sm12 93

________________________________________________________________________
PROBLEM (12.93) Redo Prob. 12.92 for a beam supported at midspan C by a spring of stiffness
k = 200 kN/m, as shown in Fig. P12.93.
SOLUTION
See solution of Prob. 12.92
k
B
A
L/
2
C
L/
2
h
W
R
st
R
k
δ =
R
W=196.2 N
33
3
()
0.65 10
48 48
st WRL RL R
EI EI k
δ
−
−
==×−
=
or
3
61
650 10 ( )
48
L
RkEI
−
×=+ 3
61(2)
10 [ ]
0.2 48(0.07)(0.72)
R
−
=+
or
650 (5 3.307), 78.2
R
RN
=
+= and 118WR N
−
=
Hence
3
78.2 0.39
200 10
st Rmm
k
δ == =
×
Maximum stress occurs at midspan:
6
118(2)(0.03) 2.46
4(0.72 10 )
st Mc
M
Pa
I
σ
−
== =
×
3
2(0.05)
11 17
0.39 10
K− =+ + =
×
Continued on next slide
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(a)
max 17(0.39) 6.65vm==m
(b) max 17(2.46) 41.82
M
Pa
σ
==
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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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