01-01ChapGere.0010

01-01ChapGere.0010 - length? (Obtain the weight densities...

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Solution 1.3-1 Hanging wire of length L Solution 1.2-12 Rotating Bar 10 CHAPTER 1 Tension, Compression, and Shear v 5 angular speed (rad/s) A 5 cross-sectional area g 5 weight density 5 mass density g g Consider an element of mass dM at distance ± from the midpoint C . The variable ± ranges from x to L . dF 5 Inertia force (centrifugal force) of element of mass dM (a) T ENSILE STRESS IN BAR AT DISTANCE x (b) M AXIMUM TENSILE STRESS x 5 0 Ê s max 5 g v 2 L 2 2 g s x 5 F x A 5 g v 2 2 g ( L 2 2 x 2 ) F x 5 # B D dF 5 # L x g g A v 2 j d j 5 g A v 2 2 g ( L 2 2 x 2 ) dF 5 ( dM )( j v 2 ) 5 g g A v 2 j d j dM 5 g g A d j C B L x v dM ± d ± D We wish to find the axial force F x in the bar at Section D, distance x from the midpoint C . The force F x equals the inertia force of the part of the rotating bar from D to B . Mechanical Properties of Materials Problem 1.3-1 Imagine that a long steel wire hangs vertically from a high-altitude balloon. (a) What is the greatest length (feet) it can have without yielding if the steel yields at 40 ksi? (b) If the same wire hangs from a ship at sea, what is the greatest
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Unformatted text preview: length? (Obtain the weight densities of steel and sea water from Table H-1, Appendix H.) W 5 total weight of steel wire g S 5 weight density of steel 5 490 lb/ft 3 g W 5 weight density of sea water 5 63.8 lb/ft 3 (b) W IRE HANGING IN SEA WATER F 5 tensile force at top of wire 5 13,500 ft 5 40,000 psi (490 2 63.8)lb / ft 3 (144 in. 2 / ft 2 ) L max 5 s max g S 2 g W F 5 ( g S 2 g W ) AL s max 5 F A 5 ( g S 2 g W ) L 5 11,800 ft L max 5 s max g S 5 40,000 psi 490 lb / ft 3 (144 in. 2 / ft 2 ) L A 5 cross-sectional area of wire s max 5 40 ksi (yield strength) (a) W IRE HANGING IN AIR W 5 g S AL s max 5 W A 5 g S L A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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