---
title: "Short column 450x300, 1500 kN, M30"
subject: "Design of RCC Structure"
chapter: 10
key: "semester_7/design_of_rcc_structure:short-column-450x300-1500-kn-m30"
source: https://www.bctengineer.com/q/semester_7/design_of_rcc_structure/short-column-450x300-1500-kn-m30
site: BCT Engineering
---

# Short column 450x300, 1500 kN, M30

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

- Asked in: 2071 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-450x300-1500-kn-m30
- Whole chapter: https://www.bctengineer.com/md/semester_7/design_of_rcc_structure/chapter-10

## Question

Design a short rectangular column of size 450 mm x 300 mm and unsupported length 3 m subjected to an axial ultimate load of 1500 kN and ultimate moments 150 kNm and 80 kNm about long major and minor axes respectively. Adopt M30 grade of concrete and Fe500 grade of steel. Sketch the final design.

## Short answer

For a 450×300 mm short column with 1500 kN axial load and biaxial moments 150 and 80 kNm, provide 8-25 mm longitudinal bars (2.91% steel) and 8 mm lateral ties at 300 mm c/c.

## Answer

#### Data and assumptions
- Column 300 mm (width $b$) × 450 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) $M_{ux}$ = 150 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) | 3000 | 450 | 6.67 | short |
| y-y (about minor) | 3000 | 300 | 10.00 | 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: $e_x = 3000/500 + 450/30 = 21.0$ mm (min. 20 mm); adopt 21.0 mm; $M_{ux,min} = P_u e = 31.5$ kN·m
- About y-y: $e_y = 3000/500 + 300/30 = 16.0$ mm (min. 20 mm); adopt 20.0 mm; $M_{uy,min} = 30.0$ kN·m

#### Design moments
- Design moments: $M_{ux} = 150.0$ kN·m, $M_{uy} = 80.0$ kN·m (not less than the minimum-eccentricity values).

#### Longitudinal reinforcement
$\dfrac{P_u}{f_{ck} b D} = \dfrac{1500000}{30 \times 300 \times 450} = 0.370$
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 | $p$ (%) | $d'/D$ | $M_{ux1}$ | $M_{uy1}$ | $P_u/P_{uz}$ | $\alpha_n$ | $(M_{ux}/M_{ux1})^{\alpha_n}+(M_{uy}/M_{uy1})^{\alpha_n}$ |
|---|---|---|---|---|---|---|---|
| 16-16 φ | 2.38 | 0.124 | 204.2 | 118.9 | 0.502 | 1.50 | 1.180 ✗ |
| 12-20 φ | 2.79 | 0.129 | 229.4 | 130.4 | 0.471 | 1.45 | 1.032 ✗ |
| 8-25 φ | 2.91 | 0.134 | 238.6 | 134.3 | 0.463 | 1.44 | 0.988 ✓ |

#### Check
$P_{uz} = 0.45 f_{ck} A_c + 0.75 f_y A_{sc} = 0.45 \times 30 \times 131073 + 0.75 \times 500 \times 3927 = 3242$ kN
$\dfrac{P_u}{P_{uz}} = \dfrac{1500}{3242} = 0.463$, so $\alpha_n = 1.44$ (IS 456 cl. 39.6; linear between 1.0 at 0.2 and 2.0 at 0.8).
$$
\left(\frac{M_{ux}}{M_{ux1}}\right)^{\alpha_n} + \left(\frac{M_{uy}}{M_{uy1}}\right)^{\alpha_n} = \left(\frac{150.0}{238.6}\right)^{1.44} + \left(\frac{80.0}{134.3}\right)^{1.44} = 0.988 \le 1.0
$$
The interaction condition is satisfied; the section is **safe**.

Provide **8-25 mm** bars ($A_{sc} = 3927$ mm², $p = 2.91\%$), within 0.8% to 4%.

#### Lateral ties
- Diameter $\ge \max(\phi_{max}/4,\ 6) = \max(25/4, 6) = 6.25$ mm → provide 8 mm.
- Pitch $\le \min$(least lateral dimension, $16\phi_{min}$, 300 mm) $= \min(300, 400, 300) = 300$ mm → provide 8 mm ties @ 300 mm c/c.

#### Detailing
```text
CROSS-SECTION 300 x 450
    +-------------------------+
    |                         |
    |    o       o       o    |
    |                         |
    |                         |
    |                         |
    |    o               o    |
    |                         |
    |                         |
    |                         |
    |    o       o       o    |
    |                         |
    +-------------------------+
   o = 25 mm bars, ties 8 mm @ 300 c/c
```

**Answer:** 300 × 450 mm column with 8-25 mm longitudinal bars ($p = 2.91\%$) and 8 mm ties @ 300 mm c/c.

## Check yourself

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

1. In the design, Mux = 150 kN-m acts about the major axis. Which depth is used for the slenderness of that axis?
   A. 300 mm
   B. 450 mm
   C. 750 mm
   D. 3000 mm
   Answer: B. Bending about the major axis uses the depth D = 450 mm; the minor axis uses b = 300 mm. (Key point: Which dimension for which axis)

2. Pu/Puz = 1500/3242 = 0.463. What is alpha_n?
   A. 1.00
   B. 1.44
   C. 1.88
   D. 2.00
   Answer: B. alpha_n = 1 + (0.463 - 0.2)/0.6, which is about 1.44. (Key point: Alpha_n value)

3. What are Mux1 and Muy1 in the interaction equation?
   A. The applied factored moments
   B. The uniaxial moment capacities about each axis at the given Pu
   C. The minimum eccentricity moments
   D. The moments at zero axial load
   Answer: B. They are the moment capacities of the section about each axis, acting separately, at the given axial load (from SP-16 charts or strain compatibility). (Key point: Reading uniaxial capacities)

4. Why is 8-25 mm (sum = 0.988) accepted while 12-20 mm (1.032) is not?
   A. 8-25 has smaller bars
   B. Only 8-25 gives a sum <= 1.0, with p = 2.91% inside 0.8-4%
   C. 12-20 has p above 4%
   D. 12-20 has less than 0.8% steel
   Answer: B. Safety needs an interaction sum <= 1.0; 12-20 gives 1.032, which fails. (Key point: Accepting the design)

5. For 25 mm bars, the ties provided are
   A. 6 mm at 400 mm
   B. 8 mm at 300 mm
   C. 25 mm at 300 mm
   D. 8 mm at 450 mm
   Answer: B. Dia >= max(25/4, 6) = 6 mm, so 8 mm is used; pitch <= min(300, 400, 300) = 300 mm. (Key point: Tie diameter and pitch)

## Close variants set in other exams

- [Short column 350x500, M30, 1500 kN](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Ashort-column-350x500-m30-1500-kn) — 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 350x350, 1440 kN, ductile detailing](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Acolumn-350x350-1440-kn-ductile-detailing) — Design of RCC Structure, chapter 10, asked 2×
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- [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
- [Rectangular footing, 450x450, uniaxial moment 240 kNm](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Arectangular-footing-450x450-uniaxial-moment-240) — Design of RCC Structure, chapter 11

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