Problem 3 (36 Pts)
The steel pipe is 0.5 m long and has an internal diameter of 60mm and an external diameter of 80 mm. The Young’s modulus E is 200GPa and the Poisson ratio ν is 0.32. The pipe experiences atwisting moment of 8 kNm and a bending moment of 3.5 kNm.
4p a) Sketch roughly how the angle of rotation and verticaldisplacement change as a function of distance from the free end ofthe pipe to the wall.
8p b) Determine the torsion angle and vertical displacement atthe free end of the pipe.
6p c) Determine the stress at the top and bottom of the beam atan arbitrary cross- section, say at a-a.
6p d) Determine (i) the principal stress, (ii) the maximum shearstress, and (iii) average normal stress if available.
4p e) Determine whether plastic deformation occurs. Here, theelastic limit for steel is 250 MPa.
4p f) The base of the rod is fastened to the wall by 4 bolts, 2vertical and 2 horizontal. Analyze different stresses (in normalstress, shear stress, or both) experienced by different bolts.
4p g) If the bolts are 6 mm in diameter and made of the samesteel. With the increase of two moments in proportion, which boltwill yield first and how will the yield look like?
