Question

An alumninum (E = 68.9 GPa) cylindrical tube has an outer diameter of 200 mm, a wall thickness of 7.5 mm, and an internal pressure of 5 MPa. It is subjected to a force with the axial and transverse components shown acting at the centroid of the free end of the tube 1. Verify that the tube meets the thin-wall criterion 2. Draw the left half of the tube, and show the equivalent force-couple system acting at the centroid of the cross- section containing points H and K; OR Draw the free-body diagram of the right half of the tube, from the cross-section containing points H and K to the free end where the load is applied At point H, located at the top of the tube (a) Determine the magnitude of the normal stress due to axial force. Report whether it is compressive or tensile (b) Determine the magnitude of the normal stress due to flexure. Report whether it is compressive or tensile (c) Determine the axial stress. (d) Determine the hoop stress. (e) Determine the magnitude of the shear stress due to flexure (f) On a two-dimensional stress element, illustrate the state of stress. Include the x-z coordinate system next to or 3. on your element. At point K, located on the side of the tube (g) Determine the magnitude of the normal stress due to axial force. Report whether it is compressive or tensile (h) Determine the magnitude of the normal stress due to flexure. Report whether it is compressive or tensile. (i) Determine the axial stress. i) Determine the hoop stress. (k) Determine the magnitude of the shear stress due to flexure. (I) On a two-dimensional stress element, illustrate the state of stress. Include the x-y coordinate system next to or 4. on your element. Use discontinuity functions or superposition tables to determine the deflection of the tube at the free end (x-7 m) 5. 3.5 m H 3.5 m 200 mm 9 kN 3 kN

Answer 1

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