68 On the Strength of Cylindrical Steam Boilers. 



Art. XII. — Remarks on the Strength of Cylindrical Steam Boilers; 

 by Walter R. Johnson, Professor of Mechanics and Natural 

 Philosophy in the Franklin Institute, Philadelphia.* 



[Read before the Institute, at the stated monthly meeting, July 26, 1832. J 



It has been generally supposed that the rolling of boiler-plate iron, 

 gives to the sheets a greater tenacity in the direction of the length, 

 than in that of the breadth. Supposing this to be correct, it has fre- 

 quently been asked, how the sheets ought to be disposed in a cylin- 

 drical boiler of the common form, in order to oppose the greatest 

 strength to the greatest strain. It has also been asked, whether the 

 same arrangement will be required for all diameters, or whether a 

 magnitude will not be eventually attained, which «^-:-yrequire the di- 

 rection of the sheets to be reversed ? 



To determine these questions in a general manner, recourse must 

 be had to mathematical formulas, assuming such symbols for each of 

 the elements as may apply to any given case of which the separate 

 data are determined either by experiment or by the conditions of t^e 

 case. The principles of the calculation require our first notice. 



1. To know the force which tends to burst a cylindrical vessel in 

 the longitudinal direction, — or, in other words, to separate the head 

 from the curved sides, we have only to consider the actual area of 

 the head, and to multiply the number of units of surface by the num- 

 ber of units offeree applied to each superficial unit. This will give 

 the total divellent force in that direction. 



To counteract this, we have, or may be conceived to have, the te- 

 nacity of as many longitudinal bars as there are linear units in the cir- 

 cumference of the cylinder. The united strength of these bars con- 

 stitutes the total retaining or quiescent force, and at the moment when 

 rupture is about to take place, the divellent and the quiescent forces 

 must obviously be equal. 



2. To ascertain the amount of force which tends to rupture the 

 cylinder along the curved side, or rather along two opposite sides, 

 we may regard the pressure as applied through the whole breadth of 

 the cylinder upon each linear unit of the diameter. Hence the total 

 amount of force which would tend to divide the cylinder in halves by 



* From the Jouraal of the Franklin Institute. 



