---
title: "Corner stresses of 500 x 900 column (300 kN)"
subject: "Concrete Technology and Masonry Structure"
chapter: 8
key: "semester_5/concrete_technology_and_masonry_structure:column-stress-500x900-300kn"
source: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/column-stress-500x900-300kn
site: BCT Engineering
---

# Corner stresses of 500 x 900 column (300 kN)

Concrete Technology and Masonry Structure · Chapter 8: Design of masonry walls for gravity loads

- Asked in: 2075 Chaitra, 8 marks
- Video: [Design of a Rectangular Column subjected to combined axial loading and biaxial bending](https://www.youtube.com/watch?v=VL2MoB0n9Tg) — Stan Academy
- 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-500x900-300kn
- 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 at all four corners.

## Short answer

Eccentricities80 mm and90 mm; A =450000 mm², Z₁ =37,5×10⁶ mm³, Z₂ =67,5×10⁶ mm³. Direct stress0.667 N/mm², bending stresses0.640 and0.400 N/mm². Corner stresses: A =1.707, B =0.907, C =0.427, D =−0.373 N/mm² (tension at D).

## 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.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Load is 170 mm from the 900 mm face and 360 mm from the 500 mm face. What are e1 and e2?
   A. e1 = 170 mm, e2 = 360 mm
   B. e1 = 250-170 = 80 mm, e2 = 450-360 = 90 mm
   C. e1 = 80 mm, e2 = 360 mm
   D. e1 = 250 mm, e2 = 450 mm
   Answer: B. Eccentricity is the half-dimension minus the distance from the face. (Key point: Eccentricities)

2. What is Z1 for bending across the 500 mm side?
   A. 500 x 900^2 / 6
   B. 900 x 500 / 6
   C. 900 x 500^2 / 6 = 37.5 x 10^6 mm^3
   D. 500 x 900^2 / 12
   Answer: C. Z1 = (width along the other side) x (500)^2 / 6. (Key point: Section modulus)

3. What is the stress at corner D?
   A. -0.373 N/mm^2 (tension)
   B. +0.373 N/mm^2 compression
   C. 0.667 N/mm^2
   D. 0
   Answer: A. 0.6667 - 0.6400 - 0.4000 = -0.3733. (Key point: Corner D)

4. Why does tension occur?
   A. The load is at the centroid
   B. P/A is negative
   C. Section is too long
   D. 6e1/500 + 6e2/900 = 1.56 > 1, the load is outside the kernel
   Answer: D. A load outside the middle-third kernel produces tension at the far corner. (Key point: Kernel)

## Close variants set in other exams

- [Corner stresses of 400 x 800 column (250 kN)](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Acolumn-stress-400x800-250kn) — Concrete Technology and Masonry Structure, chapter 8, asked 7×
- [Corner stresses of 400 x 800 column (200 kN)](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Acolumn-stress-400x800-200kn) — Concrete Technology and Masonry Structure, chapter 8, asked 7×

## Related in Concrete Technology and Masonry Structure

- [Column 500 x 900: stress intensities, critical corner](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Acolumn-stress-500x900-critical) — Concrete Technology and Masonry Structure, chapter 8
- [Corner stresses of 450 x 750 column (150 kN)](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Acolumn-stress-450x750-150kn) — Concrete Technology and Masonry Structure, chapter 8