144 RESISTANCE OF MATERIALS 



or, since cd = 4 ab, 



c* 

 (202) p = w> 



which gives the required maximum stress. 



For a square .plate a = b and c = a V2, and formula (202) reduces 

 to formula (201) for square plates, obtained in the preceding article. 



APPLICATIONS 



241. The cylinder of a locomotive is 20 in. internal diameter. What must be 

 the thickness of the steel end plate if it is required to withstand a pressure of 

 160 lb./in. 2 with a factor of safety of 6 ? 



242. A circular cast-iron valve gate ^ in. thick closes an opening 6 in. in diam- 

 eter. If the pressure against the gate is due to a water head of 150 ft., what is the 

 maximum stress in the gate ? 



243. Show that the maximum concentrated load which can be borne by a 

 circular plate is independent of the radius of the plate. 



244. A cast-iron manhole cover 1 in. thick is elliptical in form and covers an ellip- 

 tical opening 3 ft. long and 18 in. wide. How great a uniform pressure will it stand ? 



245. What must be the thickness of a wrought-iron plate covering an opening 

 4 ft. square in order to carry a load of 200 lb./ft. 2 with a factor of safety of 5 ? 



246. A wrought-iron trap door is 5ft. long, 3ft. wide, and | in. thick. How 

 great a uniform load will it bear? 



247. The steel diaphragm separating two expansion chambers of a steam turbine 

 is subjected to a pressure of 150 lb./in. 2 on one side and 80 lb./in. 2 on the other. 

 Find the required thickness for a factor of safety of 10. 



248. The cylinder of a hydraulic press is made of cast steel, 10 in. inside diam- 

 eter, with a flat end of the same thickness as the walls of the cylinder. Find the 

 required thickness for a factor of safety of 20. Also find how much larger the 

 factor of safety would be if the end was made hemispherical . Assume w = 1200 lb./in . 2 



249. The cylinder of a steam engine is 16 in. inside diameter and carries a steam 

 pressure of 125 lb./in. 2 If the cylinder head is mild steel, find its thickness for a 

 factor of safety of 10. 



250. A cast-iron valve gate 10 in. in diameter is under a pressure head of 200 ft. 

 Find its thickness for a factor of safety of 15. 



251. A cast-iron elliptical manhole cover is 18 in. x 24 in. in size and is designed 

 to carry a concentrated load of 1000 Ib. If the cover is ribbed, how thick must it 

 be for a factor of safety of 20, assuming that the ribs double its strength ? 



252. Thurston's rule for the thickness of cylinder heads for steam engines is 



where h = thickness of head in inches, 



D = inside diameter of cylinder in inches, 

 w = pressure in lb./in. 2 



Compare this formula with Bach's, assuming the material to be wrought iron and 

 using the data of problem 249. 



