## Buoyancy

Archimedes Principle
Any body immersed in a fluid is subjected to an upward force called buoyant force equal to the weight of the displaced fluid.

Archimedes (287-212 B.C.)

$BF = \gamma V_D$

Where
$BF$ = buoyant force
$\gamma$ = unit weight of fluid
$V_D$ = volume of fluid displaced by the body

## Analysis of Gravity Dam

Dams are structures whose purpose is to raise the water level on the upstream side of river, stream, or other waterway. The rising water will cause hydrostatic force which will tend the dam to slide horizontally and overturn about its downstream edge or toe. The raised water level on the upstream edge or heel will also cause the water to seep under the dam. The pressure due to this seepage is commonly called hydrostatic uplift and will reduce the stability of the dam against sliding and against overturning.

## Problem 353 | Equilibrium of Non-Concurrent Force System

Problem 353
The forces acting on a 1-m length of a dam are shown in Fig. P-353. The upward ground reaction varies uniformly from an intensity of p1 kN/m to p2 kN/m at B. Determine p1 and p2 and also the horizontal resistance to sliding.

## Problem 266 | Resultant of Non-Concurrent Force System

Problem 266
Determine the resultant of the three forces acting on the dam shown in Fig. P-266 and locate its intersection with the base AB. For good design, this intersection should occur within the middle third of the base. Does it?