COLLAPSE OF TEXAS TOWER NO. 4 195 



STATIC AND DYNAMIC FORCES DIFFERENTIATED 



Mr. Brewer. Yes. A static analysis, I think we could use as an 

 analogy, perhaps, a diving board, a springboard. 



If you simply went to the end of the diving board and stood there, 

 you would bend the diving board, and you would have stresses all 

 along the diving board as a simple cantilever beam, and the stresses 

 would be a function of your weight at the end of the diving board. 



If you jump up and down on the diving board you would mipart 

 greater forces and greater stresses to the diving board. This would be 

 a dynamic loading of a cantilever beam. 



Now, if you jump up and down at just the right frequency, and 

 that corresponds with the frequency of the diving board, you can get 

 tremendous stresses and forces into the diving board, so that if the 

 frequency of the dynamic loading corresponds with the resonant 

 frequency— that is the frequency at which the structure itself naturally 

 vibrates at — you can get tremendous vibrations, and this is like a 

 violin string. 



When you work a bow over the string, and you do it at just the 

 right frequency, you get very high amplitudes, and it makes a sound. 

 So that dynamic loading, if it is in the right frequency spectrum, can 

 produce loads, produce stresses, in a structure very much higher than 

 the same load would do if it were quite static. 



Again, like a person, he still weighs the same amount of weight, but 

 if he jumps up and down on the diving board, he can impart a weight 

 three or four times his own weight to the diving board. 



Mr. French. Now, in view of your findings that 10-foot waves 

 caused greater stresses than waves of 30-feet in height, would it be 

 reasonable at least to suggest the possibility that a dynamic force 

 analysis should have been made in computing the design of this tower? 



Mr. Brewer. That question, of course, is one that comes up after 

 this was observed. 



Now, in the original design, and I was not in on this, and I am 

 merely speaking from what small knowledge I have of the original 

 design, but in the initial design it was assumed by the designer that 

 the underwater bracing would be tight and would be effective, and that 

 the natural frequencies would be about 37 cycles a minute. 



When the tower was constructed, the actual frequencies were very 

 much less ; they were 19 cycles, and this means that the tower had much 

 greater motion for the same amount of force on it because of the very 

 much lower natural frequency. 



So that this condition was recognized at once by the designers and 

 by the people who were responsible for the structure as being bad, 

 and, at the time we were there, they were making strenuous efforts to 

 correct the structure beneath the sea. 



In fact, the divers were down, and they were making attempts to 

 put collars on where there had been some damage, and they were 

 making every effort that could be made to try to restore the integrity 

 of the subsea structure. So I cannot really answer that question 

 directly. 



The only thing I can say is that if the tower had such a low fre- 

 quency at the beginning, as a design fact, then certainly it would have 

 been well to look into the dynamics of tilings. 



