A 50 mm diameter cylindrical aluminum block is connected to 2 hollowed cylindrical steel blocks as shown in Figure. Both hollowed steel cylinders are of 60 mm and 40 mm outer and inner diameters respectively. The assembly is then connected to a rigid steel plate. Four bolts of diameter 10 mm are then used to rigidly fix the assembly to a wall. A force P is then applied to the assembly. The Modulus of elasticity(E) of steel is 200 GPa while aluminum has Modulus of elasticity(E) of 70 GPa. Both steel and aluminum have a yield strength (σy) of 250 MPa. The bolts have a yield stress (σy) of 800 MPa. All connections and joints are considered rigid. All lengths are in mm. a. Determine the allowable value of P that can be applied to the assembly taking into consideration the yielding of all parts of the assembly and bolts. Use a factor of safety of 1.5. b. Based on the value of P obtained part (a), determine the total elongation of the cylindrical steel block. c. Based on the value of P obtained in part (a), determine the change in diameter of the cylindrical aluminum block (the Poisson’s ratio for aluminum is 0.35).
A 50 mm diameter cylindrical aluminum block is connected to 2 hollowed cylindrical steel blocks as shown in Figure. Both hollowed steel cylinders are of 60 mm and 40 mm outer and inner diameters respectively. The assembly is then connected to a rigid steel plate. Four bolts of diameter 10 mm are then used to rigidly fix the assembly to a wall. A force P is then applied to the assembly. The Modulus of elasticity(E) of steel is 200 GPa while aluminum has Modulus of elasticity(E) of 70 GPa. Both steel and aluminum have a yield strength (σy) of 250 MPa. The bolts have a yield stress (σy) of 800 MPa. All connections and joints are considered rigid.
All lengths are in mm.
a. Determine the allowable value of P that can be applied to the assembly taking into consideration the
yielding of all parts of the assembly and bolts. Use a factor of safety of 1.5.
b. Based on the value of P obtained part (a), determine the total elongation of the cylindrical steel block.
c. Based on the value of P obtained in part (a), determine the change in diameter of the cylindrical
aluminum block (the Poisson’s ratio for aluminum is 0.35).
Step by step
Solved in 4 steps with 4 images
