2

It is defined as a solid wall, curved in plan,standing across the entire width of the rivervalley, in a single span.

Structurally behave:

Partly as a cantilever retaining wall standing upfrom its base, and

Partly, the load will be transferred to the two endsof the arch span by horizontal arch action.

3

Transfer a large part of their loading bycantilever action.

Depending upon the shape consideration:

Constant radius arch dams

Variable radius arch dams

Constant angle arch dams

4

Constant radius arch damsExtrados and Intrados

5

Variable radius arch damsExtrados and Intrados

6

Constant angle arch damsExtrados and Intrados

Water Pressure

Uplift Pressure

Pressure due to Earthquake forces

Silt Pressure

Wave Pressure

Ice Pressure

8

Thin cylinder theory

Method gives wrong results and can relied onlyupon rough estimation of dimensions of arches.

Theory of Elastic arches

Dam divided into horizontal independent arches.

The Trial Load method

Dam divided into

The horizontal arches

The vertical cantilevers

9

Thin cylinder theory

t

rh

t

R w

t

rhf w

c

rhR w Reaction,

Compressive stress,

Allowable compressive stress,

10

Central angle for minimum concrete

trV )2(

)2(2

rf

hV

c

w

sin2

Lr

431332 0

11

Limitation of Thin cylinder theory

The arch sections are not thin cylinders. They arealso not free at abutments, as assumed in theory.

The theory does not consider shear and bendingstresses in the arch.

Analysis is based only on hydrostatic pressure. Icepressure and temperature stresses, though areimportant, not considered in the theory.

Stressed due to yielding of abutments and thosedue to rib shortening have not been accounted.

Plastic flow of concrete and shrinkage of concretenot accounted for.

12

Thin Elastic theory

Temperature stresses, due to temperaturechanges

Shrinkage stresses, due to setting of concrete

Stresses due to yielding of abutments

No abutment is rigid and yields to an extentdepends upon the nature of rock.

Stresses due to rib shortening

Caused due to restriction of change in span.

13

General formulas

yHL

xMMMM ABA

14

. Deck slab typeMultiple arch type

15

Simply SupportedSlab type

Buttress spacing andDeck slope

Most economical spacingof buttresses

minimum thickness ofconcrete is fully utilised.

16

Simply Supported Slab type

Buttress spacing and Deck slope

Height, thickness and spacing of buttresses

Height of buttress Slenderness ratio = = 12 – 15

Thickness of buttress

Spacing of buttress Massiveness factor = = 2.5 – 3

Thickness of buttress

Concrete quantity/ mlength of dam

cot

1208.0 2

sc F

HV

17

18

Multiple Arch type

Daniel Jhonson Dam, Quebec, CanadaMultiple arch and buttress dam (Height – 216m)

19

Multiple Arch type

20

Other types

Multiple Dome type

Coolidge Dam, Arizona,USA Multiple domeand buttress dam(Height – 75.95m)

21

Other types

Massive Head type

22

Massive Head type Advantages

The construction work is easier.

Since water pressure acts radially in a cylindricaltype, and perpendicular in a diamond type, allpressures are normally compressive.

Since the deck is not to ne reinforced, there is noquestion of failure by rusting of steel.

For smaller heights, they prove to give moreeconomical buttress spacing.

Such a dam body offers more resistance to sliding,because it is considerably heavier.

23

Other types

Columnar Buttress type Disadvantages :

Require very strong and stable foundations

More skill is required in constructing the buttresses.

24 Hydraulic Structures