Chap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 919 



function of the structure has been determined.^' Seismic resistance may 

 be defined as the ratio of ultimate stress U to the stress X corresponding 

 to an amplitude a: at a given point. For example, in a low structure where 

 shear predominates over flexure, the stress is approximately X = ^Xh/H, 

 where y is rigidity and Xh is the amplitude at the elevation H. The build- 

 ing amplitude a: is a function of the static magnification V, the ground 

 amplitude a, and the frequency factor /. In other words, x is dependent 

 on the magnification function of the building. Therefore, the seismic 

 resistance R = U p^, where U = ^{xb)u/H, with (xh)vi as the critical build- 

 ing amplitude at the elevation H. Since X = }xxh/H and Xh = Vco a(fd), 



where (/d) = / 2 ~2 2 T^ ^^ ^ damped frequency factor, the seis- 

 V (coo — CO ) -|- 4e CO 



mic resistance becomes 



^ = ^^•VU-co^)' + 4e^col (12-8) 



Determination of static magnifications appears to have been made 

 hitherto only on low buildings. On such structures the static magnifica- 

 tions ranged from 0.8 to 2 and the dynamic magnifications (at resonance) 

 from 2 to 20, the high figures indicating that the buildings were poorly 

 damped. 



Dynamic vibration tests are of practical value in industrial plants where 

 large machines are used in connection with a light framework. Structures 

 of this kind may eventually be shaken to pieces when the machine vibra- 

 tions resonate with the building and particularly when machine, struc- 

 ture, and ground are in resonance. It is sometimes possible to avert 

 damage by a slight change in the speed of the machine. Koehler de- 

 scribes investigations of a coal dressing plant whose vibration amplitude 

 could be reduced 77 per cent by increasing the speed of a screening machine 

 by only 11 per cent. 



2. Dynamic ground tests. In a dynamic ground test the site under 

 investigation is set into forced oscillation by a vibrator and the vibrations 

 are recorded either at the source or at one or several points some distance 

 away. The shakers are fairly heavy, cover a surface of about 10 square 

 feet, and are arranged for reinforcement of the vertical and cancellation of 

 the horizontal components of the centrifugal force. Vibrations are re- 

 corded by the usual electromagnetic vertical component seismographs em- 

 ployed in seismic exploration. Other possibilities, in respect to vibrators 

 and detectors, are discussed on pp. 915-917. Higher frequency agitators 



8' Heiland, loc. cit. 



" Zeit. Geophys., 12(4), 148-166 (1936). 



