Thermal Strain
Two vertical steel rods support the rigid bar as shown. Initially, the rods are stress-free. Neglect the weight of the bar and use E = 200 GPa for steel.
At what temperature ΔT change would the stresses for both rods be equal?
Use α = 11.7 x 10-6 mm/mmC°
Homework Answers
Problem 1. Before hanging the weight, W = 90 kN, both the Steel and Bronze rods...
Problem 1. Before hanging the weight, W = 90 kN, both the Steel and Bronze rods were stress free as they were connected to rigid but weightless (originally) horizontal bar as shown in the figure. With W, determine (a) Stress in the Steel rod (b) Strain in the bronze rod Bronze L = 3 m A = 1300 mm E = 83 GPa Steel A = 320 mm E = 200 GPa 1m- 2.5 m - 1.5 m w
Determine F1 in left steel bar F2 in right steel bar Normal Stress in left steel...
Determine F1 in left steel bar
F2 in right steel bar
Normal Stress in left steel bar
Normal stress in right steel bar
A = 1200 mm h2 h A = 300 mm B A 41 12 The figure above shows a rigid bar ABC, pin connected to two vertical steel bars and a pin support at B. The two steel bars have heights of h1 = 1.2 m, h2 = 1.5 m and are placed from B at distances...
2) The rigid bar CDE is attached to a pin support at E and rests on...
2) The rigid bar CDE is attached to a pin support at E and rests on the 30-mm diameter brass cylinder BD. A 22-mm-diameter steel rod AC passes through a hole in the bar and is secured by a nut which is snugly fitted when the temperature of the entire assembly is 20°C. The temperature of the brass cylinder is then raised to 50°C while the steel rod remains at 20°C. Assuming that no stresses were present before the temperature...
2) The rigid bar CDE is attached to a pin support at E and rests on...
2) The rigid bar CDE is attached to a pin support at E and rests on the 30-mm diameter brass cylinder BD. A 22-mm-diameter steel rod AC passes through a hole in the bar and is secured by a nut which is snugly fitted when the temperature of the entire assembly is 20°C. The temperature of the brass cylinder is then raised to 50°C while the steel rod remains at 20°C. Assuming that no stresses were present before the temperature...
The composite bar is firmly fixed at both ends. The bar is stress-free at 60°F Compute the stress in each material after the 50-kip force 42 in is applied and the temperature is increased to 120°...
The composite bar is firmly fixed at both ends. The bar is stress-free at 60°F Compute the stress in each material after the 50-kip force 42 in is applied and the temperature is increased to 120°F. Use α-6.5 x 10-6/°F for steel and α-1 2.8 x 10-6/°F for aluminum. At what temperature will the aluminum and steel have stresses of equal magnitude after the 50-kip force is applied? Problem 4(25 Points) The rigid bar ABCD is supported by a pin...
M5.14 Coaxial bars with temperature change scenes AT-105°C 110 mm2 160 GPa 17.71א / 2600 mm...
M5.14 Coaxial bars with temperature change scenes AT-105°C 110 mm2 160 GPa 17.71א / 2600 mm 450 mm (1) 40 GPa 1300 mm 1300 mm (2) 23.7x10 /oC (2) A (kN) F. P= 15 kN A rigid horizontal bar ABC is supported by three vertical rods (properties given). The system is stress free before the load is applied. After the load P is applied, the temperature of all three rods is raised by the indicated AT. Determine: the internal force...
0.7 mm 6 BL Problem 3 - Thermal Stress (25 pts) The center rod CD of...
0.7 mm 6 BL Problem 3 - Thermal Stress (25 pts) The center rod CD of the assembly is heated from T, = 25°C to T2 = 200°C using electrical resistance heating. At the lower temperature T, the gap between C and the rigid bar is 0.7 mm. Determine the force in the rods AB and EF caused by the increase in temperature. Rods AB and EF are made of steel, and each has a cross-sectional area of 125 mm²....
100 KN 150 mm 450 mm ΑΙ B G С The three cylinder rods made of...
100 KN 150 mm 450 mm ΑΙ B G С The three cylinder rods made of A-36 steel and have equal cross-sectional areas support a vertical load of 100kN as shown. The bar ABC is fully rigid. Determine: a) The force at A, B and C. b) The diameter of the rods consider safety factor of 1.5, rounded to the nearest even number. c) The displacement of point A, B, C. A 36 steel, Modulus of elasticity E = 200...
A steel cylinder is enclosed in a bronze sleeve, both simultaneously support a vertical compressive load...
A steel cylinder is enclosed in a bronze sleeve, both simultaneously support a vertical compressive load of 250 kN which is applied to the assembly through a horizontal bearing plate. The lengths of the cylinder and the sleeve are equal. Compute the temperature change that will cause a zero load in the steel. Also, determine the temperature change that will cause a zero load in bronze. For the steel cylinder, the area is 7,200 sq mm, E is 200 GPa,...
The pin-connected structure shown in Fig. 5 consists of a rigid bar ABCD and two 1,500-mm-long...
The pin-connected structure shown in Fig. 5 consists of a rigid bar ABCD and two 1,500-mm-long bars. Bar (1) is steel [E=200 GPa] with a cross-sectional area of A1 = 510 mm2. Bar (2) is an aluminium alloy [E-70 GPa] with a cross-sectional area of A2 1,300 mm2. All bars are unstressed before the load P is applied. If a concentrated load of P 200 kN acts on the structure at D determine: (a) the normal stresses in both bars...
Problem 1. Before hanging the weight, W = 90 kN, both the Steel and Bronze rods were stress free as they were connected to rigid but weightless (originally) horizontal bar as shown in the figure. With W, determine (a) Stress in the Steel rod (b) Strain in the bronze rod Bronze L = 3 m A = 1300 mm E = 83 GPa Steel A = 320 mm E = 200 GPa 1m- 2.5 m - 1.5 m w
Determine F1 in left steel bar
F2 in right steel bar
Normal Stress in left steel bar
Normal stress in right steel bar
A = 1200 mm h2 h A = 300 mm B A 41 12 The figure above shows a rigid bar ABC, pin connected to two vertical steel bars and a pin support at B. The two steel bars have heights of h1 = 1.2 m, h2 = 1.5 m and are placed from B at distances...
2) The rigid bar CDE is attached to a pin support at E and rests on the 30-mm diameter brass cylinder BD. A 22-mm-diameter steel rod AC passes through a hole in the bar and is secured by a nut which is snugly fitted when the temperature of the entire assembly is 20°C. The temperature of the brass cylinder is then raised to 50°C while the steel rod remains at 20°C. Assuming that no stresses were present before the temperature...
2) The rigid bar CDE is attached to a pin support at E and rests on the 30-mm diameter brass cylinder BD. A 22-mm-diameter steel rod AC passes through a hole in the bar and is secured by a nut which is snugly fitted when the temperature of the entire assembly is 20°C. The temperature of the brass cylinder is then raised to 50°C while the steel rod remains at 20°C. Assuming that no stresses were present before the temperature...
The composite bar is firmly fixed at both ends. The bar is stress-free at 60°F Compute the stress in each material after the 50-kip force 42 in is applied and the temperature is increased to 120°F. Use α-6.5 x 10-6/°F for steel and α-1 2.8 x 10-6/°F for aluminum. At what temperature will the aluminum and steel have stresses of equal magnitude after the 50-kip force is applied? Problem 4(25 Points) The rigid bar ABCD is supported by a pin...
M5.14 Coaxial bars with temperature change scenes AT-105°C 110 mm2 160 GPa 17.71א / 2600 mm 450 mm (1) 40 GPa 1300 mm 1300 mm (2) 23.7x10 /oC (2) A (kN) F. P= 15 kN A rigid horizontal bar ABC is supported by three vertical rods (properties given). The system is stress free before the load is applied. After the load P is applied, the temperature of all three rods is raised by the indicated AT. Determine: the internal force...
0.7 mm 6 BL Problem 3 - Thermal Stress (25 pts) The center rod CD of the assembly is heated from T, = 25°C to T2 = 200°C using electrical resistance heating. At the lower temperature T, the gap between C and the rigid bar is 0.7 mm. Determine the force in the rods AB and EF caused by the increase in temperature. Rods AB and EF are made of steel, and each has a cross-sectional area of 125 mm²....
100 KN 150 mm 450 mm ΑΙ B G С The three cylinder rods made of A-36 steel and have equal cross-sectional areas support a vertical load of 100kN as shown. The bar ABC is fully rigid. Determine: a) The force at A, B and C. b) The diameter of the rods consider safety factor of 1.5, rounded to the nearest even number. c) The displacement of point A, B, C. A 36 steel, Modulus of elasticity E = 200...
The pin-connected structure shown in Fig. 5 consists of a rigid bar ABCD and two 1,500-mm-long bars. Bar (1) is steel [E=200 GPa] with a cross-sectional area of A1 = 510 mm2. Bar (2) is an aluminium alloy [E-70 GPa] with a cross-sectional area of A2 1,300 mm2. All bars are unstressed before the load P is applied. If a concentrated load of P 200 kN acts on the structure at D determine: (a) the normal stresses in both bars...
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> I have the same homework and this is very helpful. May I request for another answer? The requirement is to find the deformation of the Steel Rod @ B. Many thanks.
Mai Sakurajima Fri, Nov 26, 2021 12:55 AM