02-07ChapGere.0005

02-07ChapGere.0005 - 164 A-PDF Axially Loaded : Purchase...

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164 CHAPTER 2 Axially Loaded Members P 1 P 2 d 1 d 1 d 2 P 2 P 1 d 0 5 20mm d 1 5 d 2 5 25mm Fillet radius: R 5 2mm Allowable stress: s t 5 80MPa (a) C OMPARISON OF BARS 5 (80 MPa) ¢ p 4 (20 mm) 2 5 25.1 kN Prismatic bar: Ê P 1 5 s t A 0 5 s t ¢ p d 0 2 4 Stepped bar: See Fig. 2-65 for the stress- concentration factor. R 5 2.0mm D 1 5 D 2 5 Enlarging the bar makes it weaker , not stronger. The ratio of loads is (b) D IAMETER OF PRISMATIC BAR FOR THE SAME ALLOWABLE LOAD d 0 5 d 1 Ï K < 20 mm Ï 1.75 < 15.1 mm P 1 5 P 2 Ê s t ¢ p d 0 2 4 5 s t K ¢ p d 1 2 4 Ê d 0 2 5 d 1 2 K P 1 / P 2 5 K 5 1.75 < 14.4 kN 5 ¢ 80 MPa 1.75 ≤¢ p 4 mm) 2 P 2 5 s nom A 1 5 s max K A 1 5 s t K A 1 s nom 5 P 2 p 4 d 1 2 5 P 2 A 1 Ê s nom 5 s max K R / D 1 5 0.10 Ê D 2 / D 1 5 1.25 Ê K < 1.75 Problem 2.10-6 A prismatic bar of diameter d 0 5 20 mm is being compared with a stepped bar of the same diameter ( d 1 5 20 mm) that is enlarged in the middle region to a diameter d 2 5 25 mm (see figure). The radius of the fillets in the stepped bar is 2.0 mm.
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