sm10 154

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PROBLEM (10.154) A propped cantilever beam AB is subjected to loads as shown in Fig. P10.154.
Calculate the reactions at each support.
SOLUTION
Select
A
R
as redundant.
Draw
M
EI diagrams (see Table A.4).
110 50
1( )(10)
2AA
R
R
AEI EI ==
21 80 320
()(8)
2
AEI EI =− =−
31 90 180
()(6)
3
AEI EI =− =−
Place reference tangent at B:
0.
B
θ
=
Also
12
22
[ (10)] [ (8) 2]
33
AB
tA A
=
++
31
[10 (6)] 0
4
A
+
−=
Then
50 20 320 28 180
() () (8.5)0
33
A
AB R
tEI EI EI =−−=
or
13.55
A
R
kN=↑
Equilibrium:
10 30 13.55 26.45
B
R
kN=+− = ↑
34.5
B
M
kN m
=
⋅
x
M
/E
I
M
B
A
1
x
B
M/EI
A
-80
A
2
R
A RB
10 RA
C
5 kN/m
-90
10 kN
Parabolic
Spandrel
A
3