The composite shaft, consisting of aluminum, copper, and steel sections, is subj
ID: 2073678 • Letter: T
Question
The composite shaft, consisting of aluminum, copper, and steel sections, is subjected to the loading shown. The cross-sectional areas of sections AB, BC , and CD are AAB = 0.09 in2 , ABC = 0.11 in2 , and ACD= 0.07 in2 , respectively. The modulus of elasticity for each section are shown in the figure. Neglect the size of the collars at B and C.
Determine the displacement of B with respect to C of the composite shaft.
Copper E 1010) ks Ecu 18(10)ksi E 29(10) ksi Aluminum Steel 3.50 kip1.75 kip 2.00 kip 1.50 kip 50 ki 18 in12 in16 inExplanation / Answer
From free body diagram, the forces acting at section AB =FAB= 2 kip ( tensile in nature).
Displacement = FAB L /AE = 2*18 / (0.09*10*103) = 0.04 in.
Forces acting at section BC by taking equilibrium of forces from left end = 2-3.5 = -1.5 kip ( compressive in nature)
Displacement = FBCL/AE = -1.5*12 / 0.11*18*103 = - 0.009 in.
Let us consider section CD the forces acting on this section are FCD = 2-3.5+1.75 = 0.25 kip ( tensile in nature)
Displacement = FCDL/AE = 0.25*16 / (0.07*29*103) = 0.001970 in.
Displacement of B with respect to C = 0.04-0.009+0.001970=0.0329 in
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