Problem 3 (36 Pts) The steel pipe is 0.5 m long and has an internal diameter...

Problem 3 (36 Pts)

The steel pipe is 0.5 m long and has an internal diameter of 60 mm and an external diameter of 80 mm. The Young’s modulus E is 200 GPa and the Poisson ratio ν is 0.32. The pipe experiences a twisting moment of 8 kNm and a bending moment of 3.5 kNm.

4p a) Sketch roughly how the angle of rotation and vertical displacement change as a function of distance from the free end of the pipe to the wall.

8p b) Determine the torsion angle and vertical displacement at the free end of the pipe.

6p c) Determine the stress at the top and bottom of the beam at an arbitrary cross- section, say at a-a.

6p d) Determine (i) the principal stress, (ii) the maximum shear stress, and (iii) average normal stress if available.

4p e) Determine whether plastic deformation occurs. Here, the elastic limit for steel is 250 MPa.

4p f) The base of the rod is fastened to the wall by 4 bolts, 2 vertical and 2 horizontal. Analyze different stresses (in normal stress, shear stress, or both) experienced by different bolts.

4p g) If the bolts are 6 mm in diameter and made of the same steel. With the increase of two moments in proportion, which bolt will yield first and how will the yield look like?

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Expert Solution

samet mamat answered 4 months ago

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