THICK CYLINDERS AND GUNS 57 



543. A concrete beam 14 inches deep, 8 inches wide, and 10 feet 

 span, with supported ends, has two |-inch square steel rods placed 

 1 inch from the bottom. Supposing that the concrete offers no tensile 

 resistance, find the total uniform load for the beam if the maximum 

 compressive unit-stress in the concrete is 500 pounds per square inch. 

 What is then the tensile unit-stress in the steel ? 



544. Solve Problem 543 for a concrete beam 8 inches broad, 10 

 inches deep, and 15 feet span, which is reinforced on the tensile side 

 by six J-inch steel rounds with their centers 2 inches from the 

 bottom of the beam. 



545. A concrete beam 8 inches broad and 10 inches deep is 

 reinforced by steel rods placed with their centers 2 inches from the 

 bottom of the beam. Neglecting the tensile strength of the concrete, 

 find the area of the steel reinforcement necessary to make the beam 

 equally strong in tension and compression. What is then the safe 

 bending moment for a factor of safety of 6 ? 



XIII. THICK CYLINDERS AND GUNS 



546. A cylinder 1 foot inside and 2 feet outside diameter is sub- 

 jected to an internal pressure of 600 pounds per square inch and an 

 external pressure of 15 pounds per square inch. Determine the tan- 

 gential unit-stresses at the inside and outside surfaces of the cylinder. 



547. The steel cylinder of an hydraulic press has an internal diam- 

 eter of 5 inches and an external diameter of 7 inches. How great an 

 internal pressure can the cylinder withstand with a factor of safety 

 of 4? 



548. Find the internal pressure to burst a cast-iron cylinder 10 

 inches inside diameter and 5 inches thick. Compare the result with 

 that obtained when considering it a thin cylinder. 



549. Determine the internal pressure for a cast-iron pipe 10 inches 

 inside diameter and 2 inches thick, for a factor of safety of 8. Con- 

 sider it first as a thick and then as a thin cylinder. 



550. If a gun of 3 inches bore has an internal pressure of 2000 

 pounds per square inch, what should be its thickness so that the 

 greatest stress in the material shall not exceed 3000 pounds per 

 square inch? 



