The pin-connected structure consists of a rigid bar ABC, a solid bronze [E = 107 GPa, a = 16.5 x 10-6/°C] rod (1), and a solid aluminum alloy [E = 75 GPa, a = 20.1 x 10-6/°C] rod (2). Bronze rod (1) has a diameter of 24 and aluminum rod (2) has a diameter of 17 mm. The bars are unstressed when the structure is assembled at 24°C. After assembly, the temperature of rod (2) is decreased by 37°C, while the temperature of rod (1) remains constant at 24°C. Determine the normal stresses 0₁, 02 in both rods for this condition (positive if tensile, negative if compressive). 210mm (1) 220mm 480mm (2) 510mm

The pin-connected structure consists of a rigid bar ABC, a solid bronze [E = 107 GPa, a = 16.5 x 10-6/°C] rod (1), and a solid aluminum alloy [E = 75 GPa, a = 20.1 x 10-6/°C] rod (2). Bronze rod (1) has a diameter of 24 and aluminum rod (2) has a diameter of 17 mm. The bars are unstressed when the structure is assembled at 24°C. After assembly, the temperature of rod (2) is decreased by 37°C, while the temperature of rod (1) remains constant at 24°C. Determine the normal stresses 0₁, 02 in both rods for this condition (positive if tensile, negative if compressive). 210mm (1) 220mm 480mm (2) 510mm

Materials Science And Engineering Properties

1st Edition

ISBN:9781111988609

Author:Charles Gilmore

Publisher:Charles Gilmore

Chapter8: Engineering Materials

Section: Chapter Questions

Problem 8.3P

See similar textbooks

Similar questions

Steel, Brass, and Copper rods are connected as shown in the figure. Initially, the temperature was 15 degrees Celsius and the stress on the bars is zero. Eventually, the temperature increased to 25 degrees Celsius. Determine the total deformation on the steel. Steel Brass Copper Est = 200 GPa Ebr = 100 GPa Ecu = 120 GPa %3D ast = 12(10-6)/°C abr = 21(10¬6)/°C acu = 17(10-)/°C %3D Acu = 515 mm² |Ast = 200 mm? Abr = 450 mm² %3D 300 mm- 200 mm 100 mm O -0.0058mm O 0.0165mm O -0.0165mm O 0.0058mm
For the two element rod shown, element (1) is steel with: E₁ = 210 GPa, A₁ = 1000 mm², L₁= 2 m, and coefficient of thermal expansion, a₁ = 12X106/°C. Element (2) is a titanium alloy with E2 = 120 GPa, A2 = 1500 mm², L2 = 1.5 m, and coefficient of thermal expansion, a₂ = 8X10-6/°C. a) Determine the axial stress ₁ and ₂ in the two rods if the temperature in both is increased by 100°C. b) Determine the deflection of point B following the temperature increase. A₁, E₁, 0₁ L₁ B UB A2, E2, 02 -L₂
Problem 2 14600ksi, apr For the shown structure, AB is made by C83400-red-brass (Ebr 9.8 × 10-6/ °F) and BC is made by 2014-T6-aluminum (Eal 10600ksi, a al = 12.8 × 10-6/°F). AB and BC are joined at the collar B and fixed connected at their ends. The cross sectional area of each member is 1.75 in². If there is no load in the = member when T₁ 50 °F. Now the temperature for both members are increased to T₂ = 120 °F. Determine (1) Reaction forces at fixed end C (2) The average normal stress in the member AB (3) The average normal stress in the member BC (4) Eventually, how far will the collar B be displaced? = = 3 ft 2 ft
Increase the carbon content in steel results less in__- a. Life O b. Ductility c. Strength O d. Cost
-6 The aluminum shell is fully bonded to the brass core and the assembly is unstressed at a temperature of 16°C. It is known thatE = 105 GPa and a = 20.9 × 10 °C for the brass core and E = 71 GPa and a = 23.8 × 10¯6°C for the aluminum shell. Considering only axial deformations, determine the stress in the aluminum when the temperature reaches 185°C. 25 mm σα MPa -63 mm
Problem 1 An axial force of P is applied to the center of the rigid end plate shown below. If the portion of the load carried by the aluminum plates is half the portion of the load carried by the brass core, (a) determine the value of h, (b) the total load if the stress in the brass is 50 MPa. Brass core (E = 105 GPa) Aluminum plates (E = 70 GPa) Rigid end plate 300 mm 60 mim 40 mm
The pin-connected structure shown consists of a rigid bar ABCD and two axial members. Bar (1) is steel [E = 200 GPa; a = 11.7x 10-6/°C], with a cross-sectional area of A1 = 370 mm2. Bar (2) is an aluminum alloy [E = 70 GPa; a = 22.5 x 10-6/°C], with a cross- sectional area of A2 = 380 mm?. The bars are unstressed when the structure is assembled. Assume a=360O mm, b=620 mm, c=730 mm, P=20 kN, and L=890 mm. After a concentrated load of P = 20 kN is applied and the temperature is increased by 35°C, determine (a) the normal stresses in bars (1) and (2). (b) the deflection of point D on the rigid bar. A (1) B (2)
The pin-connected structure shown consists of a rigid bar ABCD and two axial members. Bar (1) is steel [E = 200 GPa; a = 11.7 x 10-6/°C], with a cross-sectional area of A₁ = 400 mm². Bar (2) is an aluminum alloy [E = 70 GPa; a = 22.5 x 10-6/°C], with a cross-sectional area of A₂ = 400 mm². The bars are unstressed when the structure is assembled. After a concentrated load of P = 36 KN is applied and the temperature is increased by 25°C, determine (a) the normal stresses in bars (1) and (2). (b) the deflection of point D on the rigid bar. 350 mm 600 mm 900 mm (1) (2) A B 36 kN 720 mm D
The aluminum (E=15x10^10psi, α=11.6x10^-6/°F) shell is fully bonded to the brass (E=10.6x10^6psi, α=12.9x10^-6/°F) sore, and the assembly is unstressed at a temperature of 78°F. Considering only axial deformations, determine the stress when the temperature reaches 180°F (a) in the brass core (b) in the aluminum shell
Rigid bar ABCD is supported by a pin connection at A and by two axial bars (1) and (2). Bar (1) is a 34-in.-long bronze [E = 15000 ksi, α=α= 9.2 × 10−6/°F] bar with a cross-sectional area of 1.75 in.2. Bar (2) is a 42-in.-long aluminum alloy [E = 10300 ksi, α=α= 11.9 × 10−6/°F] bar with a cross-sectional area of 2.25 in.2. Both bars are unstressed before the load P is applied. Assume L1=34 in., L2=42 in., a=30 in., b=42 in., and c=16 in. If a concentrated load of P = 27 kips is applied to the rigid bar at D and the temperature is decreased by 120°F, determine:
A brass (? =5.6 ? 10^6 ???) and aluminum (? = 3.7 ? 10^6 ???) cylinders are bonded together at B, and are attached to fixed supports A and C. Determine (a) The torsion in AB, (b) The torsion in BC, (c) The maximum shearing stress in AB (d) The maximum shearing stress in BC.
Rigid bar ABCD is supported by a pin connection at A and by two axial bars (1) and (2). Bar (1) is a 34-in.-long bronze [E = 15000 ksi, α=α= 9.2 × 10−6/°F] bar with a cross-sectional area of 1.75 in.2. Bar (2) is a 42-in.-long aluminum alloy [E = 10300 ksi, α=α= 11.9 × 10−6/°F] bar with a cross-sectional area of 2.25 in.2. Both bars are unstressed before the load P is applied. Assume L1=34 in., L2=42 in., a=30 in., b=42 in., and c=16 in. If a concentrated load of P = 27 kips is applied to the rigid bar at D and the temperature is decreased by 120°F, determine:(a) the normal stresses in bars (1) and (2).(b) the normal strains in bars (1) and (2).(c) the deflection of the rigid bar at point D.