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- Rectangular bars of copper and aluminum are held by pins at their ends, as shown in the figure. Thin spacers provide a separation between the bars. The copper bars have cross-sectional dimensions 0.5 in. × 2.0 in., and the aluminum bar has dimensions 1.0 in. × 2.0 in. Determine the shear stress in the 7/16-in. diameter pins if the temperature is raised by 100°F. (For copper, Et= 18,000 ksi and ac = 9.5 × 10-6/?; for aluminum, Ea= 10,000 ksi and aa= 13 × 10-6/?.) Suggestion: Use the results of Example 2-10A copper rod with 0.15 cm diameter is enclosed by a steel tube that has an outside diameter of 0.3 cm and an internal diameter of 0.2 cm. The assembly is fixed at each end. Determine the stresses in the rod and tube if the temperature is at 220oC; at 10oC, there is no longitudinal stress. Based on laboratory results for steel, E = 2.1 x 105 N/mm2, a = 11x10-6/oC, and for copper, E = 1 x 105 N/mm2, a = 18x10-6/oC1. A thin-walled cylinder with a diameter of 20 cm and a wall thickness of 2 mm is filled with gas at a pressure of 2 MPa. Calculate the longitudinal stress, and circumferential stress in the cylinder wall.
- Pressure inside the cylinder is 10 bars Is this a thin walled cylinder when the thickness is 10 mm. Estimate theoretically the hoop andlongitudinal stressesa) A cylinder with a 0.30-m inner diameter and a 0.40-mouter diameter is internally pressurized to 100 MPa. Determinethe maximum shear stress at the outer surfaceof the cylinder. b) A thin-walled cylinder containing pressurized gas isfixed by its two ends between rigid walls. Obtain anexpression for the wall reactions in terms of cylinderlength l, thickness th, radius r, and internal pressure pi.An engineering machine component operating in a high temperature environment consists of a copper pipe having a cross-sectional area of 2 000 mm2 and 0.3 m long, which is placed between two rigid caps. Four M22 steel bolts are symmetrically arranged around the tube and parallel to the axis of the tube and are lightly tightened. 3.1 Find the stress in the pipe and the bolts if the temperature of the assembly is increased from 25 0C to 95 0C. 3.2 What load will each bolt carry at the raised temperature? 3.3 Make a neat sketch of the assembly. (ESt = 200 GPa, ECu = 100 GPa, αSt = 12 × 10-6/ oC, αCu = 16 × 10-6/ oC)
- Question 3 - Strain Energy A brass tube with an outside diameter of 20 mm and 4 mm wall thickness is 80 mm long.It is joined to the end of a solid brass rod with a diameter of 20 mm and 120 mm long toform a compound assembly. This assembly is subjected to tension due to a mass of 150kg moving at a speed of 0.4 m/s.3.1. Determine the stresses induced in the rod and the tube respectively.3.2. Determine the change in length of each part, as well as the total change in length ofthe assembly.3.3 Determine the equivalent impact load (in kg) required to have the same effect(produce the same amount of energy) if falls freely from a height of 10 cm onto acollar attached to the bottom of the assembly if the assembly is vertically attachedat its top.3.4 How much strain energy is absorbed by each section of the assembly?(For brass: E = 100 GPa and α = 18×10-6/ 0C)A cylindrical component 0.3 m long is solid for 1/3 of its length and hollow with inner diameter ½ the outer diameter for the rest of the length. At 300C a gap of 0.1 mm exists between the component and the rigid supports. The outer diameter is 60 mm and the stress is not to exceed 150 MN/m2. Determine the maximum temperature that will not cause failure of the component. Take α as 1.3x10-5/0c and E as 200 GN/m2Q2 A rod is 3m long at a temperature of 15°C. Find the expansion of the rod, when the temperature is raised to 95°C. If this expansion is prevented, find the stress induced in the material of the rod. Take E=1x105 N/mm2 and α=0.000012/°C.
- The steel rails of a railroad are 12 m with a clearance of 3 mm at 15 oC. Calculate: 1.1 The change in temperature that will cause the rails to touch. 1.2 The stresses that would be induced at this new temperature if there were no initial clearance (E = 200 GPa and α = 12 × 10-6 /oC).The rigid bar ABC is supported by a hinge at B and two vertical steel rods at A and C as shown in Figure. Initially, the bar is horizontal, and the rods are stress-free. The coefficient of thermal contraction, α is 11.7x10-6 /oC and modulus of elasticity, E = 200 GPa for steel. If the temperature of the steel rod at A is decreased by 35oC while the temperature of steel rod at C remains constant, determine : The stress in the steel rod at A (in MPa). The stress in the steel rod at C (in MPa). The deformation of the steel rod at C. Include negative sign if contraction (in mm, in 3 decimal places). The deformation of the steel rod at A. Include a negative sign if contraction (in mm, in 3 decimal places)5. In the CN Railwayproject,steel railroad rails of 9.5meters long are to be installed.If the modulus of elasticity of steel is207GPa, and if the lowest temperature considered is 18°C and a maximum temperature of 36°C is designed for, determine the clearance between the rails such that adjoining will just touch at maximum design temperature. Assume α for steel is 11.6 x 10-6/°C