68 RESISTANCE OF MATERIALS 



expression for d, by its equal it becomes 



(58) 



e 



5 pi* 



The total angular deflection for half the beam in this case is 



(59} tan 6 = = . 



E I 24 E I 



The deflection may also be obtained by regarding the moment 

 diagram as representing the load on the beam. Since the total area 



of the moment diagram is , each reaction will then be , and 



therefore, taking moments about the center to find the deflection at 

 this point, the result is, as before, 



Ceo) d = ( -- 1\ = 



V*V jjiT \ 9/1 9 94 1A I 



Jjjj_ \ ^T: ^j ^y A JL O / 



APPLICATIONS 



136. A 15-in. I-beam weighing 60 Ib./f t. carries a 25-ton load at the center of 

 a 12-ft. span. Find the maximum deflection. 



137. In building construction the maximum allowable deflection for plastered 

 ceilings is ^^ of the span. A floor is supported on 2 in. x 10 in. wooden joists 

 of 14-ft. span and spaced 16 in. apart on centers. Find the maximum load per 

 square foot of floor surface, in order that the deflection may not exceed the 

 amount specified. 



138. Determine the proper spacing, center to center, for 12-in. steel I-beams 

 weighing 35 Ib./f t., for a span of 20 ft. and a uniform floor load of 100 lb./ft. 2 , in 

 order that the deflection shall not exceed ^^ of the span. 



139. A structural steel shaft 8 in. in diameter and 6 ft. long between centers of 

 bearings carries a 25-ton flywheel midway between the bearings. Find the maxi- 

 mum deflection of the shaft, considering it as a simple beam. 



140. A wrought-iron bar 2 in. square is bent to a right angle 4 ft. from one 

 end. The other end is then embedded in a concrete block so that it stands upright 

 with the 4ft. length horizontal. If the upright projects 12ft. above the concrete, 

 and a load of 300 Ib. is hung at the end of the horizontal arm, find the deflection 

 at the end of this arm. 



141. A wooden cantilever 2 in. x 10 in. in section, with the longer side vertical, 

 projects 10 ft. from the face of a wall and carries a concentrated load of 600 Ib. at 

 a point 6 ft. from the wall. Find the deflection at the free end of the beam. 



142. A 10-in. steel I-beam weighing 40 lb./ft. spans an opening 16 ft. wide and 

 supports a total load of 40 tons. Find how much greater the maximum deflection 

 of the beam is when this load is concentrated at its center than when it is distri- 

 buted uniformly over the beam. 



