---
title: "Minimum safe width of 18 m elementary profile"
subject: "Hydropower Engineering"
chapter: 4
key: "semester_7/hydropower_engineering:elementary-profile-min-width-18m"
source: https://www.bctengineer.com/q/semester_7/hydropower_engineering/elementary-profile-min-width-18m
site: BCT Engineering
---

# Minimum safe width of 18 m elementary profile

Hydropower Engineering · Chapter 4: Headworks of Storage Plants

- Asked in: 2079 Baishakh, 4 marks
- Video: [003_DHS- Elementary Profile of a Gravity Dam](https://www.youtube.com/watch?v=D484z7gorPs) — Athul Mangalath Madhu
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/hydropower_engineering/elementary-profile-min-width-18m
- Whole chapter: https://www.bctengineer.com/md/semester_7/hydropower_engineering/chapter-4

## Question

Find the minimum safe width for an elementary profile of a gravity dam of 18 m height. The specific gravity of the dam material is 2.25. Consider both no uplift and full uplift conditions.

## Short answer

For no uplift: B = 18/√2.25 = 12.0 m. For full uplift: B = 18/√(2.25−1) = 16.1 m. These are minimum safe widths to avoid tension.

## Answer

For the elementary profile (right-angled triangle, vertical u/s face, apex at the water level) the minimum width to avoid tension (resultant at the lower third point, $e=B/6$) is

$$
B=\frac{H}{\sqrt{S_c-K}}
$$

where $K$ is the uplift coefficient ($K=0$ for no uplift, $K=1$ for full uplift at the heel). Here $H=18$ m, $S_c=2.25$.

#### a) No uplift ($K=0$)
$$
B=\frac{18}{\sqrt{2.25}}=\frac{18}{1.5}=12.00\ \text{m}
$$

#### b) Full uplift ($K=1$)
$$
B=\frac{18}{\sqrt{2.25-1}}=\frac{18}{\sqrt{1.25}}=16.10\ \text{m}
$$

Uplift increases the width needed by about 34%.

**Answer: minimum safe width = 12.0 m without uplift and 16.1 m with full uplift.** (The friction coefficient is not given, so the sliding width $H/\mu(S_c-K)$ is not checked.)

## Check yourself

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

1. The minimum width B = H/sqrt(Sc-K) of an elementary profile is derived from which condition?
   A. Resultant at the lower third point (e = B/6), so no tension
   B. Sliding factor of safety equal to 1
   C. Overturning factor of safety equal to 1.5
   D. Toe stress equal to the permissible stress
   Answer: A. The width at which the resultant just stays within the middle third (e = B/6) gives B = H/sqrt(Sc-K). (Key point: Basis of the formula)

2. For H = 18 m and Sc = 2.25 with no uplift (K = 0), what is the minimum width?
   A. 8.0 m
   B. 16.1 m
   C. 18.0 m
   D. 12.0 m
   Answer: D. B = 18/sqrt(2.25) = 18/1.5 = 12.0 m. (Key point: No uplift width)

3. With full uplift (K = 1), the minimum width is
   A. 12.0 m
   B. 16.1 m
   C. 24.0 m
   D. 10.8 m
   Answer: B. B = 18/sqrt(2.25-1) = 18/sqrt(1.25) = 16.1 m. (Key point: Full uplift width)

4. How does full uplift change the required width?
   A. It reduces it
   B. It has no effect on width
   C. It increases it by about 34%
   D. It doubles it
   Answer: C. Uplift reduces the net effective weight, so the width must increase from 12.0 m to 16.1 m, about 34% more. (Key point: Effect of uplift)

## Related in Hydropower Engineering

- [Elementary profile of gravity dam](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Aelementary-profile-definition-proportioning) — Hydropower Engineering, chapter 4
- [Design elementary profile of masonry dam](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Aelementary-profile-stone-masonry-design) — Hydropower Engineering, chapter 4
- [Gravity dam stresses with drainage gallery uplift](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Agravity-dam-stresses-2080-baishakh) — Hydropower Engineering, chapter 4
- [Base width of 20 m high trapezoidal gravity dam](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Agravity-dam-base-width-trapezoidal-20m) — Hydropower Engineering, chapter 4
- [Gravity dam forces and stability checks (2081 Baishakh)](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Agravity-dam-forces-stresses-2081-baishakh) — Hydropower Engineering, chapter 4
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