STRENGTH OF MATERIALS 



which give the radial and hoop stresses in a thick cylinder subjected 

 to internal and external pressure. Equations (77) are known as 

 Lamp's formulas. 



111. Maximum stress in thick cylinder under uniform internal 

 pressure. Consider a thick circular cylinder which is subjected only 

 to internal pressure. Then w e = 0, and equations (77) become 



(78) 



Since p h is negative, the hoop stress in this case is tension. 



Since p r and p h both increase as r decreases, the maximum stress 

 occurs on the inner surface of the cylinder, where 



"* + &*) 

 r = b = iff and _--tL__. 



Therefore the equivalent stress for a point on the inner surface of the 



cylinder is l * + fr) 



or 



(79) 



If TO = 3^, this formula becomes 



(80) p. -^-^ (.7 6' + 1 .3 a). 



Problem 134. Find the thickness necessary to give to a steel locomotive cyl . 

 of 22 in. internal diameter, if it is required to withstand a maximum steam pressure 

 of 150 lb./in. 2 with a factor of safety of 10. 



Problem 135. In a four-cycle gas engine the cylinder is of steel with ;m int. 

 diameter of 6 in., and the initial internal pressure is 200 lb./in.* absolute.* With 

 a factor of safety of 16, how thick should the walls of the cylinder be made ? 



Problem 136. The steel cylinder of an hydraulic press has an internal diameter 

 of 5 in. and an external diameter of 7 in. With a factor of safety of 3, how great 

 an internal pressure can the cylinder withstand ? 



* By absolute pressure is meant the pressure mi-asuroil from a vacuum. Absolute 

 pressure therefore includes the atmospheric pressure, which must be deducted from it in 

 order to obtain the effective pressure. 



