Question

Problem 3. An aluminum beam is shown in the figure with a rectangular cross section. The beam is pinned to the ground at one end and supported by a round steel rod with hooks formed on the ends. Use Castigliano's method to find deflection at point B. T 100 lbf 7-in dia. 12 in 2 in 1-in thick B . 04_P0-—. 7 in 12 in — 6 in

Answer 1

VAN 100k O A D B The elongatari for me hod is ynored as its young's modules is not provided EM=0 → Våx6 = 100X5+6) > VA= 183-33 lbf. EFy=o. - Vot VAT U ZEI

Consider an enginesy load 'p' at poent B - - €Mg =O > VA = 1100 + P818 183.33+3P {Fy=0 Vo=(100+P) VA = -83-33-2P Strani enespy, o QEI 26 26 I + /6 83.33 +28) 23 dx ZEI 189 cowy + 2 xilova[n+ 7) + peatos de ET 2E1 83.330+4822 + 33332px?) dx 261

r 2 a EI 2 ET 2EI 2 EI EI ou i spuide 8 333-32x² dx Nove as the reel value of einapinary load P=Og all the terms having P can be equeted to O. hence deflectori at B, 1 = "favox(x+)dx+ 9333:3zi do 2 EI J 2EI x 2614 s I 179416.67+ 11999.52] EI z 91416.18 EI The cle of aluminum rod il Irich :: It fol. 9,23*20.167 mick inches o asinch : A = 5401 - 548497.08 unimin