88 APPLIED MECHANICS 
To make the existence of the turning or bending and the sliding or 
shearing actions more evident, consider the case of a block BC (Fig. 111) 
resting on a_hori- 
zontal plane YY. 
Let this block be | 
pushed by a hori- Y 
zontal force R as 
shown. If the re- Ye Bo Re 
sistance to sliding ; pie 
on YY be not too Fia. 110. Fia. 111. Fia. 112. 
great the block will _* 
slide to the left into, say, the position shown by the dotted lines. But 
if the resistance to sliding is great enough the force R will cause the 
block BC to tilt over, as shown by the dotted lines in Fig. 112, provided 
the resistance to tilting is not too great. R, is the resistance to sliding 
at YY, and R, is the effect of R transmitted, by reason of the rigidity 
of BC, from section to section downwards to YY. 
It is evident that the magnitude of the shearing action at YY depends 
only on the magnitude of R, and not on the distance of R from YY. 
But the turning or bending action at YY depends on both the magni- 
tude of R and the distance of R from YY. 
100. Positive and Negative Bending and Shearing. — When a 
horizontal beam is bent by thé action of the loads on it, it will either 
“sag” or “hog,” that is, it will either become concave or convex on the 
pokes oth te 
+ Bending. — Bending. + Shearing. — Shearing. 
----7 
C\ 
(?) 
a 
—w 
< 
ies 
pa 
— 
y 
a, 
r 
1 
‘ 
‘ 
R 
‘ 
\ 
\ 
‘ 
\ 
y 
Fig. 113. Fia. 114. Fie. 115. Fiq. 116. 
top, and it will be convenient to call one of these, say the first (Fig. 113), 
positive(+) bending, and the other (Fig. 114) negative ( —) bending. 
Again, in considering the shearing action at a section of the beam the 
loads will tend either to cause the portion to the right of the section 
to descend and the portion to the left to ascend, or vice versa, and it will 
be convenient to call one of these, say the first (Fig. 115), positive (+) 
shearing, and the other (Fig. 116) negative ( — ) shearing. 
101. Bending Moment and Shearing Force Diagrams.—If the 
bending moments and shearing forces at a sufficient number of sections of 
a beam be determined and the results plotted to scale at right angles to 
a base line representing the length of the beam, diagrams are obtained by 
joining the points plotted, which are called the bending moment and 
shearing force diagrams. In cases where there is both positive and 
negative bending, or positive and negative shearing on the same beam, 
it is necessary to distinguish between the positive and negative quantities 
by measuring them on opposite sides of the base line, and it is desirable 
in all cases to measure positive bending moments and positive shearing 
