--- title: "Box column of teak planks, 400 kN" subject: "Design of Steel and Timber Structure" chapter: 11 key: "semester_6/design_of_steel_and_timber_structure:timber-column-teak-box" source: https://www.bctengineer.com/q/semester_6/design_of_steel_and_timber_structure/timber-column-teak-box site: BCT Engineering --- # Box column of teak planks, 400 kN Design of Steel and Timber Structure · Chapter 11: Design of Compression Members - Asked in: 2081 Chaitra, 10 marks - 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/timber-column-teak-box - Whole chapter: https://www.bctengineer.com/md/semester_6/design_of_steel_and_timber_structure/chapter-11 ## Question Design a built-up box column to carry axial load of 400 kN having length 4.5 m. Use 50 mm thick Teak planks. ## Short answer Built-up box column of 50mm thick Teak planks per IS 883:1994 cl. 7.6.2. Trial 300×300mm overall, 200×200mm inside (A=50,000mm²). S/√(d1²+d2²)=12.48, K9=17.72, intermediate column; fc=q·fcp[1-⅓(S/K9√(d1²+d2²))⁴]=8.63 N/mm². Capacity P=fc·A=431 kN > 400 kN. Safe. Inside location, Grade I, staggered fasteners ≤200mm pitch, solid end blocks. ## Answer **Approach.** Box (built-up) column designed to IS 883:1994 cl. 7.6.2: the planks are nailed or bolted to form a hollow square section; the strength depends on $S/\sqrt{d_1^2 + d_2^2}$, where $d_1$ is the overall side and $d_2$ the inside side of the box. #### Data and permissible stresses Length $S = 4.50$ m, axial load $N = 400$ kN, plank thickness $t = 50$ mm. Pin ends, effective length $= S$. **Species:** Teak (Tectona grandis), Group B. **Location:** inside. **Grade:** Grade I (standard) (Table 1 values are for Grade I). Permissible stresses (IS 883:1994 Table 1, inside location): | Property | Table 1 value (N/mm²) | Used (N/mm²) | |---|---|---| | Bending / tension along grain $f_b$ | 15.5 | 15.50 | | Compression parallel to grain $f_{cp}$ | 9.4 | 9.40 | | Compression perpendicular to grain $f_{cn}$ | 4.5 | 4.50 | | Horizontal shear $H$ | 1.15 | 1.15 | | Modulus of elasticity $E$ | 9970 | 9970 | Location is not stated, so **inside** and Grade I are assumed. For plank thickness 50 mm (cl. 7.6.2.5): $U = 0.6$, $q = 1.0$ (values given for 25 mm and 50 mm planks). #### Trial section Square box, overall side $d_1 = 300$ mm, inside side $d_2 = 300 - 2\times50 = 200$ mm. $$ A = d_1^2 - d_2^2 = 300^2 - 200^2 = 50,000\ \text{mm}^2 $$ $$ \begin{aligned} \frac{S}{\sqrt{d_1^2 + d_2^2}} &= \frac{4500}{\sqrt{300^2 + 200^2}} = \frac{4500}{360.6} = 12.48 \\ K_9 &= \frac{\pi}{2}\sqrt{\frac{UE}{5qf_{cp}}} = \frac{\pi}{2}\sqrt{\frac{0.6\times9970}{5\times1.0\times9.40}} = 17.72 \end{aligned} $$ $8 < 12.48 < K_9 = 17.72$, so it is an **intermediate column**: $$ f_c = q f_{cp}\left[1 - \frac{1}{3}\left(\frac{S}{K_9\sqrt{d_1^2 + d_2^2}}\right)^4\right] = 1.0\times9.40\left[1 - \frac{1}{3}\left(\frac{12.48}{17.72}\right)^4\right] = 8.63\ \text{N/mm}^2 $$ #### Check $$ P = f_cA = 8.63\times50,000/10^3 = 431\ \text{kN} > N = 400\ \text{kN} $$ Safe. #### Arrangement ```text +------------------------------+ | plank 50 mm thick | | +----------------------+ | | | hollow | | outside 300 x 300 mm | | 200 x 200 | | | +----------------------+ | +------------------------------+ ``` The 50 mm thick planks are fixed with staggered nails or bolts at a pitch not exceeding about 150 mm to 200 mm so that they act as one unit; the ends are fitted with solid end blocks. #### Answer Provide a box column of overall size **300 mm × 300 mm** formed with 50 mm thick Teak planks (inside 200 mm). Capacity 431 kN $>$ 400 kN. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What values of U and q are used for 50 mm thick planks in the box column? A. U = 0.8, q = 1.0 B. U = 0.6, q = 1.0 C. U = 0.6, q = 0.8 D. U = 1.0, q = 0.6 Answer: B. IS 883 cl. 7.6.2.5 gives U = 0.6 and q = 1.0 for 50 mm planks (U = 0.8 for 25 mm). (Key point: Plank constants) 2. For a 300 mm overall box with 50 mm planks, what are d2 and A? A. d2 = 250 mm, A = 27,500 mm^2 B. d2 = 200 mm, A = 50,000 mm^2 C. d2 = 200 mm, A = 90,000 mm^2 D. d2 = 150 mm, A = 67,500 mm^2 Answer: B. d2 = 300 - 2x50 = 200 mm, and A = 300^2 - 200^2 = 50,000 mm^2. (Key point: Inside dimension) 3. S/sqrt(d1^2 + d2^2) = 12.48 with K9 = 17.72. What class is the column? A. Short, since it is above 8 B. Long, since it is above 8 C. Intermediate, since 8 < 12.48 < K9 D. Cannot be classified without U Answer: C. Between 8 and K9 the column is intermediate, so fc = q fcp[1 - (1/3)(ratio/K9)^4]. (Key point: Classification) 4. What is the final result for the teak box column? A. P = 431 kN > 400 kN, safe B. P = 431 kN > 400 kN but fails detailing C. P = 350 kN < 400 kN, unsafe D. P = 500 kN, so a smaller box must be chosen Answer: A. fc = 8.63 N/mm^2 and P = 8.63 x 50,000 = 431 kN, which exceeds 400 kN. 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