861_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

861_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 ; ...
View Full Document

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.

Ask a homework question - tutors are online