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Unformatted text preview: Solution 5.1211 Concrete wall 364 CHAPTER 5 Stresses in Beams h  height of wall t  thickness of wall b  width of wall (perpendicular to the figure) g c  weight density of concrete g w  weight density of water d  depth of water W  weight of wall W  bht g c F  resultant force for the water pressure M AXIMUM WATER PRESSURE  g w d A  bt S TRESSES AT THE BASE OF THE WALL ( d  DEPTH OF WATER ) Eq. (1) Eq. (2) s c   W A  M S   h g c  d 3 g w t 2 s t   W A  M S   h g c  d 3 g w t 2 S  1 6 bt 2 M  F d 3  1 6 bd 3 g w F  1 2 ( d )( g w d )( b )  1 2 bd 2 g w (a) S TRESSES AT THE BASE WHEN d  h h  6.0 ft  72 in. d  72 in. t  1.0 ft  12 in. Substitute numerical values into Eqs. (1) and (2): s t   6.042 psi  93.600 psi  87.6 psi s c   6.042 psi  93.600 psi   99.6 psi (b) M AXIMUM DEPTH FOR NO TENSION Set s t  0 in Eq. (1): d max  28.9 in. d 3  (72 in.)(12 in.) 2 145 62.4  24,092 in. 3 d 3  ht 2 g c g w  h g c  d 3 g w t 2  g w  62.4 lb ft 3  62.4 1728 lb in. 3 g c  145 lb ft 3  145 1728 lb in. 3 h d t M W W F d/ 3 V Eccentric Axial Loads Problem 5.1212 A circular post and a rectangular post are each compressed by loads that produce a resultant force P acting at the edge of the cross section (see figure). The diameter of the circular post and the depth of the rectangular post are the same. (a) For what width b of the rectangular post will the maximum tensile stresses be the same in both posts? (b) Under the conditions described in part (a), which post has the larger compressive stress? Solution 5.1212 Two posts in compression SECTION 5.12 Eccentric Axial Loads 365 P P b d d C IRCULAR POST Tension: Compression: R ECTANGULAR POST A  bd Tension: Compression: s c   P A  M S   P bd  3 P bd   4 P bd s t   P A  M S   P bd  3 P bd  2 P bd M  Pd 2 S  bd 2 6   20 P p d 2 s c   P A  M S   4 P p d 2  16 P p d 2 s t   P A  M S   4 P p d 2  16 P p d 2  12 P p d 2 M  Pd 2 S  p d 3 32 A  p d 2 4 E QUAL MAXIMUM TENSILE STRESSES or (Eq. 1) (a) Determine the width b of the rectangular post From Eq. (1): (b) Compressive stresses Circular post: Rectangular post: Rectangular post has the larger compressive stress.   24 P p d 2 s c   4 P bd   4 P ( p d 6) d s c   20 P p d 2 b  p d 6 6 p d  1 b 12 P p d 2  2 P bd Problem 5.1213 Two cables, each carrying a tensile force P  1200 lb, are bolted to a block of steel (see figure). The block has thickness t  1 in. and width b  3 in....
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This note was uploaded on 10/01/2009 for the course MEGR 2144 taught by Professor Sharpe during the Fall '08 term at UNC Charlotte.
 Fall '08
 Sharpe

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