--- title: "Built-up laced column, 10 m, 1000 kN" subject: "Design of Steel and Timber Structure" chapter: 6 key: "semester_6/design_of_steel_and_timber_structure:builtup-1000kn-10m-lacing" source: https://www.bctengineer.com/q/semester_6/design_of_steel_and_timber_structure/builtup-1000kn-10m-lacing site: BCT Engineering --- # Built-up laced column, 10 m, 1000 kN Design of Steel and Timber Structure · Chapter 6: Compression Members - Asked in: 2075 Bhadra, 14 marks; 2072 Magh, 12 marks (asked 2 times) - Video: [lacing system| built up section design of compression member| design of laced column](https://www.youtube.com/watch?v=m2bngwyy0A0) — Engineering Studio - 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-1000kn-10m-lacing - Whole chapter: https://www.bctengineer.com/md/semester_6/design_of_steel_and_timber_structure/chapter-6 ## Question Design a built up column 10 m long to carry a factored axial compressive load of 1000 kN. The column is restrained in position but not in direction at both ends. Design the column with connecting system as lacing (single lacing) with bolted (or welded) connection. Use two channel back to back. Assume steel of grade Fe 410, E250 C and bolts grade 4.6. ## Short answer Two ISMC 300 channels back to back with190 mm clear gap. Single lacing:60×10 mm flats at45°, each bolted with one M20 bolt. End tie plates360×280×6 mm with two M20 bolts. ## Answer **Given:** factored axial load $P=1000$ kN, length 10 m, held in position but not restrained in direction at both ends → $K=1.0$, $KL=10$ m. Two channels back to back with single bolted lacing; E250 ($f_y=250$, $f_u=410$); bolts M20 grade 4.6. Built-up members belong to **buckling class c** (IS 800:2007 Table 10, $\alpha=0.49$). #### 1. Trial section: 2 ISMC 300 $A=2\times4564=9128$ mm², $I_{xx}=2\times6362.6\times10^4$ mm⁴, $r_{xx}=118.1$ mm, $C_{yy}=23.6$ mm, $b_f=90$ mm. - $\lambda_{xx}=\dfrac{KL}{r_{xx}}=\dfrac{10000}{118.1}=84.7$ - Effective slenderness of laced column $=1.05\lambda=88.9$ (cl. 7.6.1.4) - $f_{cc}=\dfrac{\pi^2E}{\lambda^2}$, $\lambda_n=\sqrt{f_y/f_{cc}}$, $\phi=0.5[1+0.49(\lambda_n-0.2)+\lambda_n^2]$, $f_{cd}=\dfrac{f_y/\gamma_{m0}}{\phi+\sqrt{\phi^2-\lambda_n^2}}=122.6$ N/mm² - $P_d=A f_{cd}=9128\times122.6\times10^{-3}=1119$ kN $>1000$ ✓ #### 2. Spacing of channels (so that $I_{yy}\ge I_{xx}$) $$ \left(C_{yy}+\frac{s}{2}\right)^2\ge\frac{I_{xx}-I_{yy}}{A_{ch}}\Rightarrow C_{yy}+\frac{s}{2}\ge115.2\Rightarrow s\ge183\ \text{mm} $$ Provide a clear gap $s=190$ mm between the webs. Then $I_{yy}=2[I_{yy,ch}+A_{ch}(C_{yy}+s/2)^2]=13461\times10^4$ mm⁴, $r_{yy}=121.4$ mm, $\lambda_{yy}=82.3\ (<\lambda_{xx})$, $1.05\lambda_{yy}=86.5$, $P_{dy}=1153$ kN ✓. #### 3. Lacing (single, bolted) ```text |\ /| | \ / | theta = 45 deg to axis | \ / | S = distance between bolt lines | / \ | | / \ | ``` - Distance between bolt lines (at the middle of the flanges) $S=s+b_f=190+90=280$ mm - Transverse shear $V=2.5\%P=25.0$ kN; two lacing planes: $V_p=12.50$ kN per plane - Lacing at $\theta=45°$ (limits 40°-70°): force $F=\dfrac{V_p}{\sin\theta}=17.68$ kN - Length of bar between end bolts $l=\dfrac{S}{\sin\theta}=396$ mm - Thickness $t\ge\dfrac{l}{40}=10$ mm (single lacing); width $\ge3d=60$ mm → **flat 60 × 10 mm** - Slenderness $\lambda=\dfrac{l}{t/\sqrt{12}}=137<145$ ✓; $f_{cd}=68$ N/mm² → compressive strength $=41.0$ kN $>F$ ✓; tension $T_{dn}=\dfrac{0.9(60-22)t f_u}{1.25}=112.2$ kN $>F$ ✓ - Bolt connection: $V_{dsb}=45.3$ kN (single shear), bearing on 10 mm $=99.4$ kN → **1 M20 bolt at each end** - Spacing of lacing points on one channel $=\dfrac{2S}{\tan\theta}=560$ mm; slenderness of the channel between them $=\dfrac{560}{26.1}=21.5\le\min(50,\,0.7\times89)$ ✓ (cl. 7.6.3). #### 4. Tie plates The lacing ends at tie (batten) plates at each end: length $\ge S$ + edges $=360$ mm, depth $\ge S=280$ mm for a plate at the end, thickness $\ge S/50=6$ mm: **tie plate 360 × 280 × 6 mm**, connected by 2 M20 bolts to each channel. **Answer: 2 ISMC 300 back to back, clear gap 190 mm, single lacing of 60 × 10 mm flats at 45° with M20 bolts, tie plates at the ends.** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which buckling class and imperfection factor are used for built-up members? A. Class c, alpha = 0.49 B. Class a, alpha = 0.21 C. Class b, alpha = 0.34 D. Class d, alpha = 0.76 Answer: A. IS 800 Table 10 assigns built-up members to class c. (Key point: Buckling class) 2. For a laced column, the effective slenderness used is A. 1.05 x lambda B. lambda / 1.05 C. lambda D. 2 x lambda Answer: A. Cl. 7.6.1.4: laced columns use 1.05 times the slenderness to allow for shear deformation. (Key point: Effective slenderness) 3. The spacing s is chosen so that A. Iyy = 0.5 Ixx B. s = flange width C. Iyy >= Ixx D. Ixx = 0 Answer: C. Iyy at least equal to Ixx makes the column equally strong about both axes. (Key point: Channel spacing) 4. How is the lacing force found? A. Axial load divided by number of bars B. P x sin theta C. 5% P D. Transverse shear 2.5% P, shared by lacing planes, divided by sin theta Answer: D. V = 2.5% P = 25 kN; Vp = 12.5 kN per plane; F = Vp/sin 45 = 17.68 kN. (Key point: Lacing force) ## Close variants set in other exams - [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× - [Built-up column, lacing, 8 m, 1100 kN](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Abuiltup-lacing-1100kn-8m-fe410) — Design of Steel and Timber Structure, chapter 6, asked 4× ## Related in Design of Steel and Timber Structure - [Built-up laced column 7.5 m, 1250 kN](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Abuiltup-laced-1250kn-7-5m) — Design of Steel and Timber Structure, chapter 6 - [Built-up column, single lacing, 8 m, 1100 kN](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Abuiltup-lacing-1100kn-8m-e250) — Design of Steel and Timber Structure, chapter 6 - [Built-up column with battens, 4 m, 1000 kN](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Abuiltup-battens-1000kn-4m) — Design of Steel and Timber Structure, chapter 6, asked 2× - [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× - [Built-up column, single lacing, 900 kN, 5 m](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Abuiltup-single-lacing-900kn-5m) — Design of Steel and Timber Structure, chapter 6 - [Laced two-channel column, 800 kN, 6 m](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Acolumn-two-channels-800kn-laced) — Design of Steel and Timber Structure, chapter 6 ## Related in other subjects - [Column 35x40 cm, not restrained against rotation](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Acolumn-35x40-cm-not-restrained-against) — Design of RCC Structure, chapter 10 - [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 - [Fixed-end column 4 m, 1000 kN](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Afixed-end-column-4-m-1000) — Design of RCC Structure, chapter 10 - [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