sm10 158

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PROBLEM (10.158) A continuous beam ABC of two spans, carries moments M0 at each end A
and C as shown in Fig. P10.158. Determine the reactions RA , RB , and RC for the beam.
SOLUTION
Select A
R
as redundant. Requirement:
0
AB
t
=
012
()() ( )()( )
22 3
A
MRL
LL
LL
EI EI
=+−
or
23
0
023
A
ML
R
L
EI EI
=−
Solving
0
32
AM
RL
=
↓
Equilibrium:
0
3
0: () () 0
2
BC
M
MLRL
L
=
−=
∑
or
0
32
CM
RL
=
↓
00
33
0: 0
22
yB
MM
FR
LL
=−−=
∑
or 0
3
BM
RL =↑
B
L
2L/3
x
M/EI
A
A
2
M0
A
1
L/
2
3M0/2EI
M
0
C
B
A
M
0
L
R
C
RB
L