05-02ChapGere.0015

05-02ChapGere.0015 - amount of material at the top and...

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Solution 5.6-21 Retaining wall 318 CHAPTER 5 Stresses in Beams (Basic Topics) t s q (1) P LANK AT THE BOTTOM OF THE DAM t 5 thickness of plank 5 3 in. b 5 width of plank (perpendicular to the plane of the figure) p 2 5 maximum soil pressure 5 400 lb/ft 2 5 2.778 lb/in. 2 s 5 spacing of piles q 5 p 2 b s allow 5 1200 psi S 5 section modulus M max 5 s allow S or Solve for s : (2) V ERTICAL PILE h 5 5 ft 5 60 in. p 1 5 soil pressure at the top 5 100 lb/ft 2 5 0.6944 lb/in. 2 q 1 5 p 1 s q 2 5 p 2 s d 5 diameter of pile 5 12 in. s 5 B 4 s allow t 2 3 p 2 5 72.0 in. p 2 bs 2 8 5 s allow ¢ bt 2 6 M max 5 qs 2 8 5 p 2 bs 2 8 Ê S 5 bt 2 6 Divide the trapezoidal load into two triangles (see dashed line). M max 5 s allow S or Solve for s : P LANK GOVERNS s max 5 72.0 in. s 5 3 p s allow d 3 16 h 2 (2 p 1 1 p 2 ) 5 81.4 in. sh 2 6 (2 p 1 1 p 2 ) 5 s allow ¢ p d 3 32 S 5 p d 3 32 M max 5 1 2 ( q 1 )( h ) ¢ 2 h 3 1 1 2 ( q 2 )( h ) ¢ h 3 5 sh 2 6 (2 p 1 1 p 2 ) h q 1 q 2 Problem 5.6-22 A beam of square cross section ( a 5 length of each side) is bent in the plane of a diagonal (see figure). By removing a small
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Unformatted text preview: amount of material at the top and bottom corners, as shown by the shaded triangles in the figure, we can increase the section modulus and obtain a stronger beam, even though the area of the cross section is reduced. (a) Determine the ratio b defining the areas that should be removed in order to obtain the strongest cross section in bending. (b) By what percent is the section modulus increased when the areas are removed? a a C z y b a b a A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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