---
title: "Rectangular column with working-load moment"
subject: "Design of RCC Structure"
chapter: 10
key: "semester_7/design_of_rcc_structure:rectangular-column-with-working-load-moment"
source: https://www.bctengineer.com/q/semester_7/design_of_rcc_structure/rectangular-column-with-working-load-moment
site: BCT Engineering
---

# Rectangular column with working-load moment

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

- Asked in: 2065 Shrawan (old course), 13 marks
- Video: [Design of a Rectangular Column subjected to combined axial loading and biaxial bending](https://www.youtube.com/watch?v=VL2MoB0n9Tg) — Stan Academy
- 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/rectangular-column-with-working-load-moment
- Whole chapter: https://www.bctengineer.com/md/semester_7/design_of_rcc_structure/chapter-10

## Question

Design a rectangular column supporting an axial load of 1200 kN along with bending moment of 150 kN-m at working loads. Use M25 concrete mix, Fe415 steel and the section reinforced equally on two sides only.

## Short answer

Use a 350×500 mm column with 12 bars of 20 mm diameter (6 per face, p=2.15%) and 8 mm ties at300 mm c/c. At ultimate axial load 1800 kN and moment 225 kN·m, the uniaxial moment capacity 252.3 kN·m exceeds the design moment, so the column is safe.

## Answer

#### Data and assumptions
- Column 350 mm (width $b$) × 500 mm (depth $D$); $P_u = 1800$ 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: $M_{ux}$ = 225 kN·m.
- Working loads are converted to ultimate: $P_u = 1.5 \times 1200 = 1800$ kN, $M_u = 1.5 \times 150 = 225$ kN·m. Short column with $L = 3$ m is assumed (not stated). Section size is selected by trial.
- 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 | 500 | 6.00 | short |
| y-y (about minor) | 3000 | 350 | 8.57 | 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: $e_x = 3000/500 + 500/30 = 22.7$ mm (min. 20 mm); adopt 22.7 mm; $M_{ux,min} = P_u e = 40.8$ kN·m
- About y-y: $e_y = 3000/500 + 350/30 = 17.7$ mm (min. 20 mm); adopt 20.0 mm; $M_{uy,min} = 36.0$ kN·m

#### Design moments
- Design moments: $M_{ux} = 225.0$ kN·m (not less than the minimum-eccentricity values).

#### Longitudinal reinforcement
$\dfrac{P_u}{f_{ck} b D} = \dfrac{1800000}{25 \times 350 \times 500} = 0.411$
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 |
|---|---|---|---|---|---|
| 10-20 φ | 1.80 | 0.116 | 215.6 | 225.0 | 1.044 not ok |
| 4-32 φ | 1.84 | 0.128 | 215.3 | 225.0 | 1.045 not ok |
| 12-20 φ | 2.15 | 0.116 | 252.3 | 225.0 | 0.892 ok |

#### Check
$M_{ux} = 225.0$ kN·m $\le M_{ux1} = 252.3$ kN·m. Minimum eccentricity about the minor axis: $P_u e_y = 36.0$ kN·m $\le M_{uy1} = 125.7$ kN·m. Both are satisfied; the section is **safe**.

Provide **12-20 mm** bars ($A_{sc} = 3770$ mm², $p = 2.15\%$), 6 on each 350 mm face, within 0.8% to 4%.

The two layers are $500 - 2 \times 58 = 384$ mm apart, which is more than the 300 mm maximum spacing along the periphery (IS 456 cl. 26.5.3.1), so also provide one 12 mm nominal bar at mid-depth of each 500 mm face (not counted in the design).

#### Lateral ties
- Diameter $\ge \max(\phi_{max}/4,\ 6) = \max(20/4, 6) = 6$ mm → provide 8 mm.
- Pitch $\le \min$(least lateral dimension, $16\phi_{min}$, 300 mm) $= \min(350, 320, 300) = 300$ mm → provide 8 mm ties @ 300 mm c/c.

#### Detailing
```text
CROSS-SECTION 350 x 500
    +-------------------------+
    |   o   o  o   o  o   o   |
    |                         |
    |                         |
    |                         |
    |                         |
    |   x                 x   |
    |                         |
    |                         |
    |                         |
    |                         |
    |   o   o  o   o  o   o   |
    +-------------------------+
   o = 20 mm bars, x = 12 mm nominal side bars, ties 8 mm @ 300 c/c
```

**Answer:** 350 × 500 mm column with 12-20 mm longitudinal bars ($p = 2.15\%$), 6 on each 350 mm face, plus one 12 mm nominal bar on each 500 mm face, 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. Working loads are 1200 kN and 150 kN-m. What design values are used?
   A. 1200 kN and 150 kN-m
   B. 1800 kN and 225 kN-m (factor 1.5)
   C. 1560 kN and 195 kN-m (factor 1.3)
   D. 2400 kN and 300 kN-m (factor 2)
   Answer: B. Limit state design uses a load factor of 1.5 on service loads. (Key point: Working to factored loads)

2. Because steel is on two sides only, the design is
   A. Biaxial with alpha_n
   B. Uniaxial about the major axis with a minimum-eccentricity check on the minor axis
   C. Done as a pure axial column
   D. Based on a slender column formula
   Answer: B. Only Mux is applied; the minor axis is checked only for Pu x emin <= Muy1. (Key point: Reinforced on two sides)

3. Why are 10-20 and 4-32 rejected?
   A. Their Mux1 (215.6 and 215.3) is less than the required 225 kN-m
   B. They exceed 4% steel
   C. Their ties are wrong
   D. They violate slenderness
   Answer: A. Capacity must be >= 225 kN-m; 12-20 gives 252.3 kN-m. (Key point: Trial selection)

4. Pu/(fck b D) = 1,800,000/(25 x 350 x 500) is used for
   A. Choosing the chart curve in SP-16 together with p/fck and d'/D
   B. Finding tie spacing
   C. Finding slenderness
   D. Finding bar length
   Answer: A. The SP-16 chart is entered with Pu/(fck b D), d'/D and p/fck to obtain Mu/(fck b D^2). (Key point: Non-dimensional ratio)

5. For 20 mm bars in a 350 mm column, the tie pitch is
   A. 300 mm, the least of 350, 320 and 300 is 300 mm
   B. 320 mm
   C. 350 mm
   D. 150 mm
   Answer: A. Pitch <= min(least lateral dimension 350, 16 x 20 = 320, 300) = 300 mm. (Key point: Ties)

## Related in Design of RCC Structure

- [Biaxial column 400x500, equal steel all sides](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Abiaxial-column-400x500-equal-steel-all) — Design of RCC Structure, chapter 10
- [Column design, 1350 kN, 3.4 m](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Acolumn-design-1350-kn-3-4) — Design of RCC Structure, chapter 10
- [Footing for 30x35 cm column, M25](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Afooting-for-30x35-cm-column-m25) — Design of RCC Structure, chapter 11
- [Footing 300x400 column, factored moment 120 kNm](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Afooting-300x400-column-factored-moment-120) — Design of RCC Structure, chapter 11
- [Short column 35x45 cm, 1800 kN](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Ashort-column-35x45-cm-1800-kn) — Design of RCC Structure, chapter 10
- [Footing, 1250 kN column load, depth 1.8 m](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Afooting-1250-kn-column-load-depth) — Design of RCC Structure, chapter 11

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