WORLD FOR CIVIL

Topic 3.6: Assignment Problems - Statically Indeterminate

1. In the structure shown, steel rod AB and aluminum rod BC are joined together and then held between two rigid walls as shown. A force of 40,000 lb acting to the left is applied at junction B. This force will compress the steel member while stretching the aluminum member. The cross sectional areas and lengths of the steel and aluminum rods are respectively 1.5 in², 6 ft, 1 in², 10 ft as shown in the diagram. Young's modulus for steel is 30 x 10⁶ lb/in²; Young's modulus for aluminum is 10 x 10⁶ lb/in². Determine the stress that develops in each member, and determine the deformation of the aluminum rod.
(answers: F_aluminum = 4,700 lb., F_steel = 35,300, Stress-Al = 4700 psi, Stress-St = 23, 500 psi)
(answers: Deformation-Al = .0565")

2. In the structure shown, steel rod AB, aluminum rod BC, and brass rod CD are joined together and then held between two rigid walls as shown. A force of 40,000 lb acting to the left is applied at junction B, and a force of 20,000 lb acting to the left is applied at junction C. The cross sectional areas and lengths of the steel, aluminum, and brass rods are respectively 1.5 in², 6 ft; 1 in², 10 ft; .75 in², 8 ft as shown in the diagram. Young's modulus for steel is 30 x 10⁶ lb/in²; Young's modulus for aluminum is 10 x 10⁶ lb/in²; Young's modulus for brass is 15 x 10⁶ lb/in². Determine the stress that develops in each member, and determine the deformation of the aluminum rod.
(answers: F_st = 44,800 lb. comp., F_al = 4,800 lb.comp., F_br = 15,000 lb. tens. )
(answers: Stress_st = 29,900 psi., Stress_al = 4,800 psi., Stress_br = 20,000 psi, def.-al = -.0576")

3 In the structure shown, member ABCD is pinned to the ceiling at point A, and is supported by two steel rods, FB and EC, as shown in the Diagram. A load of 8000 lb. is applied at point D. Young's modulus for Steel is 30 x 10⁶ lb/in². Determine the stress in each rod, and the movement of point D.(answers: Stress_FB = Stress_EC = 8150 psi; M_d=.0448")

4. In the structure shown, two aluminum rods and a threaded steel rod connect to vertical plates, as shown in the diagram. If the structure is initially unstressed and the nut on the threaded steel rod in screwed in .25 inches, what is the stress that develops in the aluminum and steel members?
(answers: Stress_ST = 71,300 psi., Stress_Al = 80,200 psi.)

5. In the structure shown, solid rigid member ABCDE is pinned to the wall at point A, and supported by steel member BG and aluminum member DF, with lengths and dimensions as shown. A load of 20,000 lb. is applied a point C. Determine the stress that develops in the steel and aluminum members, and the movement of point E. (answers: Stress_ST = 12,860 psi., Stress_Al = 8570 psi.)
(Movement of E = .123")