________________________________________________________________________
PROBLEM (*11.28) A column AB of length L and flexural rigidity EI has a support at its
base that does not permit rotation but allows horizontal displacement and is pinned at its top as
shown in Fig. P11.28. Determine the critical load Pcr .
*SOLUTION
Differential equation for a free-body of a segment of x is given by Eq.(11.1):
2
20
dv
EI Pv
dx +=
or
22
20
dv P
pv p
dx EI
+= =
General solution is
(1) sin cosvA pxB px=+
Boundary conditions :
(0) 0: 0 0 0, 0vB=++= = B
=
'( ) 0: cos 0, 0v L AP pL Ap==
Since
0:A≠
cos or 0
PL
EI =()
2
PLn
EI
π
=
For 2
2
1, 4
P
nEI L
π
==
Therefore
2
2
4
cr EI
PL
π
=
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