54 



RESISTANCE OF MATERIALS 



102. In an inclined railway the angle of inclination with the horizontal is 

 80. The stringers are 10 ft. 6 in. apart, inside measurement, and the rails are 



placed 1 ft. inside the stringers. The 

 ties are 8 in. deep and 6 in. wide, and 

 the maximum load transmitted by each 

 rail to one tie is 10 tons. Calculate the 

 maximum normal stress in the tie. 



Solution. The bending moment is 

 the same for all points of the tie be- 

 tween the rails, and is 20,000 ft.-lb. 

 The components of the moment with 

 respect to the axes of the_ section 

 FIG. 49 



(Fig. 49) are ^ = 240,000 I - 



and My = 240,000 () in.-lb., and the section moduli with respect to these axes are 

 Z 2 = 64 in. 8 and Z y = 48 in. 8 Therefore the maximum normal stress is 



240,000 



Pmax = 



240,0001- 



64 



= 57441b./in. 2 



103. A rectangular cantilever projects a distance I from a brick wall and 

 bears a single concentrated load P at its end. How far must the inner end 

 of the cantilever be em- 

 bedded in the wall in 

 order that the pressure 

 between this end and 

 the wall shall not exceed 

 the crushing strength 

 of the brick ? 



Solution. Let b denote 

 the width of the beam 

 and x the distance it 

 extends into the wall. 

 For equilibrium the re- 

 action between the beam 

 and the wall must con- 

 sist of a vertical force 

 and a moment. If p a 

 denotes the intensity of 



the vertical stress, and it is assumed to be uniformly distributed over the area 6x, 



p 

 then p a bx = P ; whence p a = (see Fig. 50, a). 



ox 



Similarly, let p b denote the maximum intensity of the stress forming the stress 

 couple. Then, taking moments about the center C of the portion AB, since the 

 stress forming the couple is also distributed over the area 6x, we have 



X 



a! 



and 



