02-02ChapGere.0013

02-02ChapGere.0013 - (3, 4) S UBSTITUTE INTO COMPATIBILITY...

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Problem 2.4-5 Three steel cables jointly support a load of 12 k (see figure). The diameter of the middle cable is 3 / 4 in. and the diameter of each outer cable is 1 / 2 in. The tensions in the cables are adjusted so that each cable carries one-third of the load (i.e., 4 k). Later, the load is increased by 9 k to a total load of 21 k. (a) What percent of the total load is now carried by the middle cable? (b) What are the stresses s M and s O in the middle and outer cables, respectively? ( Note: See Table 2-1 in Section 2.2 for properties of cables.) Solution 2.4-5 Three cables in tension 92 CHAPTER 2 Axially Loaded Members P 1 2 in. 1 2 in. 3 4 in. A REAS OF CABLES (from Table 2-1) Middle cable: A M 5 0.268 in. 2 Outer cables: A O 5 0.119 in. 2 (for each cable) F IRST LOADING P 1 5 12 k S ECOND LOADING P 2 5 9k (additional load) E QUATION OF EQUILIBRIUM © F vert 5 02 P O 1 P M 2 P 2 5 0 (1) E QUATION OF COMPATIBILITY d M 5 d O (2) ¢ Each cable carries P 1 3 or 4 k. F ORCE - DISPLACEMENT RELATIONS
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Unformatted text preview: (3, 4) S UBSTITUTE INTO COMPATIBILITY EQUATION : (5) S OLVE SIMULTANEOUSLY E QS . (1) AND (5): F ORCES IN CABLES Middle cable: Force 5 4 k 1 4.767 k 5 8.767 k Outer cables: Force 5 4 k 1 2.117 k 5 6.117 k (for each cable) (a) P ERCENT OF TOTAL LOAD CARRIED BY MIDDLE CABLE (b) S TRESSES IN CABLES ( s 5 P/A ) Outer cables: s O 5 6.117 k 0.119 in. 2 5 51.4 ksi Middle cable: s M 5 8.767 k 0.268 in. 2 5 32.7 ksi Percent 5 8.767 k 21 k (100%) 5 41.7% 5 2.117 k P o 5 P 2 A o A M 1 2 A O 5 (9 k) 0.119 in. 2 0.506 in. 2 5 4.767 k P M 5 P 2 A M A M 1 2 A O 5 (9 k) 0.268 in. 2 0.506 in. 2 P M L EA M 5 P O L EA O P M A M 5 P O A O d M 5 P M L EA M d O 5 P o L EA o P 2 = 9 k P O P O P M A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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