/0.6 = 1.58. (Key point: Alpha_n)

3. The interaction sum is 1.074. What is concluded?
   A. Safe, because Mux < Mux1
   B. Not safe, because the sum exceeds 1.0
   C. Safe, because Muy is small
   D. Cannot be checked
   Answer: B. Even though Mux < Mux1 individually, the combined biaxial sum must be <= 1.0; 1.074 fails. (Key point: Conclusion)

4. Why are the given moments used rather than minimum-eccentricity moments?
   A. They are larger than Pu x emin (about 40 kN-m)
   B. The column is slender
   C. Minimum eccentricity does not apply to biaxial columns
   D. Fe415 has no minimum
   Answer: A. The applied 350 and 50 kN-m exceed Pu x emin, so they govern. (Key point: Use of given moments)

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