--- title: "Check 200x200 Debdar column, 30 kN + 1.5 kNm" subject: "Design of Steel and Timber Structure" chapter: 11 key: "semester_6/design_of_steel_and_timber_structure:timber-column-check-debdar-200x200" source: https://www.bctengineer.com/q/semester_6/design_of_steel_and_timber_structure/timber-column-check-debdar-200x200 site: BCT Engineering --- # Check 200x200 Debdar column, 30 kN + 1.5 kNm Design of Steel and Timber Structure · Chapter 11: Design of Compression Members - Asked in: 2075 Bhadra, 8 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-check-debdar-200x200 - Whole chapter: https://www.bctengineer.com/md/semester_6/design_of_steel_and_timber_structure/chapter-11 ## Question Check the safety of a square column 200×200 mm in cross section. The effective length of the column is 2.5 m, the axial load and bending moment in the column are 30 kN and 1.5 kN-m respectively. The material is Debdar wood and the column is located outside the building. ## Short answer Column is safe. Permissible axial stress 6.64 N/mm² (intermediate column), bending 8.70 N/mm²; combined stress ratio 0.24 < 1. ## Answer **Approach.** Combined axial compression and bending, IS 883:1994 cl. 7.7.1: the column is safe if $\dfrac{f_{ac}}{f_c} + \dfrac{f_{ab}}{f_b} \le 1$. #### Data and permissible stresses Section 200 × 200 mm, effective length $S = 2500$ mm, $N = 30$ kN, $M = 1.5$ kN·m. **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 | The column is located outside the building, so the **outside** values are taken; the grade is not stated, so Grade I (standard). #### Permissible axial stress $$ \begin{aligned} S/d &= 2500/200 = 12.5 \\ K_8 &= 0.584\sqrt{E/f_{cp}} = 0.584\sqrt{9480/6.9} = 21.65 \end{aligned} $$ $11 < S/d < K_8$, so it is an intermediate column: $$ f_c = f_{cp}\left[1 - \frac{1}{3}\left(\frac{S/d}{K_8}\right)^4\right] = 6.9\left[1 - \frac{1}{3}\left(\frac{12.5}{21.65}\right)^4\right] = 6.644\ \text{N/mm}^2 $$ #### Actual stresses $$ \begin{aligned} f_{ac} &= \frac{30\times10^3}{200\times200} = 0.750\ \text{N/mm}^2 \\ f_{ab} &= \frac{6M}{bd^2} = \frac{6\times1.5\times10^6}{200^3} = 1.125\ \text{N/mm}^2 \end{aligned} $$ #### Check $$ \frac{f_{ac}}{f_c} + \frac{f_{ab}}{f_b} = \frac{0.750}{6.644} + \frac{1.125}{8.7} = 0.113 + 0.129 = 0.242 $$ **Answer: the interaction value is 0.24 < 1, so the column is safe.** (Depth is 200 mm, so no form factor is applied to the bending stress.) ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why are the 'outside' stresses used? A. The column is located outside the building B. The column is short C. The timber is Group C D. The load is small Answer: A. The question states the column is outside the building, so outside Table 1 values are used. (Key point: Location values) 2. S/d = 12.5, K8 = 21.65. What class is it? A. Short, since S/d is small B. Intermediate, since 11 < S/d < K8 C. Long, since S/d > 11 D. Spaced Answer: B. S/d lies between 11 and K8, so the intermediate formula gives fc = 6.644 N/mm^2. (Key point: Classification) 3. What is the check and result? A. fac/fc + fab/fb = 0.24 < 1, safe B. fac/fc + fab/fb = 1.24 > 1, unsafe C. fac + fab = 1.875 < fc, safe but marginal D. Only fac/fc = 0.113 is checked Answer: A. 0.113 + 0.129 = 0.242, well below 1, so the column is safe. (Key point: Safety criterion) 4. Why is no form factor applied to the bending stress? A. It applies only to circular sections B. Depth is 200 mm, which does not exceed 300 mm C. Bending is neglected for small moments D. Form factor is applied only to Select grade Answer: B. The form factor is only needed for depths above 300 mm. 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