Page 426 - Civil Engineering Formulas

352 CHAPTER TWELVE

M o
Extrados H o
P t
p Center line
Intrados

Crown

R d
r
R a
H a
φ
M a Abutment

Center of
curvature
FIGURE 12.30 Constant-thickness circular arch, fixed at abutments. (Davis—
Handbook of Hydraulics, McGraw-Hill.)

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:

MK 1
Rotation due to moment, α (12.193)
E r t 2
Deflection due to thrust, β HK 2 (12.194)
E r
VK 3
Deflection due to shear, (12.195)
E r
Rotation due to twist, M t K 4 (12.196)
E r t 2
VK 5
Rotation due to shear α (12.197)
E r t
MK 5
Deflection due to moment, (12.198)
E r t
*Vogt, Fredrik—Ueber dis Berehnung der Fundamentdeformation, Det Norske Videnskapa-akademi.