sm10 67

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PROBLEM (10.67) Before linearly varying load of maximum intensity w0 is applied to the beam
shown in Fig. 10.67, a small gap δA= 1/16 in. exists between the beam AB and the support at A.
Determine the reaction at each support developed after the loading.
Assumption: The bearing block is taken to be rigid.
Given: w0 = 2.4 kips/ft, L = 10 ft, E =10 x 106 psi, I = 65 in.4
SOLUTION
Resolve Example 10.12a with (0) A
v
δ
=
− to obtain: 2A CEI
δ
=
−.
Hence,
0
10
AwL
R
K=− 2
0
0
2
515
BB
wL
R
wL K M KL=+ =+
where
6
33
33(30 10 )(65)(0.0625) 0.2116
(120)
A
EI
Kkips
L
δ
×
== =
Substitute the given data:
(2.4 12)120 0.2116
10
A
R=−2.188 kips
=
↑
2(2.4 12)120 0.2116
5
B
R=+9.82 kips
=
↑
2
(2.4 12)(120) 0.2116(120)
15
B
M=+217.4 .kip in
=
⋅
y
w0
B
R
A
M
B
R
B
δ
A
L