---
title: "Design of a square timber column"
subject: "Design of Timber and Masonry Structures"
chapter: 3
key: "semester_5/design_of_timber_and_masonry_structures:design-axially-loaded-timber-column"
source: https://www.bctengineer.com/q/semester_5/design_of_timber_and_masonry_structures/design-axially-loaded-timber-column
site: BCT Engineering
---

# Design of a square timber column

Design of Timber and Masonry Structures · Chapter 3: Structural Elements of Timber Structures

- Asked in: year not given, 8 marks
- Video: [Design of Timber Column](https://www.youtube.com/watch?v=W6Sy4_gAtyE) — Humaira lone
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/design_of_timber_and_masonry_structures/design-axially-loaded-timber-column
- Whole chapter: https://www.bctengineer.com/md/semester_5/design_of_timber_and_masonry_structures/chapter-3

## Question

Design a square timber column to carry an axial load of 150 kN. The column is 3.6 m long and is hinged at both ends. Take $\sigma_{cc} = 8.0$ N/mm² and $E = 10500$ N/mm². Use the IS 883 expressions for permissible stress with the column slenderness and select a section in multiples of 5 mm.

## Short answer

Assume a square section and iterate. Effective length 3600 mm, K8=25.43, intermediate slenderness. Trial 160 mm: le/d=22.5, permissible stress 6.37 N/mm², actual 5.86 N/mm², safe. Provide 160 mm × 160 mm timber column.

## Answer

#### Method
The permissible stress depends on slenderness, which depends on the section, so we try sections and compare the capacity with 150 kN.

Effective length $l_e = L = 3600$ mm (hinged both ends). For a square section $d \times d$, $l_e/d = 3600/d$.

$$
K_8 = 0.702\sqrt{\frac{E}{\sigma_{cc}}} = 0.702\sqrt{\frac{10500}{8}} = 0.702 \times 36.23 = 25.43
$$

For $11 < l_e/d < K_8$ (intermediate):
$$
\sigma_c' = 8\left[1 - \frac{1}{3}\left(\frac{l_e/d}{25.43}\right)^4\right]
$$

#### Trial sections
| Section $d$ (mm) | $l_e/d$ | Type | $\sigma_c'$ (N/mm²) | $P = \sigma_c' d^2$ (kN) | Result |
|---|---|---|---|---|---|
| 150 | 24.0 | Intermediate | 5.89 | 132.4 | Not safe |
| 160 | 22.5 | Intermediate | 6.37 | 163.0 | Safe |
| 175 | 20.6 | Intermediate | 6.86 | 210.0 | Safe, uneconomical |

#### Check of 160 mm × 160 mm
$$
\begin{aligned}
\frac{l_e}{d} &= \frac{3600}{160} = 22.5 < 25.43 \\
\sigma_c' &= 8\left[1 - \frac{1}{3}(0.8848)^4\right] = 8\,[1 - 0.2043] = 6.37\ \text{N/mm}^2 \\
\sigma_{c,\text{actual}} &= \frac{150\,000}{160 \times 160} = 5.86\ \text{N/mm}^2 < 6.37\ \text{N/mm}^2
\end{aligned}
$$

The column is safe. Its self-weight (about $0.16^2 \times 3.6 \times 7 \approx 0.6$ kN) is less than 0.5 percent of the load and raises the stress only to about 5.88 N/mm², which is still below 6.37 N/mm².

**Answer: Provide a 160 mm × 160 mm timber column (capacity 163 kN > 150 kN, $l_e/d = 22.5$).**

## Check yourself

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

1. Why is the column section chosen by trial?
   A. The code gives no stress values
   B. The permissible stress depends on slenderness, which depends on the section
   C. The load is unknown
   D. Square sections cannot be designed directly
   Answer: B. l_e/d depends on d, and the permissible stress depends on l_e/d, so sections are tried and the capacity is compared with 150 kN. (Key point: Trial-and-check method)

2. For sigma_cc = 8 N/mm^2 and E = 10500 N/mm^2, K8 is about:
   A. 36.2
   B. 22.5
   C. 25.4
   D. 11.0
   Answer: C. K8 = 0.702 x sqrt(10500/8) = 0.702 x 36.23 = 25.43. (Key point: K8 value)

3. Why is the 150 mm x 150 mm section not adequate?
   A. It is a long column
   B. l_e/d = 3600/150 = 24 gives only about 132 kN, less than 150 kN
   C. Its capacity is 163 kN but it is uneconomical
   D. It exceeds the slenderness limit
   Answer: B. At l_e/d = 24 (intermediate), sigma_c' is 5.89 N/mm^2 and P = 132.4 kN < 150 kN. (Key point: Rejecting 150 mm section)

4. Why is 160 mm x 160 mm chosen rather than 175 mm?
   A. 160 mm is safe (163 kN > 150 kN; 5.86 < 6.37 N/mm^2) and 175 mm is uneconomical
   B. 175 mm is not safe
   C. 160 mm is a long column
   D. 160 mm is the only size in multiples of 5 mm
   Answer: A. At l_e/d = 22.5 the permissible stress is 6.37 N/mm^2, above the actual 5.86 N/mm^2; 175 mm is safe but uses more timber. (Key point: Final section)

## Related in Design of Timber and Masonry Structures

- [Safe axial load on a timber column](https://www.bctengineer.com/question.md?key=semester_5%2Fdesign_of_timber_and_masonry_structures%3Aaxial-capacity-timber-column) — Design of Timber and Masonry Structures, chapter 3
- [Timber column under axial load and bending](https://www.bctengineer.com/question.md?key=semester_5%2Fdesign_of_timber_and_masonry_structures%3Atimber-column-combined-bending-axial) — Design of Timber and Masonry Structures, chapter 3
- [Masonry pier under axial load and in-plane moment](https://www.bctengineer.com/question.md?key=semester_5%2Fdesign_of_timber_and_masonry_structures%3Amasonry-pier-axial-moment-check) — Design of Timber and Masonry Structures, chapter 7
- [Design of a simply supported timber beam](https://www.bctengineer.com/question.md?key=semester_5%2Fdesign_of_timber_and_masonry_structures%3Adesign-timber-floor-beam) — Design of Timber and Masonry Structures, chapter 3
- [Permissible compressive stress of masonry as per IS 1905](https://www.bctengineer.com/question.md?key=semester_5%2Fdesign_of_timber_and_masonry_structures%3Amasonry-permissible-stress-factors-code) — Design of Timber and Masonry Structures, chapter 5
- [Design of a nailed timber lap joint](https://www.bctengineer.com/question.md?key=semester_5%2Fdesign_of_timber_and_masonry_structures%3Anailed-lap-joint-design) — Design of Timber and Masonry Structures, chapter 2

## Related in other subjects

- [Brick column design for 80 kN axial load](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Abrick-column-80kn-roof) — Concrete Technology and Masonry Structure, chapter 8
- [Square deodar column 4 m, 350 kN, outside](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Atimber-column-deodar-square-4m-350kn) — Design of Steel and Timber Structure, chapter 11
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