Hydraulic Structures: Fourth Edition

2. Determine a profile for the dam using thin-ring theory and, assuming
   that DFL loading applies, calculate the thickness required at vertical
   intervals of 10 m.


3. Confirm the upstream and downstream face stresses at mid-height in
   terms of thick-ring theory and estimate the abutment stress.

Solutions

1. Select central subtended angle, 290° (range 70°–110°). Hence
   Ru65/[sin(90° )]92 m. From equation (3.46),

h 0.61 MN m^2.

2. Using equation (3.46), and taking h2.5 MN m^2 ,

Level (m AOD) T (m)

140 01.50 (given)
130 04.05
120 07.73
110 11.41
100 15.09

3. At level 120, from equations (3.44) and (3.45), with Ru92 m,
   RD 92 7.7384.27 m, and

pw0.21 MN m^2 ,

giving (equation (3.44))

hu0.21(92)^2  
[(92)^2 (84.27)^2 ]

hu0.21 2.50 MN m^2

and (equation (3.45))

hd2.61 MN m^2

(note the variation in stress through the arch ring). To correct for

maximum abutment stress, Ru/T11.4, and hence Kr(Fig. 3.17)

1.9, giving hd maxat abutment2.611.94.96 MN m^2.

0.42(92)^2



(7.73)(9284.27)

(15 565)



1363

(92)^2 (84.27)^2



88.13^2

10  21



103

10  1  92



1.5

pwRu



TT

WORKED EXAMPLES 187