steel bar is held by two fixed supports as shown ne figure and is subjected to an increase -mperature AT = 100°C. If the coefficient of therm xpansion and Young's modulus of elasticity of sto e 11x10-6°C and 200 GPa, respectively, agnitude of thermal stress (in MPa) induced in t
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- A steel pipe with a 50 mm outside diameter and a 43.75 mm inside diameter surrounds a solid brass rod 37.5 mm in diameter as shown. Both materials are joined to a rigid cover plate at each end. The assembly is free to expand longitudinally. The assembly is stress free at a temperature of 27 degree C. For steel, Young's modulus is 200 GN/m^2, and the coefficient of linear thermal expansion is 11.7 x 10^-6 1/degree C. For brass, Young's modulus is 93.33 GN/m^2, and the coefficient of linear thermal expansion is 1.872 x 10^-5 1/degree C. What is the stress in the steel tube when the temperature is raised to 121 degree C?Q2) ACED frame is pinned at C and support by two identical wires at A and B. The two wires have modulus of elasticity E = 70 GPa, cross sectional area A = 250m * m ^ 2 and thermal expansion coefficient alpha=23*10^ -6 1/C . a) IfP P = 1000N , Determine the force in each wire. b) If in addition to the load P, the temperature of two wires raised by 120 Determine the force in each wire. c) To what value the temperature will increased in order to make the slack? C. wire at BTemperature stresses A composite bar is comprised of a concentric circular rod of copper and a tube of aluminium, each of length 500 mm, that are attached rigidly to above one another at both ends. The diameter of the copper rod is 30 mm, while the inner and outer diameters of the aluminium rod are 50 and 60 mm, respectively. The Young’s modulus and coefficients of thermal expansion for copper and aluminium are given as, 120 GPa and 80 GPa, and17 × 10−6 oC and 23 × 10−6/ o?, respectively Please show all formulas and substitutions into formulas 1 Calculate the magnitude of the stresses that are induced in the copper bar and aluminium rod if the composite bar is exposed to a temperature change of 500 oC, and state their senses. 2 Calculate the elongations of the constituents of the composite bar.
- The round bar shown (Figure 1) has a diameter of 6.4 cmcm and a length of 8 mm . The modulus of elasticity is E� = 130 GPaGPa and the linear coefficient of thermal expansion is 1.1×10−5 1K1K . Part A - Calculate thermal stress If the bar originally has no internal normal forces and the temperature decreases by ΔTΔ� = 28 KK , what is the thermal stress developed in the bar?Abrass rod is stress free at room temperature (20 Deg. C) It is then heated up, but prevented from lengthening at its ends by external forces. At what temperature does the stress in the rod reach -172 MPa? Assume the modulus of elasticity is 100 GPa, the linear coefficient of thermal expansion is 20 x 10%-6/Deg. <Consider the thermal effects on materials The rails of a railroad track are welded together at their ends (to form continuous rails and thus eliminate the clacking sound of the wheels) when the temperature is 60°F. What compressive stress s is produced in the rails when they are heated by the sun to 120° F if the coefficient of thermal expansion a=6.5x 10^6°F and the modulus of elasticity E=30x10^6 psi?
- 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 20-ft steel rod under a fixed support has an initial temperature40°F. Up to what temperature must the rod be heated if theallowable thermal stress developed in the rod is 80 ksi. Themodulus of elasticity for steel is 29 x 106 psi and coefficient ofthermal expansion of steel is a = 6.5 x 10-6 Answers: Tf = ___________________stress and strain A steel rod is 0.02 mi n diameter, and 2.5 m in length. The modulus of elasticity of this material is 210 GPa and a Poison's Ratio of 0.2. The change in diameter after applying a tensile force of 150 KN is
- A plastic bar ACB having two different solid circular cross sections isheld between rigid supports, asshown in the figure. The diameters in the left-and right-hand parts are 50 mm and 75 mm. respectively. The corresponding lengths are 225 mm and 300 mm. Also, the modulus of elasticity E is 6.0 GPa. and the coeffident of thermal expansion a is 100 x10-6 l°C. The bar issubjected to a uniform temperature increase of 30°C.(a) Calculate the following quantities:(I) the compressive force Nin thebar.(2) the maximum compressive stress a/, and (3) the displacementScof point C.(b) Repeat part (a) if the rigid support at A is replaced by an elastic support having spring constant k = 50 MN/m (see figure part b;assume that only the bar ACB is subject to the temperature increase).A composite bar is comprised of a concentric circular rod of copper and a tube of aluminum, each of length 500 mm, that are attached rigidly to above one another at both ends. The diameter of the copper rod is 30 mm, while the inner and outer diameters of the aluminum rod are 50 and 60 mm, respectively. The Young's modulus and coefficient of thermal expansion for copper and aluminum are given as, 120 GPa and 80 GPa, and 0.000017/degrees Celsius and 0.000023/degrees Celsius. 2.1)Calculate the magnitude of the stresses that are induced in the copper bar and aluminum rod if the composite bar is exposed to a temperature change of 50 degrees Celsius, and state their senses. 2.2)Calculate the elongation of the constituents of the composite bar.A 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.