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Unformatted text preview: 11Ch11.qxd 9/27/08 3:39 PM Page 869 869 SECTION 11.4 Columns with Other Support Conditions Solution 11.4-9 Fixed-end column
BUCKLING EQUATION deflection in the y direction
DIFFERENTIAL EQUATION (EQ.11-3)
œœ M El
œœ + k2 M0 P k P
EI 2 M0
EI B.C. 2 ¿ (0)
P ‹ C2 0 C1 k cos kx ‹ cos kL k2 C1 sin kx + C2 cos kx +
1 (0) 3 (L) M0
P 00 cos kL) and kL 2p 4p2 4p2 1 CRITICAL LOAD GENERAL SOLUTION B.C. B.C. ‹ C1 2p 2
L 0 cos kx) P
EI 2 L 4p2EI BUCKLED MODE SHAPE L
2 deflection at midpoint a x
P d cos p ‹d M0
P 2M 0
2 Problem 11.4-10 An aluminum tube AB of circular cross section
has a guided support at the base and is pinned at the top to a horizontal
beam supporting a load Q 200 kN (see figure).
Determine the required thickness t of the tube if its outside diameter
d is 200 mm and the desired factor of safety with respect to Euler buckling
is n 3.0. (Assume E 72 GPa.) L2 ; L2 Let d C2 k sin kx 0 Pcr a cos p)
2 cos 2px
L Q ; 200 kN B 1.0 m 1.0 m 2.0 m
d A 200 mm ...
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.
- Fall '11