C__DOCUME~1_msoft_MYDOCU~1_EXAMPL~1_EX42~1[1]

C__DOCUME~1_msoft_MYDOCU~1_EXAMPL~1_EX42~1[1] - EXAMPLE 4.2...

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Unformatted text preview: EXAMPLE 4.2 The assembly shown in Fig. 4—7a consists of an aluminum tube AB having a cross-sectional area of 400 mmz. A steel rod having a diameter of 10 mm is attached to a rigid collar and passes through the tube. If a tensile load of 80 kN is applied to the rod, determine the displacement of the end C of the rod. Take Est : 200 GPa. E31 = 70 GPa. Solution Internal Force. The free-body diagram of the tube and rod, Fig. 4—715, shows that the rod is subjected to a tension of 80 kN and the tube is subjected to a compression of 80 kN. Displacement. We will first determine the displacement of end C with respect to end B. Working in units of newtons and meters, we have 5 p]; [+80(103) N](0.6 m) ”B 7 AE w 77(0005 n1)2[200{109) N/mz] — +0.003056 m —> The positive sign indicates that end C moves to the right relative to end B, since the bar elongates. The displacement of end B with respect to the fixed end A is _ PL [—80(103) N}(0.4 m) AE l [400 mm2(10’6) mz/mm2][70(109) N/mz] : "0.001143 m = 0.001143 me 58 Here the negative sign indicates that the tube shortens, and so B moves to the right relative to A. Since both displacements are to the right, the resultant displacement of C relative to the fixed end A is therefore (i>) 6C = 53 + 8cm = 0.001143 m + 0003056111 = 0.00420m = 4.20 mine ...
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