02-02ChapGere.0002 - elongation of the lower half of the bar L h B A C Solution 2.3-10 Prismatic bar hanging vertically W 5 Weight of bar(a D

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Solution 2.3-9 Wood pile with friction SECTION 2.3 Changes in Lengths under Nonuniform Conditions 81 F ROM FREE - BODY DIAGRAM OF PILE : (Eq. 1) (a) S HORTENING d OF PILE : At distance y from the base: © F vert 5 0 Ê c 1 T 2 Ê fL 2 P 5 0 Ê f 5 P L N ( y ) 5 axial force N ( y ) 5 fy (Eq. 2) (b) C OMPRESSIVE STRESS s c IN PILE At the base ( y 5 0): s c 5 0 See the diagram above. At the top( y 5 L ): s c 5 P A s c 5 N ( y ) A 5 fy A 5 Py AL d 5 PL 2 EA d 5 # L 0 d d 5 f EA # L 0 ydy 5 fL 2 2 EA 5 PL 2 EA d d 5 N ( y ) dy EA 5 fy dy EA L y P f dy f = P L s c = Py AL P A 0 Compressive stress in pile Friction force per unit length of pile Problem 2.3-10 A prismatic bar AB of length L , cross-sectional area A , modulus of elasticity E , and weight W hangs vertically under its own weight (see figure). (a) Derive a formula for the downward displacement d C of point C , located at distance h from the lower end of the bar. (b) What is the elongation d B of the entire bar? (c) What is the ratio b of the elongation of the upper half of the bar to the
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Unformatted text preview: elongation of the lower half of the bar? L h B A C Solution 2.3-10 Prismatic bar hanging vertically W 5 Weight of bar (a) D OWNWARD DISPLACEMENT d C Consider an element at distance y from the lower end. (b) E LONGATION OF BAR ( h 5 0) (c) R ATIO OF ELONGATIONS Elongation of lower half of bar: b 5 d upper d lower 5 3 / 8 1 / 8 5 3 d lower 5 d B 2 d upper 5 WL 2 EA 2 3 WL 8 EA 5 WL 8 EA d upper 5 3 WL 8 EA Elongation of upper half of bar ¢ h 5 L 2 ≤ : d B 5 WL 2 EA L h y B A C dy d C 5 W 2 EAL ( L 2 2 h 2 ) 5 W 2 EAL ( L 2 2 h 2 ) d C 5 # L h d d 5 # L h Wydy EAL N ( y ) 5 Wy L Ê d d 5 N ( y ) dy EA 5 Wydy EAL A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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This note was uploaded on 09/20/2009 for the course COE 3001 taught by Professor Armanios during the Spring '08 term at Georgia Institute of Technology.

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