sm10 66

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PROBLEM (10.66) Before the uniform load of intensity w is applied to the beam shown in Fig.
P10.66, a small gap δB = 1/8 in. exists between the beam AC and the support at B. What is the reaction at
each support developed subsequent to the loading ?
Given: w = 1.2 kips/ft, L=12 ft, EI = 400(106) lb
⋅
in.2
SOLUTION
Example 10.10 is resolved with the last of Eqs.(c) in page 498 is modified as
() B
vL
δ
=− .
In so doing
2
7
32 8
AK
MwL
=
+ 13
24 8
AK
RwL
L
=+ 19
24 8
BK
RwL
L
=−
where
6
22
24 24(400 10 )(0.125)
(12 12)
B
EI
KL
δ
×
== ×57.87 .kip in
=
⋅
Thus,
2
7 1.2 57.87
( )(144) 460.8 .
32 12 8
A
M
kip in
=
+= ⋅
13 1.2 57.87
( )(144) 7.85
24 12 8(144)
A
R
kips=+=↑
19 1.2 57.87
( )(144) 11.35
24 12 8(144)
B
R
kips=−=↑
R
A
A
C
B
M
A
y
w
R
B
δ
B
L
L
/2