130 APPLIED MECHANICS 
Reactions at Supports.— 
R,=F,=82'5 tons. RB,=F,+F,=117-5+57-38 = 174-88 tons. 
RB, =F, + F,= 42°62 + 48°26 = 90°88 tons. R,=F,=31°74 tons. 
Bending Moments.— 
For span AB. M-=82-5a-— %a?, where x is the distance of the section 
from A. M is zero when ¢= 0, or 132. Maximum positive value of 
M = 2723 when «= 66. 
For span BC. M= —2799+57-38«— 42°, where x is the distance of 
the section from B. M is zero when «=70°3, or 159°2. Maximum 
positive value of M=493°2 when =114°8. 
For spanCD. M=31-74a—- 42%, where x is the distance of the section 
from D. M is zero when «=0, or 127. Maximum positive value of 
M=1007 when w= 63°5. 
All the bending moment curves are parabolas whose axes are vertical 
and pass through the points of zero shear and maximum positive bending 
moment, as shown in Fig. 171. 
136. Advantages and Disadvantages of Continuous Girders.—The 
chief advantage which a continuous girder has over separate girders for 
each span will be clearly seen by reference to Fig, 172, in which the 
bending moment and ucts 
shearing force dia- Piet a 3 Bending Moments. 
grams for the example 
of a continuous gir- | hegre sfett We 
der, discussed in the HIN \ 1 
ae 
preceding Article, are 
reproduced with the 
addition of the bend- 
ing moment and 
shearing force  dia- 
grams for the three 
spans when covered ar 
with separate girders. My a 
The diagrams for the , 
continuous girder are ‘ 
shaded, while the \) 
boundaries of the dia- 
grams for the separate 
girders are shown dotted where they do not coincide with the boundaries — 
of the others. 
It will be seen that one effect of converting the separate girders into 
one continuous girder is to considerably reduce the bending moments in 
the neighbourhood of the middle of each span, and to produce bending 
moments at the supports, and also to increase the bending moments in 
the neighbourhoods of the supports. If the bending moments at the 
supports of the continuous girder are greater than at the other points, 
which is Senerally the case, the girders may be strengthened in the 
neighbourhoods of the supports, and the increase in weight will not, to 
any considerable extent, affect the bending moment diagram, the additional 
weight coming over or near the piers. A continuous girder will therefore 
Shearing Forces 
Fie. 172. 
