EXAMPLES XIX 317 



(12) A cantilever AB, of length I ft., A being the fixed end, 

 carries a load of W tons at a point C distant b ft. from A. Find 

 expressions for the bending moment, the slope, and the deflection 

 for the two parts AC and CB of the cantilever. What is the 

 deflection at C, and the deflection at B ? 



(18) A beam AB, of length 2a ft., is supported at the ends and 

 carries equal loads, each W tons, at points D and E on either side 

 of the centre C and at distances b ft. from it. Find expressions 

 for the bending moment, the slope, and the deflection for the 

 two parts CE and EB of the beam. What is the greatest deflec- 

 tion, and what is the deflection under one of the loads ? 



(14) ACB is a cantilever of length / ft. A is the fixed end and 

 C is a point situated at a distance b ft. from A. The part AC 

 carries a uniformly distributed load of to tons per foot run, while 

 the part CB is unloaded. Find expressions for the bending 

 moment, the slope, and the deflection for the two parts AC and 

 CB of the cantilever. What are the deflections at C and B ? 



(15) ADCEB is a beam, of length 2a ft., supported at the ends 

 A and B ; C is the centre and D and E are points situated at 

 equal distances b ft. on either side of C. The part DE of the 

 beam carries a uniformly distributed load of w tons per foot run, 

 while the remainder is unloaded. Find expressions for the bend- 

 ing moment, the slope, and the deflection for the two parts CE 

 and EB of the beam. What is the maximum deflection and what 

 is the deflection at E ? 



(16) If = -=-^, -j = S and -j- = w. Let w be a constant, find 



c dx 2 dx dx 



S. Let S = W, a constant, when x = 1. Find M and let M = 



dii 

 when x = I, c is a given constant, find -j- and let its value be 



when x = 0. Find y and let its value be when x = 0. (B. of E., 

 1908.) 



(17) There are two cantilevers of equal length and of the same 

 cross section. The first carries a load which decreases uniformly 

 from 2 tons at the fixed end to at the free end, and the second 

 carries a uniformly distributed load of w tons per foot run. What 

 must be the value of w so that the free ends of the cantilevers 

 will be deflected to the same amount, and what is the ratio of the 

 deflections at the mid points ? 



(18) If the section Fig. 63 is subjected to a shearing force of 

 1000 lb., what is the intensity of the shear stress at the neutral 

 axis ? What are the intensities of the shear stresses at the under 

 edge of the flange and at the top of the web ? 



(19) If the section Fig. 73, No. 5, is subjected to a shearing 

 force of 1000 lb., what is the intensity of the shear stress at the 

 neutral axis (1) when the web is vertical (2) when the web is 

 horizontal ? 



