---
title: "Brick and mortar: wall 175 kN/m, 4.2 m"
subject: "Concrete Technology and Masonry Structure"
chapter: 8
key: "semester_5/concrete_technology_and_masonry_structure:wall-eccentric-175kn-4-2m"
source: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/wall-eccentric-175kn-4-2m
site: BCT Engineering
---

# Brick and mortar: wall 175 kN/m, 4.2 m

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

- Asked in: 2081 Baisakh, 10 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/wall-eccentric-175kn-4-2m
- Whole chapter: https://www.bctengineer.com/md/semester_5/concrete_technology_and_masonry_structure/chapter-8

## Question

A wall is 4.2 m long between cross walls and the clear height of the wall is 3.2 m between RCC slabs of 12 cm thick at top and bottom. The brick wall carries an eccentric load of 175 kN/m (eccentricity of loading at 1/12) inclusive of self weight. What should be the strength of brick and grade of mortar? Use Nepal Standard Brick and joints are not raked.

## Short answer

Required basic compressive stress 0.72 N/mm². Use bricks of crushing strength not less than 10 N/mm² with M2 mortar (cement:sand 1:6); permissible stress 0.81 N/mm².

## Answer

#### Data and assumptions

- Thickness not given: Nepal standard brick $230\times110\times55$ mm, so a one-brick wall of 230 mm is adopted (joints not raked). Load 175 kN/m inclusive of self weight, $e/t=1/12$.
- Wall 4.2 m long between cross walls, clear height 3.2 m between 12 cm RCC slabs, so $H=3.2+0.12=3.32$ m.
- Design code: IS 1905:1987 (Tables 4 to 10); NBC 109 follows the same permissible-stress method.
- Brick masonry unit weight 19 kN/m$^3$ (IS 875 Part 1); modular brick, height/width $\le 0.75$, so $k_p=1$.

#### Step 1: Effective height, length and slenderness ratio (IS 1905 cl. 4.3, 4.4, 4.6)

Height between slab centres $H = 3.32$ m. Effective height $h_{ef} = 0.75 H = 0.75\times3.32 = 2.490$ m. Effective length (wall supported by a cross wall at each end, Table 5 Sl. 3) $L_{ef} = 1.0L = 4.20$ m. The lesser value governs:

$$
SR = \frac{h_{ef}}{t} = \frac{2.490}{0.230} = 10.83\ (<27,\ \text{Table 7, cement mortar})
$$

#### Step 2: Design load per metre run at the base

Load at the base (self weight already included) $P = 175.00$ kN/m.

Stress on the wall:

$$
\sigma = \frac{P}{A} = \frac{175.00\times10^3}{230\times10^3\ \text{mm}^2/\text{m}} = 0.761\ \text{N/mm}^2
$$

#### Step 3: Reduction factors

- Stress reduction factor $k_s$ (Table 9, $SR=10.83$, $e/t=0.083$, by linear interpolation) $= 0.845$
- Area reduction factor $k_a$ (cl. 5.4.1.2): area per metre 0.23 m$^2$ is not less than 0.2 m$^2$, so $k_a = 1.0$
- Shape factor $k_p = 1.0$ (modular bricks, height/width $\le 0.75$, Table 10)
- Since $e/t > 1/24$, a 25 percent increase in permissible stress is allowed (cl. 5.4.1.4 a), factor 1.25

#### Step 4: Required basic compressive stress

$$
\sigma \le f_b\,k_s\,k_a\,k_p\times1.25 \Rightarrow f_b \ge \frac{0.761}{0.845\times1.0\times1.0\times1.25} = 0.720\ \text{N/mm}^2
$$

(Without the 25 percent increase the requirement would be $f_b \ge 0.900$ N/mm$^2$.)

#### Step 5: Strength of brick and grade of mortar (IS 1905 Table 8)

Smallest standard unit strength giving $f_b \ge 0.720$ N/mm$^2$:

| Mortar (IS 1905 Table 1) | Min. unit strength (N/mm²) | Table 8 $f_b$ (N/mm²) |
|---|---|---|
| M2 (cement:sand 1:6) | 10 | 0.81 |
| M1 (cement:sand 1:5) | 7.5 | 0.74 |
| H2 (cement:sand 1:4) | 7.5 | 0.74 |
| H1 (cement:sand 1:3) | 7.5 | 0.75 |

**Answer: use bricks of crushing strength not less than 10 N/mm$^2$ with mortar M2 (cement:sand 1:6)** ($f_b = 0.81$ N/mm$^2$ $\ge$ 0.720). Other combinations in the table are also acceptable; a stronger mortar allows a weaker brick.

## Check yourself

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

1. Thickness is not given. What is adopted?
   A. 110 mm
   B. 230 mm, one Nepal standard brick (230x110x55)
   C. 345 mm
   D. 115 mm
   Answer: B. A one-brick wall of 230 mm is adopted from Nepal standard brick size. (Key point: Wall thickness)

2. With H = 3.2 + 0.12 = 3.32 m and RCC slabs at both ends, h_ef and SR are:
   A. 2.49 m and 10.83
   B. 3.32 m and 14.4
   C. 2.49 m and 21.7
   D. 1.66 m and 7.2
   Answer: A. h_ef = 0.75 x 3.32 = 2.49 m; SR = 2.49/0.23 = 10.83. (Key point: Effective height)

3. sigma = 175,000/230,000 = 0.761 N/mm^2, k_s = 0.845 and 25 percent increase give f_b of about:
   A. 0.900 N/mm^2
   B. 0.720 N/mm^2
   C. 0.35 N/mm^2
   D. 1.25 N/mm^2
   Answer: B. 0.761/(0.845 x 1.25) = 0.720 N/mm^2. (Key point: Required f_b)

4. Which unit strength with M2 mortar is needed?
   A. 7.5 N/mm^2 (f_b 0.59)
   B. 10 N/mm^2 (f_b 0.81)
   C. 5 N/mm^2 (f_b 0.44)
   D. 3.5 N/mm^2 (f_b 0.35)
   Answer: B. 0.59 < 0.720, so 10 N/mm^2 units (0.81) with M2 mortar are required. (Key point: Selection)

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