RESTRAINED, OR BUILT-IN, BEAMS 89 



ince the supports are assumed to be at the same level, the total 

 deflection of A with respect to the tangent at B is zero. Con- 

 sequently, 



N_ PI} Pffi 

 3 El ZEI 2 El 

 whence 



("2) * 



Also 



(113) B' 



A V 



The moment at the fixed end B is then 



(114) M B = Kl - Pl z = - 



and the moment at the load C is 



(115) M c = Rl, = ^i (2 1 + y. 



The maximum deflection may be found by the method explained 

 in article 48. 



APPLICATIONS 



156. One end of a beam is built into a wall, and the other end is supported at 

 the same level by a post 12 ft. from the wall. The beam carries a uniform load of 

 100 Ib. per linear foot. Find the position and amount of the maximum moment 

 and also of the maximum deflection. 



157. One end of a beam is built into a wall, and the other end rests on a prop 

 20ft. from the wall at the same level. The beam bears a concentrated load of 

 1 ton at a point 8 ft. from the wall. Find the position and amount of the maximum 

 moment and also of the maximum deflection. 



158. A cantilever of length I is loaded uniformly. At what point of its length 

 should a prop be placed, supporting the beam at the same level as the fixed end, 

 in order to reduce the bending stress as much as possible, and what proportion of 

 the load is then carried by the prop ? 



159. A 20-in. steel I-beam weighing 65 Ib./ft. is built into a wall at one end 

 and rests on a support 20 ft. from the wall at the other end. A load of 25 tons 

 rests on the beam at a point distant 15 ft. from the wall. Find the reaction of the 

 support and the maximum deflection. 



160. A beam of uniform section is built into a wall at one end, projecting 16 ft. 

 from the face of the wall, and rests on a column at 12 ft. from the wall. The 

 beam carries a uniform load of 5 tons per foot run. Find the load on the column. 



