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Unformatted text preview: 11Ch11.qxd 9/27/08 2:21 PM Page 855 855 SECTION 11.3 Critical Loads of Columns with Pinned Supports Problem 11.3-8 A slender bar AB with pinned ends and length
L is held between immovable supports (see figure).
What increase T in the temperature of the bar will produce
bucking at the Euler load? ΔT A B L Solution 11.3-8 Bar with immovable pin supports
A cross-sectional area
E modules of elasticity
I moment of inertia
a coefficient of increase in temperature
¢ T uniform increase in temperature
AXIAL COMPRESSIVE FORCE IN BAR (EQ. 2-17)
P p2EI EULER LOAD Pcr L2 INCREASE IN TEMPERATURE TO PRODUCE BUCKLING
P Pcr p2EI EAa ( ¢ T) ¢T L2 EAa ( ¢ T) p2I
aAL2 ; P Problem 11.3-9 A rectangular column with cross-sectional dimensions
b and h is pin-supported at ends A and C (see figure). AT midheight, the
column is restrained in the plane of the figure but is free to deflect
perpendicular to the plane of the figure.
Determine the ratio h/b such that the critical load is the same
for buckling in the two principal planes of the column. C X L
2 X b
2 b Section X-X A Solution 11.3-9 Column with restraint at midheight
Critical loads for buckling about axes 1-1 and 2-2:
2 L P2 p2EI2
2 (L/2) FOR EQUAL CRITICAL LOADS
P1 P2 ‹ I1 4I2 bh3
12 I2 hb 3
12 bh3 4hb 3 h
b 2 4p2EI2
L2 ; ...
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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