3. A steel bar 600mm long and having 30mm diameter, is turned down to 25mm diameter for one fourth of its length. It is heated at 30 C above room temperature, clamped at both ends and then allowed to cool to room temperature. If the distance between the clamps is unchanged, the maximum stress in the bar ( a 12.5 x 10 per C and E 200 GN/m) is
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- 1.3 A furnace wall is to be constructed of brick having standard dimensions of Two kinds of material are available. One has a maximum usable temperature of 1040°C and a thermal conductivity of 1.7 W/(m K), and the other has a maximum temperature limit of 870°C and a thermal conductivity of 0.85 W/(m K). The bricks have the same cost and are laid in any manner, but we wish to design the most economical wall for a furnace with a temperature of 1040°C on the hot side and 200°C on the cold side. If the maximum amount of heat transfer permissible is 950 , determine the most economical arrangement using the available bricks.A wine of length L = 4 ft and diameter d = 0.125 in. is stretched by tensile forces P = 600 lb. The wire is made of a copper alloy having a stress-strain relationship that may be described mathematically by =18,0001+30000.03(=ksi) in which is nondimensional and has units of kips per square inch (ksi). (a) Construct a stress-strain diagram for the material. (bj Determine the elongation, of the wire due to the Forces P. (c) IF the forces are removed, what is the permanent set of the bar? (d) If the forces are applied again, what is the proportional limit?Kindly show a step-by-step solution. Thank you A 6m rod with a 4mm gap between one of its ends and the surface of the wall next to it is secured solidly between two walls at 25°C. Calculate the highest temperature that the rod can withstand in degrees celsius while taking into account the maximum limiting stress of 67 MPa, where a = 19.5 m/mC°, and E = 130 GPa.
- A short bar of copper, 25 mm in diameter, is enclosed centrally within a steel tube of external diameter 36 mm and thickness 3 mm. At 0°C the ends of the bar and tube are rigidly fastened together and the complete assembly heated to 80°C. Calculate the stress in the bar and in the tube if E for copper is 100 000 N/mm?, E for steel is 200 000 N/mm? and the coefficients of linear expansion of copper and steel are 0.000 01/°C and 0.000 006/°C, respectively.In 2012, a new fiber-optic cable of handling 40,000 telephone calls simultaneously was laid under the Pacific Ocean from California to Japan, a distance of 13,300 km. The cable was unreeled from shipboard at a mean temperature of 22oC and dropped to the Ocean floor having a mean temperature of 5oC. The coefficient of linear expansion of the cable is 75×10-6 /degree celsius. Determine the length of cable that must be carried on the ship to span the 13,300 Km. Also, find the percent change in lengthA steel rod, 12 mm in diameter, passes centrally through a copper tube 2.5 m long and having 36 mm and 48 mm as internal and external diameters respectively. The tube is closed at each end by 24 mm thick steel plates which are secured by nuts. The nuts are tightened until the copper tube is reduced in length by 0.50. The whole assembly is then raised in temperature by 60 degrees Celsius. Steel: Coefficient of expansion = 1.2x10^-5/degrees Celsius, Es = 200 GPa Copper: Coefficient of expansion = 1.75x10^-5/degrees Celsius, Ec = 100 GPa Calculate the stress in copper and stress in steel after the rise of temperature if the thickness of the plates remains unchanged. Indicate if the answer is tensile, tension, compression.
- A steel rod, 12 mm in diameter, passes centrally through a copper tube 2.5 m long and having 36 mm and 48 mm as internal and external diameters respectively. The tube is closed at each end by 24 mm thick steel plates which are secured by nuts. The nuts are tightened until the copper tube is reduced in length by 0.50. The whole assembly is then raised in temperature by 60 degrees Celsius. Steel: Coefficient of expansion = 1.2x10^-5/degrees Celsius, Es = 200 GPa Copper: Coefficient of expansion = 1.75x10^-5/degrees Celsius, Ec = 100 GPa Calculate the stress in copper before the rise of temperature if the thickness of the plates remains unchanged. Indicate if the answer is tensile, tension or compressionA steel cylinder is enclosed in a bronze sleeve; both simultaneously support a vertical compressive load of 180 kN which is applied to the assembly through a horizontal bearing plate. The length of the cylinders and sleeves are equal. For the steel cylinder, A= 8000 mm2, E= 200 GPa, and α= 11.7 μm/(m°C). For the bronze sleeve, A= 16 x 103 mm2, E= 83 GPa, and α= 19.0 μm/(m°C). Compute the temperature change that will cause a zero load in the steel.A prismatic bar with a length L = 1 m andcross-sectional area A = 1200mm2 is supported atthe ends. The bar is then subjected to a temperatureincrease of ΔT = 25°C. Calculate the complete state ofstress acting on an inclined section rs that is cut throughthe bar at an angle θ = 45°. Use E = 200 GPa and thecoefficient of thermal expansion α = 12 x 10 -6 / °C .
- A copper rod 6cm in diameter is placed within a steel tube, 8cm external diameter and 6cm internal diameter, of exactly the same length. The two pieces are rigidly fixed together by two transverse pins 20mm in diameter,one at each end passing through both rod and the tube. Calculate the stresses induced in the copper rod, steel tube and the pins if the temperature of the combination is raised by 50°C, take: E,= 210 GPa and a,= 0.0000115 per deg C. E= 105 GPa and a,= 0.000017 per deg C. Calculate the stresses induced in the copper rod. steel tube. Calculate the stresses induced in the pins if the temperature of the combination is raised by 50°C,Consider a steel alloy plate that is 10 ft long and 6 ft wide and is insulated on its flat surfaces. Suppose that left edge is maintained at 1000 °F and the other three edges are all maintained at 50°F. Solve for the temperature profile. Please show complete solution.Steel railroad reels 15 m long are laid with a clearance of 5 mm at a temperature Ti = 34 °C. Assume α = 11.7 μm/(m·°C) and E = 200 GPa. At what temperature in °C will the rails just touch?