---
title: "Strip footing vs 2:1 method"
subject: "Soil Mechanics"
chapter: 8
key: "semester_4/soil_mechanics:strip-footing-vs-2-1-method"
source: https://www.bctengineer.com/q/semester_4/soil_mechanics/strip-footing-vs-2-1-method
site: BCT Engineering
---

# Strip footing vs 2:1 method

Soil Mechanics · Chapter 8: Vertical Stresses Below Applied Loads

- Asked in: 2078 Poush, 2+2 marks
- Video: [2:1 Method and Simpson's Rule for Stress Dissipation in Soil](https://www.youtube.com/watch?v=W-RUs__3dkQ) — Math and Engineering with Dr. A
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/soil_mechanics/strip-footing-vs-2-1-method
- Whole chapter: https://www.bctengineer.com/md/semester_4/soil_mechanics/chapter-8

## Question

A strip footing of width 2 m carries a load of 500 kN/m. Calculate the maximum stress at a depth of 5 m below the center of the footing. Compare the result with the 2:1 distribution method.

## Short answer

From the Boussinesq strip formula, maximum stress at 5 m depth is 62.0 kN/m2. The 2:1 method yields 71.4 kN/m2, about 15% higher and thus conservative.

## Answer

#### Given

Strip footing $B = 2$ m, load $Q = 500$ kN/m. Contact pressure $q = 500/2 = 250$ kN/m². Depth $z = 5$ m, below the centre (where stress is maximum).

#### Boussinesq (strip load)

$$
\Delta\sigma_z = \frac{q}{\pi}\left[\alpha + \sin\alpha\cos(\alpha + 2\delta)\right]
$$

Below the centre, $\delta = 0$, so $\Delta\sigma_z = \dfrac{q}{\pi}\left(\alpha + \sin\alpha\right)$ where $\alpha = 2\tan^{-1}\left(\dfrac{B/2}{z}\right) = 2\tan^{-1}(0.2) = 0.3948$ rad (22.62°).

$\sin\alpha = 0.3846$

$$
\Delta\sigma_z = \frac{250}{\pi}(0.3948 + 0.3846) = 79.58\times0.7794 = 62.0\ \text{kN/m}^2
$$

#### 2:1 method

$$
\Delta\sigma_z = \frac{Q}{B+z} = \frac{500}{2+5} = 71.4\ \text{kN/m}^2
$$

#### Comparison

| Method | $\Delta\sigma_z$ (kN/m²) |
|---|---|
| Boussinesq (strip, centre) | 62.0 |
| 2:1 distribution | 71.4 |

**Answer: Maximum stress at 5 m depth $= 62.0$ kN/m² (Boussinesq); the 2:1 method gives 71.4 kN/m², about 15% higher (conservative).**

## Check yourself

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

1. For a 2 m wide strip carrying 500 kN/m, the contact pressure q is
   A. 1000 kN/m2
   B. 500 kN/m2
   C. 250 kN/m2
   D. 125 kN/m2
   Answer: C. q = 500/2 = 250 kN/m2. (Key point: Contact pressure)

2. Below the centre of a strip footing the Boussinesq stress is
   A. (q/pi)(alpha + sin alpha), alpha = 2 tan^-1((B/2)/z)
   B. q/(B+z)
   C. q alpha
   D. (q/pi)(alpha - sin alpha)
   Answer: A. With delta = 0 the general strip equation reduces to (q/pi)(alpha + sin alpha). (Key point: Boussinesq strip formula)

3. At z = 5 m the Boussinesq and 2:1 results are respectively
   A. 71.4 and 62.0 kN/m2
   B. 62.0 and 62.0 kN/m2
   C. 62.0 and 71.4 kN/m2
   D. 79.6 and 71.4 kN/m2
   Answer: C. Boussinesq gives 62.0 kN/m2; 2:1 gives 500/(2+5) = 71.4 kN/m2. (Key point: Results)

4. How does the 2:1 method compare with Boussinesq here?
   A. It gives lower stress (unsafe)
   B. It gives about 15% higher stress (conservative)
   C. It gives identical results
   D. It cannot be used for strips
   Answer: B. 71.4 is about 15% higher than 62.0, so 2:1 is conservative. (Key point: Comparison)

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## Related in other subjects

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