VIBRATORY MOVEMENTS AND THEIR EFFECTS. 41 
In the calculations above we have supposed the pipe so firmly embedded in the sur- 
rounding earth that it moves with the earth; under this supposition the strength of the 
pipe to resist rupture due to vibrations would not be changed by altering the thickness 
of the pipe; but if the pipe slips in the ground, as it might if it were very straight for 
distances of half a wave-length or more, it might be strengthened by making it thicker ; 
but it is hardly practicable to lay pipes straight for such distances, and therefore we 
should not seek to strengthen pipes in the ground by making them thicker; but they 
would be strengthened by selecting a material with a large ratio of its breaking strength 
to its Young’s modulus. Wrought-iron pipes would yield by crushing rather than by 
tension, whereas cast-iron would yield first by tension; but it would require a stronger 
vibration to pull apart a cast-iron pipe than to crush one of wrought-iron. In general, 
however, the joints are the weakest spots and the ruptures occur there. 
The Spring Valley Water Company sends water to San Francisco thru three pipes 
(map No. 21, and fig. 22). The San Andreas pipe draws directly from the lake of the 
same name; altho it starts at the fault-line it was ruptured at one place only, where 
it crosses a marsh at Baden Station on a trestle. The pipe here was weakened by an 
extension joint, the two ends being held together by wires passing over lugs on the pipes; 
these lugs were pulled out. The lack of injury to the pipe at other places shows that, 
where buried in the ground, it was quite strong enough to stand the compressions and 
extensions due to the vibrations, and makes it probable that the many injuries received 
by the two other pipes, not along the fault-line, and of which we have no details, were due 
to some special causes of weakness at the points where they occurred. When the pipe 
was buried, it was prevented from bending and was then strong enough to remain intact, 
but where it was carried on a high trestle, or on a trestle over a soft marsh, bending was 
possible and its power of resistance was similar to that of a column under compression ; 
as is well known, a column yields, not by crushing, but by bending. 
The Pilarcitos 30-inch wrought-iron pipe is carried across Large Frawley Canyon 
on a high trestle about half a mile east of the fault (plate 1004); the pipe is buried on 
each side of the canyon, the intervening length being 100 feet; this portion was broken 
into two pieces of practically equal lengths which, together with the greater part of the 
trestle, were thrown into the canyon and left side by side, 50 or 60 feet from their original 
position. The ruptures occurred at riveted joints, the two pieces being otherwise intact. 
It is clear that the portion of the pipe on the trestle must have acted like a column with 
fixt ends. The formula which most accurately represents the strength under these 
conditions is known as Rankine’s formula,’ and is 
Ve 
ea ee cL? /k®” 
where p is the pressure in tons per square inch necessary to cause the collapse, and f and c 
are constants, the first dependent upon the material of the column only, the second both 
upon the material and upon the character of the ends; L is the length of the column and k 
is the radius of gyration of the cross-section. For wrought-iron f is 16 tons per square 
2 
inch; c is 1: 36,000 for a pipe with fixt ends; k? = = where d is the average of the 
inside and outside diameters; so that the formula becomes 
16 
Eo pee TL: 
* + 7500 G) 
The length of the pipe over Large Frawley Canyon is 100 feet and the diameter 2.5 feet, 
2 . 
therefore (3) is 1,600, and p, the pressure necessary to break it, becomes 11.8 tons per 


1 Ewing’s Strength of Materials, p. 178. 
