From the circle, R cos 2 45 cos 2 55 75 0. Determine a the orientation of the principal planes, b the principal stress max, c the maximum in-plane shearing stress. Draw line OK from origin tangent to the circle at K. Triangle OCK is a right triangle. Hint: Consider both in-plane and out-of-plane shearing stresses. Point Z corresponding to the z axis is located at O between A and B. We have R Point Z is located between A and B.

The largest of the 3 circles is still the circle z through A and B, and we still have R Point Z is now outside the circle through A and B. The largest circle is the circle through Z and A. Point Z corresponding to the z axis is located at O, outside the circle drawn through A and B. Point Z is located between B and A. The largest of the 3 circles is the one drawn z through A and B. Point Z is located outside the circle drawn through A and B.

R 12 ksi xy Lines marked a show the limits on max. Limit on max is max 2 max 18 ksi. If yield does not occur, determine the corresponding factor of safety. Using the maximum-distortion-energy criterion, determine whether yield will occur when a 0 MPa, b 0 MPa, c 0 MPa. Using the maximum-distortion-energy criterion, determine whether Y yield will occur when a xy 9 ksi, b xy 18 ksi, c xy 20 ksi. Using the maximum-distortion-energy criterion, determine whether yield will occur when a xy 9 ksi, b xy 18 ksi, c xy 20 ksi.

Using the maximum-shearing-stress criterion, determine the magnitude of the torque T for which yield occurs when P kN. Using the maximum-shearingstress criterion, determine the magnitude of the torque T for which yield occurs when P kN. The 1. Using the maximum-shearing-stress criterion, determine the magnitude of the torque T for which yield occurs when P 60 kips.

Using UT d determine the magnitude off the torque T for which faiilure should b expected. Knowing that the gage pressure in the container is increased from zero for which E GPa and to 1. Knowing that the ultimate stress in the steel used is U 60 ksi, determine the factor of safety with respect to tensile failure.

U max 60 ksi Knowing that a factor of safety of 4. Knowing that the internal pressure is 75 psi, determine the maximum normal stress and the maximum shearing stress in the container. Determine the normal stress in the wall when the basketball is inflated to a kPa gage pressure. Determine the maximum height h to which it can be filled with water if a factor of safety of 4.

At a time when the internal pressure of the tank is 1. Knowing that the tank has an outer diameter of mm and a wall thickness of 3 mm, determine the maximum normal stress and the maximum shearing stress in the tank. Knowing that the specific weight of water is Knowing that the allowable stress normal to the weld is 75 MPa, determine the largest gage pressure that can be used in the tank.

Knowing that the butt-welded seams form an angle 50 with the longitudinal axis of the tank and that the gage pressure in the tank is 1. Determine the largest value of that can be used if the normal stress perpendicular to the weld is not to be larger than 85 percent of the maximum stress in the tank.

Knowing that the allowable normal stress perpendicular to the weld is 12 ksi, determine the largest allowable gage pressure in each case. For a gage seams forming an angle pressure of 85 psi, determine a the normal stress perpendicular to the weld, b the shearing stress parallel to the weld. The gage pressure p insidde the vessel is psi and kkip centric axxial forces P and a P are appplied to the end plates.

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