Rigid bar ABC is supported by two identical solid bronze [E - 96 GPa, a = 18.2 x 10-6/°C] rods, and a solid steel [E - 210 GPa, a =9.9 × 10-6/°C] rod. The bronze rods (1) each have a diameter of 16 mm and they are symmetrically positioned relative to the centerrod (2) and the applied load P. Steel rod (2) has a diameter of 27 mm. The bars are unstressed when the structure is assembled at22°C. Assume L = 0.3 m. When the temperaturedecreases to -15°C, determine:(a) the normal stresses in the bronze and steel rods o1,02 (positive if tensile, negative if compressive).(b) the normal strains in the bronze and steel rods e1, €2 (positive if stretched, negative if shortened).(1)(1)LAnswers:iMPa, 02 =iMPa.iHE, E2 =iμε.= I3

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Answered: (a) the normal stresses in the bronze…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Problem 3 The aluminum rod BC (G = 26 GPa) is bonded to the brass rod AB (G = 39 GPa). Knowing that each rod is solid and has a diameter of 12 mm, determine the angle of twist (a) at B, (b) at C. 200 mm Brass - Aluminum 300 mm C 100 N. m
Compound axial member ABC has a uniform diameter of d = 1.25 in. • Segment (1) is an aluminum [E1 = 10000 ksi] alloy. The length of segment (1) is L1 = 100 in. %3D Segment (2) is a copper [E2 = 17000 ksi] alloy. The length of segment (2) is L2 = 140 in. %3D When axial force Pis applied, a strain gage attached to copper segment (2) measures a normal strain of ɛ2 = 1500 uin./in. in the longitudinal direction. What is the total elongation of member ABC? L1 P L2 A Aluminum В d Copper c'P Answer: AL = in. %3D
The pin-connected structure consists of a rigid beam ABCD and two supporting bars. Bar (1) is an aluminum alloy [E = 79 GPa] with a cross-sectional area of A₁ = 700 mm². Bar (2) is a bronze alloy [E = 106 GPa] with a cross-sectional area of A₂ = 480 mm². Assume L₁=1.8 m, L₂=2.1 m, a=0.5 m, b=1.6 m, and c=0.8 m. All bars are unstressed before the load P is applied; however, there is a 3.4-mm clearance in the pin connection at A. If a load of P = 53 kN is applied at B, 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) determine the downward deflection VA of point A on the rigid bar. (1) A Answers: (a) σ₁ = (b) 1 (c) VA = i a L₁ B b (2) L2 MPa, 0₁ = με, €2 = mm. i i D MPa. με.
The pin-connected structure consists of a rigid beam ABCD and two supporting bars. Bar (1) is an aluminum alloy [E = 72 GPa] with a cross-sectional area of A₁ = 820 mm². Bar (2) is a bronze alloy [E = 104 GPa] with a cross-sectional area of A₂ = 470 mm². Assume L₁=3 m, L₂=3.5 m, a=0.8 m, b=1.7 m, and c=1.2 m. All bars are unstressed before the load P is applied; however, there is a 4-mm clearance in the pin connection at A. If a load of P = 38 kN is applied at B, 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) determine the downward deflection VA of point A on the rigid bar. (1) Answers: (a) 6₁ = (b) &₁ = (c) VA = i i L₁ B b ล с L2 MPa, 0₁ = με, εξ = i mm. D MPa. με.
The pin-connected structure consists of a rigid beam ABCD and two supporting bars. Bar (1) is an aluminum alloy [E = 62 GPa] with a cross-sectional area of A₁ = 880 mm². Bar (2) is a bronze alloy [E = 92 GPa] with a cross-sectional area of A2 = 570 mm². Assume L₁=1.9 m, L₂=2.3 m, a=0.7 m, b=1.5 m, and c=1.3 m. All bars are unstressed before the load P is applied; however, there is a 1.5-mm clearance in the pin connection at A. If a load of P = 54 kN is applied at B, 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) determine the downward deflection VA of point A on the rigid bar. (1) (a) σ₁ = MPa, 0₁ = i MPa. (b) 1 = i με, εξ = i με. (C) VA = mm. a L₁ B P b (2) C L2 C D
The pin-connected structure consists of a rigid beam ABCD and two supporting bars. Bar (1) is an aluminum alloy [E = 74 GPa] with a cross-sectional area of A₁ = 820 mm². Bar (2) is a bronze alloy [E = 117 GPa] with a cross-sectional area of A₂ = 420 mm². Assume L₁=1.9 m, L₂=2.5 m, a=0.7 m, b=1.9 m, and c=1.3 m. All bars are unstressed before the load P is applied; however, there is a 1.4-mm clearance in the pin connection at A. If a load of P = 34 KN is applied at B, 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) determine the downward deflection VA of point A on the rigid bar. (1) A Answers: (a) σ₁ = (b) ₁: (c) VA = = tel i L₁ B b L2 mm. C MPa, σ₁ = με, εξ = i i D MPa. με.
The pin-connected structure consists of a rigid beam ABCD and two supporting bars. Bar (1) is an aluminum alloy [E = 75 GPa] with a cross-sectional area of A = 790 mm2. Bar (2) is a bronze alloy [E = 108 GPa] with a cross-sectional area of A2 = 540 mm?. Assume L1= 2.5 m, L,= 3.0 m, a= 0.5 m, b= 1.7 m, and c= 1.3 m. All bars are unstressed before the load P is applied; however, there is a 3.2-mm clearance in the pin connection at A. If a load of P = 56 kN is applied at B, determine: (a) the normal stresses o1,02, in both bars (1) and (2). (b) the normal strains &1, 82, in bars (1) and (2). (c) determine the downward deflection va of point A on the rigid bar. (2) (1) L2 L1 A B D b Answers: (a) oj = i MPa, oj = i MPa. ( b) ε - HE, E2 = i HE. (c) VA = i mm.
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 a = 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 L4=30 in., L2=48 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) b
The static Indeterminacy of the structure shown below is. G -Hinge E Dog
The pin-connected structure consists of a rigid beam ABCD and two supporting bars. Bar (1) is an aluminum alloy [E = 60 GPa] with a cross-sectional area of A1 = 870 mm?. Bar (2) is a bronze alloy [E = 92 GPa] with a cross-sectional area of Ay = 520 mm?. Assume L$=2.6 m, La=2.9 m, a=0.7 m, b= 1.3 m, and c= 1.1 m. All bars are unstressed before the load P is applied; however, there is a 3.9-mm clearance in the pin connection at A. If a load of P= 58 kN is applied at B, determine: (a) the normal stresses 01, 02, in both bars (1) and (2). (b) the normal strains € , E2, in bars (1) and (2). (c) determine the downward deflection vA of point A on the rigid bar.
B found that the member AC is fabricated A frame shown in the above figure, it was When fabricating the pin-jointed plane members after assembly. All members hay 60° 30° 30° 30° A 30° D a Jrame shown in the above figure, u was Jound that the member AC is fabricated A too long. Determine the forces in the members after assembly. All members hav same axial stiffness (AE)

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(a) the normal stresses in the bronze and steel rods o1,02 (positive if tensile, negative if compressive). (b) the normal strains in the bronze and steel rods &1, ɛ2 (positive if stretched, negative if shortened).