246 
OF THE PARTS OF 
[sect. VII. 
Of the Strength of Pipes and Working Cylinders. 
516. The thickness for pipes and cylinders of solid metal is more frequently 
determined by the condition, that the castings may be sound and perfect, than by 
a regard to strength; yet it is necessary to show the proportions essential for 
strength, that a mistake in this respect may not occur. 
The data required are the tensile strain a square inch of the metal will bear 
without permanent alteration at the proposed temperature, the pressure of the 
steam on a circular inch including such allowance as is proper for the risk of 
increase, and the diameter of the cylinder. I advise to take double the whole force 
of the steam when it escapes at the safety valve of the boiler. 
We may safely consider the cylinder to be of equal resistance throughout its 
length; and hence, if we take the stress upon an inch of that length, that stress 
will be equal to the diameter in inches, multiplied by the greatest possible force on 
a square inch, and the resistance will be twice the thickness of the cylinder, by 
one-fourth of the limit of tensile strain of the metal, the tension being considered 
to be unequal on the resisting part. Thus we have the following rule. 
517. Rule. For the thickness of solid metal, pipes, or cylinders to bear a 
given stress, the whole being of an equal temperature:— 
Multiply 2'54 times the internal diameter of the cylinder, by the greatest 
force of steam on a circular inch ; divide by the tensile force the metal will bear 
without permanent alteration, the result is the thickness in inches. 
Example. To determine the thickness of a cast iron cylinder, 60 inches dia 
meter, for a pressure not exceeding 3'2 lbs. per circular inch, in addition to the 
atmospheric pressure. In this case twice the force is 30 lbs. on the circular inch, 
and the resistance of cast iron is 15,000 lbs. per square inch ; hence, 
2-54 x 60 x_30 = 0 . 305 inches 
loOOO 
518. Were there the direct force alone to consider, we see that a very thin 
cylinder or pipe is sufficient, but the pressure is often aided by a powerful strain 
from unequal expansion. If e be the extension the metal will bear without 
alteration, and t its thickness, a being the diameter of the pipe, we have 
t ' ' 2 e a 
e : : a : — > 
the greatest quantity which the expansion of one side of the pipe should exceed the 
other, = h c, when h = the excess of heat, and e = the expansion for one degree. 
In cast iron, e = 2200 ’ &ml e = 162000 ’ hence,