H.W.7: A pin-connected structure is supported as shown in Figure load P is applied. Bar (1) is made of brass [oy = 18,000 psi; E = 17 x 106 psi], and it has a length of L, = 8.0 ft. Bar (2) is made of an aluminum alloy [oy 40,000 psi; E = 10 x 10° psi], and it has a length of L = 5.5 ft. Bars (1) and (2) each have cross- sectional areas of 0.75 in.2. Assume that a = 4.0 ft, b 6.0 ft, and c = 1,5 ft. If the minimum factor of safety required for bars (1) and (2) is 2.50, calculate the maximum load P that can be applied to the rigid bar at D. . Member ABCD is rigid and horizontal before %3D %3D %3D %3D %3D Nadhof Shu (1) B FIGURE

H.W.7: A pin-connected structure is supported as shown in Figure load P is applied. Bar (1) is made of brass [oy = 18,000 psi; E = 17 x 106 psi], and it has a length of L, = 8.0 ft. Bar (2) is made of an aluminum alloy [oy 40,000 psi; E = 10 x 10° psi], and it has a length of L = 5.5 ft. Bars (1) and (2) each have cross- sectional areas of 0.75 in.2. Assume that a = 4.0 ft, b 6.0 ft, and c = 1,5 ft. If the minimum factor of safety required for bars (1) and (2) is 2.50, calculate the maximum load P that can be applied to the rigid bar at D. . Member ABCD is rigid and horizontal before %3D %3D %3D %3D %3D Nadhof Shu (1) B FIGURE

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

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3. A cylindrical rod is fixed between two walls. The rod is composed of two materials. Section AC is made of one material (GAC = 2G) while section CD is made of a different material (GcD = G). A torque, T, is applied at point B, as shown below. Jac = JcD = J = 2 in. GẠC = 2G = 20 x 10ʻ psi T= 300 kip in. GCD = G = 10 × 106 psi A D 2L Determine the reactions at the wall, Ta, and Tp. Specify the direction for each. (Note: this is an example of a no calculator problem.) Ans: TA = 250 kip in ( Tp=50 kip in ( T Fixed Fixed to wall to wall
An aluminum alloy [E = 8400 ksi] pipe with a cross-sectional area of A₁ = 4.20 in.² is connected at flange B to a steel [E = 23800 ksi] pipe with a cross-sectional area of A₂ = 2.96 in.². The assembly is connected to rigid supports at A and C. Assume L₁= 154 in., L₂= 200 in., and P = 56 kips. For the loading shown, determine: (a) the normal stresses in aluminum pipe (1) and steel pipe (2) (₁, ₂ use positive if tensile, negative if compressive). (b) the deflection ug (use positive if it moves to the right and negative if it moves to the left) of flange B. Answers: (a) 6₁ (b) ug = (1) L₁ Save for Later B eTextbook and Media L2 ksi, 0₂ = i in. ksi, Attempts: 0 of 5 used Submit Answer
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 16 mm and a length of L₁= 2.3 m. They are symmetrically positioned relative to middle rod (2) and the applied load P. Bronze rod (2) has a diameter of 16 mm and a length of L₂ = 1.5 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 = 46 kN is applied to the rigid bar. L₁ A B C P Answer: 0₁ = i 02= i L₂ (2) (1) (1) MPa MPa
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
The pin-connected structure consists of a rigid bar ABCD and two axial members. Bar (1) is bronze [E = 95 GPa] with a cross-sectional area of A₁ = 630 mm². Bar (2) is an aluminum alloy [E = 67 GPa] with a cross-sectional area of A₂ = 290 mm². All bars are unstressed before the load P is applied; however, there is a 8.3-mm clearance in the pin connection at A. Assume L₁=700 mm, L₂=460 mm, a=580 mm, b=330 mm, and c=1280 mm. If a concentrated load of P = 91 kN acts on the structure at D, determine: (a) the normal stresses 01, 0₂ in both bars (1) and (2). (b) the normal strains 1, 2 in bars (1) and (2). (c) the downward deflection vp of point D on the rigid bar. a b Answers: (a) σ₁ = (b) €₁ = (c) vd = i i i (1) Save for Later L₁ L2 2 e Textbook and Media B C C MPa, 0₂ = με, εξ mm. = i i με.. MPa. Attempts: 0 of 5 used Submit Answer
A hollow steel [E = 30,000 ksi] tube (1) with an outside diameter of 3.125 in. and a wall thickness of 0.250 in. is fastened to a solid aluminum [E = 10,000 ksi] rod (2) that has a 1.875-in.-diameter and a solid 1.250-in.-diameter aluminum rod (3). The bar is loaded as shown. Assume L₁ = 70 in., L₂= 45 in., L3= 27 in., R = 36 kips, Q = 12 kips, and P = 24 kips. Determine (a) the change in length of steel tube (1). (b) the deflection of joint D with respect to the fixed support at A. (c) the maximum normal stress in the entire axial assembly. Answers: L₁ (a) 8₁ = (b) up= (c) Omax = GO Tutorial B Save for Later i tel R eTextbook and Media R L2 C L3 in. in. ksi Attempts: 0 of 5 used Submit Answer
H.W.6: A hollow circular cold-rolled bronze [G, = 6,500 ksi] tube (1) with an outside diameter of 1.75 in. and an inside diam- eter of 1.25 in. is securely bonded to a solid 1.25-in.-diameter cold-rolled stainless steel [G2 = 12,500 ksi] core (2) as shown in Figure and the allowable shear stress of core (2) is 60 ksi. Determine . The allowable shear stress of tube (1) is 27 ksi, (a) the allowable torque T that can be applied to the tube-and- core assembly. (b) the corresponding torques produced in tube (1) and core (2). (c) the angle of twist produced in a 10-in. length of the assembly by the allowable torque T. (1) T TA FIGURE
H.W.6: A hollow circular cold-rolled bronze [G, = 6,500 ksi] tube (1) with an outside diameter of 1.75 in. and an inside diam- eter of 1.25 in. is securely bonded to a solid 1.25-in.-diameter cold-rolled stainless steel [G2 = 12,500 ksi] core (2) as shown in Figure and the allowable shear stress of core (2) is 60 ksi. Determine . The allowable shear stress of tube (1) is 27 ksi, (a) the allowable torque T that can be applied to the tube-and- core assembly. (b) the corresponding torques produced in tube (1) and core (2). (c) the angle of twist produced in a 10-in. length of the assembly by the allowable torque T. (1) (2) T. FIGURE
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.
3. The bar shown below is composed of two pieces, AC and CD. The bar is attached to the wall at point A. The length L = 10 in. The cross sectional areas are: AAC = 4 in? and AcD = 2 in?. The Young's Moduli are: EAC =20 Msi and Ecd= 15 Msi Two forces are applied at points B and D: PB = 50 kips and PD = 20 kips. Determine: (a) the reaction force at A (specify –→ or +) and (b) the deflection of point D (specify → or +). (Hint for (b): Think about how many pieces you must subdivide the rod into.) Ans: RA = 30 kips (+), dp = 7.9167×10-3 in (E) A В C D Pp L 2L L
A load P is supported by a structure consisting of rigid bar ABC, two identical solid bronze [E = 17200 ksi] rods, and a solid steel [E = 31400 ksi] rod, as shown. The bronze rods (1) each have a diameter of 0.69 in. and they are symmetrically positioned relative to the center rod (2) and the applied load P. Steel rod (2) has a diameter of 0.53 in. Assume L₁=45 in and L₂=67 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 = 16 kips is applied. (1) Answers: 01 02 = i i L2 (2) Save for Later B P eTextbook and Media (1) ksi. ksi. L₁ Attempts: 0 of 5 used Submit Answer
Rigid bar ABCD is supported by a pin connection at A and by two axial bars (1) and (2). Bar (1) is a 30-in.-long bronze [E = 15900 ksi, 9.4x 10-6/°F] bar with a cross-sectional area of 1.00 in.?. Bar (2) is a 48-in-long aluminum alloy [E = 9200 ksi, a = 12.6 x 10-6/°F] bar with a cross-sectional area of 2.50 in.?. Both bars are unstressed before the load Pis applied. Assume L1=30 in., L2=48 a = %3D in., a=32 in., b=44 in., and c=14 in. If a concentrated load of P = 29 kips is applied to the rigid bar at Dand 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. (2) L2 A B D L1 (1)