235_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

235_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_2.8-2.12.qxd 9/25/08 11:44 AM Page 229 229 SECTION 2.10 Stress Concentrations SUBSTITUTE NUMERICAL VALUES: s nom R D1 (0.0040 in.)(25 * 106 psi) 2(5 in.) a 0.2 in. 1.0 in. 1.0 2 b + 20 in. 1.4 Use the dashed curve in Fig. 2-65. K 3,984 psi max K nom 1.53 (1.53)(3984 psi) ; 6100 psi 0.2 Problem 2.10-6 A prismatic bar of diameter d0 20 mm is being compared with a stepped bar of the same diameter (d1 20 mm) that is enlarged in the middle region to a diameter d2 25 mm (see figure). The radius of the fillets in the stepped bar is 2.0 mm. P1 (a) Does enlarging the bar in the middle region make it stronger than the prismatic bar? Demonstrate your answer by determining the maximum permissible load P1 for the prismatic bar and the maximum permissible load P2 for the enlarged bar, assuming that the allowable stress for the material is 80 MPa. (b) What should be the diameter d0 of the prismatic bar if it is to have the same maximum permissible load as does the stepped bar? P2 d0 d1 P1 d2 d1 P2 Solution 2.10-6 Prismatic bar and stepped bar Fillet radius: R Allowable stress: 2 mm 80 MPa t (a) COMPARISON OF BARS st a stA0 Prismatic bar: P1 p (80 MPa) a b (20mm)2 4 pd2 0 b 4 ; 25.1 kN Stepped bar: See Fig. 2-65 for the stress-concentration factor. R 2.0 mm R/D1 d0 20 mm d1 20 mm d2 25 mm s nom 0.10 P2 p2 d 41 D1 20 mm D2/D1 P2 s nom A1 D2 1.25 smax K K 25 mm 1.75 ...
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

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