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01-01ChapGere.0018

# 01-01ChapGere.0018 - 1 8,0 3 e e 0 e 0.03 s 5 ksi in which...

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Solution 1.4-4 Magnesium bar in tension 18 CHAPTER 1 Tension, Compression, and Shear Problem 1.4-4 A circular bar of magnesium alloy is 800 mm long. The stress-strain diagram for the material is shown in the figure. The bar is loaded in tension to an elongation of 5.6 mm, and then the load is removed. (a) What is the permanent set of the bar? (b) If the bar is reloaded, what is the proportional limit? ( Hint: Use the concepts illustrated in Figs. 1-18b and 1-19.) (MPa) 0 0 200 100 0.005 0.010 ( PL ) 2 ( PL ) 1 A B 0 R B E L 800 mm 5.6 mm ( PL ) 1 initial proportional limit 88 MPa (from stress-strain diagram) ( PL ) 2 proportional limit when the bar is reloaded I NITIAL SLOPE OF STRESS - STRAIN CURVE From - e diagram: At point A : ( PL ) 1 88 MPa e A 0.002 Problem 1.4-5 A wire of length L 4 ft and diameter d 0.125 in. is stretched by tensile forces P 600 lb. The wire is made of a copper alloy having a stress-strain relationship that may be described mathematically by the
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Unformatted text preview: 1 8,0 3 e e } 0 # e # 0.03 ( s 5 ksi) in which e is nondimensional and s has units of kips per square inch (ksi). (a) Construct a stress-strain diagram for the material. (b) Determine the elongation of the wire due to the forces P . (c) If the forces are removed, what is the permanent set of the bar? (d) If the forces are applied again, what is the proportional limit? S TRESS AND STRAIN AT POINT B From s-e diagram: s B 5 ( s PL ) 2 5 170 MPa E LASTIC RECOVERY e E R ESIDUAL STRAIN e R e R 5 e B 2 e E 5 0.007 2 0.00386 5 0.00314 (a) P ERMANENT SET e R L 5 (0.00314)(800 mm) 5 2.51 mm (b) P ROPORTIONAL LIMIT WHEN RELOADED ( s PL ) 2 5 s B 5 170 MPa e E 5 s B Slope 5 ( s PL ) 2 Slope 5 170 MPa 44 GPa 5 0.00386 e B 5 d L 5 5.6 mm 800 mm 5 0.007 Slope 5 ( s PL ) 1 e A 5 88 MPa 0.002 5 44 GPa A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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