CIVIL ENGINEERING FORMULAS

352 CHAPTER TWELVE

Rock Movements. Considerations of rock movements and their effects on the
section of arch dams may be based on approximate formulas.* If the ends of the
arch elements are vertical, and the bases of the cantilever elements, horizontal,
rock rotations and deflections of elements with parallel sides 1 ft apart may be
calculated by the following equations:

Rotation due to moment, (12.193)

Deflection due to thrust, (12.194)

Deflection due to shear, (12.195)

Rotation due to twist, (12.196)

Rotation due to shear (12.197)

Deflection due to moment,  (12.198)

MK 5

Ert

α

VK 5

Ert

 

MtK 4

Ert^2



VK 3

Er

β

HK 2

Er

α

MK 1

Ert^2

FIGURE 12.30 Constant-thickness circular arch, fixed at abutments. (Davis—

Handbook of Hydraulics, McGraw-Hill.)

p

P Extrados

Center line

Intrados

Mo

Ho

t

Crown

Center of

curvature

Abutment

H

a Ra

Rd

r

Ma φ

*Vogt, Fredrik—Ueber dis Berehnung der Fundamentdeformation, Det Norske Videnskapa-akademi.