---
title: "Footing size from plate load test curve"
subject: "Foundation Engineering"
chapter: 6
key: "semester_5/foundation_engineering:plate-load-footing-size-3200kn"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/plate-load-footing-size-3200kn
site: BCT Engineering
---

# Footing size from plate load test curve

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

- Asked in: 2075 Asoj, 8 marks
- Video: [Finding Allowable Load of Foundation Using Plate Load Test Data|Plate Load Test Solved Problem](https://www.youtube.com/watch?v=scn5NfsZqqU) — Master Civil Engineering
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/plate-load-footing-size-3200kn
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-6

## Question

The figure below shows the load-settlement curve obtained from a plate load test conducted on a sandy soil. The size of the plate used was 30 cm × 30 cm. Determine the size of a square column footing to carry a net load of 3200 kN with a maximum settlement of 25 mm. [Figure: load-settlement curve, pressure axis 0 to 800 kN/m², settlement axis 0 to 50 mm, curve not reproducible from the scan.]

## Short answer

Using the plate load test curve and Terzaghi-Peck settlement relation for sand, a footing size of 3.3 m × 3.3 m yields a pressure of 294 kN/m² and settlement below 25 mm. Provide a 3.3 m square footing.

## Answer

**Given:** plate $B_p = 0.3$ m on sand. Net load $Q = 3200$ kN, allowable footing settlement $S_f = 25$ mm, square footing $B \times B$.

The figure could not be read exactly, so the plate readings below are **assumed** (typical for sand): pressure (kN/m²) 0, 100, 200, 300, 400, 500, 600, 700, 800 against settlement (mm) 0, 1.5, 4, 7.5, 12, 17.5, 24, 33, 45. If your curve differs, repeat the same steps with your own readings.

#### Method (Terzaghi–Peck, sand)
The settlement of a footing and a plate under the same pressure are related by

$$
\frac{S_f}{S_p} = \left[\frac{B(B_p + 0.3)}{B_p(B + 0.3)}\right]^2 = \left[\frac{2B}{B + 0.3}\right]^2 \quad (B_p = 0.3\ \text{m})
$$

So for each trial size $B$: the pressure is $q = 3200/B^2$; the plate settlement equivalent to 25 mm is $S_p = 25\left(\dfrac{B+0.3}{2B}\right)^2$; read the plate settlement from the curve at pressure $q$ and compare.

| $B$ (m) | $q = 3200/B^2$ (kN/m²) | Required $S_p$ (mm) | $S_p$ from curve (mm) |
|---|---|---|---|
| 3.0 | 355.6 | 7.56 | 10.0 |
| 3.2 | 312.5 | 7.48 | 8.06 |
| 3.3 | 293.8 | 7.44 | 7.28 |
| 3.4 | 276.8 | 7.40 | 6.69 |

The plate settlement read from the curve equals the required value at $B \approx 3.27$ m (pressure $\approx 299$ kN/m²). At $B = 3.3$ m the curve gives 7.28 mm, which is below the required 7.44 mm, so the footing settles less than 25 mm.

#### Safety check
The pressure is $\approx 300$ kN/m², which is well below the failure region of the curve (the curve keeps rising smoothly up to 800 kN/m²), so shear failure is not critical. The ultimate capacity of the footing is $q_{up} \times B/B_p$ (about 11 times the plate value), which gives a large factor of safety.

**Answer: provide a square footing of about 3.3 m × 3.3 m** (pressure $\approx 294$ kN/m², settlement below 25 mm), on the assumed curve.

## Check yourself

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

1. Sf/Sp for Bp = 0.3 m is
   A. B/0.3
   B. (B/0.3)^2
   C. [B/(B+0.3)]
   D. [2B/(B+0.3)]^2
   Answer: D. Terzaghi-Peck relation for sand. (Key point: Settlement ratio)

2. How is footing size found?
   A. Trial B: q = Q/B^2, required Sp from ratio, compare with curve
   B. Use plate pressure directly
   C. Scale by B/Bp only
   D. Take qu of plate
   Answer: A. Iterate until the curve value equals required Sp. (Key point: Procedure)

## Related in Foundation Engineering

- [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
- [Bearing capacity from plate load curve](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Abc-from-load-settlement-sand) — Foundation Engineering, chapter 6
- [Rectangular footing size, 6000 kN](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Afooting-6000kn-rectangular-sand) — Foundation Engineering, chapter 6
- [Square footing under eccentric load, min depth](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Asquare-footing-eccentric-2000kn) — Foundation Engineering, chapter 6
- [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
- [Limitations of plate load test](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Aplate-load-test-limitations) — Foundation Engineering, chapter 6, asked 5×

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