---
title: "Footing size in sand, 150 tons"
subject: "Foundation Engineering"
chapter: 6
key: "semester_5/foundation_engineering:footing-sand-150-tons"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/footing-sand-150-tons
site: BCT Engineering
---

# Footing size in sand, 150 tons

Foundation Engineering · Chapter 6: Bearing Capacity and Settlement of Shallow Foundations

- Asked in: 2076 Chaitra, 7 marks
- Video: [How to decide the size of footing?  | Area of footing | Design of RCC footing | Civil Tutor](https://www.youtube.com/watch?v=HAyyvpl0vlY) — Civil Tutor
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/footing-sand-150-tons
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-6

## Question

Determine the size of the footing resting over sand to carry a column load of 150 tons. The bottom of the footing is 1.5 m below the ground level and water table is located at 3 m below the footing. Take unit weight of sand is $20\ \text{kN/m}^3$. Assume $N_c = 55.2$, $N_q = 39.51$ and $N_\gamma = 40.13$.

## Short answer

For sand, q_u = γ D_f N_q + 0.4 γ B N_γ. With FS=3, solving for B by trial gives B=1.7 m, providing a safe load of 1668 kN. Provide a 1.7 m × 1.7 m square footing.

## Answer

**Given:** column load $= 150$ t $= 150 \times 9.81 = 1471.5$ kN, $D_f = 1.5$ m, $\gamma = 20$ kN/m³, sand ($c = 0$), $N_q = 39.51$, $N_\gamma = 40.13$ (and $N_c = 55.2$, not needed). The water table is 3 m below the footing, which is more than $B$, so it has no effect.

**Assumptions:** square footing, FS = 3 (not given), Terzaghi's equation, general shear, weight of footing included in the load.

$$
\begin{aligned} q_u &= \gamma D_f N_q + 0.4\gamma B N_\gamma \\ &= 20 \times 1.5 \times 39.51 + 0.4 \times 20 \times 40.13\,B \\ &= 1185.3 + 321.0\,B\ \text{kN/m}^2 \end{aligned}
$$

Safe load: $\dfrac{q_u}{3}B^2 = 1471.5$, giving (by trial) $B = 1.61$ m.

| $B$ (m) | $q_u$ (kN/m²) | Safe load $q_uB^2/3$ (kN) |
|---|---|---|
| 1.6 | 1699.0 | 1449.8 |
| 1.7 | 1731.1 | 1667.6 |
| 1.8 | 1763.2 | 1904.2 |

**Answer: provide a square footing of 1.7 m × 1.7 m** (safe load 1668 kN > 1471.5 kN).

## Check yourself

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

1. Why does the 3 m deep WT have no effect?
   A. It is deeper than B below the base
   B. Sand is dry
   C. c = 0
   D. Nq is large
   Answer: A. Beyond B below the base, no effect. (Key point: Water table)

2. Which equation is used?
   A. qu = 1.3cNc
   B. qu = gamma Df Nq + 0.4 gamma B Ngamma
   C. qu = 0.3 gamma B Ngamma only
   D. qu = gamma Df Nc
   Answer: B. c = 0 for sand; square uses 0.4. (Key point: Square formula)

## Related in Foundation Engineering

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- [Rectangular footing size, 6000 kN](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Afooting-6000kn-rectangular-sand) — Foundation Engineering, chapter 6
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## Related in other subjects

- [Uniform sand, water table 2 m, capillary](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Auniform-sand-effective-stress-capillary) — Soil Mechanics, chapter 6
- [Footing, 1250 kN column load, depth 1.8 m](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Afooting-1250-kn-column-load-depth) — Design of RCC Structure, chapter 11
- [Clay over sand, effective stress at depths](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aclay-sand-profile-effective-stress-depths) — Soil Mechanics, chapter 6
- [Rectangular footing, 600x600 column, 1150 kN](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Arectangular-footing-600x600-column-1150-kn) — Design of RCC Structure, chapter 11