sm10 60 61

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________________________________________________________________________
PROBLEMS (10.60 and *10.61) A beam is loaded and supported as shown in Fig. P10.60 and
P10.61. Determine the deflection at the free end .
SOLUTION (10.60)
Use Table B.14
() ()
BBPBQ
vv v=+
where,
() () ()(2)
BP CP CP
vv a
θ
=+
32 3
4
(2 )
32 3
Pa Pa Pa
a
EI EI EI
=− − =−
() () ()()
BQ DQ DQ
vv a
θ
=+
32 3
(2 ) (2 ) 14
()
32 3
Qa Qa Qa
a
EI EI EI
=− − =−
Thus, 3
2(2 7 )
3
Ba
vPQ
EI
=+↓
SOLUTION (*10.61)
Continued on next slide
A
P
=
+
B
Actual
Loading
Q
a
a
C
Equivalent Loadings
a
D
A
P
B
a
C
A
B
Q
a
D
A
P
=
+
B
Actual
Loading
L/
2
L/
2
C
M0
L/
2
A
P
M
0
a
C
A
B
()
BM
θ
C
B
P
D
M0

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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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Copyright Act without the permission of the copyright owner is unlawful.
Use Table B.14 (cases 7, 9, and 2):
,
() ()
D
BMP DM
vv v=+
where,
,,
() () ()
2
DMP BMP L
v
θ =
20
() ()
16 2 3 2
ML
PL L L
EI EI
=− −
() () ()()
DQ DQ DQ
vv a
θ
=+
2
0(2)
() 2
DM ML
vEI =−
Hence, 2
0
(3 28 )
96
DL
vPLM
EI
=−