sm10 129 130

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________________________________________________________________________
PROBLEMS (10.129 and 10.130) A beam ABC with an overhang BC supports a lod as shown in
Figs. P10.129 and P130. Determine:
(a) The angle of rotation at support B.
(b) The deflection at the free end C.
SOLUTION (10.129)
22
12
13 1
(3 ) ( )
22 22
Pa Pa Pa Pa
Aa Aa
EI EI EI EI
=− =− =− =−
23 3
/1 2
23 10
(2 ) ( )
333
CA aPaPa Pa
tAaA EI EI EI
=+ =−−=−
2
/1 3
() 2
BA Pa
tAa EI
==−
2
/
1
32
ABA
Pa
t
aEI
θ =− =
(a) /1AB A B A
θ
θθ =−=
222
113
22
BA Pa Pa Pa
AEI EI EI
θθ =−= − =
(b) 33
//
41043
()
3332
CCA BA Pa Pa
vt t EI EI
=− =− −−
3
4
3Pa
EI
=↓
Continued on next slide
t
B
/A
x
B
4P
/
3
C
M/EI
B
A
θ
A
C
A1
P/
3
C
v
P
2a/3
tC/A
-Pa/EI
A
2
a
3a
2a
A
4tA/B/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 (10.130)
23
122
(2 )
323
wa wa
Aa
EI EI
=− =
23 23
23
11
(2 ) ( )
22 2 32 6
wa wa wa wa
AaAa
EI EI EI EI
=− =− =− =−
44
/1 2
424
() ( ) 0
336
AB awawa
tAaA EI EI
=+ =−− =
(a) /
10
2
BAB
t
a
θ == Thus '"0CC
=
.
(b) 4
/3
3
()
48
CB awa
tA EI
==−
4
/8
CCB
wa
vt EI
== ↓
B
A
C
B
B
θ
A
tB/A
C
C
v
-wa2/2E
I
M/EI
a
wa2
/
2E
I
x
w
2a
Spandrel
parabola
tan
g
ent at B
C’
C’
’
tC/B
y
Parabola
A
1
A
2
A
3
B
θ