and for the 10-second wave, 



, ,M Ib.-ft. 



[K]c - 32,000 -^ 



, ,,, , Ib.-ft. 

 M''L = 43 



(T = 10 sec.) 



M/f 



ft. 



The overturning moments about point B are obtained from Equation 7-75, 



[^'b)c " 23,900 - 9.0 (2,100) = 5,000 -^^ , 



[K)t 



(T = 6 sec.) 



and for the 10-second wave. 



, ,„ Ib.-ft. 



[K)c = 8,400-^, 



(T = 10 sec.) 



(Mb). 



As in the examples in Sections 7.323 and 7.324, various combinations of 

 appropriate wave conditions for the two sides of the structure can be 

 assumed and resulting moments and forces computed. 



************************************* 

 7o33 BREAKING WAVE FORCES ON VERTICAL WALLS 



Waves breaking directly against vertical-face structures exert high, 

 short duration, dynamic pressures that act near the region where the wave 

 crests hit the structure. These impact or shock pressures have been 

 studied in the laboratory by Bagnold (1939), Denny (1951), Ross (1955), 

 Nagai (1961 b) , Carr (1954), Leendertse (1961), Kamel (1968), Weggel (1968), 

 and Weggel and Maxwell (1970 a, and b) . Some measurements on full-scale 

 breakwaters have been made by deRouville, et al . , (1938). Wave tank experi- 

 ments by Bagnold (1939) led to an explanation of the phenomenon. Bagnold 

 found that impact pressures occur at the instant that the vertical, front 

 face of a breaking wave hits the wall and only when a plunging wave entraps 

 a cushion of air against the wall. Because of this critical dependence 

 on wave geometry, high impact pressures are infrequent against prototype 

 structures. However, the possibility of high impact pressures must be 

 recognized, and considered in design. The high impact pressures are 

 short (of the order of hundredths of a second) , and their importance in 

 the design of breakwaters against sliding or overturning is questionable. 

 However, lower dynamic forces which last longer are important. 



7-145 



