---
title: "Built-up column, lacing, 8 m, 1100 kN"
subject: "Design of Steel and Timber Structure"
chapter: 6
key: "semester_6/design_of_steel_and_timber_structure:builtup-lacing-1100kn-8m-fe410"
source: https://www.bctengineer.com/q/semester_6/design_of_steel_and_timber_structure/builtup-lacing-1100kn-8m-fe410
site: BCT Engineering
---

# Built-up column, lacing, 8 m, 1100 kN

Design of Steel and Timber Structure · Chapter 6: Compression Members

- Asked in: 2079 Chaitra, 14 marks
- Video: [Design of double Laced column | Steel column connection details | 3d animation](https://www.youtube.com/watch?v=_omCPfxJGGM) — Comten Consulting Engineers
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/design_of_steel_and_timber_structure/builtup-lacing-1100kn-8m-fe410
- Whole chapter: https://www.bctengineer.com/md/semester_6/design_of_steel_and_timber_structure/chapter-6

## Question

Design a built-up column 8 m long to carry a factored axial compressive load of 1100 kN. The column is restrained in position but not in direction at both ends. Design the column with connecting system as lacing with bolted connections. Use two channel sections back to back. Use steel of grade Fe 410.

## Short answer

Use 2 ISMC 300 back to back (webs facing) with 190 mm clear gap. Provide single lacing of 60×10 mm flats at 45°, connected by M20 bolts, and end tie plates 360×280×6 mm.

## Answer

**Given/assumptions:** factored load $P_u=1100$ kN; length 8 m, restrained in position but not in direction at both ends → $K=1.0$, $KL=8$ m. Two channels back to back, single bolted lacing (M20, grade 4.6); Fe410 / E250 ($f_y=250$, $f_u=410$).

#### 1. Section: 2 ISMC 300 back to back (webs facing, flanges outward)
$A=2\times4564=9128$ mm², $I_{xx}=2\times6362.6\times10^4$ mm⁴, $r_{xx}=118.1$ mm, $C_{yy}=23.6$ mm, $b_f=90$ mm. Built-up members use **buckling class c** (IS 800:2007 Table 10, $\alpha=0.49$).
- $\lambda_{xx}=\dfrac{KL}{r_{xx}}=\dfrac{8000}{118.1}=67.8$
- Laced column: $\lambda_e=1.05\lambda=71.1$ (cl. 7.6.1.4)
- $f_{cd}=\dfrac{f_y/\gamma_{m0}}{\phi+\sqrt{\phi^2-\lambda_n^2}}$ with $\phi=0.5[1+0.49(\lambda_n-0.2)+\lambda_n^2]$, $\lambda_n=\sqrt{f_y/f_{cc}}$, $f_{cc}=\pi^2E/\lambda_e^2$ → $f_{cd}=150.4$ N/mm²
- $P_d=A f_{cd}=1373$ kN $\ge P_u=1100$ kN ✓

#### 2. Clear gap for equal stiffness
The centroid of each section is at $x_c=23.6+s/2$ from the column axis. For $I_{yy}\ge I_{xx}$:
$$
x_c\ge\sqrt{\frac{I_{xx}-I_{yy,ch}}{A_{ch}}}=115.2\ \text{mm}\ \Rightarrow\ s\ge183\ \text{mm}
$$
Provide **$s=190$ mm**. Then $I_{yy}=2[I_{yy,ch}+A_{ch}x_c^2]=13461\times10^4$ mm⁴, $r_{yy}=121.4$ mm, $\lambda_{yy}=65.9$, $1.05\lambda_{yy}=69.2$, $P_{dy}=1402$ kN $\ge P_u$ ✓.

#### 3. Design of lacing (single lacing, two planes)
```text
   |\     /|
   | \   / |    theta = 45 deg to the axis
   |  \ /  |    S = distance between connection lines
   |  / \  |
   | /   \ |
```
- Distance between connection lines $S=s+b_f=190+90=280$ mm
- Transverse shear $V=2.5\%\,P_u=27.5$ kN; per lacing plane $V_p=13.75$ kN
- Force in lacing bar $F=\dfrac{V_p}{\sin\theta}=19.45$ kN
- Length of bar $l=\dfrac{S}{\sin\theta}=396$ mm; effective length $=l$ (between the inner end bolts)
- $t\ge l/40=10$ mm; width $\ge3d=60$ mm → **flat 60 × 10 mm**
- $\lambda=\dfrac{l}{t/\sqrt{12}}=137<145$ ✓ (cl. 7.6.3); $f_{cd}=68$ N/mm², $P_c=41.0$ kN $>F$ ✓
- Tension: $T_{dn}=\dfrac{0.9(w-d_0)tf_u}{\gamma_{m1}}=112.2$ kN $>F$ ✓
- Connection: M20 (4.6) $V_{dsb}=45.3$ kN, bearing on 10 mm $=99.4$ kN → **1 bolt at each end**
- Lacing angle $\theta=45°$ lies between 40° and 70° ✓
- Spacing of lacing points on one section $=\dfrac{2S}{\tan\theta}=560$ mm; slenderness of the section between them $=\dfrac{560}{26.1}=21.5\le\min(50,\ 0.7\lambda_{max})$ ✓ (cl. 7.6.3)

#### 4. Tie plates
Tie (end) plates at both ends of the lacing system: length $\ge S+$ edges $=360$ mm, depth $\ge S=280$ mm, thickness $\ge S/50=6$ mm → **360 × 280 × 6 mm** at each end, connected to each section by 2 bolts.

**Answer: 2 ISMC 300 back to back (webs facing, flanges outward), clear gap 190 mm, single lacing of 60 × 10 mm flats at 45°, tie plates 360 × 280 × 6 mm at the ends.**

## Check yourself

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

1. For 2 ISMC 300 back to back with lacing, lambda_xx = 67.8. What slenderness is used for f_cd?
   A. 67.8
   B. 1.05 x 67.8 = 71.1
   C. 1.1 x 67.8 = 74.6
   D. 0.7 x 67.8 = 47.5
   Answer: B. Laced columns use 1.05 times slenderness (cl. 7.6.1.4): 71.1. (Key point: Back-to-back arrangement and effective slenderness)

2. Why was a clear gap of 190 mm provided between the channel webs?
   A. To fit the lacing bolts
   B. To make I_yy at least I_xx (s >= 183 mm)
   C. To reduce the weight
   D. Because the gusset needs 190 mm
   Answer: B. The gap is found from x_c >= 115.2 mm so that I_yy >= I_xx; s >= 183 mm gives 190 mm. (Key point: Clear gap)

3. The lacing bar is 396 mm long and 10 mm thick. What does the slenderness check show?
   A. lambda = 137 < 145, acceptable
   B. lambda = 137 > 120, unacceptable
   C. lambda = 20, very stocky
   D. lambda = 200, acceptable
   Answer: A. lambda = l/(t/sqrt12) = 137, below the 145 limit for lacing in IS 800 cl. 7.6.3. Thickness is at least l/40 for single lacing. (Key point: Lacing bar design)

4. With P_u = 1100 kN and two lacing planes at 45 degrees, what force acts in a bar?
   A. 19.45 kN
   B. 27.5 kN
   C. 13.75 kN
   D. 38.9 kN
   Answer: A. V = 2.5% x 1100 = 27.5 kN, V_p = 13.75 kN, and F = 13.75/sin 45 = 19.45 kN. (Key point: Lacing force)

## Close variants set in other exams

- [Built-up laced column, 10 m, 1000 kN](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Abuiltup-1000kn-10m-lacing) — Design of Steel and Timber Structure, chapter 6, asked 4×
- [Built-up column with battens, 10 m, 1080 kN](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Abuiltup-battens-1080kn-10m) — Design of Steel and Timber Structure, chapter 6, asked 4×

## Related in Design of Steel and Timber Structure

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- [Braced built-up column, 3 m, 1600 kN](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Abraced-builtup-1600kn-3m) — Design of Steel and Timber Structure, chapter 6, asked 2×
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