Rigid bar ABC is supported by two identical solid bronze [oy = 331 MPa; E = 105 GPa; a = 22.0 x 10-6/°C] rods and a single solid steel [oy = 250 MPa; E = 200 GPa; a = 11.7x10-6/°C] rod. Bronze rods (1) each have diameters of d₁ = 17 mm and lengths of L₁ = 3.8 m. Steel rod (2) has a length of L₂ = 5.1 m. (a) Calculate the diameter d₂ required for steel rod (2) so that the deflection of joint B is zero for any change in temperature. (b) Using the value of d₂ determined in part (a), determine the maximum temperature decrease that is allowable for this assembly if a factor of safety of 2.3 is specified for the normal stress in each rod. Since the temperature is decreasing, the answer should be negative. (1) (1) 4₁ Answer: (a) d₂ = i (b) AT = i (2) B 42 mm °C

Rigid bar ABC is supported by two identical solid bronze [oy = 331 MPa; E = 105 GPa; a = 22.0 x 10-6/°C] rods and a single solid steel [oy = 250 MPa; E = 200 GPa; a = 11.7x10-6/°C] rod. Bronze rods (1) each have diameters of d₁ = 17 mm and lengths of L₁ = 3.8 m. Steel rod (2) has a length of L₂ = 5.1 m. (a) Calculate the diameter d₂ required for steel rod (2) so that the deflection of joint B is zero for any change in temperature. (b) Using the value of d₂ determined in part (a), determine the maximum temperature decrease that is allowable for this assembly if a factor of safety of 2.3 is specified for the normal stress in each rod. Since the temperature is decreasing, the answer should be negative. (1) (1) 4₁ Answer: (a) d₂ = i (b) AT = i (2) B 42 mm °C

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

Rigid bar ABCD is supported by a smoth pin at D and by vertical aluminum alloy [E=10,000 ksi] bars attached at joints A and C. Bar (1) was fabricated to its intended length L1=40 in. Bar (2) was intended to have a length of 60 in.; however, its actual length after fabrication was found to be L2=59.88 in. To connect it to the pin at C on the rigid bar, bar (2) will need to be manually stretched by Δ=0.12 in. After bar (2) has been stretched and connected to the pin at C, a load P=20 kips is applied to the rigid bar at B. Use the following additional properties and dimensions: A1=A2=0.75 in2, a = 36 in, b =54 in, and c = 48 in. Determin: a) The normal stresses in bars (1) and (2). b) The deflection at A of the rigid bar.
A 0.5-in.-diameter steel [E= 30,000 ksi] bolt (1) is placed in a copper tube (2). The copper [E= 16,000 ksi] tube has an outside diameter of 1.00 in., a wall thickness of 0.125 in., and a length of L= 8.0 in. Rigid washers, each with a thickness of t= 0.125 in., cap the ends of the copper tube. The bolt has 20 threads per inch. This means that each time the nut is turned one complete revolution, the nut advances 0.05 in. (i.e., 1/20 in.). The nut is hand-tightened on the bolt until the bolt, nut, washers, and tube are just snug, meaning that all slack has been removed from the assembly but no stress has yet been induced. What stresses are produced in the bolt and in the tube if the nut is tightened an additional quarter turn past the snug-tight condition?
A hollow steel [E = 30,000 ksi] tube (1) with an outside diameter of 3.50 in. and a wall thickness of 0.219 in. is fastened to a solid 2.00-in.-diameter aluminum [E = 10,000 ksi] rod. The assembly is attached to unyielding supports at the left and right ends and is loaded as shown. Assume P=18 kips, Q=10 kips, L1=6 ft, L2=7 ft, and L3=7 ft. (A) Calculate the cross-sectional area of steel tube (1), A1, and the cross-sectional area of the aluminum rods (2) and (3). in inches squared (B) Find the force in the steel tube (1), F1, and the forces F2 and F3, which are the forces in the aluminum rods. Use the correct sign for each force. By convention, a tension force is positive, and a compression force is negative. IN kips (C) Find σ1, σ2, and σ3, the normal stresses in members (1), (2), and (3), respectively. By convention, a tension stress is positive, and a compression stress is negative. IN KSI (D) Determine δ1 and δ2, the deformations of members (1) and (2), respectively. By…
Rigid bar ABCD is loaded and supported. Bars (1) and (2) are unstressed before the load P is applied. Bar (1) is made of bronze [E= 100 GPa] and has a cross-sectional area of 400 mm2. Bar (2) is made of aluminum [E= 70 GPa] and has a cross-sectional area of 600 mm2. After the load P is applied, the force in bar (1) is found to be 60 kN (in compression). Determine: (a) the stresses in bars (1) and (2).(b) the vertical deflection of point A.(c) the load P.
A load P is supported by a structure consisting of rigid bar ABC, two identical solid aluminum alloy [E = 73 GPa] rods (1), and a solid bronze [E = 105 GPa] rod (2). The aluminum rods (1) each have a diameter of 10 mm and a length of L₁ = 2.7 m. They are symmetrically positioned relative to middle rod (2) and the applied load P. Bronze rod (2) has a diameter of 25 mm and a length of L₂ = 1.7 m. If all bars are unstressed before the load P is applied, determine the normal stresses in the aluminum and bronze rods after a load of P = 70 KN is applied to the rigid bar. L₁ B Answer: 01 = i 0₂ i L2 (2) (1) (1) MPa MPa
1. A 0.015 meter diameter bar of steel is stress tested and the following stress-strain curve is produced Stress (psix 10 60 50 8 20 10 1 MPa 300 100 psi (x 10%) 50 200-30 OL 40- 20- 10 0.05 0.005 1 L 0.010 0.10 Strain a. What is the ultimate tensile strength (MPa)? d. What is the yield strength(MPa)? 0.15 c. What is the percent plastic elongation at the time of fracture? e. What is the Modulus of Elasticity (GPa)? 400 300 200 Stress (MPa) b. What is the greatest load that can be place on this bar before failure(N)? 100 10 0.20
An aluminum alloy [E = 10,000 ksi; oy = 40 ksi] pipe (1) is connected to a bronze [E = 16,000 ksi; ay = 45 ksi] pipe at flange B. The pipes are attached to rigid supports at A and C. Pipe (1) has an outside diameter of 2.425 in., a wall thickness of 0.21 in., and a length of L₁ = 8 ft. Pipe (2) has an outside diameter of 5.00 in., a wall thickness of 0.20 in., and a length of L₂ = 14 ft. If a minimum factor of safety of 2.1 is required for each pipe, determine: (a) the maximum load P that may be applied at flange B. (b) the deflection of flange B at the load determined in part (a). Deflection to the right is positive. (2) (1) C Answer: (a) P = i (b) Ug = i P< L₁ B L₂ ! kips in.
A load P is supported by a structure consisting of rigid bar ABC, two identical solid bronze [E = 15800 ksi] rods, and a solid steel [E = 27600 ksi] rod, as shown. The bronze rods (1) each have a diameter of 0.62 in. and they are symmetrically positioned relative to the center rod (2) and the applied load P. Steel rod (2) has a diameter of 0.41 in. Assume L₁=30 in and L₂-62 in. If all bars are unstressed before the load P is applied, determine the normal stresses in bronze rods (1) and steel rod (2) after a load of P=32 kips is applied. Answers: 0₁ = 02 = i L₂ B ksi. ksi.
A load P is supported by a structure consisting of rigid bar ABC, two identical solid bronze [E = 15,000 ksi] rods, and a solid steel [E = 30,000 ksi] rod, as shown. The bronze rods (1) each have a diameter of 0.615 in. and they are symmetrically positioned relative to the center rod (2) and the applied load P. Steel rod (2) has a diameter of 0.320 in. If all bars are unstressed before the load P is applied, determine the normal force in steel rod (2) after a load of P = 44 kips is applied. ... (2) 60 in. (1) (1) 24 in.
A copper [E = 106 GPa, a = 17.5x10-6/°C] rod (2) is placed within a steel [E = 212 GPa, a = 11.2x10-6/°C] tube (1) of the same length. The two components are connected at each end by pins that pass through both the tube and the rod. The outside diameter of the steel tube is D₁ = 97 mm, its inside diameter is d₁ = 84 mm, and its cross-sectional area is A₁ = 1849 mm². The diameter of the solid copper rod is d₂ = 60 mm, and its cross-sectional area is A₂ = 2828 mm². Calculate the normal stress in the copper rod if the temperature of the entire assembly is raised by 40°C. Pin Answer: 02= i Steel Tube (1) Pin MPa Copper Rod (2)
A steel [E = 30,300 ksi; a = 6.7 x 106/°F] pipe column (1) with a cross-sectional area of A₁ = 5.70 in.² is connected at flange B to an aluminum alloy [E = 10,100 ksi; a = 12.7 x 10-6/°F] pipe (2) with a cross-sectional area of A₂ = 4.30 in.². The assembly (shown in the figure) is connected to rigid supports at A and C. It is initially unstressed at a temperature of 90°F. Assume L₁ = 126 in., L₂ = 156 in., P = 34 kips. (a) At what temperature will the normal stress in steel pipe (1) be reduced to zero? (b) Determine the normal stresses (positive if tensile, negative if compressive) in steel pipe (1) and aluminum pipe (2) when the temperature reaches -11°F. A Answers: (a) T= (b) σ₁ = 0₂ = L₁ tel i L2 °F ksi ksi
Q-A solid 75-mm-diameter Aluminum [E = 80 GPa and 0.3 Poisson ratio] shaft that is 1.25-m long extends through and is completely bonded to a hollow brass |G = 25 GPa] tube, as shown in Figure. Brass tube (1) has an outside diameter of 10 cm, an inside diameter of 75 mm, and a length of 0.75 m. Both the aluminum shaft and the brass tube are securely attached to the wall support at A. When the two torques shown are applied to the composite shaft, determine: (a) The maximum shear stress magnitude in brass tube (1) and Aluminum shaft segment (2) and (3). (b) The rotation angle of joint B and the rotation angle of end c. (1) 30 KN m 12 kN-m Figure 0.5 m