KIC000101

# KIC000101 - I CE332 Deflection of Beams by Virtual Work...

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I, CE332 - Deflection of Beams by Virtual Work - Examples Example 1: Calculate the vertical deflection at B (i.e. OBv) for the following structure. EI is constant. 5k RAY 2 klft. RAx-Ef ! E B C D M A A 4 ft. 4 ft. 10 ft. REV 2 klft. d ! ! ! Fcx~ 5k D RAY J Fey RAXii~ {CY REy -----.-F cx B C MA A For the right portion, ++:EFx=O=F cx -+ F cx = 0 +) :EMc= 0 = -(2 k)(lO ft.)(5 ft.) + REy(lOft.) -+ R Ey = to k i t:EF y = 0 = Fcy - (2 k/ft)(10 ft.) + 10k -+ Fey = 10k i Step 1: Is the structure determinate? r = 6, n = 2, 2(3) - 6 = 0 -+ statically determinate Step 2: Calculate the support reactions. Break the structure at the hinge. Notice that the left portion is stable on its own, while the right portion must be supported by the left.

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M A = 100ft-k) RAY = 15 kj For the left portion: ~I:Fx = 0 =RAX -+ -Ij I:MA= 0 = M A - (5 k)(4 ft.) - (10 k)(8 ft.) -+ iI:Fy=O=RAy -(5 k)-(IOk) -+ RAX=O 15 k ~ --o-_--;;;:, ........ ",~--..,. 10 k IL.- ~ :------- ~ -10 k Step 3: Draw the moment diagram due to the real external loads (i.e. the M p diagram) 25 ft.-k -100 ft.-k Q~ I k 1 k oB ~~_{~_-o-o_-------" 4ft.-k B A _4ft.-k~ c
25 ft.-k Step 5: Apply the virtual work equation and use visual integration.

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