--- title: "Column 500 x 900: stress intensities, critical corner" subject: "Concrete Technology and Masonry Structure" chapter: 8 key: "semester_5/concrete_technology_and_masonry_structure:column-stress-500x900-critical" source: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/column-stress-500x900-critical site: BCT Engineering --- # Column 500 x 900: stress intensities, critical corner Concrete Technology and Masonry Structure · Chapter 8: Design of masonry walls for gravity loads - Asked in: 2081 Baisakh, 8 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/column-stress-500x900-critical - Whole chapter: https://www.bctengineer.com/md/semester_5/concrete_technology_and_masonry_structure/chapter-8 ## Question A column section 500 mm $\times$ 900 mm carries a load of 300 kN acting at 170 mm from the 900 mm face and 360 mm from the 500 mm face. Determine the stress intensities. Which one is critical? ## Short answer Eccentricities80 mm,90 mm; corner stresses: A =1.707, B =0.907, C =0.427, D =−0.373 N/mm². Corner A has the highest compression (1.707 N/mm²), corner D is in tension (−0.373 N/mm²). Both are critical because masonry cannot resist tension and compression must not exceed permissible stress. ## Answer Distances are measured from the faces. The 170 mm distance is across the 500 mm side (from the 900 mm face) and the 360 mm distance is along the 900 mm side (from the 500 mm face). Hence $e_1 = 250-170 = 80$ mm and $e_2 = 450-360 = 90$ mm. #### Data Section 500 mm $\times$ 900 mm, $P=300$ kN. The load acts 170 mm from the 900 mm face and 360 mm from the 500 mm face. #### Eccentricities $$ \begin{aligned} e_{1} &= 80\ \text{mm (across the 500 mm side)}\\ e_{2} &= 90\ \text{mm (along the 900 mm side)} \end{aligned} $$ #### Section properties $$ \begin{aligned} A &= 500\times900 = 450000\ \text{mm}^2\\ Z_1 &= \frac{900\times500^2}{6} = 37500000\ \text{mm}^3\\ Z_2 &= \frac{500\times900^2}{6} = 67500000\ \text{mm}^3 \end{aligned} $$ #### Stresses $$ \begin{aligned} \sigma_0 &= \frac{P}{A} = \frac{300\times10^3}{450000} = 0.6667\ \text{N/mm}^2\\ \sigma_{b1} &= \frac{Pe_1}{Z_1} = \frac{300\times10^3\times80}{37500000} = 0.6400\ \text{N/mm}^2\\ \sigma_{b2} &= \frac{Pe_2}{Z_2} = \frac{300\times10^3\times90}{67500000} = 0.4000\ \text{N/mm}^2 \end{aligned} $$ Corner stresses $\sigma=\sigma_0\pm\sigma_{b1}\pm\sigma_{b2}$ (positive = compression, N/mm²): | Corner | Position | Working | Stress | |---|---|---|---| | A | near the 900 face and near the 500 face | $0.6667 + 0.6400 + 0.4000$ | **1.7067** | | B | near the 900 face, far from the 500 face | $0.6667 + 0.6400 - 0.4000$ | **0.9067** | | C | far from the 900 face, near the 500 face | $0.6667 - 0.6400 + 0.4000$ | **0.4267** | | D | far from both faces | $0.6667 - 0.6400 - 0.4000$ | **-0.3733** | Check: $\sigma_0$ = average of the four corners = 0.6667. Corner D is in **tension** (-0.3733 N/mm²) because $6e_1/500+6e_2/900 = 1.560 > 1$, i.e. the load lies outside the kernel (middle-third) of the section. **Answer: A = 1.707, B = 0.907, C = 0.427, D = -0.373 N/mm²** (compression positive); maximum 1.707 N/mm² at A. #### Critical stress - The **maximum compressive stress is at corner A = 1.707 N/mm$^2$**, the corner nearest the load. This must be compared with the permissible compressive stress of the masonry ($f_b k_s k_a k_p$). - Corner D has a **tension of 0.373 N/mm$^2$** because the load is outside the kernel of the section. Masonry and plain concrete have little tensile strength (IS 1905 cl. 5.4.2 permits none for vertical loads), so the corner would crack and the compression at A would be even higher than 1.707 N/mm$^2$. Therefore corner A (compression) and corner D (tension) both govern; the column must be enlarged or the eccentricity reduced. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which corner has the maximum compression and its value? A. Corner D, 0.373 N/mm^2 B. Corner B, 0.907 N/mm^2 C. Corner A, 1.707 N/mm^2 D. Corner C, 0.427 N/mm^2 Answer: C. A is nearest the load in both directions: 0.6667 + 0.64 + 0.40. (Key point: Maximum compressive corner) 2. Why is corner D in tension? A. Load lies outside the kernel (6e1/500 + 6e2/900 = 1.56 > 1) B. Because P is too small C. Because masonry has negative stress D. Because the section is square Answer: A. Bending stress exceeds direct stress at D. (Key point: Tension corner) 3. What happens in masonry with tension at D? A. Nothing, masonry resists tension well B. It cracks, so compression at A would be even higher than 1.707 C. Stress at A reduces D. The load shifts to centroid Answer: B. No tension is allowed for vertical loads, so the effective section shrinks. (Key point: Effect of cracking) 4. What should be done as both A and D govern? A. Increase the load B. Use weaker mortar C. Ignore corner D D. Enlarge the column or reduce eccentricity Answer: D. The design is not acceptable as given. 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