---
title: "Rectangular footing size, 6000 kN"
subject: "Foundation Engineering"
chapter: 6
key: "semester_5/foundation_engineering:footing-6000kn-rectangular-sand"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/footing-6000kn-rectangular-sand
site: BCT Engineering
---

# Rectangular footing size, 6000 kN

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

- Asked in: 2081 Bhadra, 6 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-6000kn-rectangular-sand
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-6

## Question

An RCC column footing rectangular in shape ($L/B = 1.5/1$) rests 1.5 m below the ground surface. The total load to be transmitted including the weight of column and footing is 6000 kN. If the saturated density of sand be 2.0 g/cc for $\phi = 34^\circ$, $N_q = 41.4$, $N_\gamma = 42.4$, find the suitable size of foundation considering the rise of water table to the ground surface. Use FoS = 3. (Values of $N_q$, $N_\gamma$ as read from the scan.)

## Short answer

Using Terzaghi’s equation for rectangular footing with water table at ground surface (γ' = 9.81 kN/m³), qu = qNq + 0.5(1–0.2B/L)γ'BNγ. Solving for B from safe load 6000 kN with FS=3 gives B=3.2 m, so footing size 3.2 m × 4.8 m.

## Answer

**Given:** $L/B = 1.5$, $D_f = 1.5$ m, $Q = 6000$ kN, $\phi = 34^\circ$, $N_q = 41.4$, $N_\gamma = 42.4$, $c = 0$, $\gamma_{sat} = 2.0\ \text{g/cc} = 19.62$ kN/m³, FS = 3, water table at ground surface (worst case). Use $\gamma_w = 9.81$ kN/m³.

**Assumptions:** Terzaghi's equation for a rectangular footing with $B/L = 1/1.5 = 0.667$. The load of 6000 kN includes the weights of column and footing, so the gross allowable pressure is $q_u/F$.

$$
\begin{aligned} \gamma' &= 19.62 - 9.81 = 9.81\ \text{kN/m}^3 \\ q &= \gamma' D_f = 9.81 \times 1.5 = 14.715\ \text{kN/m}^2 \\ q_u &= qN_q + 0.5\left(1 - 0.2\tfrac{B}{L}\right)\gamma' B N_\gamma \\ &= 14.715 \times 41.4 + 0.5(1 - 0.133)(9.81)(42.4)B \\ &= 609.2 + 180.3\,B\ \text{kN/m}^2 \end{aligned}
$$

Load capacity: $Q = \dfrac{q_u}{3} \times B \times L = \dfrac{609.2 + 180.3B}{3} \times 1.5B^2 = 6000$

Solving for $B$ by trial and error gives $B = 3.185$ m.

| $B$ (m) | $L = 1.5B$ (m) | $q_u$ (kN/m²) | Safe load $= q_uBL/3$ (kN) |
|---|---|---|---|
| 3.0 | 4.5 | 1149.9 | 5174.7 |
| 3.2 | 4.8 | 1186.0 | 6072.2 |
| 3.3 | 4.95 | 1204.0 | 6555.8 |

**Answer: provide a rectangular footing of 3.2 m × 4.8 m** (safe load 6072 kN > 6000 kN).

## Check yourself

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

1. With water table at ground surface, which unit weight is used?
   A. 19.62 kN/m3
   B. 9.81 kN/m3 for q only
   C. gamma_w only
   D. gamma' = gamma_sat - gamma_w = 9.81 kN/m3
   Answer: D. Both the surcharge and gamma term use submerged weight. (Key point: Submerged weight)

2. Which gamma-term factor is used for B/L = 0.667?
   A. 0.5(1 - 0.2B/L)
   B. 0.4
   C. 0.5(1 + 0.3B/L)
   D. 1.3
   Answer: A. Terzaghi's rectangular factor reduces from 0.5 for a strip. (Key point: Rectangular factor)

3. What is q at Df = 1.5 m?
   A. 29.43 kN/m2
   B. 14.715 kN/m2
   C. 19.62 kN/m2
   D. 9.81 kN/m2
   Answer: B. q = 9.81 * 1.5. (Key point: Surcharge)

4. Which equation is solved for B?
   A. qu * B * L = 6000
   B. (qu/3) * B = 6000
   C. (qu/3) * B * 1.5B = 6000
   D. qu/3 = 6000
   Answer: C. Gross safe pressure times area equals load. (Key point: Load equation)

## Related in Foundation Engineering

- [Footing size in sand, 150 tons](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Afooting-sand-150-tons) — Foundation Engineering, chapter 6
- [Square footing size in clay, 750 kN](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Asquare-footing-clay-750kn) — Foundation Engineering, chapter 6
- [Footing size from plate load test curve](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Aplate-load-footing-size-3200kn) — Foundation Engineering, chapter 6
- [Rectangular footing 3 m × 4 m, water table cases](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Arect-footing-3x4-backfilled) — Foundation Engineering, chapter 6
- [Footing 2 m × 3 m, chart factors, eccentricity](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Afooting-2x3-eccentric-skempton) — Foundation Engineering, chapter 6
- [Circular footing depth, 2000 kN](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Acircular-footing-depth-2000kn) — Foundation Engineering, chapter 6

## Related in other subjects

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- [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
- [RC wall footing, 1000 kN total load](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Arc-wall-footing-1000-kn-total) — Design of RCC Structure, chapter 11
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