32 PROBLEMS IN STRENGTH OF MATERIALS 



274. A wrought-iron beam 14 feet long, supported at its ends and 

 of circular section, is loaded with a total uniform load of 200 pounds 

 per linear foot. Find its diameter for a factor of safety of 4. 



275. A simple wooden beam 20 feet long and 12 inches square 

 supports a load of 2 tons at the middle. Find the factor of safety, 

 considering the weight of the beam. 



276. A cast-iron rectangular beam resting upon end supports 12 feet 

 apart carries a load of 2000 pounds at the center. If the breadth is 

 one half the depth, find the area of cross-section for a factor of safety 

 of 4. Neglect weight of beam. 



277. Round and square beams of the same material are equal 

 in length and have the same loading. Find the ratio of the diameter 

 to the side of the square so that the two beams may be of equal 

 strength. 



278. Compare the relative strengths of a square beam and a circular 

 beam which is the inscribed cylinder. 



279. Compare the strength of a square beam with a side vertical, to 

 that of the same beam with a diagonal vertical. 



280. Compare the relative strengths of a cylindrical beam and the 

 strongest rectangular beam that can be cut from it. 



281. A wrought-iron beam 8 feet in length and supported at its 

 ends bears a total uniform load of 2000 pounds per linear foot. Its 

 section is like Fig. 19, where b 1 = 5 2 = 4, t l = t 2 = t = l } and d = 6 

 inches. Find the factor of safety. 



282. Find the factor of safety for the beam of Problem 281, if its 

 section is like Fig. 15, with b = 4, d = 6, ^ = 2, and d = 4 inches. 



283. The beam of Problem 281 has a section like Fig. 21, with 

 6 = 4, j = t = 1, and d = 8 inches. Find the factor of safety. 



284. Determine the factor of safety for a wrought-iron beam 8 feet 

 in length and supported at its ends, with a concentrated load of 8000 

 pounds 3 feet from the left end. Its section is like Fig. 19, with \ = 

 5 2 = 4, tfj = t 2 = t = 1, and d = 6 inches. Neglect weight of beam. 



285. The beam of Problem 284 has a section like Fig. 15, with 

 I = 4, d = 6, &j = 2, and d^ = 4 inches. Find the factor of safety. 



286. Find the factor of safety for a circular wrought-iron simple 

 beam 3 inches in diameter and 6 feet in length, with concentrated 

 loads of 1000 pounds 2 feet from each end. Neglect weight of beam. 



