sm10 155 156

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________________________________________________________________________
PROBLEMS (10.155 and 10.156) A beam AB is supported and loaded as shown in Figs.
P10.155 and P10.156. Determine the reactions at supports A and B.
SOLUTION (10.155)
Consider
A
R
as redundant.
/0
AAB
vt
=
=
0
B
θ
=
2
111
()
22
AA
ARLLRL==
2
211
()
22 2 8
PL L
APL=− =−
/12
25
0()()
36
AB LL
EIt A A== +
or
5
16
A
R
P=↑
Statics:
11
16
B
R
P=↑ 3
16
B
M
PL=
Continued on next slide
B
2L
/
3
L/
2
M
B
C
A
1
C
x
tangent at A
B
M
A
P
A
-PL/2
L/2
A
2
R
A RB
L/2
RAL
L/
3

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instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other
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SOLUTION (10.156)
Consider
A
R
and A
M
as redundants.
2
111
()
22
AA
ARLLRL==
2A
AML
=
−
22
00
31()
46 24
wL wL
AL
EI EI
=− =−
00
/123
0
AB B A AAA
θθθ =−==++
or
2
0
11
224
AA
M
RL wL−+ = (1)
123
24
0()()()
325
AB LL L
EIt A A A== + +
or
2
0
21
315
AA
M
RL wL−+ = (2)
From Eqs.(1) and (2):
2
0
1
30
A
M
wL= 0
3
20
A
R
wL
=
↑
Statics:
0
7
20
B
R
wL=↑ 2
0
1
20
B
M
wL=
M
B
A
1
x
B
M
A
-w0L2/6
R
A RB
MA
RAL
2L
/
3
L
Cubic
4L/5
Tangent at B w0
-MA
L/
2
A
3
A
2