Art. 16. 



SHEARS. 



13 



2000 Jbs. 



h-*'-r * 



I 20' 



k~*4.ooo (bs. zsoo 



the reactions R^ and R. This is a case of much practical import- 

 ance. The shearing stresses may be considered separately from 

 the bending stress which also occurs ; if the maximum (principal) 

 stress were wanted at any point, the resultant would have to be 

 found. (76). 



16. Shears. The shear, at any section of a body, is equal 

 to the algebraic sum of all the components of the external forces 

 taken parallel to the section and acting on either side of it, 



and is equal to the shearing stress 

 on the section. Thus in Figure 

 10, the shear (vertical) between 

 Ri and Pi equals 4000 Ibs. act- 

 ing up; between Pi and P 2 , 2000 



Fig. 10. Ibs. acting up; between P? and 



A, 1000 Ibs. acting down; at the section pq, 1600 Ibs. (1000 

 +3X200) acting down; just to the left of #2, 2500 Ibs. (1600 

 +4%X200) acting down; and just to the right of #2, there is 

 zero shear (25002500), as there should be. In Fig. 9, there is, 

 in like manner an "up" shear 011 each section between R^ and 

 P, equal to R lt and between P and R 2 , a down shear equal to 

 R P, (since P is larger than R^) or to E 2 . 



An "up" shear simply denotes that the part to the left of 

 the section tends to move up, past the part to the right, or the 

 part to the right tends to move down, past the part to the left. 

 Beginning at the right, 'ive get the sam.e results if we apply the 

 terms up and down to the part on the left as before. Shears are 

 usually spoken of as positive and negative, an "up" shear, going 

 from left to right, being positive. 



At a load, the shear changes abruptly, sometimes passing 

 through zero, so that we speak of the shear just to the left or 

 just to the right of the load, never at the load. Since loads car- 

 ried by trusses act at the panel points, the shear can change only 

 at the panel points, and is constant in the panels, hence we speak 



of the shear in a panel. In Fig. ll y 

 the shear in the first panel is equal to 

 R L ; in the second panel, to R^P^ ; in 

 the third, to R^P^P^-, in the 

 fourth, to R 1 P i P 2 P s or to R 2 . 

 It is evident, in this case, that the 



11. 



