---
title: "Square column with 80 mm eccentricity"
subject: "Design of RCC Structure"
chapter: 10
key: "semester_7/design_of_rcc_structure:square-column-with-80-mm-eccentricity"
source: https://www.bctengineer.com/q/semester_7/design_of_rcc_structure/square-column-with-80-mm-eccentricity
site: BCT Engineering
---

# Square column with 80 mm eccentricity

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

- Asked in: 2067 Asar (old course), 8 marks
- Video: [Design of a Square Column subjected to combined axial loading and biaxial bending](https://www.youtube.com/watch?v=ZTv--3b0gVs) — 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/square-column-with-80-mm-eccentricity
- Whole chapter: https://www.bctengineer.com/md/semester_7/design_of_rcc_structure/chapter-10

## Question

Design a square shaped reinforced concrete column that has to carry ultimate factored load of 800 kN inclusive of live load, at an eccentricity of 80 mm in both X and Y directions. Use concrete grade M20 and steel grade Fe415.

## Short answer

For 350x350 mm column, Pu=800 kN with 80 mm eccentricity in both directions, provide 8-20 mm bars (Asc=2513 mm2, p=2.05%) and 8 mm ties at 300 mm c/c; interaction ratio is 0.998.

## Answer

#### Data and assumptions
- Column 350 mm (width $b$) × 350 mm (depth $D$); $P_u = 800$ kN; $f_{ck} = 20$ MPa, $f_y = 415$ MPa. Clear cover 40 mm (IS 456 cl. 26.4.2.1), 8 mm ties.
- Moments: about major axis (x-x) $M_{ux}$ = 64 kN·m; about minor axis (y-y) $M_{uy}$ = 64 kN·m.
- Moments from eccentricity: $M_{ux} = M_{uy} = P_u e = 800 \times 0.08 = 64$ kN·m.
- Short column assumed; unsupported length 3 m assumed for the minimum-eccentricity check.
- 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 | 350 | 8.57 | 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: $e_x = 3000/500 + 350/30 = 17.7$ mm (min. 20 mm); adopt 20.0 mm; $M_{ux,min} = P_u e = 16.0$ kN·m
- About y-y: $e_y = 3000/500 + 350/30 = 17.7$ mm (min. 20 mm); adopt 20.0 mm; $M_{uy,min} = 16.0$ kN·m

#### Design moments
- Design moments: $M_{ux} = 64.0$ kN·m, $M_{uy} = 64.0$ kN·m (not less than the minimum-eccentricity values).

#### Longitudinal reinforcement
$\dfrac{P_u}{f_{ck} b D} = \dfrac{800000}{20 \times 350 \times 350} = 0.327$
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 | $p$ (%) | $d'/D$ | $M_{ux1}$ | $M_{uy1}$ | $P_u/P_{uz}$ | $\alpha_n$ | $(M_{ux}/M_{ux1})^{\alpha_n}+(M_{uy}/M_{uy1})^{\alpha_n}$ |
|---|---|---|---|---|---|---|---|
| 10-16 φ | 1.64 | 0.160 | 88.3 | 95.1 | 0.468 | 1.45 | 1.192 ✗ |
| 12-16 φ | 1.97 | 0.160 | 102.7 | 102.7 | 0.437 | 1.39 | 1.035 ✗ |
| 8-20 φ | 2.05 | 0.166 | 105.8 | 105.8 | 0.430 | 1.38 | 0.998 ✓ |

#### Check
$P_{uz} = 0.45 f_{ck} A_c + 0.75 f_y A_{sc} = 0.45 \times 20 \times 119987 + 0.75 \times 415 \times 2513 = 1862$ kN
$\dfrac{P_u}{P_{uz}} = \dfrac{800}{1862} = 0.430$, so $\alpha_n = 1.38$ (IS 456 cl. 39.6; linear between 1.0 at 0.2 and 2.0 at 0.8).
$$
\left(\frac{M_{ux}}{M_{ux1}}\right)^{\alpha_n} + \left(\frac{M_{uy}}{M_{uy1}}\right)^{\alpha_n} = \left(\frac{64.0}{105.8}\right)^{1.38} + \left(\frac{64.0}{105.8}\right)^{1.38} = 0.998 \le 1.0
$$
The interaction condition is satisfied; the section is **safe**.

Provide **8-20 mm** bars ($A_{sc} = 2513$ mm², $p = 2.05\%$), within 0.8% to 4%.

#### 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 350
    +-------------------------+
    |                         |
    |   o        o        o   |
    |                         |
    |                         |
    |                         |
    |   o                 o   |
    |                         |
    |                         |
    |                         |
    |   o        o        o   |
    |                         |
    +-------------------------+
   o = 20 mm bars, ties 8 mm @ 300 c/c
```

**Answer:** 350 × 350 mm column with 8-20 mm longitudinal bars ($p = 2.05\%$) 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. Why were the 10-16φ and 12-16φ trials rejected?
   A. Their steel percentage exceeded 4%
   B. The interaction sum was greater than 1
   C. Their bars were thinner than 12 mm
   D. Pu/Puz was below 0.2
   Answer: B. Their interaction values were 1.192 and 1.035, both above 1.0, so the section was unsafe. (Key point: Trial and error on steel)

2. What is Pu/(fck b D) used for in the design with SP-16 charts?
   A. It gives the steel percentage directly
   B. It is the non-dimensional axial load used to read the uniaxial moment capacity from the chart
   C. It is the slenderness ratio
   D. It is the required tie spacing
   Answer: B. Pu/(fck b D) = 0.327 is the chart axis from which Mux1 and Muy1 at that axial load are found. (Key point: Axial load ratio)

3. Which expression gives the axial capacity Puz of the section used for αn?
   A. 0.45 fck Ac + 0.75 fy Asc
   B. 0.67 fck Ag + fy Asc
   C. 0.45 fck Ag + 0.75 fy Ag
   D. 0.87 fy Asc only
   Answer: A. Puz = 0.45 fck Ac + 0.75 fy Asc, with Ac the concrete area excluding steel. (Key point: Puz formula)

4. For 350 mm square column with 20 mm bars, what limits the tie pitch to 300 mm?
   A. Least lateral dimension 350 mm
   B. 16 x smallest bar diameter = 320 mm
   C. The 300 mm upper limit
   D. 12 x bar diameter
   Answer: C. Pitch is the least of 350, 16 x 20 = 320 and 300 mm, so the 300 mm limit governs. (Key point: Tie pitch)

## Related in Design of RCC Structure

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