A 20 m long steel rod is at a temperature of 20°C. The rod is heated so that temperature rises by 50°C. If rod is allowed to expand by 14 mm, what will be the stress induced in rod? Take E = 200 GPa and α = 12 × 10-6/°C. (a) 20 MPa (c) 68 MPa (b) 35 MPa (d) None of these
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- A solid 45 mm diameter beryllium copper (E = 131 GPa; α = 17.0 × 10−6 /°C) rod is stress free when securely attached to the unyielding supports shown in the figure below. If the compressive normal stress in the rod must not exceed 450 MPa, what is the maximum temperature increase (rounded down to the nearest degree) that can be allowed for the rod? Use L1 = 300 mm.(a) Figure Q2 shows a steel bar held between two rigid supports. The bar has a cross sectional area of 0.25 m? and is 6.0 m in length. The structure is stress free before a force P = 3×106 N is applied at the point shown. Steel has a Young's modulus E = 210 GPa and its coefficient of thermal expansion is equal to a = 12 ×10-6 K-1. (i) What is the stress in the bar to the left of the applied load? (ii) What change in temperature would cause the stress on the right of the applied load to go to zero? 4.0 m 2.0 m P Figure Q2 -Constrained metal bar.A steel rod, which is free to move, has a length of 200 mm and diameter of 20 mm at a temperature of 15°C. If the rod is heated uniformly to 115°C,determine the length and the diameter of this rod to the nearest micron at the new temperature if the linear coefficient of thermal expansion of steel is 12.5 * 10-6m/m/C. Is there a stress on the rod at 115°C?If the rod is snugly fitted against two immovable nonconducting walls at a temperature of 15°C and then heated uniformly to115°C, what is its length at 115°C? If the modulus of elasticity of steel is207 GPa, what is the stress induced in the bar? Is this stress tension or compression?
- PROBLEM 4: As shown in the diagram shown, there is a gap of 0.5 mm between the rods at 10°C. Determine the stress in each rod if the temperature is raised to 150°C. The properties of each material are shown in the diagram. 0.5 mm FINAL ANSWERS 300 mm -250 mm MPa O alum O steel MPа Aluminum Stainless steel A = 2000 mm2 E = 75 GPa a = 23 × 10-6°C A = 800 mm? E = 190 GPa 17.3 x 10-6/°CA brass wire of diameter d = 2.33 mm is stretched tightly between rigid supports so that the tensile force is T = 93 N (see figure). T The coefficient of thermal expansion for the wire is 19.5 x 106/°c, and the modulus of elasticity is E = 110 GPa. (a) What is the maximum permissible temperature drop (in °C) if the allowable shear stress in the wire is 60 MPa? (Enter the magnitude.) °C (b) At what temperature change (in °C) does the wire go slack? °CA rigid horizontal bar of negligible mass is connected to two rods as shown in Fig. If the system is initially stress-free. Calculate the temperature change that will cause a tensile stress of 80 MPa in the brass rod. Assume that both rods are subjected to the change in temperature. Brass L=2 m A = 1200 mm? E= 100 GPa a= 18.7 um/(mC) 3 m - 2 m - Соpper L= 3m A = 1500 mm E = 120 GPa a = 16.8 um/(m"C)
- steel rod, which is free to move, has a length of 200 mm and diameter of20 mm at a temperature of 15°C. If the rod is heated uniformly to 115°C,determine the length and the diameter of this rod to the nearest micron atthe new temperature if the linear coefficient of thermal expansion of steel is12.5 X 10-6 m/m/°C. Is there a stress on the rod at 115°C?3. An aluminum rod is rigidly attached between a steel rod and a bronze rod as shown in the figure. Axial loads are applied at the positions indicated. Find the maximum value of P that will not exceed a stress in steel of 140 MPa, in aluminum of 13.05 ksi, or in bronze of 100 MPа. Aluminum A = 400 mm? Bronze A = 200 mm Steel A = 500 mm? 2P 4D 2.5 m 2.0 m 1.5 mA 20 m long steel rod is at a temperature of 20°C. The rod is heated so that temperature rises by 50°C. If rod is allowed to expand by 14 mm, what will be the stress induced in rod? Take E = 200 GPa and α = 12 x 10-6/°C.
- A steel rod with a cross-sectional area of 0.25in2 is stretched between two fixed points. The tensile force in the rod at 70°F is 1200lb. If a = 6.5x10-6/°F and E = 29x106 psi, What will be the stress at 0°F? At what temperature will the stress be zero? A bronze bar 3m long with a cross-sectional area of 320mm2 is placed between two rigid walls. At ta temperature of -20°c, the gap A = 25mm. Find the temperature at which the compressive stress of the bar will be 35 MPa. Use a = 18x10-6 m/ (m. °C) and E = 80GPA.A steel bar, 300 mm long and 24 mm diameter, is turned down to 18 mm diameter for one third of its length. It is heated 30°C above room temperature, clamped at both end and then allowed to cool to room temperature. If the distance between the clamps is unchanged, the maximum stress in the bar (α = 12.5x10-6 per °C & E=200GN/m² is)A steel rod, which is free to move, has a length of 200 mm and diameter of20 mm at a temperature of 15°C. If the rod is heated uniformly to 115°C,determine the length and the diameter of this rod to the nearest micron atthe new temperature if the linear coefficient of thermal expansion of steel is12.5 * 10-6 m/m/°C. Is there a stress on the rod at 115°C?