86 



STEENGTH OF MATERIALS 



The deflection of a beam bearing a static load P' at the center is D = -^-^ 



(Problem 75), or, substituting in this the value of P', D = -^j^ Assi; 



E = 30,000,000 lb./in. 2 , and replacing p, I, and e by the values given in the problem, 



D = .288 in. 

 Consequently, the work of deformation is 



W= - P'D = 

 2 



= 2442 in. Ib. 



Therefore, from the equality \P f D = P(h + D), we have 



= .75P(6- 

 P = 518 Ib. 



whence 



Problem 94. From what height can a weight of half a ton fall on the 

 of the beam in the preceding problem without producing a stress greater than 

 40,000 lb./in. 2 ? 



74.* Influence line for bending moment. As a load moves over a 

 structure the bending moment and shear at any given point change 



continuously. This v, 

 \P 



B 



tion of the bending moment, 

 shear, or any similar funr- 

 tiuii at a ^ivtMi ti.v.l point 

 due to a moving load can U* 

 represented graphical 1 

 a curve (>r straight lim-) 

 called an influence line. 



To obtain tin- influence 

 line for bending moment for 



a simple beam of length /, let d denote the distance of the ghvn ; 



A from the left support 0, and x the distance of a movable load /' t'n .m 



(Fig. 67). Then, if P is on the right of A, K, = P(l ~ ' r) 

 the moment at A is 



_P(l-x)d 

 I 



Now let P be a unit load (say one pound or one ton). Then 





FIG. 67 



and hence 



* For a brief course the remainder of this chapter may be omitted. 



