--- title: "Square deodar column 4 m, 250 kN, open shed" subject: "Design of Steel and Timber Structure" chapter: 11 key: "semester_6/design_of_steel_and_timber_structure:timber-column-deodar-4m-250kn" source: https://www.bctengineer.com/q/semester_6/design_of_steel_and_timber_structure/timber-column-deodar-4m-250kn site: BCT Engineering --- # Square deodar column 4 m, 250 kN, open shed Design of Steel and Timber Structure · Chapter 11: Design of Compression Members - Asked in: 2076 Baisakh, 6 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-deodar-4m-250kn - Whole chapter: https://www.bctengineer.com/md/semester_6/design_of_steel_and_timber_structure/chapter-11 ## Question Design a square Deoder wood column of length 4m to be used in an open shed, to carry an axial load of 250kN. ## Short answer Solid square Deodar column per IS 883:1994. Trial 225×225mm (A=50,625mm²). S/d=17.8, K8=21.65, intermediate column; fc=fcp[1-⅓(S/d/K8)⁴]=5.85 N/mm². Capacity P=fc·A=296 kN > 250 kN. Safe. Grade I, outside location, pin-ended, S/d<50 satisfied. ## Answer **Approach.** Working stress design to IS 883:1994 (cl. 7.6 for columns, cl. 7.7 for combined axial compression and bending). Ends are taken as pin-ended, so the effective length equals the unsupported length $S$ (cl. 7.6.1.5). #### Data and permissible stresses Length $S = 4.00$ m = 4000 mm. Axial load $N = 250$ kN. **Species:** Deodar (Cedrus deodara), Group C. **Location:** outside. **Grade:** Grade I (standard) (Table 1 values are for Grade I). Permissible stresses (IS 883:1994 Table 1, outside location): | Property | Table 1 value (N/mm²) | Used (N/mm²) | |---|---|---| | Bending / tension along grain $f_b$ | 8.7 | 8.70 | | Compression parallel to grain $f_{cp}$ | 6.9 | 6.90 | | Compression perpendicular to grain $f_{cn}$ | 2.1 | 2.10 | | Horizontal shear $H$ | 0.7 | 0.70 | | Modulus of elasticity $E$ | 9480 | 9480 | An open shed is an **outside** location. The grade is not stated, so Grade I (standard) is taken. #### Trial section Try **225 mm × 225 mm** (square). Area $A = 50,625$ mm²; least dimension $d = 225$ mm. #### Slenderness and permissible axial stress (cl. 7.6.1) $$ \begin{aligned} S/d &= \frac{4000}{225} = 17.8 \\ K_8 &= 0.584\sqrt{\frac{E}{f_{cp}}} = 0.584\sqrt{\frac{9480}{6.90}} = 21.65 \end{aligned} $$ $11 < S/d = 17.8 < K_8 = 21.6$, so it is an **intermediate column**: $$ f_c = f_{cp}\left[1 - \frac{1}{3}\left(\frac{S/d}{K_8}\right)^4\right] = 6.90\left[1 - \frac{1}{3}\left(\frac{17.8}{21.6}\right)^4\right] = 5.85\ \text{N/mm}^2 $$ $S/d = 17.8 < 50$ (cl. 7.6.1.4). OK. #### Check $$ P = f_cA = 5.85\times50,625/10^3 = 296.3\ \text{kN} \ge N = 250\ \text{kN} $$ Safe. #### Answer Provide a solid Deodar column of **225 mm × 225 mm** cross-section (Grade I (standard), outside location). Capacity $296$ kN $> 250$ kN. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why are the 'outside' Table 1 stresses used for the column in an open shed? A. Because the column is Group C timber B. Because an open shed is exposed to weather, so it is an outside location C. Because the grade is Select D. Because the length is over 3 m Answer: B. An open shed is not enclosed, so IS 883 outside-location stresses (lower than inside) apply. (Key point: Location and stress values) 2. S/d = 17.8 and K8 = 21.65. How is the column classified and which fc formula is used? A. Short; fc = fcp B. Intermediate (11 < S/d < K8); fc = fcp[1 - (1/3)(S/d / K8)^4] C. Long; fc = 0.329E/(S/d)^2 D. Intermediate; fc = 0.329E/(S/d)^2 Answer: B. S/d lies between 11 and K8, so the intermediate-column formula with the fourth power applies. (Key point: Column classification) 3. With 225 x 225 mm and fc = 5.85 N/mm^2, what is the conclusion? A. P = 296 kN > 250 kN, safe B. P = 296 kN > 250 kN, but S/d exceeds 50 so it fails C. P = 350 kN, over-designed and rejected D. P = 250 kN exactly Answer: A. P = fc x A = 5.85 x 50,625 = 296 kN, greater than 250 kN; S/d = 17.8 is also below the 50 limit. 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