COE 3001 Final Study Guide
COE 3001 Final Study Guide coe 3001 I
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This 0 page Study Guide was uploaded by Eleanor Notetaker on Tuesday December 1, 2015. The Study Guide belongs to coe 3001 I at Georgia Institute of Technology taught by Dr. Kennedy in Summer 2015. Since its upload, it has received 30 views. For similar materials see Deformable Bodies in Engineering and Tech at Georgia Institute of Technology.
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Date Created: 12/01/15
COE 3001 Mechanics of Deformable Bodies Final Study Guide 1 An aluminum bar AD see figure has a crosssectional area of A250 mm2 and is loaded by forces P17560 N P25340 N and P35780 N The lengths of the segments of the bar are a1525 mm b610 mm and c910 mm a Assuming that the modulus of elasticity E72 GPa calculate the change in length of the bar Does the bar elongate or shorten b By what amount P should the load P3 be increased so that the bar does not change in length when the three loads are applied c If P3 remains at 5780 N what revised crosssectional area for segment AB will result in no change of length when all three loads are applied 2 The composite shaft shown in the figure is manufactured by shrinkfitting a steel sleeve over a brass core so that the two parts act as a single solid bar in torsion The outer diameters of the two parts are d140 mm for the brass core and d250 mm for the steel sleeve The shear moduli of elasticity are Gb36 GPa for the brass and GS80 GPa for the steel a Assuming that the allowable shear stresses in the brass and steel are Tb48 MPa and quot880 MPa respectively determine the maximum permissible torque Tlmx that may be applied to the shaft COE 3001 Mechanics of Deformable Bodies Final Study Guide 3 Draw a beam under a pure bending moment deformed Be sure to include ds d1 dB and p 4 Determine the maximum stress in the beam v rn a n i v n nr 5 Find the de ection equation for the following beam COE 3001 Mechanics of Deformable Bodies Final Study Guide 6 Draw Mohr39s circle COE 3001 Mechanics of Deformable Bodies Final Study Guide Answers 1 622961umAP317503NAAB49103 m2 Total elongation 5HP1P2 P3aP2 P3b P3cl 1 75605340 5780 1525 5340 578061 578091 72x10925 Z Z 2961um 02 P1P2P3aP2P3bP3Cl0 P3abcP1P2 61sz P1P2aP2b 7560 5340 1525 534061 7 abc 15256191 5303N P3 A P3 75303 5780 17503 N P3 must increase by 17503 N in order for the bar to feel no elongation 0 AaP1P2 P3 25152575605340 5780 249103 m2 cP3 P2 P3b 915780 5340 578061 The new crosssectional area should be 49103 mm3 COE 3001 Mechanics of Deformable Bodies Final Study Guide 2 Tmax15212Nm P1p2 Gprb T T b 0 GbIPbGSIP GsIP T T 0 GbIPbGSIP S GbIPb9O478N mZGSIPS28981Nm2 solid16T Gb Pb maxsolid d3 quotWk GbIPbGSIPS 16 T Tm dnd3 GprbGsts 48x106H043 9047828981 max 16 Gb Pb 16 90478 325353 Nm hollow quotmquot Hd24 dl4 GSIPS Tmaxhollow d24d14 quotW GbIPbGSIP 16d2 TmathZlowHd24 d14 GbIPGSIP T b s quotW5 16d2 GSIP Z 80x106 054 044 9047828981 15212Nm 1605 28981 15212 lt 25353 Tmax is 15212 COE 3001 Mechanics of Deformable Bodies Final Study Guide 3 COE 3001 Mechanics of Deformable Bodies Final Study Guide 4 Omax 18887 psi h Mmax 2 Omax IZ 3 3 h 2t Izz Z U 1787Z4 12 2 12 Looking at the figure we can see that the maximum bending moment occurs at L2 1 2 1 2 qu I 8 231251bft23751bE6 ML2RA Omax18887 psi COE 3001 Mechanics of Deformable Bodies Final Study Guide 5 ZFyzochARBPRBP L 1 ZMB0 RAL P 0 RA7P SL Vixi x PxgtL 3 EId Vx dx xSLxgtL 3 3 EId gz PEId gzp dx 2 dx 2 2 MEId Zz Pxc1MEId 1Pxd1 dx 2 dx Mx0201OM x3L 03PLd1Ld1 3PL 2 2 2 2PxxSL M 3 Px PLxgtL 2 d2 d x2cszL EI 1MzEId V1 3 dx x Px2 PLxd2xgtL 2 2 x3czxc3xSL 12 ogtEIvx 1 3 ng3 ZPLx2d2xd3xgtL COE 3001 Mechanics of Deformable Bodies Final Study Guide COE 3001 Mechanics of Deformable Bodies Final Study Guide 6
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