24 PROBLEMS IN STRENGTH OF MATERIALS 



500 pounds at distances of 2, 5, and 8 feet respectively from 

 the fixed end. 



182. Show analytically that the maximum moment occurs in a 

 cantilever beam and in a simple beam at that section where the shear 

 passes through zero. 



In the following problems find also the position of the danger 

 section. 



183. A simple beam of length I, with two equal concentrated loads 

 at the quarter points. Neglect weight of beam. 



184. A simple beam of length I, with two equal concentrated loads 

 at the quarter points, and a uniform load of w pounds per linear foot. 



185. A simple beam of length 10 feet, with 200 pounds 4 feet from 

 the left end. Weight of beam neglected. 



186. A simple beam 12 feet in length, with 300 pounds 4 feet from 

 the left end, and a uniform load of 20 pounds per linear foot. 



187. A simple beam 20 feet long, weighing 12 pounds per linear 

 foot, with a load of 240 pounds 5 feet from the left end. 



188. A simple beam 8 feet in length, with a concentrated load of 

 1000 pounds 2 feet from the left end, and a uniform load of 500 

 pounds per linear foot. 



189. A simple beam 6 feet long, with concentrated loads of 1000 

 pounds 2 feet from each end, if weight of beam is neglected. 



190. A simple beam 12 feet long, with a uniform load of 40 pounds 

 per linear foot, and concentrated loads of 2000 pounds at 3 feet from 

 each end. 



191. A simple beam 12 feet in length, with 240 pounds 3 feet from 

 the left end, and 360 pounds 4 feet from the right end, if weight of 

 beam is neglected. 



192. The beam of Problem 191 has in addition to the concentrated 

 loads a uniform load of 60 pounds per linear foot. 



193. A simple beam 20 feet long, with concentrated loads of 2000 

 pounds 4 feet from the left end, and 1000 pounds 2 feet from the 

 right end, and also a uniform load of 100 pounds per linear foot. 



194. A simple beam 6 feet in length, there being concentrated loads 

 of 4000 and 1000 pounds 1 and 2 feet respectively from the left end, 

 and no uniform load. 



