##### Document Text Contents

Page 1

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Page 2

Cornell University Library

TC 540.B64 1916

Damsand weirs; an analytical and practic

3 1924 004 065 664

Te5M6

m

Qforttell InittctBitg SIthratg

Strata, BJcm ^atk

BOUGHTW[TH THE INCOMEOF THE

SAGEENDOWMENTFUND

THE GIFT OF

HENRYW. SAGE

1891

ENGINEERINGLIBRARY

Page 116

104 DAMSANDWEIRS

8 1 . Support of Vertical Water Loads in Arched Dams.

When the back of an arched dam is incHned, the weight of the

water over it is supported by the base, the horizontal pressure of

the water alone acting on the arch and being conveyed to the

abutments. In the case of inclined arch buttress dams, however, a

portion of the vertical load is carried by the arch, increasing its

thrust above what is due to the horizontal water pressure alone.

This is due to overhang, i. e,, when the e.g. falls outside the base.

82, Crest Width. The crest width of arched dams can be

safely made much less than that of gravity dams and a rule of

i..|v7j (23)

would seem to answer the purpose, unless rein-

forcement is used, when it can be made less.

EXAMPLESOF ARCHEDDAMS

The following actual examples of arched

dams will now be given.

83. Bear Valley Dam. This small work,

Fig. 59, is the most remarkable arched dam in

existence and forms a valuable example of the

enormous theoretical stresses which this type

of vertical arch can stand. The mean radius

being 335 feet according to formula (21) the

unit stress will be

—r- —= 60 tons, nearly

Fig. 59. Section of Old Bear

Valley Dam

This section would be better if reversed. The

actual stress is probably half this amount.

This work has now been superseded by a new dam built below it,

Fig. 77, section 103.

84. Pathfinder Dam. This immense work, Fig. 60, is built

to a radius of 150 feet measured to the center of the crest. That,

however, at the extrados of the base of the section is 186 feet and this

quantity has to be used for the value of R in the long formula (22).

The unit stress then works out to 18 tons, nearly. The actual stress

in the lowest arch ring is undoubtedly much less, for the reason

Page 117

DAMSANDWEIRS 105

that the base must absorb so large a proportion of the thrust that

very Httle is transmitted to the sides of the canyon. The exact

determination of the proportion transmitted in the higher rings

is an indeterminate problem, and the only safe method is to assume

with regard to tangential arch stress that the arch stands clear of

RAD. 150'

Fig. 60. Section of Pathfinder Dam

the base. This will leave a large but indeterminate factor of safety

and enable the adoption of a high value for 5, the maximum unit

stress.

The profile of the dam is nearly equiangular in outline. This

is necessary in so high a dam in order to bring the vertical resultants

(W) R, E. and (iV) R. F. as near the center as possible with the

object of bringing the ratio of maximum to mean stress as low as

possible.

The estimation of the exact positions of Wand of N is made

analytically as below.

pfifPIWi

wm

mwM\J;l

Page 2

Cornell University Library

TC 540.B64 1916

Damsand weirs; an analytical and practic

3 1924 004 065 664

Te5M6

m

Qforttell InittctBitg SIthratg

Strata, BJcm ^atk

BOUGHTW[TH THE INCOMEOF THE

SAGEENDOWMENTFUND

THE GIFT OF

HENRYW. SAGE

1891

ENGINEERINGLIBRARY

Page 116

104 DAMSANDWEIRS

8 1 . Support of Vertical Water Loads in Arched Dams.

When the back of an arched dam is incHned, the weight of the

water over it is supported by the base, the horizontal pressure of

the water alone acting on the arch and being conveyed to the

abutments. In the case of inclined arch buttress dams, however, a

portion of the vertical load is carried by the arch, increasing its

thrust above what is due to the horizontal water pressure alone.

This is due to overhang, i. e,, when the e.g. falls outside the base.

82, Crest Width. The crest width of arched dams can be

safely made much less than that of gravity dams and a rule of

i..|v7j (23)

would seem to answer the purpose, unless rein-

forcement is used, when it can be made less.

EXAMPLESOF ARCHEDDAMS

The following actual examples of arched

dams will now be given.

83. Bear Valley Dam. This small work,

Fig. 59, is the most remarkable arched dam in

existence and forms a valuable example of the

enormous theoretical stresses which this type

of vertical arch can stand. The mean radius

being 335 feet according to formula (21) the

unit stress will be

—r- —= 60 tons, nearly

Fig. 59. Section of Old Bear

Valley Dam

This section would be better if reversed. The

actual stress is probably half this amount.

This work has now been superseded by a new dam built below it,

Fig. 77, section 103.

84. Pathfinder Dam. This immense work, Fig. 60, is built

to a radius of 150 feet measured to the center of the crest. That,

however, at the extrados of the base of the section is 186 feet and this

quantity has to be used for the value of R in the long formula (22).

The unit stress then works out to 18 tons, nearly. The actual stress

in the lowest arch ring is undoubtedly much less, for the reason

Page 117

DAMSANDWEIRS 105

that the base must absorb so large a proportion of the thrust that

very Httle is transmitted to the sides of the canyon. The exact

determination of the proportion transmitted in the higher rings

is an indeterminate problem, and the only safe method is to assume

with regard to tangential arch stress that the arch stands clear of

RAD. 150'

Fig. 60. Section of Pathfinder Dam

the base. This will leave a large but indeterminate factor of safety

and enable the adoption of a high value for 5, the maximum unit

stress.

The profile of the dam is nearly equiangular in outline. This

is necessary in so high a dam in order to bring the vertical resultants

(W) R, E. and (iV) R. F. as near the center as possible with the

object of bringing the ratio of maximum to mean stress as low as

possible.

The estimation of the exact positions of Wand of N is made

analytically as below.