76 STRENGTH OF MATERIALS 



Fig. 58, the shear will tend to slide these layers one upon another. 

 By Hooke's law, the amount of this sliding for different layers wiJ 



, . B t also vary as the ordinates to a parabola, 



I I being zero at top and bottom and a maxi- 



I W mum at the center. Therefore, if the 



/^ y elongations and contract ions of the fiben 



f ^j due to bending stress are combined with 



t ^7 the sliding due to shear, the result ant 



D'* 'C' deformation of the prism will be as rq- 



FlG ' 59 resented in Fig. 59. 



68. Effect of shear on the elastic curve. In addition to the hori- 

 zontal shearing stress acting at any point in a beam, there is a si 



ing stress of equal intensity acting in a vertical direction. The etVe.-t 

 of this vertical shear is to slide each cross section past its adjacent 

 cross section, as represented in Fig. 60, and 

 thus increase the deflection of the beam. 



In extended treatises on the strenut h >f mate- 

 rials formulas are derived by means of wliieh 

 the amount of this shearing deflection can be 

 calculated. It is found, however, that in all 

 ordinary cases the shearing deflection is so 

 small that it can be neglected, in comparison 



with the deflection due to bending strain. The v **Jc' 



point to be remembered, then, is that the 

 shearing deflection is negligible but not ze 



In precise laboratory experiments for the determination of Young's 

 modulus it should always be ascertained whether or not the shearing de- 

 formation can be neglected without affecting the precision of the result 



69. Built-in beams. If the ends of a beam are secured in such a 

 way as to be immovable, the beam is said to be built-in. Kxamples of 

 built-in beams are found in reenforced concrete construction, in wliieh 

 all parts are monolithic. Thus a floor beam in a building constructed 

 of reenforced concrete is of one piece with its supporting girders, and 

 consequently its ends are immovable. 



Since the tangents at the ends of a built-in beam are horizontal. 

 dy 

 ~ = at these points. Also, from Fig. 61, it is obvious that the. 



