---
title: "Short column 350x500, M30, 1500 kN"
subject: "Design of RCC Structure"
chapter: 10
key: "semester_7/design_of_rcc_structure:short-column-350x500-m30-1500-kn"
source: https://www.bctengineer.com/q/semester_7/design_of_rcc_structure/short-column-350x500-m30-1500-kn
site: BCT Engineering
---

# Short column 350x500, M30, 1500 kN

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

- Asked in: 2075 Chaitra, 14 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/short-column-350x500-m30-1500-kn
- Whole chapter: https://www.bctengineer.com/md/semester_7/design_of_rcc_structure/chapter-10

## Question

Design a short rectangular column of size 350 mm x 500 mm and unsupported length of 3.30 m subjected to an axial factored load of 1500 kN and factored moments 130 kN-m and 80 kN-m about major and minor axes respectively. Adopt M30 grade concrete and Fe500 grade steel. Sketch the reinforcement details.

## Short answer

Short column; no slenderness effect. Use 8-16 mm bars (p=0.92%) and 8 mm ties @250 mm c/c; biaxial interaction ratio is 0.918, so safe.

## Answer

#### Data and assumptions
- Column 350 mm (width $b$) × 500 mm (depth $D$); $P_u = 1500$ kN; $f_{ck} = 30$ 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) $M_{ux}$ = 130 kN·m; about minor axis (y-y) $M_{uy}$ = 80 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) | 3300 | 500 | 6.60 | short |
| y-y (about minor) | 3300 | 350 | 9.43 | 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: $e_x = 3300/500 + 500/30 = 23.3$ mm (min. 20 mm); adopt 23.3 mm; $M_{ux,min} = P_u e = 34.9$ kN·m
- About y-y: $e_y = 3300/500 + 350/30 = 18.3$ mm (min. 20 mm); adopt 20.0 mm; $M_{uy,min} = 30.0$ kN·m

#### Design moments
- Design moments: $M_{ux} = 130.0$ kN·m, $M_{uy} = 80.0$ kN·m (not less than the minimum-eccentricity values).

#### Longitudinal reinforcement
$\dfrac{P_u}{f_{ck} b D} = \dfrac{1500000}{30 \times 350 \times 500} = 0.286$
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 | $p$ (%) | $d'/D$ | $M_{ux1}$ | $M_{uy1}$ | $P_u/P_{uz}$ | $\alpha_n$ | $(M_{ux}/M_{ux1})^{\alpha_n}+(M_{uy}/M_{uy1})^{\alpha_n}$ |
|---|---|---|---|---|---|---|---|
| 8-16 φ | 0.92 | 0.112 | 210.5 | 138.2 | 0.510 | 1.52 | 0.918 ✓ |

#### Check
$P_{uz} = 0.45 f_{ck} A_c + 0.75 f_y A_{sc} = 0.45 \times 30 \times 173392 + 0.75 \times 500 \times 1608 = 2944$ kN
$\dfrac{P_u}{P_{uz}} = \dfrac{1500}{2944} = 0.510$, so $\alpha_n = 1.52$ (IS 456 cl. 39.6; linear between 1.0 at 0.2 and 2.0 at 0.8).
$$
\left(\frac{M_{ux}}{M_{ux1}}\right)^{\alpha_n} + \left(\frac{M_{uy}}{M_{uy1}}\right)^{\alpha_n} = \left(\frac{130.0}{210.5}\right)^{1.52} + \left(\frac{80.0}{138.2}\right)^{1.52} = 0.918 \le 1.0
$$
The interaction condition is satisfied; the section is **safe**.

Provide **8-16 mm** bars ($A_{sc} = 1608$ mm², $p = 0.92\%$), 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 500
    +-------------------------+
    |   o        o        o   |
    |                         |
    |                         |
    |                         |
    |                         |
    |   o                 o   |
    |                         |
    |                         |
    |                         |
    |                         |
    |   o        o        o   |
    +-------------------------+
   o = 16 mm bars, ties 8 mm @ 250 c/c
```

**Answer:** 350 × 500 mm column with 8-16 mm longitudinal bars ($p = 0.92\%$) 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. With le = 3300 mm, 350 x 500 section, how is the column classified?
   A. Slender because 3300/350 = 9.43 > 3
   B. Short because both le/dimension ratios are below 12
   C. Short because the load is under 2000 kN
   D. Slender about the minor axis only
   Answer: B. Ratios are 6.60 and 9.43, both below 12, so it is short and needs no additional moment. (Key point: Slenderness check)

2. About the minor axis, e = 3300/500 + 350/30 = 18.3 mm. What value is adopted?
   A. 18.3 mm
   B. 20 mm
   C. 30 mm
   D. 0 mm
   Answer: B. The minimum eccentricity is 20 mm, so 20 mm applies, though the design moment 80 kN·m is larger anyway. (Key point: Minimum eccentricity effect)

3. Why are the given moments 130 and 80 kN·m used as the design moments?
   A. They exceed the minimum-eccentricity moments
   B. They are always used regardless of minimum values
   C. They are lower than the minimum values
   D. They are averaged
   Answer: A. The design moment is the larger of the applied moment and Pu x emin (34.9 and 30 kN·m), so the applied ones govern. (Key point: Design moments)

4. The interaction sum is 0.918 with αn = 1.52. What does this mean?
   A. The section is unsafe
   B. The section is safe and 8-16φ is adequate
   C. More steel is needed
   D. The column is slender
   Answer: B. 0.918 is not more than 1.0, so the section satisfies IS 456 cl. 39.6. (Key point: Interaction result)

## Close variants set in other exams

- [Short column 450x300, 1500 kN, M30](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Ashort-column-450x300-1500-kn-m30) — Design of RCC Structure, chapter 10, asked 2×

## Related in Design of RCC Structure

- [Short column 300x500, 2000 kN, M30](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Ashort-column-300x500-2000-kn-m30) — Design of RCC Structure, chapter 10
- [Column 350x550 with major axis moment](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Acolumn-350x550-with-major-axis-moment) — Design of RCC Structure, chapter 10
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