---
title: "Corner stresses of 400 x 800 column (250 kN)"
subject: "Concrete Technology and Masonry Structure"
chapter: 8
key: "semester_5/concrete_technology_and_masonry_structure:column-stress-400x800-250kn"
source: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/column-stress-400x800-250kn
site: BCT Engineering
---

# Corner stresses of 400 x 800 column (250 kN)

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

- Asked in: 2079 Bhadra, 8 marks; 2078 Kartik, 6 marks; 2076 Ashwin, 8 marks; 2073 Shrawan, 10 marks; 2071 Chaitra, 8 marks (asked 5 times)
- Video: [EX 04 | BENDING STRESSES | RECTANGULAR COLUMN | ECCENTRIC LOADING ANYWHERE IN COLUMN](https://www.youtube.com/watch?v=Fe-ftpSHkV8) — Structural Funda by:- KheNiSiR
- 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-400x800-250kn
- Whole chapter: https://www.bctengineer.com/md/semester_5/concrete_technology_and_masonry_structure/chapter-8

## Question

A column section 400 mm $\times$ 800 mm carries a load of 250 kN acting at 160 mm from the 800 mm face and 350 mm from the 400 mm face. Determine the stress intensities at all four corners.

## Short answer

Eccentricities from centroid are 40 mm and 50 mm. Section area 320000 mm², Z1=21.33×10⁶ mm³, Z2=42.67×10⁶ mm³. Stress intensities (compression positive): corner A 1.543, B 0.957, C 0.605, D 0.020 N/mm²; maximum 1.543 N/mm² at A.

## Answer

Distances are measured from the faces. The 160 mm distance is across the 400 mm side (from the 800 mm face), and the 350 mm distance is along the 800 mm side (from the 400 mm face). Hence the eccentricities from the centroid are $e_1 = 200-160 = 40$ mm and $e_2 = 400-350 = 50$ mm.

#### Data

Section 400 mm $\times$ 800 mm, $P=250$ kN. The load acts 160 mm from the 800 mm face and 350 mm from the 400 mm face.

#### Eccentricities

$$
\begin{aligned} e_{1} &= 40\ \text{mm (across the 400 mm side)}\\ e_{2} &= 50\ \text{mm (along the 800 mm side)} \end{aligned}
$$

#### Section properties

$$
\begin{aligned} A &= 400\times800 = 320000\ \text{mm}^2\\ Z_1 &= \frac{800\times400^2}{6} = 21333333\ \text{mm}^3\\ Z_2 &= \frac{400\times800^2}{6} = 42666667\ \text{mm}^3 \end{aligned}
$$

#### Stresses

$$
\begin{aligned} \sigma_0 &= \frac{P}{A} = \frac{250\times10^3}{320000} = 0.7812\ \text{N/mm}^2\\ \sigma_{b1} &= \frac{Pe_1}{Z_1} = \frac{250\times10^3\times40}{21333333} = 0.4688\ \text{N/mm}^2\\ \sigma_{b2} &= \frac{Pe_2}{Z_2} = \frac{250\times10^3\times50}{42666667} = 0.2930\ \text{N/mm}^2 \end{aligned}
$$

Corner stresses $\sigma=\sigma_0\pm\sigma_{b1}\pm\sigma_{b2}$ (positive = compression, N/mm²):

| Corner | Position | Working | Stress |
|---|---|---|---|
| A | near the 800 face and near the 400 face | $0.7812 + 0.4688 + 0.2930$ | **1.5430** |
| B | near the 800 face, far from the 400 face | $0.7812 + 0.4688 - 0.2930$ | **0.9570** |
| C | far from the 800 face, near the 400 face | $0.7812 - 0.4688 + 0.2930$ | **0.6055** |
| D | far from both faces | $0.7812 - 0.4688 - 0.2930$ | **0.0195** |

Check: $\sigma_0$ = average of the four corners = 0.7812. All four corners are in compression, because the load lies inside the kernel ($6e_1/400+6e_2/800 = 0.975 < 1$).

**Answer: A = 1.543, B = 0.957, C = 0.605, D = 0.020 N/mm²** (compression positive); maximum 1.543 N/mm² at A.

## Check yourself

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

1. The load is 160 mm from the 800 mm face on the 400 mm side. What is e1?
   A. 40 mm (200 - 160)
   B. 160 mm
   C. 200 mm
   D. 360 mm
   Answer: A. Eccentricity is the distance from the centroid, 200 - 160 = 40 mm. (Key point: Eccentricities)

2. What is the direct stress P/A?
   A. 1.25 N/mm^2
   B. 0.7812 N/mm^2
   C. 0.3125 N/mm^2
   D. 7.81 N/mm^2
   Answer: B. 250000/320000 = 0.7812 N/mm^2. (Key point: Direct stress)

3. How is the bending stress due to e1 found?
   A. P e1 / A
   B. P / Z1 only
   C. P e1 / Z1, with Z1 = 800 x 400^2 / 6, giving 0.4688 N/mm^2
   D. P e1 / Z2 giving 0.2930
   Answer: C. Z1 = 21333333 mm^3 and 250000 x 40 / Z1 = 0.4688. (Key point: Bending stress)

4. What is the maximum corner stress and why are all corners compressive?
   A. 0.0195 N/mm^2 at D; the load is outside the kernel
   B. 1.543 N/mm^2 with tension at D
   C. 0.957 N/mm^2 at B
   D. 1.543 N/mm^2 at A; the load lies inside the kernel
   Answer: D. sigma0 + sb1 + sb2 = 1.543, and 6e1/400 + 6e2/800 = 0.975 < 1 so no tension. (Key point: Maximum stress)

## Close variants set in other exams

- [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×
- [Corner stresses of 500 x 900 column (300 kN)](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Acolumn-stress-500x900-300kn) — 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
- [Brick and mortar for 250 mm wall (350 kN/m)](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Awall-eccentric-250mm-350kn) — Concrete Technology and Masonry Structure, chapter 8, asked 7×

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