02-05ChapGere.0006

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Solution 2.7-3 Three-story column SECTION 2.7 Strain Energy 139 H 5 10.5 ft E 5 30 3 10 6 psi A 5 15.5 in. 2 P 1 5 40 k P 2 5 P 3 5 60 k To find the strain energy of the column, add the strain energies of the three segments (see Eq. 2-40). Upper segment: N 1 52 P 1 Middle segment: N 2 ( P 1 1 P 2 ) Lower segment: N 3 ( P 1 1 P 2 1 P 3 ) S TRAIN ENERGY [ Q ] 5 (40 k) 2 1 (100 k) 2 1 (160 k) 2 5 37,200 k 2 2 EA 5 2(30 3 10 6 psi)(15.5 in. 2 ) 5 930 3 10 6 lb 5 5040 in.-lb U 5 (10.5 ft)(12 in. / ft) 930 3 10 6 lb [37,200 k 2 ] 5 H 2 EA [ Q ] 5 H 2 EA [ P 1 2 1 ( P 1 1 P 2 ) 2 1 ( P 1 1 P 2 1 P 3 ) 2 ] U 5 a N i 2 L i 2 E i A i P 1 P 2 P 3 H H H Problem 2.7-4 The bar ABC shown in the figure is loaded by a force P acting at end C and by a force Q acting at the midpoint B . The bar has constant axial rigidity EA . (a) Determine the strain energy U 1 of the bar when the force P acts alone ( Q 5 0). (b) Determine the strain energy U 2 when the force Q acts alone ( P 5 0). (c) Determine the strain energy U 3 when the forces P and Q act simultaneously upon the bar.
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This note was uploaded on 09/20/2009 for the course COE 3001 taught by Professor Armanios during the Spring '08 term at Georgia Tech.

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