434_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

434_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 05Ch05.qxd 9/24/08 428 4:59 AM Page 428 CHAPTER 5 Stresses in Beams (Basic Topics) Solution 5.6-21 Retaining wall (1) PLANK AT THE BOTTOM OF THE DAM t thickness of plank 3 in. b width of plank (perpendicular to the plane of the figure) p2 maximum soil pressure 400 lb/ft2 2.778 lb/in.2 s spacing of piles q p2b sallow 1200 psi S section modulus Mmax Mmax A qs 8 2 p2bs 8 s allow S 2 or S bt 6 p2bs 2 8 Solve for s: s 4sallow t 2 3p 2 72.0 in. q1 q2 d 12 in. Divide the trapezoidal load into two triangles (see dashed line). 2 Mmax bt 2 sallow a b 6 S 1 2h (q1) (h) a b 2 3 pd 3 32 Mmax sh 2 (2p1 + p2) 6 sh2 (2p1 6 1 h (q2)(h) a b 2 3 sallow S sallow a p2) or pd 3 b 32 Solve for s: s (2) VERTICAL PILE h 5 ft 60 in. p1 soil pressure at the top 100 lb/ft 2 0.6944 lb/in.2 p1s p2s diameter of pile 3psallow d 3 16h2 (2p1 + p2) PLANK GOVERNS smax 81.4 in. 72.0 in. Problem 5.6-22 A beam of square cross section (a length of each side) is bent in the plane of a diagonal (see figure). By removing a small 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? ; y a z ba C a ba ...
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