124 [RESISTANCE OF MATERIALS 



77. Bursting pressure for thick cylinder. Let u t denote the ulti- 

 mate tensile strength of the material of which the cylinder is com- 

 posed. Then, from equation (176), the maximum allowable internal 

 pressure w i is obtained from the equation 



whence 







Equation (178) gives the maximum internal pressure w t which the 

 cylinder can stand without bursting. 



78. Maximum stress in thick cylinder under uniform external 

 pressure. Consider a thick circular cylinder subjected only to 

 external pressure. In this case w t ,= and equations (174) become 



Since p h is positive, the hoop stress in this case is compression. 

 For a point on the inner surface of the cylinder r = 6, p r = 0, and 



79. Comparison of formulas for the strength of tubes under uni- 

 form internal pressure. 



I. Thin Cylinder f-^.O23j. From article 73 the formula for 

 the hoop (or circumferential) stress in a thin circular cylinder is 



(180) ft = g, 



and from article 74, when the ends of the cylinder are closed, the 

 longitudinal stress is 



