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05-05ChapGere.0012

# 05-05ChapGere.0012 - 900.64 5 90 3 10 6 pascals 900.64 A T...

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Problem 5.12-7 Because of foundation settlement, a circular tower is leaning at an angle to the vertical (see figure). The structural core of the tower is a circular cylinder of height h , outer diameter d 2 , and inner diameter d 1 . For simplicity in the analysis, assume that the weight of the tower is uniformly distributed along the height. Obtain a formula for the maximum permissible angle if there is to be no tensile stress in the tower. Solution 5.12-7 Leaning tower SECTION 5.12 Beams with Axial Loads 361 C OMPRESSIVE STRESS 41.82 T 858.83 T 900.64 T ( c pascals) s c N A Mc I 0.90631 T 21.677 10 3 m 2 (0.96306 T )(0.13 m) 145.778 10 6 m 4 A LLOWABLE TENSILE FORCE
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Unformatted text preview: 900.64 5 90 3 10 6 pascals 900.64 A T THE BASE OF THE TOWER N 5 W cos a T ENSILE STRESS ( EQUAL TO ZERO ) M AXIMUM ANGLE a a 5 arctan d 2 2 1 d 1 2 4 hd 2 ∴ cos a A 5 hd 2 sin a 4 I Ê tan a 5 4 I hd 2 A 5 d 2 2 1 d 1 2 4 hd 2 s t 5 2 N A 1 Mc I 5 2 W cos a A 1 W I ¢ h 2 sin a ≤ ¢ d 2 2 ≤ 5 M 5 W ¢ h 2 ≤ sin a c 5 d 2 2 I A 5 d 2 2 1 d 1 2 16 h d 1 d 2 a W 5 weight of tower a 5 angle of tilt C ROSS SECTION 5 p 64 ( d 2 2 2 d 1 2 )( d 2 2 1 d 1 2 ) I 5 p 64 ( d 2 4 2 d 1 4 ) A 5 p 4 ( d 2 2 2 d 1 2 ) N V M 2 W A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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