sm10 145

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________________________________________________________________________
PROBLEM (10.145) In the fixed beam AB shown in Fig. P10.145, the left-hand support has settled
a distance δ0 below the right-hand support. Determine the support reactions.
SOLUTION
Consider
A
R
and A
M
as redudants.
2
12
1
2
AA
M
LRL
AA
EI EI
==−
00
/12BA B A AA
θθθ =−=+
Thus,
2
AA
M
RL= (1)
23
/01 2
2
() ( )
2323
AA
AB
M
LRL
L
tAAL
EI EI
δ =− = + = −
or
0
2
6
23
AA
EI
RL M L
δ
−+=− (2)
From Eqs. (1) and (2):
00
32
12 6
AA
EI EI
RM
LL
δ
δ
=− ↓ =−
Continued on next slide
R
A
M
A/EI
A
1
A
M/EI
B
M
A
L
x
B
x
RB
MB
R
A
A
-R
A
L/E
I
M
A
δ
0
L/
2
A
2
2L/3

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Symmetry dictates that
BA BA
R
RMM=− ↑ =