A copper [E = 104 GPa, a = 17.1x10-6/°C] rod (2) is placed within a steel [E = 208 GPa, a=113x10-6/°C] tube (1) of the same length. The two components are connected at each end by pins that pass through both the tube and the rod. The outside diameter of the steel tube is D₁ = 88 mm, its inside diameter is d₁ = 69 mm, and its cross-sectional area is A₁ = 2343 mm². The diameter of the solid copper rod is d₂ = 45 mm, and its cross-sectional area is A₂ = 1591 mm². Calculate the normal stress in the copper rod if the temperature of the entire assembly is raised by 40°C. Pin Answer: 02. i Steel Tube (1) Pin MPa Copper Rod (2)

A hollow steel [E = 30,000 ksi] tube (1) with an outside diameter of 3.50 in. and a wall thickness of 0.219 in. is fastened to a solid 2.00-in.-diameter aluminum [E = 10,000 ksi] rod. The assembly is attached to unyielding supports at the left and right ends and is loaded as shown. Assume P=18 kips, Q=10 kips, L1=6 ft, L2=7 ft, and L3=7 ft.  (A) Calculate the cross-sectional area of steel tube (1), A1, and the cross-sectional area of the aluminum rods (2) and (3). in inches squared (B) Find the force in the steel tube (1), F1, and the forces F2 and F3, which are the forces in the aluminum rods.  Use the correct sign for each force.  By convention, a tension force is positive, and a compression force is negative. IN kips (C) Find σ1, σ2, and σ3, the normal stresses in members (1), (2), and (3), respectively. By convention, a tension stress is positive, and a compression stress is negative. IN KSI (D) Determine δ1 and δ2, the deformations of members (1) and (2), respectively.  By…

A circular column is made of concrete [Ec = 4.2(103)ksi] while being reinforced with six steel rods [Est = 29 (103 )ksi]. It is acted upon by an axial force of 30 kip as shown in the figure to the right. Each rod has a diameter of 0.85 in.    c) Stress in each steel rod, σst = ____________________ ksi  d) Stress in the concrete, σc = ____________________ ksi

An aluminum alloy [E = 10,000 ksi; oy = 40 ksi] pipe (1) is connected to a bronze [E = 16,000 ksi; ay = 45 ksi] pipe at flange B. The pipes are attached to rigid supports at A and C. Pipe (1) has an outside diameter of 2.425 in., a wall thickness of 0.21 in., and a length of L₁ = 8 ft. Pipe (2) has an outside diameter of 5.00 in., a wall thickness of 0.20 in., and a length of L₂ = 14 ft. If a minimum factor of safety of 2.1 is required for each pipe, determine: (a) the maximum load P that may be applied at flange B. (b) the deflection of flange B at the load determined in part (a). Deflection to the right is positive. (2) (1) C Answer: (a) P = i (b) Ug = i P< L₁ B L₂ ! kips in.

The assembly shown below consists of a brass shell (1) fully bonded to a ceramic core (2). The brass shell [E = 115 GPa; α = 18.7 x 10-6 /°C] has an outside diameter of 50 mm and an inside diameter of 35 mm. The ceramic core [E = 290 GPa; α = 3.1 x 10-6 /°C] has a diameter of 35 mm. At a temperature of 15°C, the assembly is unstressed. Determine the largest temperature increase that is acceptable for the assembly if the normal stress in the longitudinal direction of the brass shell must not exceed 80 MPa.

Rigid bar ABC is supported by two aluminum alloy (E = 10,000 ksi) rods as shown below. The horizontal distance between rods (1) and (2) is a = 150 in. Rod (1) has a length of L₁ = 99 in. and a cross-sectional area of A₁ = 0.55 in.². Rod (2) has a length of L₂ = 96 in. and a cross-sectional area of A₂ = 0.95 in.². Rigid bar ABC is to remain horizontal under a load of P = 35 kips. Determine the distance x from joint A to the location of load P so that bar ABC remains horizontal. L Answer: X= i (1) eTextbook and Media Save for Later x in. B (2) L2 Attempts: 0 of 5 used Submit Answer

A steel [E = 30,300 ksi; a = 6.7 x 106/°F] pipe column (1) with a cross-sectional area of A₁ = 5.70 in.² is connected at flange B to an aluminum alloy [E = 10,100 ksi; a = 12.7 x 10-6/°F] pipe (2) with a cross-sectional area of A₂ = 4.30 in.². The assembly (shown in the figure) is connected to rigid supports at A and C. It is initially unstressed at a temperature of 90°F. Assume L₁ = 126 in., L₂ = 156 in., P = 34 kips. (a) At what temperature will the normal stress in steel pipe (1) be reduced to zero? (b) Determine the normal stresses (positive if tensile, negative if compressive) in steel pipe (1) and aluminum pipe (2) when the temperature reaches -11°F. A Answers: (a) T= (b) σ₁ = 0₂ = L₁ tel i L2 °F ksi ksi

Q-A solid 75-mm-diameter Aluminum [E = 80 GPa and 0.3 Poisson ratio] shaft that is 1.25-m long extends through and is completely bonded to a hollow brass |G = 25 GPa] tube, as shown in Figure. Brass tube (1) has an outside diameter of 10 cm, an inside diameter of 75 mm, and a length of 0.75 m. Both the aluminum shaft and the brass tube are securely attached to the wall support at A. When the two torques shown are applied to the composite shaft, determine: (a) The maximum shear stress magnitude in brass tube (1) and Aluminum shaft segment (2) and (3). (b) The rotation angle of joint B and the rotation angle of end c. (1) 30 KN m 12 kN-m Figure 0.5 m

A steel [E = 30,100 ksi; a = 6.3 x 10-6/°F] pipe column (1) with a cross-sectional area of A₁ = 5.80 in.² is connected at flange B to an aluminum alloy [E = 10,700 ksi; a = 13.1 x 10-6/°F] pipe (2) with a cross-sectional area of A₂ = 3.50 in.². The assembly (shown in the figure) is connected to rigid supports at A and C. It is initially unstressed at a temperature of 92°F. Assume L₁ = 115 in., L₂ = 149 in., P = 22 kips. (a) At what temperature will the normal stress in steel pipe (1) be reduced to zero? (b) Determine the normal stresses (positive if tensile, negative if compressive) in steel pipe (1) and aluminum pipe (2) when the temperature reaches -11°F. A (1) L₁ B P P L2 с