02-05ChapGere.0006

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Solution 2.7-3 Three-story column SECTION 2.7 Strain Energy 139 H 10.5 ft E 30 10 6 psi A 15.5 in. 2 P 1 40 k P 2 P 3 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 P 1 Middle segment: N 2 ( P 1 P 2 ) Lower segment: N 3 ( P 1 P 2 P 3 ) S TRAIN ENERGY [ Q ] (40 k) 2 (100 k) 2 (160 k) 2 37,200 k 2 2 EA 2(30 10 6 psi)(15.5 in. 2 ) 930 10 6 lb 5040 in.-lb U (10.5 ft)(12 in. ft) 930 10 6 lb [37,200 k 2 ] H 2 EA [ Q ] H 2 EA [ P 1 2 ( P 1 P 2 ) 2 ( P 1 P 2 P 3 ) 2 ] U 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 0). (b) Determine the strain energy U 2 when the force Q acts alone ( P 0). (c) Determine the strain energy U 3 when the forces P and Q act simultaneously upon the bar.
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