Quiz 2 –Home Assignment ----------- Given the state of stress described in the Figure below, determine the principal stresses and the angle of rotation for the principal stresses.

------------- The stresses at a point are given by the stress-matrix shown. Determine the overall maximum shear stress.

----------- The  thin-­‐walled  pipe  has  an  inner  diameter  of  0.5in.  and  a  wall  thickness  of  0.025in..  If  it  is  subjected  to  an  internal  pressure  of  500psi  and  to  the  axial  tension  and  torsional  loadings  shown,  determine  the  state  of  stresses  on  element  A.  Use  x-­‐xis  as  horizontal  and  y-­‐axis  as  vertical  upwards.  

 -­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐  For purpose of analysis, a segment of the crankshaft in a vehicle is represented as shown below. The load P equals 1.0kN, and b1=80mm, b2=120mm and b3=40mm. The diameter of the upper shaft is d=20mm. Determine the state of stresses at point A, which is located on the surface of the shaft at the zo-axis. Determine the principal stresses and maximum shear stress at point A. Determine the state of stresses at point B, which is located on the surface of the shaft at the yo-axis.

 -­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐  A 2.5-in.-diameter solid aluminum post is subjected to a horizontal force of V = 3 kips, a vertical force of P = 7 kips, and a concentrated torque of T = 11 kip-in., acting in the directions shown. Determine the normal and shear stresses acting at point H (in ksi). Assume L = 3.5 in.

----------------- The non-zero stress components are: σxx=150MPa, σyy=70MPa, σzz=-80MPa, and τxy=-45MPa. Determine the principal stresses, the maximum shear stress and the angle for the principal stresses. -----------