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PROBLEM (10.157) A fixed-guided roller beam AB carries a uniform load of intensity w as
shown in Fig. P10.157. Determine the reactions RA , MA , and MB for the beam.
SOLUTION
Equilibrium:
0: ( ) 0
2
AAB
L
MMMwL
=
+− =
∑(1)
0:
yA
FRwL==
∑
Since both tangent at A and tangent
at B are horizontal, 0
BA
θ
=.
Thus 2
1
0( )() ( )()
32
B
BA MwL
LL
EI EI
θ
== + −
or
2
6
BwL
M=
Equation (1) gives then
2
3
AwL
M=
x
B
MB
M/EI
MB
O
-wL2/2
w
Parabolic
spandrel
A
1
B
tangent at A
R
A
MA
A
2
L
L/3
B
A
tan
g
ent at B
1
/
1
100%