861_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 861_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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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 L length 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 h B L — 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: I1 P1 p2EI1 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.

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